Classroom Discourse and the Space of Learning

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Classroom Discourse

and the Space of Learning



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Classroom Discourse

and the Space of L earning

Ference

Marton, Goteborg Universi ty

Am y B. M. Tsui,

The

Un iversity

of

Ho n g K o n g

With

Pakey P. M .

Chik

PoYukKo

M un Ling 33Lo

Ida

A . C. Mok

Dorothy F . P. Ng

M i n g F ai Pang

Wing Yan Pong

Ulla Runesson

IEA

1

•

LAWRENCE ERLBAUM ASSOCIATES, PUBLISHERS

2004 Mahwah, New Jersey London



C o p y r ig h t ©

2004

b y L awren ce E r lbau m A s s oc ia t es , I n c .

A ll

r i g h t s

reserved.

No part o f th i s book m ay be rep roduced in

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m eans ,

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Jersey

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Cover des ign by John Leung

Library

of Congress

C a t a l o g i n g - i n - P u b l i c a t io n D a t a

Marlon , Ference .

Class room d iscourse and the

space

o f l ea rn ing / Ference Mar ton ,

A m y B . M .

Ts u i w i t h Pakey

P . M.

C h i k

. . . [et

al . ] .

p. cm.

I nc l ude s

b ib l i o g rap h i ca l r e f e ren ces

a nd

i n d ex .

I S B N

0-8058-4008-7 (c lo th :

alk . paper)

I S B N

0-8058-4009-5

( pbk . : a lk . paper )

1 .

C o m m u n i c a t i o n

in

ed u ca t i o n .

2.

L e a r n i n g .

3.

Class room

envi ronment .

I . Ts u i , Am y . II . Ti t l e .

L B 1 0 3 3 . 5 . M 2 6 5

2003

371.102'2^c21

2003047019

C I P

Books publ ished

by

L awrence Erlb aum Associates

are

printed

on

acid-

free paper, and their bindings are chosen for strength and durabili ty.

Pr in ted in the Un i ted S ta tes o f A m er ica

1 0 9 8 7 6 5 4 3 2 1



C o n t e n t s

Contributors v ii

P re f a c e ix

Part

I O n

Learning

and

Language

1 The

Space

of

Learning

3

Ference M arlon , Ulla Runesson, and Amy B. M. Tsui

Part II O n Learning

2

Vanation

and the Secret of the

Virtuoso

43

Po Yuk Ko and Ference Marlon

3

Discernment

and the

Question, "What

Can Be

Learned?"

63

Ulla Runesson and Ida A. C. Mok

4 Simultaneity and the Enacted Object of Learning 89

Pakey P. M. Chik and Mun Ling Lo

Part

III O n Language

5

Questions

and the

Space

of

Learning

113

Amy B . M.

Tsui, Ference Marlon ,

Ida A. C. Mok,

and Dorothy F. P. Ng



V I

CONTENTS

6 The Semant ic E nr ichm ent of the Space of Learning 1 39

A m y B . M .

Tsui

7 The

Shared Space

of

L earning

1 65

Amy B. M.

Tsui

Part IV O n Improving Learning

8 Toward a Pedagogy of Learning 1 89

M un Ling

Lo , Ference Marlon , Ming F ai Pang ,

and

Wing

Y an

Pong

Epilogue

227

References 233

Au thor Index 239

Subject Index 241



Contr ibutors

Ference

M arton, Professor of Educat ion, Facul ty of Educat ion, Goteborg

Universi ty,

Sweden ,

and

Honorary Professor , Facul ty

o f

Educa t i on ,

T he

U nivers ity of Hon g K ong.

Am y B . M . Tsui , Chair Professor , Facul ty of Ed ucat ion, The Un ivers i ty of

Hong Kong .

Pakey P . M . C hik , S tuden t, Degree

of

M as ter

o f

Phi losophy, Facu l ty

of Ed-

ucat ion ,

The U nivers ity of Hong Kong.

Po Yuk Ko, Lec turer , Department

of

C urr icu lum

and

Ins t ruct ion,

The

H o n g

Kong Ins t i tu te o f Educat ion .

M u n L i n g L o , Head, Centre

for

Development

of

School Partnership

and

Field

Ex perience, The Hon g Kong Ins t itu te of Ed uca t ion.

Ida A. C.

Mok, A ssis tant Professor , Fac ul ty

o f

E duca t ion ,

Th e

Un ivers i ty

of Hong Kong .

D or ot h y F. P. N g, Teaching Fellow, Fa culty of

Educat ion ,

The U nivers ity of

Hong Kong .

M ing Fa i Pang, A ssistant Professor , Fa cul ty of Educ at ion, The Un ivers ity

of Hong Kong.

W in g Y a n P on g ,

Principal , Hong Kong Management Associat ion, David

Li

K w o k

Po

Col lege.

Ulla Runesson, Postdoctoral Fellow, Senior Lecturer, Faculty

of

E du c a -

t ion,

Goteborg Universi ty, Sweden.

V I I



Preface

This book

is

abou t learning

in

schools ,

and the

role

of

language

in

learning.

W e have tr ied to capture i ts tw o m ain ideas in the t i t le . Co ntained w ithin the

first idea is the

p rem ise

that wh atever you are trying to learn, there are cer-

tain

necessary condi t ions for succeeding. Al thou gh you cannot be sure tha t

learning w il l take place when those co ndit ions are m et , you can be sure that

no

learning w il l take place

if

they

are

not .

T he

l imits

o f

w h a t

is

possible

to

learn, w e call " the space o f learning." T he second premise is tha t langu age

p l a y s a cen tra l role in learning : that i t does not m erely convey m eaning, it

also creates

m e a n in g .

A n

understanding

of how the

space

of

learning

i s

l in-

gui s t i ca l ly co nst i tute d in the c lassroom is best achieved through invest igat-

ing "classroom discourse ," wh ich

is

w h a t

w e a im to do

here .

A teach er can never ensure that the intended learning wi l l ac tual ly take

p lace , but a teacher should try to ensure that i t

i s

possible for the studen ts to

learn

w ha t is inte nd ed. That is, the teacher sho uld ensure that the space of

learning

a l lows

for the

intended learning

to

take place .

F or

every educa-

t ional

aim, for every single thing that students are expected to learn, there

are

specif ic

c ondit ions necessary fo r that learning. In our view, f inding ou t

w h a t

these condition s are, and br inging them about , should be the teacher 's

pr imary p rofess iona l task .

A

p rerequisi te

fo r

f inding

ou t

these condit ions

is

the

rea l iza tion tha t

one's

ow n w ay o f teaching is not the only w ay. Such a re-

al izat ion can only be achieved by co nfron ting different way s of teaching the

same th ing , by exam ining how the different w ays are actual ly played out in

the c lassroom and by com paring w hat is intended with wh at is enac ted. A nd

invest igat ing

the discourse in which the teacher and the s tudents are en-

gaged

in the

classroom

is an

essential par t

of

this endeavor.

It is,

there fore ,

fundamenta l ly important that teachers—an d student teachers , for that mat-

ter— are given opportuni t ies

to

observe different teachers teaching

the

same

ix



X

P R E F A C E

th ing ,

and to analyze and ref lec t on how the c lass room d iscourse in w hic h

they

a re

engaged w i th

th e

s tuden t s m ax im izes

o r

m in im izes oppor tun it ie s

for

learning.

This book

is organized in

four

par ts . In Par t I , "On Learning and Lan-

guage," w e

p resen t

the

theo r e t i ca l backg r ound , namely

th e

theor ies tha t

wh atever you are t rying to learn, there are cer tain necessary co ndi t io ns for

succ eeding , and that langu ag e play s a central role in lea rnin g. Par t II , "On

Learning,"

com prises

three chap ters , each

o f

w hich e labora tes

on one of the

three core

e l emen t s

of our

view

o f

learn ing : va r ia t ion , d i scernm ent ,

and si-

m ultanei ty . Part I I I , "O n Language," comprises three chapters a s w e l l , each

of

which deals wi th

one of the

three aspects

of the

role

o f

la n g u a g e

in

class-

room

learn ing :

th e

role

of

quest ions

in

c ons t i t u t ing

the

space

o f

l ea r n ing ,

the

semant ic n a ture o f the space of learn ing , and the jo i n t con s t i tu t io n of tha t

space. In Par t IV, "On Improving Learning," we give three examples of

teachers

w orking

together a nd

using

the

very the oretical tools presented

in

the previous chapters .

Three

fea tures o f th i s book d is t inguish it f rom s im i lar books about learn-

ing in

schools. First ,

it is a

book about both theory

an d

p rac t ice .

I t

con ta in s

a

detai led ex pl icat ion of the theory of learnin g that m otivated the ana lyse s of

classroom teach ing in the res t of the book. I t presents deta i led an aly ses of

classroom teach ing that were dr iven by classroom discourse data in a nu m -

ber of authe nt ic cases of learn ing in school, and w h i c h w i l l be of p r ac t i ca l

relevance to teachers .

Second, th is book is m ore cul tura l ly s i tuated than most othe r books about

learning

in

schools . M ost

o f the

studie s reported

in

th is book have been ca r-

ried out in

Hong Kong .

In

every exa m ple,

it is

c lear ly demons t ra ted

how the

specif ic langu age , cu l tu re , and pedagogy m olds wha t i s happe ning in the

classroom . At the same t im e, however, w e w ou ld l ike to cla im that it i s a lso

possible

to

gen eral ize

f rom the

c u l tu r a l ly

specif ic

examples

and

a r gumen t s

presented

in

this

book. W e argue

that whatever skil ls , whatever ways

of

th ink ing th e s tudents a re expected to develop, there a re necessary condi-

t ions for the developm ent of these sk i l ls . These con d i t ions are

specif ic

to ev-

ery s pe cific sk il l , to every

specif ic

way of th ink ing , and they m us t be met

regardless o f where the learn ing is tak ing p lace , a nd rega rdless o f wha t o ther

condi tions there m ight be .

Third , th is boo k— just l ike other books— is good fo r cer tain th in gs and

not so

good

for

other th ing s .

A s

imp lied earlier ,

if you

w a n t

to f ind ou t how

cer tain specif ic capa bi l it ies (such as using elem entary ar i thme tic in

flexible

way s , d i s t ingu ish ing be tween

different

tones in Can tonese, seeing bodies in

mot ion

in

accordance wi th

a

Newtonian f ramework , r ea l iz ing

w hy

green

plants

are

essent ial

fo r l i fe on

Ear th)

can be

best developed,

you

w i l l p roba-

bly f ind

th is

book

use fu l . However,

i f you

w a n t

to f ind out

about gen eral iza-

t ions that

are

universal ,

if

they exist

a t

al l , such

as how

people become

creat ive, wh at is the best ar range m ent for learning in gen eral , the exact nu m -



P R E F A C E X I

ber of

intel l igences

or

learning styles

in

humans ,

to

what extent those

intel l igences

or

learning styles

are

biologically, eco nom ically, cultural ly,

or

l inguist ical ly

determined, and so on, this

book

is

probably

not a very good

source

o f

inspirat ion.

This

book,

w e

w ish

to

emp hasize,

is not

abou t univer-

sal general izat ions about learning,

nor is it

about

the

development

of

spe-

cific

c apa bil it ies per se.

This

book is abou t the

necessary condi t ions

for the

development of any specific capability.

W e

w ou ld l ike

to

sugg est that this book

is

best used

in field

practice

for

teacher educat ion and in-service training for teachers . W e feel that it w i ll be

of m ost pract ical use when read in conjunct ion wi th arrangem ents w hereby

teachers and

studen t teachers have o ppo rtunities

to

observe different teach-

ers teaching

th e

same topic,

an d to

investigate

teacher-student

discourse

in

l ight

o f the opportunit ies fo r learning that are afforded.

Th is book can, however, also

be

juxtapo sed w ith other theoretical accou nts

of classroom learning. Dealt w ith

in

this way,

it can be

used,

w e

believe,

in ad-

vanced

sem inars in teacher edu cation, and for courses at Master's level in ed-

ucat ional

studies.

A C K N O W L E D G M E N T S

T he

research carr ied

o ut in

Hong Kong

w as

m ade poss ib le throu gh

a

grant

awarded to Professor P aul M orris ( then Chair Professor of Edu cat ion, The

Universi ty o f

Hong Kong ,

now

President

of the

Hong Kong In s t i tu te

of Ed-

uca t ion) f rom the Standing Commit tee on Language Educat ion and Re-

search in Hong Kong (SC OL A R). W e w ould l ike to express our s incere

grat i tude to

Professor M orris ,

a

bri l l iant scho lar

and a

m ost generous col-

l eague .

1

Ference M arton and Ul la Run esson w ould like to acknow ledge the sup-

port

of The

Tercentennary Foundat ion

of the

Bank

of

Sweden ,

and the

Swedish Re search C ounc i l, w i thout w hich thei r work w ould not have been

poss ib le .

The authors of th is volum e wo uld also l ike to thank the form er D epart-

m e n t

of C urr icu lum S tudies (now part of the Facu l ty of E ducat ion) at The

U niversity of Hong Kong, fo r providing the Departmental Research Fund,

wh ich

a l lowed

the

authors

to pay for

expenses incurred

in

collaborating

with

Goteborg Universi ty

and in

securing l inguist ic edit ing assistance.

The research team included Dr. Tam m y Kw an, whose contr ibut ion to th is

book is indicated by expl ici t references to her work. V ikki W eston has car-

ried

out a w ond e rf u l job of

editing

th e

l anguage

o f the

m anuscr ip t. An nie

Chow, M iranda Cheu ng, and W inky M ok at The U nivers ity of Hong K ong,

as wel l as Lisbetth Soderberg and Barbro Stromberg at Goteborg Univer-

sity,

have,

in different but

essential w ays, helped

us to put the

m anuscr ip t

in

shape .

W e thank them al l .



X ll

P R E F A C E

Tw o reviewers , C our tney C azden of Harvard Graduate Schools and

Gaalen Er ickson of the U nivers ity of Br i t ish Columbia, have provided ex-

t r emely usefu l

and

critical

comments

that have sharpened

the

f o c u s

of the

book. W e are very

gra teful

to them . Fina l ly , th i s book w ould never have ma-

ter ial ized without

the

support

o f

N aom i S i lverman, Sen ior Ed i to r ,

and

Lori

Haw ver, A ssistant E di tor ,

o f

Law rence E r lbaum A ssocia tes , bo th

o f

w h o m

have been most encouraging, accommodat ing, and efficient . To them we

owe our deepest g rat i tude.

-—

Ference

M a r l o n

— A m y

B . M .

Tsui

E N D N O T E

'Part of the

findings from this

project have

been repo rted

previously in F.

M arton

& P.

Morris. (Eds.). (2002).

What

Mat ters: Discover ing

Crit ical

C o n d i t i o n s

o f

Classroom

Learn ing . Goteborg , Sweden :

Acta

Universitat is G othoburgensis .



O n Learn ing and Language



1

The

Space

of Learning

Ference Marton

U l l a

Runesson

A m y B . M . T s u i

Schoo l is an inst i tut ion with w hich a l l c i t izens in the industr ia l w orld have

extensive fam il iar i ty, and one that

f requent ly

a t t racts considerable public

and po li t ica l a t tent ion. T he discussions abo ut school can be heated an d the

opinions polemic : "W e should have less who le-class teaching," " W e should

have more pro jec t work," "W e should have more peer learning," "W e

shou ld have more problem -based

learning,"

"By the yea r 2006, a t least 20%

of a l l learning in our school should be information technology ( IT) sup-

ported," "Students should have more homework ," "Students should have

less homew ork," "W e should do away w i th age group ing," "W e shou ld re in-

troduce age grouping," "W e should have streaming," and so on.

A ll

these opinions about w hat should

be

done assume,

o f

course, th at

do-

ing this or doing that is bet ter than doing som ething e lse . B ut i f w e ask the

ques t ion , "Better for w hat?" the an sw er is l ikely to be, "Better for learning,

of course." "But

for the

learning

o f

w h a t?" "For

th e

learning

of

everything?"

These are the ques t ions tha t must be addressed.

Th e point is that i t is highly u nl ikely that there is any one pa r t icular way

of arrang ing for learning that is condu cive to all kinds of learning. In order

to find

effective w a y s

o f

arranging

fo r

learning, research ers need

to

first

ad-

dress what it is that should be learned in each case, and

find

the

different

con dit ions that are conducive to different kinds of learning.

It is only when we have a

fair

understanding of what learners are ex-

pe cted to learn in particu lar situations, w hat they ac tually learn in those si tu-

at ions, and w hy they learn som ething in one si tuat ion but not in another, that

pedagogy becom es a reasonably ra t ional se t of hum an a ct ivi ties . I t is the

aim

of

this book

to

provide such

an

u nders tanding.

3



M A R I O N ,

R L ' N E S S O N , T S U I

W h e n

people argue

fo r a

p ar t icu lar

way o f

ar ranging

for

l ea r n ing ,

or for a

par t icular teaching method, such as wor k ing in groups or the use of p e d a -

gogica l d rama, they should make i t c lear wh at the par t icu lar a r rang em ent , o r

the par t icular m ethod, is good for and why . Ped ag og ica l ac ts shou ld take as

their point

o f

departure

the

cap ab i l i t i es they

are

supposed

to

co n t r ibu te

to

develop ing . The po in t o f sch ool ing i s no t tha t s tude nts shou ld or sho uld no t

be

grouped together

in

ce r ta in ways un d er ce r ta in con d i t ions— such

as b e-

ing

divided

up

according

to

age, abil i ty level,

or

gender . N ei ther

is the

p o i n t

that teachers should do cer tain th in gs in cer ta in w ays, or tha t ce r t a in con ten t

should

be

covered.

T he

po in t

is

tha t

the

s tudents should develop cer ta in

ca-

pabi l i t ies . '

T H E

O B J E C T

O F

L E A R N I N G

Learn ing

is

a lways

th e

acq u i r ed knowled ge

o f

s o m e t h in g .

A n d w e

shou ld

a lways

keep in

mind w ha t t ha t " someth ing"

is , tha t is , w e

s h o u l d

b e

c l ea r

about

the

object

o f

learn ing .

In th is

book ,

the object of learning is a

capab il ity ,

and any capa b i l i ty has a

general and a sp ecif ic aspect. T he genera l aspect has to do w i th th e na tu r e of

the capabili ty, such as rem em ber ing , d i scern ing , in terpre t ing , g rasp ing , or

viewing, that

is, the

acts

o f

learn ing

ea rned

o u t .

T he specif ic

aspect

h as to do

with the th ing o r sub jec t o n w hich these ac t s are car r ied o ut , such a s fo rm u-

las , engineer ing problems, s im ultan eo us equ at io ns . W orld W ar I I . or Fran z

Kafk a ' s

l i terary heritage.

In

other words,

the

ge ne r a l

aspect

r efer s

to

ac t s

(the indirect object of learn ing) , w hereas the specific aspect r efer s to w ha t i s

acted upon ( the

direct

object

o f

learn ing) .

T he

learner s ' focus

is

no r ma l ly

on

what they

a re

trying

to

learn ( the d irect object

o f

l ea r n ing ) , w her eas

the

teacher 's focus should

be on

both;

no t

on ly

on

tha t w h i ch

the

learners

are

trying

to

learn,

bu t

also

on the way in

w h i c h

the

learners

are

t ry ing

to

m a s te r

what they

a re

trying

to

l eam .

W e

m ight assum e therefore , tha t teachers

are

trying to work toward an object

of l e ar n i ng .

This o b jec t may be m ore or less

conscious for the teacher and i t m ay be mo re or less elaborated. Bu t , w ha t-

ever

the

c i r cumstances , w hat teachers

are

striving

for is the in tended

ob jec t

of learning, an object o f the teacher 's awareness , tha t m igh t chang e dynam i-

cally during the course o f learn ing .

Th i s

is the ob jec t of learn ing as seen

from the teacher's

perspec tive,

and as

such

is

dep ic ted

i n

th is book

as

be ing

evidenced

by

wha t

the

teacher does

and

says .

W h a t is of imp or tance for the s tudents , how ever , is not so m u c h how the

t eache j intends

the

object

o f

learning

to

come

to the fore, but how the

teacher structures the conditions of learn ing so tha t i t is po ssible for the ob-

j e c t o f

learning

to

come

to the

fore

of the

learners ' awareness . What

the

s tu-

dents

encounter is the enacted object o f learn ing , and it d e f ines wh a t it is

possible to leam in the

actual sett ing, from

the

po in t

of

view

of the specif ic

object o f learning.

There

are obv ious ly cer ta in necessary cond i t ions fo r



1 . T H E

S P A C E

O F L E A R N I N G

learning one

thing

or

another.

T he

enacted object

of

learning

is the re-

searc her 's descript ion of w hether, to w hat ex tent , and in w hat form s the nec -

essary condit ions of a part icular object of learning appear in a certain

set t ing.

The enacted objec t of learning is described

from

the point of view of

a certain

research

interest and a part icular theoretical perspective.

Wh a t is of decisive importance for the students, is what actually

conies

to

the fore of their at tention, that is , w hat asp ects of the si tuation they discern

and focus o n. In the best case, they focus o n the cntical aspects of the object

of learn ing, and by doing so they learn w ha t the teacher in tended . B ut they

m ay also

fail to

discern

and

focus

on

some

of the

cri t ical aspects,

or

they

m ay discern

and

focus

on

other aspects . Wha t they a ctua l ly learn

is the

l ived

object

of learning, the o bject of learning as seen

from

the learner 's p oint of

view,

that

is, the outcome or

result

of

learning.

T h e O r i g i n

of

Powerful Ways

of A c t i n g

Learn ing is the process of becoming capable of doing som ething

("doing"

in the wide sense) as a resul t of having had cer tain experiences (of do ing

some th ing

or of som ething happen ing) . D eveloping a learner ' s cap abi l i ty

of hand ling novel si tuations in pow erful way s is

considered

to be on e of the

m o s t imp ortant educa t ional a ims. In order to address how this can be done,

w e

have

to

ref lect

on the

na ture

of powerful

w a y s

o f

act ing, that

is,

w a y s

o f

engag ing in acts ins t rum ental to ach ieving one 's goals eff iciently. Ac t ing in

powe r f u l

w ays mea ns, therefore, doing

different

th ings

to

achieve different

a i m s ,

and

doing

different

th ings

in different

s i tua t ions .

T he

power fu lnes s

o f

on e's acts is relat ive to

one 's

a ims and the s i tua t ions .

L et u s

f i rst cons ide r

the

s i tua t ions .

A s

r a t i on a l be ings ,

w e

a lways

try to

act

in

a cco rdance wi th

an y

given s i tua t ion, that

is, the

s i tuat ion

as we

per-

ce ive

i t.

W h a t k n o w l e dg e

w e

m i g h t

try to

exp lo i t depends

o n h o w w e

m a k e

sense of the s i tua t ion . Our previous exper iences

affec t

t he way i n w h ich

w e perceive

the s i tuat ion, but the way in wh ich w e perceive the situation

also

affec ts

wha t exper i ences we see as relevant in tha t par t i cu lar s i tua -

t ion . W e a re

trying

to ac t in

pow er fu l w ays , tha t

is, w e a re

t ry ing

to

ach i eve

our a i m s ,

not in

relat ion

to the

s i tuat ion

in an

obje ct ive sense,

but in

r e l a -

t ion to the s i tua t ion as we see i t . P o w e r f u l w a y s o f ac t ing spring from p o w -

erfu l w a y s

o f

seeing.

Let

u s

take

an

exam ple . Someone

is

standing

in a

lake wi th

th e

water

up to

his

knees

and

aiming

at a

fish

in the

w ater with

a

harpoon.

He

m ight

a im at

the

fish

where it appears to be, that is, where he actually sees it, or at a

sl ightly adjusted angle, that

is,

w here

he

th inks

it

should actual ly

be if he

takes

the

refraction

of the

l ight into considera t ion.

These tw o

different w a y s

of act ing are based on two different w ays of understanding the si tuation and

the

latter is

m ore

pow erful than the former. Let us take ano ther exam ple. Let

us imagine that a sales tax of 10% is introduced in Hong Kong. One car



M A R I O N , R U N E S S O N , T S U I

dealer selling expen sive cars sim ply increases the prices by 10%, while an-

other adds only 5% on to the previous prices. T he first car dealer assumes

(wrongly) that sa les tax mu st be added to the previous pr ice an d the buy er

m ust a lw ays pay for i t . However, the second one p redicts ( r igh t ly) tha t de-

m and w il l be adversely affected by the pr ice increase and real izes that even

if

10% of the net price has to be given to the tax auth or i t ies , a par t of this sum

has to be absorbed by the se ller. (A sim ilar exam ple is e laborated in chap. 8).

A gain, there are tw o different w ays of unders tanding the same s i tua t ion and

hence tw o w ays of ac t ing , one of which i s mo re po w erful than the o ther .

Let us look a t some other exam ples th at i llustra te the thesis that po w erful

w a y s

o f

actin g derive from p o w e r fu l w a y s

o f

seeing.

L et us

take

a

very s im -

ple one to

begin w ith.

A

wo rd problem

w as

given

to

some 7-year-old ch i l-

dren. T he problem is as fo l low s: "I d idn ' t have m uch m oney th i s m orn ing

w hen I w ent to schoo l . B ob gave back 4 kronor th at he had borrow ed f rom

m e last w eek, and w ith that I cou ld buy a green chocolate bar for 7 kronor.

How m u c h m o n ey did I have th i s morn ing w hen I c a m e to school?

1 1

Some of the chi ldren knew the answer a lm ost ins tant ly , w hereas o thers

struggled in vain. W as there anyth ing tha t th e form er could do tha t the latter

could not? A ctual ly none of the chi ldren had ever seen a problem l ike th is ,

nor did they remem ber any addit ion tables . Those w ho d id not do too w el l

saw the problem as one of addi t ion ; the chi ld had some kronor to begin w i th

an d

then

he got 4

more , which made

7

al together .

B u t

w ha t then caused

these children diff iculty was the ques tion: How can you add w hen you do n ' t

k n ow w h a t

to add to? Th e

chi ldren

w ho did not f ind the

problem

di ff icul t a t

all said som ething like this

to

them se lves :

"I can sa y

tha t

he had 7

kronor

a l-

together and I know that he got 4 kronor from Bob. S o I have to take aw ay 4

kronor f rom 7 kronor."

They

cont inued , "One goes aw ay: 6 . Tw o goes away :

5. Three

goes

away : 4. A nd four goes a w a y : 3. So he had 3 kronor th i s mom -

ing." O thers m igh t have said, "I have to look for the o ther part . I hav e to f ind

out how

many kronor

I

have

to add to the 4

kronor

I got from

Bob ,

to get 7

kronor a l together . So the answer is 3 ." These chi ldren s ta rted w i th wh at they

had got , w hich w as 4, then they coun ted three un i ts , 5 , 6 , 7 , and visu al ize d

the "threeness" of those three u ni ts . Or others perhaps s im ply knew tha t 7

can, among other things, be broken down into 4 and 3. Th e chi ldren w ho

cou ld come up w ith the answer easi ly did not see the problem as an addit ion /

subtraction problem but as a

part-whole

problem: the who le and one of the

parts are given, the w h o l e is 7 and the given part is 4; the m iss ing par t m us t

then be 3. So the dif ferenc e between the chi ldren who han dled the prob lem

easi ly an d the others w ho did not was not so m uc h w ha t they did, bu t ra ther

w hat they saw, that is , how they understood the prob lem . The ch i ldren w ho

could solve the problem saw i t in term s o f par ts and w ho le , and therefore

could

solve

i t easily,

whereas

the children w ho could not solve the

problem

saw it in

term s

of the

ar i thmetic operat ion, that

is,

addi t ion ,

and

therefore

had diff icult ies

solving

i t . Th e

po int here

is

tha t ,

in

ma ny cases , see ing s im-



T H E

S P A C E

O F L E A R N I N G

pie ar i thmet ic problem s

in

term s

of part-whole

relat ions

is a more

powerfu l

w ay

of seeing them than seeing them in terms of ari thmetic operat ions

(Neuman, 1987) as al ready shown. The

part-whole

way of seeing works

very wel l

for

an y

of the

p rob lem s

in

which

tw o

par ts

are

given

and you

have

to find the whole, or when the who le and one of the par ts are given and you

have

to

look

for the

other part .

For

example ,

a + b = _

a-b =

= c

a-_ = c

Seeing the prob lem as a

part-whole

relat ion en ables the ch ild to act in a

p o wer fu l w a y ,

in the

sense

o f

hav ing

a

capab i l i ty

to

deal wi th

dif ferent

prob l ems .

An other w el l-known

a nd

more complex exam ple

of how

"the ca pa bil i ty

of seeing" is of decisive im portance, is de Groot's (1965) wo rk on expertise

in

chess p lay ing .

"What

is it that chess m asters are esp ecial ly good at?" de

Groot asked, eag er

to

find

out

w hether

it is

true,

as

ma ny people bel ieve, that

w h a t

chess masters

a re

good

a t is

being able

to

m ental ly visual ize

and try out

a n u mb e r of al ternatives act ions (and their consequences) in great depth.

However ,

this

did no t in fact

turn

o ut to be the

case.

The

chess m asters

d id

not try

m ore al ternat ive courses

o f

a ct ion than other players ,

o r

follow them

up fo r longer. B ut the courses o f act ion they considered were m ost ly more

powerfu l w a y s

of

han dl ing

th e

si tuations than other cou rses

o f

ac t ion would

have

been .

S o ,

w h a t

was i t

that enabled

the

chess masters

to

find

m ore pow-

erful

w a y s

o f

handl ing

th e

si tuations?

T he

m ost striking

fact

w as

that chess

m as ters seemed

to see the

chessboard differently

to

other people:

We know

that

inc reas ing

ex p e r i en ce

and

k n o w l e d g e

in a spe cific

f ield ( che ss ,

for in-

s tance) has the

effect tha t

th ings (prope r t ies , e tc . ) which , a t

ear l ier

s tages , had to be ab-

stracted, or even inferred are apt to be immediately perceived at later stages. To a

ra the r

large

ex ten t ,

abs t rac t ion is replaced by percep t ion , but we do not k n o w m u c h

abou t how

th i s

w o r k s , n or w h e re the bord e r l ine l ies. As an effect of th is

r e p l a c e me n t ,

a

so-cal led

"given" problem s i tua t ion

is not

rea l ly g iven s ince

it is

seen

different ly

by an

expert than it is perce ived by an inexpe r i enced pe r son , (de Groot, 1965, p p . 33-34)

Al though de

Groot also found that chess masters were m uch bet ter

at re-

m em bering posi tions o n the

board

than n ovices, this w as only true w hen the

arrangements represented m eaning ful pat terns , and was not the case w hen

the

arrangements were random configurat ions .

In the

latter case,

the

chess

masters ' memories were

no t

significan tly better than that

o f

other people.



8 M A R I O N , R U N E S S O N , T S U I

These findings were replicated by Chase and S imon (1 973) w ho by ex-

amining the w a y s in w hich chess m asters reconstructed c on f igu rat ion s that

they

had

br ief ly seen,

and the

errors that they m ade

in

doing

so ,

arrived

at the

interpretation that chess

masters

can

remember

a

great number

o f

pat terns

of about e ight pieces, and that they interpret every co nf ig ura t ion on the

board in terms of a t m ost seven or e ight such pat terns.

These

pat terns form a

kind of giga ntic a lphabet com prising up to 10,000 le t ters , each one corre-

sponding to a cer ta in pat tern (c i ted in Berei ter & S carda m elia , 1993).

T h e

m a in d i f f e r ence be tween chess mas te r s

an d

less exper ienced p la y-

ers, acc ord ing to th is line of reason ing, h as to do w i th the d i f fe ren ces in

w ays of see ing the chessbo ard , and d i f fe re nc es in w ay s of see ing var iou s

co n f ig u ra t i o n s a s

m e a n in g f u l

pa t te rns .

I t is the

chess m as te r 's

w a y o f

see-

ing that enables

the

p l a y e r

to

engage

in

p o w e r fu l w a y s

o f

ac t i n g .

A n d

there

are o ther s im i la r find ings on the na ture of exper t i se . Glaser and Chi (1988)

showed that exper ts

an d

nov ice s

di f fe r as to the

p r o b l e m s t h e y

see as

s i m i -

lar and

those problems they

see as

dif ferent . P h y s i c i s t s

a re

ab le ,

for in-

s tance , to see tha t the problems of r iver cur rents , and the problems of

h e a d w i n d s an d t a i l w i n d s in a i rp l a n e s i n v o l v e s i m i l a r m a t h e m a t i c a l an d

p h y s i c a l a s p e c ts , s u c h a s r e l a t i v e v e l o c i t i e s ( B r a n s f o r d , B r o w n . &

Cocking, 2000) . S imi la r f ind ings or ig ina te from such d ive r se f ields as

e lec t ronic c i rcui t ry (Eg an & Sch w ar tz , 1 979) , rad io lo gy (L esg old , 1988) ,

com pute r p rogram m ing (E hr l i ch & So loway , 1 984) and t each ing (Sabe r s .

C u s h m g ,

&

Ber l iner , 1991) .

Rela t ing

these cases, Bra nsfo rd

et al.

(2000) stated tha t exp ertise

in a do-

m a i n is characterized by sensi t ivi ty to pat terns o f mean in g f u l i n f o r m a t i o n

that m i g h t no t be avai lable to o thers dea l ing w i th th e same p rob lem s w i t h in

the same dom ains. In this book, w e w ou ld l ike to assert that var ious degrees

of expertise, that is, the capabi l i ty of ac t ing in p o w e r fu l w a y s

w i th i n

a cer-

tain

d o m a i n ,

is

re f lec ted

in the

var ious way s

o f

see ing , tha t

is, in the

var ious

meanings seen in a par t icular scenar io or problem.

T h u s i t can be seen th a t people act not in r e l a t i o n to s i t u a t i o n s a s s u c h ,

but in re la t ion to s i t u a t i o n s as they pe rce ive , expe r ience , an d u n d e r s t a n d

them. O ne o f the m os t f r e que n t ly r ecur r ing f ind ings

f rom

our own r e -

search , as w el l as f rom oth ers ' r esearch , i s tha t w ha teve r s i tu a t io n peop le

enco unte r , they see i t , exp e r ience i t , and u n d e r s t a n d it in a l im i te d n u m b e r

of

qua l i t a t ive ly dif ferent

w ays (see M ar ton & Booth , 1997) . In r e l a t ion to

par t icu la r a im s,

some

w ays o f see ing a r e more po w er fu l than o the r s . Pow-

e'rful w a y s o f a c t ing der ive from p o w e r f u l w a y s o f see ing , and the way t h a t

s o m e t h i n g is seen o r exper ienced is a f u n d a m e n t a l

f ea ture

o f l e a r n i n g . If

w e w ant lea rners to deve lop cer ta in capa bi l i t ie s , w e m us t m ake i t po ss ib le

for them to deve lop a ce r ta in way of see ing or exper ienc ing . Conse-

quent ly , a r ranging for lea rn ing imp l ies a r ranging for deve lopin g

learners'

w a y s

o f

seeing

o r

exper ienc ing , tha t

i s ,

deve lop ing

th e

e y e s t h r o u g h w h i c h

the world is perceived.



T H E S P A C E O F L E A R N I N G

WAYS OF S E E I N G

Wh a t

does it

take

to

develop

the learner's

eyes? W hat

is

meant

by "a way of

seeing something?" Whatever we at tend to is inexhaustible, in the sense

tha t

the

inform at ion that

can in

principle

be

gained

from it is

un l im i ted.

A t

the sam e t ime , as George M iller so aptly declared, a lm ost 50 years a go, our

capac i ty for process ing inform at ion i s seriously l imited (M iller, 1 956). T he

inevitable mechanism

o f

selectivity

originates

from

the

co ntradiction

be-

tween un l im i ted in form at ion

and the

highly l imi ted capaci ty

fo r

process ing

this

in format ion wi th w hich hum ans are equipped.

W henever people at tend

to

something, they discern certain aspe cts

of it,

and by doing so pay more at tention to some things, and less at tention or

none

at all to

other things.

If one

person discerns certain aspects

of

something

and

another person

discerns par t ly o r wh ol ly different aspects, we say that the two people see

the sam e thing in different w a y s . So, a way of seeing something can be de-

f ined in

t e rm s

of the

aspects that

are

discerned

at a

certain point

in

t im e.

T he

aspects

are

thus discerned (and

attended to) at the same

t im e rather than

o ne

at a t im e . A par t icular way o f seeing something can be

defined

by the as-

pects discerned, that

is, the

cri t ical features

of

w h a t

is

seen.

A n aspect of a thing co rresponds to the way in w hich that th ing m ight di f-

fer from, or be

s imi lar

to, an y

other thing, that

is, the w ay it is

perceived

to

be, or the w ay that it is experienced by someone as different from, or similar

to

som ething else. Th e problem cited previously (a bou t the child with 7 kro-

nor)

w as

unders tood,

o r

exp erienced,

by

som e chi ldren

in

te rm s

o f its part-

w h o l e

s t ructure. Some chi ldren not iced that it had the s ame who le in it

( i .e. ,

7)

as

some other problem they

had

experienced,

and in

that respect

it

d i f -

fered from

problems

in

which

th e

whole

w as

other than

7.

Furthermore,

am ong those problems

in

wh ich

the

w ho le

w as 7, i t w as

s im i lar

to

those

in

w h i c h one of the parts was 4 and different from those problems in w hich

no ne o f the parts w as 4. Seeing the problem in terms o f its

part-whole

struc-

ture mea ns, we bel ieve, seeing w hat the par ts a nd the who le

a re

and wha t

they

are

not .

However, other children understood

the

same problem

in

terms

of the

ari thm etic operation involved. They tho ugh t

i t w as

similar

to

other addit ion

prob lems , and that i t differed from problems about subtract ion. A m ong ad-

dition

prob lems ,

i t w as

similar

to

those

in

wh ich

the

second addend

w as 4,

and different

from

those

in

w hich this

w as not the

case. They probably also

t hough t

tha t i t was similar to those addit ions in w h i c h the s um is 7, and di f-

ferent f rom those in w hich this wa s not the case. Seeing the problem in terms

of the

ari thm etic operat ion involved required

a

thou gh t process l ike this ,

w e

bel ieve.

The reason that som e children c ould solve the problem and others

could not was because they saw the same problem in different ways, that is,

because they at tended

to

different aspects . At tending

to a

certain aspect



J _0 M A R T O N , R U N E S S O N , T S U I

means compar ing something

w e

exper ience w i th o ther th ing s tha t

w e

have

experienced earl ier . Th e kin ds of thin gs broug ht into the comparison

def ine

the aspect that is attended to .

In

Lo and Ko

(2002),

the

Engl ish

lessons

of two primary

Grade

4

c lasses a re d iscussed . Eviden ce f rom the lea rn ing outcom es sug ges ts tha t

m ost chi ldren in one o f the classes un de r s tood the "s" at the end of verbs a s

s igna l ing th i rd person s ingu la r , tha t

is ,

that they "saw"

the "s" in

th is par -

t icu la r way. Th i s imp l ies ,

w e

be l ieve , tha t they m ade

an

im pl ic i t compar i-

son

o f verbs where "s" was present wi th th e same verb where " s" was

absent . In the o ther c lass , most c h i ldren d id not seem to pay a t te n t io n to the

"s." They compared, w e th ink , im pl i c i t ly , the verbs w i th o ther verbs . T he

"s" ha s to do

w i th

the

third

person

s ingu la r , t ha t

is , i t ha s to do

w i t h g r am -

m ar ; wh e reas the com par i son w i th o the r ve rbs—or o the r w ords— has to

do wi th the me aning . The m ajo r i ty of the ch i ldren in the fi r s t c lass seemed

to

attend

to

both

th e

g r a m m a t i c a l

and the

mean ing a spec t s

of the

verbs,

w hereas m ost ch i ldren in the second c lass d id not seem to a t tend to the

grammat ica l aspec t o f these verbs.

A ccording to this l ine of reason ing, a way o f seeing can be ch aracter ized

in terms of the aspects

discerned

that are attended to s imultaneously. This

defini t ion is very w ide and very narrow at the same t im e . It is very w ide be-

cause it refers to the m e a n i n g o r appearance o f a l m o s t a n y t h i n g . A nd it is

very narrow because

it

s imply a im s

a t

te l l in g apar t

d i f ferent

w a y s

o f

seeing

in respects th at a re cr i t ica l in re la t ion to the eff ic iency of the ac ts tha t spnng

from

those ways of seeing, those meanings, and those appearances.

D I S C E R N M E N T

In order

to see som ething in a cer ta in w ay, a person m us t discern ce r ta in fea-

tures of that thing. We should a lso be c lear about the

dif ference

between

discerning and be ing to ld . M edica l s tudents , for ins tance , m ig ht be advised

by

the ir professors

to try to

not ice dif ferent fea tures

o f

the i r pa t ien ts , such

as

the color of the l ips , the m oisture of the skin, the ease of breath ing , and so

on ; th is is be ing to ld . But in order to fol low th is advice , the s tuden t s m us t

experience those features, and the only w ay to

exper ience

them is to

expe ri-

ence ho w they can vary. N otic in g the color of a pa t ie nt 's l ips , for exa m ple ,

w o u l d

no t

mean ve ry m uch

if lip

color

wa s the

same

fo r

everyone.

Simi lar ly , / rawe

o f

reference

in

phys ics only mak es sense

i f we can

t h i n k

of more than on e f ram e of r eference . Even very abstract not io ns der ive the ir

m eanin g ( in the sense of the exper ience of und ersta nd ing ) throu gh var ia-

t ion. H istor ical ly, no one was aware o f na tu ra l num ber s , fo r ins t ance ,

unt i l

the re w ere o ther num bers such as nega t ive num bers . At tha t poin t , the na tu -

ra l num bers cou ld be ident i f ied as those tha t were not nega t ive num bers .

This

is wh y in a sense we of ten know very l i t t le abo ut our ow n coun try

un t i l

w e

leam about other countr ies .

A nd

th i s

i s why

teachers gene ra l ly g ive

a



1 . THE SPACE OF L E A R N I N G 1J_

number

of different

exam ples

in

order

to

explain

a new

concept

o r

principle.

If

teach ers give one exam ple only, they do so because they them selves con -

sider the other alternatives to be obvious (which, however, they m ay not be

fo r

the students). In order to explain w hat a frame o f reference is , i t is not

suff icient

to

point

out

that when

w e

consider

a

moving body

in the sk y from

the point of view of the ground, w e con sider i t from a part icular fram e of ref-

erence . W e also have to give other exam ples, su ch as considering i t from the

poin t of view of another body m oving in the sky in paral lel with the

first

one

and at the same velocity.

B y experiencing variat ion, people discern certain aspects

of

their envi-

ronmen t ;

w e

could perhaps

say

that they become "sensitized"

to

those

as-

pects . This m eans that they

are

likely

to see

future

events

in

term s

of

those

aspects; the phy sician w il l pay at tention to the c olor of the pa tient 's l ips, the

phys ic i s t w il l pay at tention to the fram e of reference

from

w hich a body in

mo ve me n t

is

co nsidered. This

is

w h a t

w e

me a n

by

learning

to see

certain

th ings in

cer tain w ays.

O ne

m ain

way of

dealing w ith novel si tuations

is to

m ake u se of previou s expe rience. It is im portant to develop the ca pa bil i ty

for profess ional se e ing , that

is,

seeing si tuations

in

term s

of

features that

are

general ly cri t ical w ithin

one 's

professiona l f ield. But i t is equa lly imp ortant

to be able to discern o ther featu res that are not cri t ical in a gen eral sense, but

that

m ay be

cri t ical

in a

specific case.

N ot

only

do you

need

to

discern fea -

tures that have proved to be e ssential in the past , but you m ust be a ble to dis-

cern new fea tures when they are cri t ical . This is in fact very central in

research

an d it is

very m uch

how new

discoveries

a re

m a de.

Bu t we

should

rem em ber tha t even the discernm ent of enti rely new features depends on the

varia tion yo u h ave enc oun tered earl ier .

The w ord "fea ture" has been used to stand for at tribute, or aspect , such as

color of l ips, f rame of

reference,

tal lness, and so on, and we ha ve pointed to

the

fact

that human beings cannot discern

a

feature wi tho ut experiencing

variation

in a

corresponding dim ension. How ever,

we no t

only discern fea -

tures,

bu t a lso discern different qu ali t ies ( i .e. , values ) in the relevant dim en-

sions such a s "blue," "ray of light," "very short," and so on.

D i s c e r n m e n t a n d Context: Parts an d W h o l e s

So far we ha ve talked about the di scernment o f features and values

wi th in

features.

Bu t i t i s a lso poss ib le to th ink abo ut discernm ent as a del im i tat ion

of wholes

from

thei r context and as a del imi tat ion of par ts w i thin wholes

(cf . Svensson, 1976).

Mar ton

and B ooth (1 997) gave an example:

W h a t

does i t take to see a mo t ion l e s s de e r a mong the dark t rees a n d b ushe s of the

n i gh t

w oods?

To see i t at all we

have

to

d isce rn

it f rom the

su r r oun d ing t re e s

a nd

b ushe s ,

w e

have to see i ts

c o n t o u r s ,

it s ou t l i ne , the l imi t s tha t d i s t i ngu i sh it from

w h a t s u r r o u n d s



\2 M A R T O N , R U N E S S O N , T S U I

it.

W e have t o see, a t least par t ia l ly , w h e r e i t s tar ts and w h e r e i t e nds . .. [ b u t ] no t o n l y

do we have to d isce rn i t from i ts

c on t e x t ,

a s a de e r in the woods , bu t we a l so have to d i s -

cern i ts par ts , the way t h ey

re la te

to each o ther , and the way t hey r e l a t e to the

w h o l e .

There fore , on s e e ing the de e r in the w oods , in s e e i n g its co n t o u r s , w e a l so s ee pa r t s o f

i ts body, i ts he a d , i ts a n t l e r s , i t s forequ ar ters , an d so on, and t h e i r r e l a t i o n s h i p i n t e r ms

of s tance , (pp. 86-87)

Discern ing the re la t ion of par ts w i th in wh oles and d iscern ing the wh ole

from the con tex t is an im por tan t aspect o f d i sce r nm en t . Eq ua l ly impo r tan t is

discern ing the w ay w holes r e la te to the con tex t . Th is i s because the way the

w hole relates to the con text shapes the d iscern m ent of the par ts

w i t h in

the

wh ole . W hat does th i s m ean? Le t us take some classroom data as exam ples.

Let us star t with th e role that context p lays in d e t e r min ing t he m e a n i n g

assigned

to a

p h e n o m e n o n .

In a

pr imary Chinese lesson

on

s e m a n t ic s ,

wh ich is d iscussed in chap te r 2, we see how one w ord took on a very

differ-

en t

mean ing when

i t w as put in di f fe rent

con tex t s .

In

th is lesson,

the

teacher

told a story about how one w ord in Chinese y ao (P u to ng hu a) [ -f|- ] (w hich

can be

translated l i terally

a s

"wan t")

w as

explo i ted

by a

barber, Afa n t i ,

to

carry the d iametr ical ly

opposed

m e a n i n g s , "give"

(gei)

( P u t o n g h u a )

[$&]

and

"keep"

(liu) ( P u t o n g h u a ) [^] in order to take his r ev enge on a cus tomer .

A h u n g , w ho kept

r e fus ing

to pay for the service. In the story, the barber

asked Ahu ng wh ether he

"w an ted" (yao buyao

(P u to ng hu a) [ - f c^ -l c - ]) h i s

eyebrows , w hereupon A hu ng rep l ied tha t

h e

"w an ted"

h is

eyebrows (yao),

m eaning he wanted to keep h is eyebrows .

A f a n t i

shaved of f A hu ng ' s eye-

b ro ws

and said, "You 'w an t '

(yao)

your eyebrows , so I ' l l g ive them to yo u "

Ahung was speech less because he had indeed sa id yao . Af te r th i s , A f a n t i

asked

Ahung i f he

"wan ted"

h i s beard , and Ahung, who had a b e a u t i f u l

beard , immediately said ,

buyao

( P u t o n g h u a ) [^ - fc ] , tha t

is ,

"don ' t want ,"

mean ing he did not w a n t

Afa n t i

to shave off his beard . However ,

Afan t i

shaved off his beard all the s ame . Aga in , A hu ng was speech less because he

h ad indeed said buyao

("don't

want") .

In

th is story,

we see

tha t

the

wordjao

w as

ass igned di f fe rent m e a n i n g s

in

relation to d i f ferent contexts . In the first in s t ance , A hun g r e l a ted it to the

context o f a

barbershop

where people had the ir hair and beard tr im m ed o r

cut , but wou ld n o t typica l ly have their eyebrows shaved off . Let us r efer to

this context as Contex t A . Therefore, when he said yao, he m ean t tha t he

wanted to

keep

his eyebrows. However,

Afa n t i

del ibera tely relate d i t to a

different

context where "wan t"

(yao)

can mean "give " Let us r efer to th i s

contex t as Contex t B . For exam ple , in the con tex t o f m ak ing an offer, such as

offer ing a dr ink, "Do you wa nt a

dr ink?"

a pos i t ive rep ly from the addressee,

yao,

wo uld entai l the person m ak ing the

offer

ac tua l ly

g iv ing

a drink to the

addressee . Then, in the second ins tance , when Ah ung used buyao to m e a n

that h e "did no t w a n t" h is beard, h e w a s relat ing y ao to the con tex t in w h i c h

Afan t i

w as operating in the previous exchange w here ya o m e a n t

"give,"

tha t



1. T H E S P A C E O F

L E A R N I N G

1 J3

is C ontext B. However, A fanti

deliberately

related buyao ("don't

want")

to

the context in which A hung w as op era ting previous ly , w here y a o m e a n t

"want" or "keep,"

that

is

C ontext

A .

T he

story

in

this lesson sugg ests that

the

context

to

which som ething

is

related

cannot necessari ly

be

taken

for

granted.

In

c lassroom learning s i tua-

tions,

it is

very important that there

is a

m utua l unders tanding (be tween

teacher and students) of the context to w h i ch the teacher re la tes the

object

o f

learning in

order

to

help learners discern

its

cri t ical

features .

Let

u s

look

at tw o

lessons

on

w riting

a book

report,

for

example, also

re-

ported by Ch ik (2002). In one lesson, the teacher (T eacher A ) used genres o f

w ri ting as the

context

for

discussing

the

com ponen ts that s tudents should

include in a

book report.

She

sp ecifically used na rrative

as a

genre

of w ri ting

and

asked the s tudents to th ink abo ut th e features that dis t ing uish a book r e-

port

from a

narrative.

In the

other lesson ,

the

teacher (Teacher

B )

used

a

dif-

ferent

context

for

discussing

a

book report , that

is,

different w a y s

o f

present ing a book report .

Specifically,

she cited the use of pic tures to pres-

ent a

book report,

a

format with which students were also familiar.

Wh i c h

is a more

power fu l

context , in the sense of be ing more

effective

in

bringing about learning? W hich w il l help learners discern

the

cr i t ical f ea -

tures of a book

report?

T he

answer

to

this question depends

o n the

aspects

of the

book report

o n

w hich the teacher wants to focus. In these tw o lessons, the ob jec t of learning

is the

essentia l comp onents

of a

book report.

O ne

could argue that pic toria l

representat ion

is one kind of

form at

and that i t can be con trasted w ith a w rit -

ten format .

B u t

there

i s

noth ing m uch tha t

can be

said apart

from

this ,

and it

does

no t

help

the

s tudents

to

discern

the

com ponen t s t ha t

are

cri t ica l

to a

book report .

O n the

o ther hand, other genres

o f

w ri ting , such

a s

narra t ives,

contain various components such as time, p lace, people, and sequence of

events

tha t

are not

found

in

book reports . What dis t inguishes

one

genre

o f

wri t ing

from

another

is the

com ponents tha t they conta in .

In

o ther w ords ,

the g e n re s

o f

wri t ing, o f wh ich book reports are one instantiation and narra-

tives

another, provides

the

context

to

w h i ch

the

cri t ica l

features o f

book

re-

ports re la te .

Let us look a t how Teacher A dealt with th e com ponents cr i t ica l to a book

report . Sh e put e ight com ponents that w ere re la ted to books on the board.

They were: price

of the book,

date

of

reading, genre, call number, author,

n a m e

of the

book, summ ary,

and

com m entary ( impression

af ter

reading) .

Am o n g th e m ,

the first

four, a l though having

to do

w i th books , were

no t

rele-

vant

to book reports. The

teacher asked

the

students

to

take away those com -

pon ents that they felt should not be included in a book report. B y asking th e

students to do that , the teacher w as doing two things. Firs t , she was a t tend-

ing to the

internal relationsh ip,

a part-whole

relationship, betw een

the

c o m -

pon ents and the book report . T he com ponen ts that rem ained on the board

were author , name

of the

book, commentary,

and

summary. These

four



J _4 M A R T O N , R U N E S S O N , T S U I

com ponents w ere related

to

each other

in the

sense th at they were co nsti tu-

tive

of a book report in such a way that if any part w as m iss ing, i t w ould no

longer be a book report . F or exam ple, if the comm entary w as m issing , the

book

report

w ould becom e a piece of text in an annotated bibl iography . Sec-

ond, she was at tending to the wa y in w hich the inclus ion of par ts that w ere

not

critical

to a

book report wou ld affect

the

who le .

F or

example ,

the

inc lu-

s ion of the pr ice of the book and the pub l isher wou ld const itu te a wh ole that

is

no

longer

a

book report,

bu t

another genre,

for

example ,

an

advert isem ent .

T he

discernmen t

of the

cr i tical com pone nts

o f a

book report

w as

b rough t

about

b y

discerning

the

book report

as an

ins tant iat ion

o f

genres

of

w ri ting.

In other words,

ge nr e s o f wri t ing

w as the con text to wh ich the book report

w as related. It is in relat io n to the book report a s a genre, as opposed to other

genres such

as the

n arra t ive , tha t discernmen t

of the

parts

w as

made poss i-

ble . In other w ords, i t i s the discernm ent of how the wh ole relates to the con-

text that enabled the discernm ent of the par ts (of the w ho le) .

VARIATION

W e i l lus t ra te the s i gn i f i cance of var ia t ion for the poss ib i l i t ies to learn by

referr ing to some s i tua t ions tha t w i l l

hope f u l l y

be eas i ly recognizab le to

the reader .

Con sider h ow w e leam w hat coldness, ta l lness , or heaviness i s . Sa ying

that

som ething is heavy does not mean an ything to us unless we experience

this agains t the background o f a difference in w e igh t , t ha t is, w e igh t t ha t can

vary.

In the

same w ay,

for

i n st ance , know ing wha t

red is

presupposes

the ex-

perience of other colors , that is , a var iat ion in colors . Even k now ing w hat

color i s presupposes an experienced variation of colors . Im ag ine for a mo-

m ent that there w as no variation of colors , tha t everything a round u s had the

same color. I t w ou ld be impo ssible for us to know w ha t red, green, or yel low

w ere, ju s t as i t wo uld be imp ossible for us to discern co lor as a feature. I f ev-

ery

object

w e

encountered

had the

same color, this

feature of the

object

w o u l d

not be discerned.

T he

s ign i f i cance

of

variat ion

for

seeing so m ething

in a new way

app l ies

to abstract objects as w el l . Research on the w ay that young chi ldren solve

simple ar i thmet ic problems has reported that chi ldren who always solve

simple addit ions ( l ike

2 + 3 =, 5 + 1 =, 1 + 4 =,

etc.)

by

start ing w ith

the first

addend, can suddenly chang e s trategy and s tar t w i th the b iggest num ber. In-

stead of 2 + 3, 1 +4 and so on, the order of the addends is chan ged , and the

child adds 3 + 2 =, 4 + 1 = (cf. Carpe nter & M oser, 1984). In this si tuation, a

variat ion of order of the addends is open ed. Y ou co uld say that an aspect that

was taken for granted or was undiscerned became a discerned aspect . By

this opening

of variat ion, a fea ture of addit ion (that is , that the sum is inde-

pendent of order of the addends) is discerned.



1 .

THE

S P A C E

OF L E A R N I N G 1 _5

O ne o f the m ain these s in th is book is that the pa t tern of var iat ion inher-

ent

in the

learning situation

is

fundamenta l

to the

developm ent

of

certain

capab i l i ti es ( see fo l low ing tex t ) . A n exper im enta l s tudy on mo tor l earn ing

(Moxley, 1979) demonstrated

the

importance

of

variation

on

l earn ing .

The exper im ent inc luded ch i ldren prac t i c ing to h i t a t a rge t w i th a ba l l .

C hi ldren in the control group alw ays threw the bal l a t the target from the

same di rec t ion , whereas ch i ldren in the exper imenta l g roup prac t i ced

throwing

the

bal l

a t the

t a rge t f rom di f ferent d i r ec t i ons . When

the two

groups were compared t rying to hi t the target

from

a di rect ion that was

new to

both groups ,

the

group tha t

had

prac t iced h i t ting

th e

target from d i f -

ferent di rect ions w as then

found

to be superior to the group tha t h ad p rac -

t iced hi t t ing the target

from

the same direct ion al l the t ime. I t can be

con cluded that var iation

in

direction seemed

to be a

cri t ical feature

of the

pract ice and thus also cr i t ical for learning. However , we are not arguing

for variation in general , and we are not saying that the more variation there

is , the bet ter the poss ib i l i t ies to learn. W hat w e bel ieve is tha t var iat ion en-

ables learners

to

experience

the

features that

a re

critical

for a

part icular

learning as wel l as for the development of cer tain capabi l i t ies . In other

w ords, these fea tures m us t be experienced as dimensions o f variat ion.

Lea rn ing ,

fo r

i n s t ance ,

to

solve

a

prob lem

in

d i f ferent w ays requi res expe-

r ience

o f

variat ion

in

solving s t rategies . U nde rs tanding

the

"manyness"

of

a

num ber requi res the exper ience of

d i f ferent

num bers , ju s t as the ab i li ty

to

throw

a

bal l from

dif ferent

di rec t ions

and

still

hit a

target requires

the

exper ience o f th row ing an ob jec t from

different

ang l es , and rea l iz ing h ow

a

genera l p r inc ip le can encom pass

d i f ferent

exam ples requ i res the exper i-

ence of at leas t tw o

d i f ferent

examples , and so on .

In m a them at ic s , different strategies for solving problem s, different n u m -

bers,

and so on all

m a ke

up

dim ensions

of

variation.

O ne

particular solving

strategy is one

va lue

in a

dimension

of

variat ion, w hereas

a

different

strat-

egy is another value in this dim ension. And thus the strategy as used in a spe-

cif ic example i s an ins tance of tha t s t ra tegy . When we exper ience

something, we discern aspects, or features, of the object and we experience

values in the corresponding dimensions of var iat ion. The experienced as-

pects

are

discerned

as

values

in dimensions of

variation.

I

experience

the ob-

ject on my table , for example, as a b lue, cyl indrical , ceramic mug with a

handle (an instance).

"Blue"

a nd "cylindrical" are values in dimens ions of

variat ion (e.g. , these are perceived in relat ion to the experience that they can

vary).

Features of the m ug , such as the color, shap e, ma terial , and so on, are

sim ultaneo usly discern ed as a pattern of dim ensions of variat ion (or to put i t

s imply, as a pattern of variat ion), and these featu res consti tute the pa rt icular

object .

In

order

to

experience

the

object

as a

blue, cylindrical , ceramic m ug ,

all of these aspects m us t be discerned and related to potential dim ensions of

variation.

A nd because these aspects are necessary for defining th e object in

quest ion, they

are

also cal led

its

cr it ica l fea tures .



M A R T O N , R U N E S S O N , T S U I

Patterns of Variation

A ccording to the preceding l ine of reasoning, i t i s necessary to pay close at -

tent ion

to

w h a t

varies

a nd

w h a t

is

invariant

in a

learning s i tuat ion,

in

order

to

understand wh at

it is

possible

to

leam

in

that si tuation

and

w ha t no t .

In

the different studies reported in th is book, w e are able to

ident i fy

certain

patterns

of

vanat ion :

1

. Con tras t. A s al ready m ent ioned, in order to experience som ething, a

person must experience something else

to

com pare

it

w i t h .

In

order

to un-

derstand wha t "three" is , for ins tance, a person m us t experience som ething

t ha t

is not

three: "two"

or

"four,"

for

exam ple . This i l lus t ra tes

h o w a

value

(three,

fo r

ins tance )

is

experienced wi thin

a

cer ta in dim ens ion

of

vanat ion ,

w h i c h

corresponds

to an

aspect (nu m erios i ty

or

"manyness") .

2.

General iza t ion. In order to fu l ly under s tand wh a t

"three"

is, w e m u s t

also experience varying appearances

of "three," for

exam ple th ree apples ,

three monkeys, three

toy

cars, three books,

and so on.

This vanat ion

is

nec-

essary in order for us to be able to grasp the ide a of "threeness" and separate

it

from i r relevant features (suc h

as the

color

o f

apples

or the

very

fact tha t

they

are apples) .

3.

Separat ion .

In

order

to

expenence

a

certain aspect

of

s o m e t h in g ,

and

in

order

to

separate th is aspect

from

other aspects ,

it

m us t vary w hi le o ther

aspects rem ain invariant . This

i s how the "angle"

aspect

o f

h i t t ing

a

target

wi th a bal l w as developed in one group o f ch i ldren in M ox ley ' s (1979) ex-

periment , m ent ioned previously .

The

expenm ent co uld a l so

be

expanded

by

sys temat ica l ly

varying

the

di s tance

to the

t a rge t ,

fo r

ins tance , w hi le o ther

aspects were kept invariant; then sy stem at ica l ly vary ing the w e i g h t of the

bal l ,

w hi le keeping other aspects invariant ,

and so on . In

th is

way the

ch i l -

dren could

be

prepared

fo r

various other s i tuat ions , such

as

hi t t ing

targets

from dis tances they have never thrown f rom, w i t h ba l l s

o f

vary ing (and

novel ) weigh ts ,

and so on.

4.

Fusion.

If

there

a re

severa l c r i t i ca l a spec t s t ha t

th e

learner

has to

take in to con s idera t ion

a t the

s a me t i me , t h e y m u s t

a l l be

exper i enced

s i-

m u l t a n e o u s l y . I n

eve ryday

l i f e , i t is

s e ldom tha t on ly

o n e

a spec t

o f

some-

th ing va r ie s a t a t ime , and so t he way i n w h ic h we re spond to a s i t ua t i o n ,

such

a s

h i t t i n g

a

t a rge t w i th

a

ba l l

o r a

p rob l em

o f

h u m a n re l a t i o n s , sp r in g

f rom

a

more

genera l ho l i s t i c perce p t ion

of the

s i t u a t i o n .

W e c a n

c o m p a re

t h i s

w i th a m ar r i age cou nse lo r ' s p ro fes s iona l w ay o f s ee ing hu m an re l a -

t i onsh ip p rob l ems . The counse lo r i s p robab ly s ee ing d i f f e r en t cases in

terms

o f a l i m i t e d n u m b e r o f a n a l y t i c a l l y s e p a ra t ed , b u t s t i l l s i m u l t a -

neous ly exper ienced, aspec t s .

O u r

c o n j e c t u r e

is

tha t see ing

a

cer ta in

c l a ss o f phen om ena i n t e rm s o f a s e t o f a spec t s tha t a re an a ly t i ca l l y s epa-

ra ted b u t s i m u l t a n e o u s l y e x p e r ie n c e d p r o v i de s a mo r e ef fec t ive bas i s fo r

p o w e r f u l

ac t i on t han

a

g l o b a l , und i f f e r e n t i a t e d

w a y o f

s ee ing

th e

s a m e



1 .

THE SPAC E O F L E A R N I N G T 7

c lass

o f

p h e n o m e n a .

W e

bel ieve th at sep arat ing

th e

aspec t s

f i rs t and

then

fus ing them

together is

more ef f i c ien t ( f rom

th e

view

o f

being able

to

adap t to chan ging condi t ions ) than never t ak ing th e cr i t ica l aspec t s apa r t .

W e also bel ieve that th is

fus ion

wi l l unavoidab ly t ake p lace th rough th e

s i m u l t a n e o u s

var ia t ion in the d imens ions o f var ia tion cor responding to

th e

cr i ti ca l aspec t s .

A nother exa m ple of th is type of

fusion

is presen ted in the com parison of

tw o

primary classes

in

Chinese languag e

in

chapter

4,

whereby different

as-

pects of the same word ( form, meaning , p ronuncia t ion) are successful ly

fused in one of the

classes,

but not in the

other.

In

chapter

8,

there

is a further

example of this type, in the comparison of two groups of secondary eco-

nomics classes .

In

this exam ple,

the

elasticity

o f

demand

and the

elasticity

of

sup ply are f irst separated and then

fused

in the classes in one group ("the

learning study" group),

but not in the

other group ("the lesson study"

group), in w hich they are only deal t w i th one at a t ime .

S I M U L T A N E I T Y AN D AWARENESS

W e

have thus m ade

the

point that

in

order

to

discern

a

feature,

a

person m us t

experience variation

in

tha t

feature .

For

example ,

in

order

to

experience

a

teenage girl as strikingly tall , w e must have encountered teenage girls as

typ ica l ly

being sho rter

or

considerably shorter than this pa rt icula r girl .

The

experience of tal lness derives

from

jux tapos ing w hat we see and w hat we

remem ber ; wha t we exper ience now and w hat we have experienced befo re .

W e

have

to be

aware

of

both

at the

same t ime.

In

general ,

to

experience variation am oun ts

to

experiencing different

in -

stances at the sam e t im e. A part icular co lor is experienced aga inst the bac k-

groun d of other colors tha t w ere experienced in the past; an act of kindn ess

is

experienced against

the

background

o f

acts

o f

kindness

o r

cruelty that

w ere experienced in the past . V ariat ion is experienced very m uc h as we ex-

perience

a

m elody. Each tune

is

experienced

in the

context

of

other tun es.

O f

course ,

we w ou ld never experience a m elody i f w e experienced each tone

separately, one at a t im e. In the sam e w ay, w e can never exp erience variat ion

in

any respect i f w e expe rience every instance one at a t im e. In order to exp e-

rience variat ion

in a

certain respe ct ,

w e

have

to

experience

the

different

in-

stances that vary

in

that respect s imul taneously , that

is , we

have

to

experience instances that

w e

have encountered

a t different

points

in

t im e,

at

the s a m e

time. W e call th is

diachronic

s imul tanei ty . This i s the s im ul taneou s

experience of different ins tances at the same t ime, which is necessary for

experiencing variat ion in a certain dim ension and for discerning the aspect

of an

instance

corresponding to the

dimension. How ever,

you

wi l l remem -

ber

that

w e

have previously defined

a way o f

seeing som ething

as the

dis-

cernment of var ious cr i t ical features of an ins tance s imul taneously . This



j_8


type of s im ul tanei ty , is cal led

synchronic s imul tane i ty ,

and is the experience

of different co-exist ing aspects of the same thing at the same t ime.

Let us br ief ly return to M oxley 's s tudy of chi ldren p ract icing to hit a tar-

get with a ball . In the ci ted exam ple, variat ion in the direction or an gle of the

throwing w as com pared to the absence of var iation, in relat ion to a group 's

abili ty

to

per form

the

task

o f

hi t t ing

the

target

f rom a

direct ion that

was new

to both groups . A s we m ent ioned, i f the chi ldren were to leam to hit a target

wi th a ny bal l , f rom any di rect ion, unde r any c ondi t ions , they w ould need to

pract ice throw ing the bal l f rom different di rect ions , w i th

different

ba l ls (e .g .

each one a different w eigh t ) , under different con di t ions (e .g ., different w i n d

force) . M as ter ing th is capab i li ty w ould am ount to be ing ab le to discern a ll

o f

those features

and

being able

to

take them

a ll

in to considerat ion

at the

same t im e ( i .e . , seeing bal l -throw ing s i tua t ions

in

t e rm s

o f

features cr i t ical

for hi t t ing a target ) . Doing so amoun t s to exper iencing th e different aspects

present at the same t ime s im ul taneous ly . In a m etaphor ica l sense , w e could

ta lk abo ut spat ial in tegrat ion o r synchronic s imul tane i ty a t one par t i cu lar

point in t ime.

W hat does

it

take

to

experience

different

aspects

o f the

s ame p h e n o me -

non? C lear ly , the aspects m ust be discerned and the person m ust be focal ly

aware o f t h em . So s imu l tanei ty in the synch ronic sense is obvious ly a func-

t ion

of

di scernm ent .

Ex per i enc ing va r i a t i on i s , however , a s w e have show n , con t i ng en t on

th e

s i mu l ta n e o u s a w a r e n e s s

o f

i n s t ances t ha t appea r

a t d i f fe ren t

p o i n t s

in

t im e . W e w ou ld no t be ab l e to s ee a s t ory a s a s to ry w i tho u t t he s im u l t a -

neous awareness o f o ther s to r ies tha t we have come across in the pas t .

T h i s is a k i n d o f t e mp o r a l i n t e g r a t i o n , a s i m u l t a n e o u s a w a r e n e s s o f w h a t

w e a re exper i enc ing and wh a t w e have exper i enced be fo re . C l ea r ly , a s

w e l l ,

i n w h a t w e a r e e x p e r i e n c i n g , w h a t w e h a ve e x p e r i e n c e d b e f o r e

m u s t be or m u s t h a ve

been

d i s ce rned in order for us to e x p e r i e n c e it . In

th i s r e spec t , no t on ly synch ron i c bu t a l so d i ach ron i c s i m u l t a n e i t y is a

fu n c t i o n

o f d i s ce rnmen t . Fu r the rmore , t he re can be no exper i ence o f

s y n c h ro n i c s i m u l t a n e i t y w i t h o u t

th e

e x p e r ie n c e

o f

d i a c h r o n i c s i m u l t a -

ne i ty ,

b e c a u s e

in order to

exper i ence

tw o

aspec t s

of the

s a me t h i n g

to -

ge the r we mus t d i s ce rn bo th s epa ra t e ly , and t h a t c a n o n l y h a p p e n b y

h a v i n g exper ienced va r i a t i on i n t he d im ens ions o f va r i a t i o n co r respond-

in g

to

e a c h

one of the

a spec t s .

There

is another

form

o f the s im ul taneo us expenenc e in the synchronic

sense, tha t is, one t ha t is different from exper iencing different aspects o f the

same th ing at the s ame t im e . W ha t w e have in m in d is the s im u l taneous ex-

perience of the w hole and i ts par ts ; the wh ole be ing, for exa m ple, a deer in

the

fores t (m ent ioned previously) ,

a

text

w e

read

in

school,

o r

bas ica l ly any-

th ing that can be m ea ning ful ly divided into com ponen t par ts .

In an example tha t appears in chapter 4, tw o teac hers ' w ays of teach ing

Chinese a re com pared. B oth teach ers w ere try ing to develop t h e s t uden t s '



1.

THE

S P A C E

OF

L E A R N I N G

1 _9

vocabula ry in the context o f the same story. O ne of the teachers deal t w i th

the story as a whole first, then wi th

different

paragraphs, sentences, and fi-

nal ly with individual words, taking each feature of the words (such as

m eaning , sp el l ing, i .e . ,

stroke

pat tern, and pronun c ia tion) o ne at a t im e . In

other words,

the

teacher dealt with

the

vocabulary i tems (words) sequen-

t ial ly and in isolation, instead of in context . T he other teacher seemed to

act in

accordance w ith

the

view tha t

the

m ean ing

of a

character

is mo di f ied

by

the

word

or phrase in

w hich

it

occurs; that

the

m ean ing

of the

wo rd

or

phrase is m odif ied by the sentence in w hich i t appears; and that the m ean -

ing of the

sentence

is

m odi f ied

by the

text

in

wh ich

it

forms

a par t . S he

tried to make sure that al l of the different levels of the text (story, para-

graph, sentence, w ord, character)

were

present in the s tudents ' awareness

at the

same t ime ,

by

deal ing with each level

in the

context

of the

nex t

superordina te

level. Furtherm ore , she deal t w i th di f ferent features of the

cha racters in the con text of each w ord, instead of deal ing w ith each char-

ac ter

as an ind ividua l un i t as the other teacher had done.

Awareness

B u t ,

where

are instances, aspec ts, parts, and wh oles w hen they are exp eri-

enced sim ultan eo usly ? In a vivid sense they are present to us. They are not

s imply s tored away somewhere deep down

in our

m e m o ry;

we can

hear

them or see them , feel them, sense them or imag ine them . They are in our

awareness .

Awareness (w e use the

word

as a

synonym

to

consc iousness)

is the to-

tality of a pe rson 's experiences of the wo rld, a t each p oint in t im e. I t i s a l l

that

is

p re sen t

on

every occas ion . A wareness changes dyna m ica l ly

all the

t ime and every s i tuat ion is experienced against the bac kg rou nd o f previ-

ous experiences. T his occurs to varying degrees of course , bu t poten t ia lly ,

aw areness is present aga inst the backg round of a very, very g reat nu m ber

of previous experiences. And to

affect

our experiences a t this very mo-

m ent , here and now, these previous experiences a l l have to be present a t

any one

t im e .

In a

wa y ,

i f we

exaggera te th ings

a

l i t t le ,

we

m i gh t

say

tha t

we are aware of everything a l l the t ime, s imply not in the same way.

Actua l ly there

are

very

few

th ings tha t

we can be focal ly ,

tha t

i s ,

sharply,

aware of at the same t ime , but a lot can affect the way in w h i ch we are

aware o f these th ings . In accordance w i th Gu rw ich ' s (1964) account , w e

mi g h t say tha t the charac te r is t ic of hum an aw areness i s tha t a l im i ted num -

ber of ob jects , aspects of objects , or s i tuat ions com e to a t t rac t our a t tent ion

( i .e. , become focused), whereas a very great number of other things are

there as bac kg rou nd. I t i s against this back grou nd that w e experience the

things that w e are foca l ly

aw are

o f, that is, the things that are the focus o f

our a t tent ion .

A

gen eral ized

and

ever chang ing f igure-grou nd st ructure

is

t hus characteris t ic

for our

awareness .



20


Discernment,

Awareness and Si mul ta ne i ty

Al though learning can be viewed as the developm ent of both cap abi l i t ies

and

values,

the

focus

o f

this

book,

as we

stated earlier,

is on

learning

as the

developm ent o f capab i l i ties . The kinds of

capabil i t ies

we

focus

on are those

that empow er learners to deal w ith s ituat ions in

power fu l

w ays , t ha t is, to si-

m ultaneously ( in the diachronic sense) focu s on features cri t ical for achiev-

ing a

certa in a im. However,

we can

o nly exper ience s im ul tane ou s ly tha t

w h i c h w e can discern; we can only discern wh at we experience to vary; and

we can only experience variation i f w e have experienced different instances

previously

and are

ho ld ing them

in our

awareness s imul taneous ly

( in the

diachronic sense). So the three (or rather

four)

key concep ts of the theory

are intimately l inked, each of them being a func t ion o f another.

T H E SPACE O F L E A R N I N G

A s w e have a lready pointed ou t , nobo dy can discern a certa in feature w i t h -

out exp eriencing varia t ion in a d im ens ion corresponding to that fea ture . L et

us assume that tw o

persons,

A and B, are engaged in a conversat ion w ith a

stranger, C , in a sm al l cot tage in a N epa le se m oun ta in v i ll age . A f t e rward , it

turns o u t tha t A had not iced that C spoke w i th a typica l southweste rn N epa-

lese dialect (a ctually all

three

o f them did so), w hile B did not notice this at

all. W hy was it

tha t

B did not

discern

C 's

d ia lec t w hereas

A

d id? W hat

w as

varying, as far as dia lects are concerned? A s it was , no th ing var ied in the ac-

tual

situation,

but A had

heard

a lot of different

Nepalese dialects previ-

ously

and he re la ted C's w ay of speaking to w ha t he had experienced and

not iced the s im ilarity w ith a pa r t icula r N epa lese d ia lec t , and the difference

w hen compared

to

other

Nepalese

dialects.

B , on the

other han d,

had

never

been ou ts ide

h is

v i l lage ,

had

never w atched

T V o r

l i s tened

to the

radio,

and

had actua l ly never heard any other dialect . He cou ld no t discern the d ia lec t

because he did not

know

of any

other.

T he

variation exp erienced

by A was a

resul t of the m em ories of past events that A brou gh t into the s i tuat io n, and

t hus a lso into his encoun ter w ith C .

Now let us

assume that

C

speaks

a

different dialect.

If this were

the

case ,

A

w ould probably not ice

th e fact, bu t

also

B

wo u l d

not ice that

C

speaks

in a w ay

that

is

different

from all the

other people

he has

ever

heard (he may even find it very

difficult

to understand C). A t the same

time,

h e

w ould probably becom e co nscious

of the fact

tha t

he

h imse l f

has a

certain

way of

speaking.

In the first

example,

the only variation w ith

respect

to dialects w as the

fac t

th at A had had previous exp erience of hearin g other dia lects , and that

C's way of

speaking

w as

juxtapo sed w i th th i s exper ience .

In the

second

example , there

is

variation

to be experienced in the

actual s i tuat ion.

T he

ins igh t th at there are

di f ferent

w a y s o f speaking can be derived from s i m -



1 . T H E S P A C E O F L E A R N I N G 21

p ly

being exposed to them in this s i tuat ion.

There

is a space created for

gaining

this

insight in the second case.

This

space is created by chal leng-

ing

th e taken-for-granted nature of the

experience

o f people's w a y s o f

speaking

in the

person

wh o h as

previously only been exposed

to one way

of speak ing . Creat ing a space m eans opening u p a dime nsion of variat ion

(as

compared

to the

taken-for-granted nature

of the

absence

o f

var ia t ion) .

As o u r exam ple i llus t rates , however , som eone w hose past experiences a re

suf f ic ien t

fo r

pe rce iving

th e

necessary pat tern

o f

variat ion

can

exper ience

variat ion w i thou t that space ( i .e .,

t h e

necessary pat tern

o f

variat ion ) being

cons t i t u t ed in the

imm edia te s i tua t ion .

T he

space o f learning re fers

to the

pat tern o f var iat ion inherent in a s i tuat ion as observed by the researche r .

This

space

is a

necessary condition

for the

learner's experience

of

that pat-

tern of var iat ion unless the learner can experience that pat tern du e to w ha t

she has encou ntered in the pas t .

N ow let us consider another type of var iat ion. W hen w e con sider a mov-

ing

body for example , w e usu al ly look at i t f rom the po in t of view of the

ground.

W e can say

that

the

ground

is

taken

as

a f rame

of

reference.

But we

could

also look

a t the

m oving body

from the

po in t

o f

view

of

another

f r ame

of

r eference;

from our own mo ving body ins tead o f the ground, for ins tance .

A nd if we do that , w e introd uce variat ion in

f rames

of re ference . T he very

idea

o f f rames of refere nce presuppo ses variat ion, as does the insight tha t

looking at a body in movement f rom th e point of view of rest (the ground)

amo unts to

adopt ing

a

par t icular f ram e

o f

re ference .

In

addit ion

to

looking

at

m oving bodies

from the

point

of

view

o f

rest ,

w e

also ha bitually look

at

them when they

a re

under

the

influence

of the

gravita-

t ional

force of the

earth.

So

wi thout being aware

of

this ,

we

take

the

gravita-

tional force for granted. In order to break this taken -for-granted natu re of our

awareness of the world, variation in the gravitational force mus t be intro-

duced.

This can be done by traveling in a space shuttle, or more

easily,

by

looking

a t

pictures

f rom a

space shuttle,

by

engaging

in a

simu lation

of the ef-

fects of varying gravitat ional force or sim ply carrying out a thoug ht experi-

ment .

These tw o

dimensions—gravity

and frame of

reference—form

a space

of learn ing . A space of learning

com prises

any

number

of

dim ensions

o f vari-

ation and denotes the aspects of a situation, or the phenomena embedded in

that

situa tion, that

can be

discerned

due to the

variation presen t

in the

situa-

t ion.

V ariation that

is not

present

in the

situation

can

still

be

discerned, how -

ever,

if variat ion is brought in by m eans o f the learner 's m em ory of previous

experience.

W e

should notice, here, that

a

space does

n ot refer to the

absence

of

constraints,

but to

something actively constituted.

It

del im i ts w hat

can be

possibly learned (in sense of discerning) in that pa rticular situation.

B ut w e are not interested in al l types o f variation. W e m ust look at the sit-

uation

from the

point

o f

view

of a

particular object

of

learning.

And by do-

ing so we can find out

whether

or not it is

possible

for the

learner

to

appropriate that part icular object o f learning in that par t icular s i tuat ion.



22


Th e Object of L e a r n i n g

The object

of

learning can be d efin ed by i ts cri tical fea tures, that is, the fea-

tures that m ust

be

discerned

in

order

to

const i tu te

the

m eaning a imed for .

The

quest ion

w e

mu s t

ask

therefore,

is to

wh at ex ten t

we f ind

variation

in

the relevant respects. A s learners can only discern that which vanes, w e

m ust look for the pattern of variat ion necessary for deve loping the required

capa bil i ty. U nless the re is variat ion in al l the respects corresp ondin g to the

cri t ical fea tures, that

is, the

necessary pattern

of

variat ion

is

presen t , this

ca-

pabil i ty cannot

be

developed.

W e a re

thus ta lking about

the

necessary p at-

tern

of

variat ion.

In

order

to

develop

a

cer tain capabi l i ty ,

the

l earner mu s t

enco unter a cer tain p at tern of var iat ion, regardless of the arrange m ents for

teach ing

tha t

are

m a de,

a nd

regardless

of the w ay in

wh ich learn ing

is

orga-

nized (e .g . , wh ether the learner par t ic ipates in an au the nt ic pract ice, or s it s

in a lecture h all with 300 students). The space o f learn ing tel ls us wh at i t is

possible

to

learn

in a

cer tain s i tuat ion.

In

th e

light

of a

specific object

of

learning ,

the

space

of

learning

is a

rather

specific

character izat ion of the in teract ion in the classroom. As al ready

pointed out ,

the

object

of

learning

is

there,

to

beg in w i th ,

as an in tended o b-

ject

o f learning as seen

from

the teacher 's perspective, then i t is somehow

realized in the

classroom

in the form of a pa rt icular space of learning. This is

the enacted object o f learning as

seen

from th e

researcher ' s po in t

of

view,

const raining w ha t i s poss ib le to leam .

W e

can see

tha t

the

space

of

learning con st i tu ted

in the

classroom

is the

enacted object

of

learning.

This is how the

object

of

l earn ing

is

con st i tu ted

in the m ost con crete sense. A nd i t is this that m atters rega rding op portuni-

t ies to learn in school . F actors such as c urr icu lum , teach er ' s in te nt ion , and

so on, are

m edia ted th rough

the

enacted object

of

l earn ing .

The way

that students see, understand,

and

make sense

of the

object

of

learning when

th e

lesson ends

and

beyond,

is the l ived object

o f

learning.

T he

pedagogical s i tuat ion

and

w h a t

the

students

actual ly

learn

can

thus

be

described

in the

same terms.

So now we can describe

learning

and

teaching

in

relat ion to one another, from the point of view of learn ing, not as a rela-

t ionship

between cause

and

effect ,

but as a

re la t ionsh ip be tween w hat

is

m ade poss ib le and w hat poss ib i l i t ies are actu al ly m ade use of .

The focu s should thus be on learning in the first instanc e and on teaching

in the second; the

focus

should be on wh at shou ld be learned and w hat i s ac-

tual ly learned.

A nd

w h a t

is

actua l ly learned should

be

understood

in

term s

of the con dit ions of learning . If learning is ac tua lly tak ing place in the class-

room, w e should try to unders tand w hat the students leam in term s of wha t

is

taking place

in the

classroom. Whatever takes place

in the

classroom

makes

differing

sense to different students. This is one of the most solid

conclusions that can be drawn f rom our own research (Marton & Booth ,

1997)

o r

tha t

of

others.

N o

co ndi t ions

of

learn ing ever

cause

lea rning. They




only m ake i t possible for learners to learn c ertain things. A nd this , in our

view,

is exact ly wha t pedagogy is about , especial ly the type of pedago gy of

learning that we are putt ing forward in this book, that is,

making

learning

poss ible. Le t us consider tw o si tuations ( tw o classroom scenarios)

from

the

point of view of learning or developing a certain c apabil ity. W e m ight de-

scribe what i t is possible to learn with view of that capabil i ty in the two

classrooms; we might descr ibe what i s taking place in each classroom in

terms o f the possibilities for learning that are brought about, an d in terms of

w h a t kind o f space of learning i s con st i tu ted. The space

of

learn ing thus de -

pic ts the possibil it ies of learning in relat ion to the ca pab il ity in qu estio n.

Th rough out th is book, w hen w e talk abo ut wha t i t i s poss ib le to learn, w e

restrict ourselves to the kind o f learn ing we h ave discussed in this chap ter,

namely learning to see certain things in certain w ays. But even bearing this

res t ric tion in m ind, there w i l l und oub tedly be a great num ber of th ings that

vary, and hence that w i ll or could be discerned. The space of learning does

not d enote al l that is possible to leam , even in the restricted sense of learn ing

(i.e., learning to see). The space of learning ca ptures o nly what i t is pos sible

to learn in a situation

from

the point of view of wha t is m eant to be learned.

W hat i s m eant to be learned is the o bject of learning, wh ich in our case is

a c apab i l ity of seeing som ething in a cer tain w ay. A s we p ointed out ear lier,

a

cer tain way o f seeing som ething can be character ized in term s of the as-

pec ts of a s i tuation or phenom enon that are discerned and focused on s imul -

taneously, or more precisely, the crit ical aspects of the situation or the

phenomenon that are discerned and focused on s imul taneously . Now the

quest ion is : How do we know w hat dimensions o f var iat ion w e should look

for?

How do we know w hat cr i t ical features there are for a certain class of

s i tuat ions

to be seen in a cer tain w ay? How can w e character ize the nature of

a certain capability?

C arlsson (1 999) investigated "the a natom y

o f

ecological u nders tanding,"

com pris ing, am ong other th ings ,

th e

unders tanding

o f

pho tosynthesis , recy -

cl ing,

an d the con servation of energy. One of the cr it ical feature s— actua l ly

the most cr i t ical feature of al l of these component capabil i t ies—was the

idea

of

transformation, that

is ,

that

one

thing turns into something qualita-

tively different: Sunl igh t and water are t ransform ed into carbohydrates a nd

oxygen in photosynthesis; material microscopic part icles from hum an be-

ings

and

an im als,

and so on, are for

instanc e rearrang ed into soil,

and

soil

re -

arranged into plants; and on e

form

of energy, such a s hea t , can be turned into

and stored in solid or l iquid form through th e conservation of energy.

In what sense

is

t ransformat ion

a

critical feature

of

ecological under-

standing

and how can i t be found or discovered? Is it by m eans of co ntem-

plat ing the concept o f ecologica l unders tanding W ell, this w as definitely

not

the way in

wh ich C arlsson found

it. In

C arlsso n's study, this critical fea -

ture (transformation) appeared empirically, as a contrast to another

frequent

w ay

o f thinking that im plied that certain things were perceived a s consum ed



24 M A R T O N , R U N E S S O N , T S U I

(e.g., sunlight, water, dead bodies, energy)

and

that other things were per-

ceived

as

independen tly produ ced (e.g., coal, oil ,

or the

chlorophyl l

in f low-

ers and

trees).

The law

o f

variation applies thus

to the

research er 's

work

as

w el l.

It is not

possible to discern a certain way o f th inking about something wi thout the

contrast

o f other

ways

of

th inking about

the

same thing.

T he crit ical feature

is

critical

in

dis t inguishing

one way of

th inking

from

another,

an d is

relative

to the group participating in the study, o r to the p opu lat ion represented by

the

sample.

F or

instance ,

if all the

p art ic ipants

in

Carlsson's study

had em-

braced the idea of transform ation, t ransform ation m ay never have shown i t-

self as a cri t ical feature. The cntical features have, at least in part , to be

found

empir ical ly—for ins tance, through interviews wi th learners and

through the analysis of w hat i s happening in the classroom — and they also

have to be fou nd for every object o f learning

specifical ly,

becau se the cnt i -

cal features are cri t ical features of spe cific obje cts of learn ing.

Th e Space of Le a r n in g Is the E n a c t e d Object of L e a r n i n g

The enacted object of learn ing is the research er 's descr ipt ion of w hethe r , to

w hat extent

an d in

what fo rms ,

the


of a

par t i cu lar

ob-

jec t of learning appear in a certain set t ing. Th e ena cted obje ct of lear nin g is

t hus what w e have also called the space of learning, thereby de pict in g w ha t

is

po ss ib le

to

l earn . W hat fo l low s from th is l ine

o f

reasoning

is tha t

w h e n

w e talk about learning, teaching , and other related mat ters, w e shou ld try to

be exp l ici t about w hat we h ave in our m inds as far as the quest ion of "W hat

is

learned?"

( i .e. , "What should be

learned?"

"What can be poss ib ly

learned?" "What

is

actu al ly learned?")

is

concerned.

In th i s way , the space o f l earn ing , w hich com pr ises different d imens ions

of variation, is con sti tuted by l ing uist ic m ean s in the inte rac tion between

teacher and students.

T H E

L I NGUI S T I C

CONSTITUTION

OF THE

SPACE

O F

L EARNI NG

In

the

previous discuss ion,

w e

descnbed

learn ing as the

process

o f

coming

to experience the world in a certain way. W e put forw ard the thes is tha t the

space o f learn ing is the space of variat ion, and that the dim ens ions of varia-

t ion that can

be

opened

up and

those tha t

are

actually opened

up

contribute

to qua l i ta t ive di f ferenc es between the wa y in w hich so m ething

c a n be

expe-

r ienced an d the

ac tua l

way in

w h i c h

it

is experienced.

T he

space

o f

l earn ing ,

therefore,

is

also

an

experiential space.

In talking abo ut the space of learning as an experiential space, w e are re-

ferring

to experience not as an in stan tiat ion , but rather as a po tentia l for ex-

periencing, seeing, and un der stan din g (see also Hal l iday & Mat th iessen ,



1 .

T H E

S P A C E

O F

L E A R N I N G

25

1999). It is in relation to this potential that learners can m ake sense of a par-

t icular object of learning. A s such , this space is elastic; i t can be w idened if

the teacher affords learners opp ortunit ies to explore the ob ject of learnin g in

a variety of ways.

A nother thesis

we put

forward

in

this volum e

is

that language plays

a

cen-

tral

role in the construal of experience,

that

it does not

simply

represent

expe-

rience, as is widely perceived, but mo re imp ortantly, it constitutes experience.

Seen in

this l ight, languag e plays

a

central role

in

learning,

and

understanding

how the learning experience is being con stituted by langu age is crucial to un-

derstanding

how

different ways

o f

experiencing

the

object

of

learning

are be-

in g

brought about

in the

classroom.

L a n g u a g e a n d t h e C o n s t r u a l o f

E x p e r i e n c e

L et

us clarify w hat w e mean by langu age and the construal of experience.

The p osi t ion that w e are adopt ing is that the same phenom enon can be expe-

rienced in qualitatively different ways, and that the different construal of

the experience w il l be ref lec ted in the lang uage used. For exam ple , le t us

imagine that the jan i tor of a school locked the door o f a com puter laboratory

and

tha t tw o teachers were t rying to open the door bu t co uld no t . Teacher A

said, "The

jani tor

locked

the

door," whereas Teacher

B

said, "The door

is

locked." The same phenomenon was construed in different w ays by these

tw o

teach ers . For Teacher A , the jani to r w as the point of departure o f the

message, whereas for Teacher B, the door was the point of departure .

Hence , for Teacher A, the m essage w as about w ha t the jan i tor did: that is ,

that he had

locked

the

door.

B y

contrast ,

for

Teacher

B, the

m essage

w as

about the state of the door, that is , that i t w as locked and therefore could no t

be opened.

The re la t ionsh ip between langu age and experience can be best seen by

examining data on chi ld language development . Hal l iday's (1973, 1975)

seminal work on Nigel ' s language development shows that for ch i ldren ,

learning language

is also learning

about

the

world through language.

Hall iday ( 1 993) observed that

Whe n c h i l d r e n lea rn langu age , they

a re no t

s imp ly engag ing

in one

type

o f

l ea rn ing

am ong m any; ra ther , they a re learning the foun dat ions o f learning itself . T he dist inc-

t ive

cha rac te r i s t i c o f

human l e a rn ing

is

tha t

it is a

process

o f

m a k i n g m e a n i n g — a

semio t i c process ;

and the

p ro to typ ica l f o rm

o f

h u m a n semio t ic

is

l a n g u a g e ,

(p. 93)

A s

the child

experiences

th e

world

and as he learns how to mean

(Hall iday, 1973), his m eaning p otent ia l is being recon st i tuted. The reconst i-

tut ion of his m eaning potent ia l finds its rea lization in the w ay the chi ld re-

constructs his

"grammar"

so that i t eventually shares the conventions of

adult gramm ar.



26 M A R T O N , R U N E S S O N ,

T S U I

Let us take for exam ple chi ld lang uag e developm ent . A t an early s tage

of language deve lopment , the ch i ld ut ters words as "annotat ions of experi-

ence"

(H alliday 1993,

p .

99).

For

example ,

on

seeing

a

round objec t ,

a

Cantonese speaking chi ld w il l say "bo bo"

[ > .

$.] (b a l l ), no m a t te r whe the r

it is a round doorknob, a balloon, or a basketball . A s adul t s comm ent on

the

chi ld 's ann ota t ions

b y

say ing , "Yes, it 's

a

bal l"

o r

"No, th a t ' s

not a

ba l l ;

it 's a

doorknob,"

they a re c lass i fy in g th ings for the ch i ld . ( In Can tonese ,

"bo" [ j& ] (bal l) is a generic term for a ll kinds of ba l ls . ) W hen the ch i ld ap-

propriates the

adul t c lass i f ica t ion

of a

round o bjec t

as "a

ball ,"

he is

also

implic i t ly c lassi fying what is not a bal l . In Hal l iday's

terms,

he is

"outclassing" (1 993,

p.

99).

2

In other words, the chi ld experiences varia tion am ong the round objects

that he sees: Objec ts tha t a re round and he can p lay w i th h i s m om m y are

called

"balls,"

and

objects that

are

round

and are

stuck

on

doors

are

"not

balls." This

experienced

variation

is

realized

in the

language that

th e

child

uses

to

m a k e

a

dis t inct ion between different k inds

o f

rou nd ob jects . Later ,

the child experiences variation within the class of "balls." He experiences

balls that can be blown up into big on es, are

l ight,

and can nse into the air,

and those that cannot. This kin d of "ball" is called a "balloon." A t this stage,

the

child

is

experiencing variation

in the

dimension

of

"ball,"

and

there

are

three values in this dim ension : "ball," "balloon," and "not ball." W ith this

further

dist inction, the ch i ld 's seman t ic sy stem of "ball" changes . It is no

longer a system w ith two term s, but w ith three term s. The m eaning of "ball"

changes

as

we l l.

"Ball" no

long er ju st means "not doorknob";

it

m eans "not

balloon"

a s w ell.

The re la t ionship between langu age and experience is dia lect ic . The ex-

perienced variation enables

the

chi ld

to

discern

th e

d is t inc t ion s tha t

are

real-

ized in languag e , and the l inguis t ic d is t inc t ion enables the ch i ld to discern

the variation. A s Ha llida y (1 978) observed, in this process:

th e

construal of reali ty is inseparable

from

th e construal of the semantic

sys tem

in

wh ich the reali ty is

encoded.

In

this sense, l anguage

is a shared

m ean ing

poten tial , at

once both a part of exper ience and an inter-subjective

interpretation

of

experience,

(pp. 1-2)

This m eaning potent ia l

is

being reco nsti tuted every t im e

the

ch ild experi-

ences language

in

use,

and

experiences what

he can do

w i th l anguage .

L a n g u a g e an d Di s t i nc t i o ns

In order to m ake sense of w hat w e have experienced, w e need to be able to

reduce the in defin i te ly varied phenom ena of the world into a mana geable

number o f phenomena of sim ilar types. A s Britton (1970) pointed out, o b-

jec ts in the wo rld do not present them selves as readi ly

classified.

T he c lassi-



1 .

T HE S P A C E O F L E A R N I N G 27

f icat ions are given by hum ans in order to handle the world, and language is

a

principal

m e a n s

o f doing this . W e say "a principal means" because there

are certain class ificat ion s that

can be

done w i thout languag e .

F o r

example ,

if

someone

is asked to class i fy all the clothes in the w ardrobe, he could pu t

all

the w inter clothes in one pile, all the

w ork

clothes in ano ther pi le, and all

the

form al evening clothes in a third pile. However, in the m ajori ty o f cases,

it is not possible to m a k e

class i f icat ions wi thout language.

F or

example ,

how

does one

dis t inguish betw een

a

m ale hum an being

who i s

related

by

blood

to

one's father

and one who i s

not ,

by

nonl inguis ti c m eans?

A s

Sapir (1961) pointed out ,

.. . language

is

pr im ari ly

a

vocal actualization

of the tendency to see

realities symbo l i-

cal ly ... an

actualization

i n

terms

of vocal express ion of the tende ncy to

master

reality

not b y direct and ad hoc hand l ing of

this

elem ent but by the reduc tion of experien ce to

famil iar

forms, (pp. 14-15)

Adopting a similar stance to Sapir, Hall iday (1978) proposed that

Language

has to in te rpre t t he

w h o l e

of our

exper ience ,

r ed uc ing the indef in i t e ly var-

ied p henom ena o f the wor ld

a round

us , and

also

of the

wor ld

inside us, the processes

of

our own co nsc iousness , to a

manageab le

num ber o f

c lasses

o f

phenom ena : types

of

proces ses, events

and ac t ions , classes o f

objects ,

peop le and ins t i tu t ions , and the

l ike. (p . 21)

W e

po in ted o ut earl ier in this chapter tha t the contradiction between the

unl imi ted and

inexhaus tib le am ount

of

inform at ion avai lable

to us an d the

l imi ted capaci ty

of the

hum an mind requi res tha t

we be

select ive

in

wha t

w e

attend to. Th e th ings that w e at tend to are th ings tha t w e discern as cr i t i ca l ,

not in a

general sense,

but

cr i t ical

in

relat ion

to a

cer tain co ntext .

F or

th is

reason ,

the

dist inctions

or

c lassi f ica t ions

that

w e

ma k e

in the

process

o f re-

ducing the indefini tely varied phenom ena of the world into a m a n a g e a b le

n u m b e r

o f

classes

o f

phenomena

a re

n ecessar i ly select ive.

Let us

take

fo r

example

the way

th ings

are

class i f ied

in

different cu l tu res .

The fam ou s B ri ti sh anthropologis t Mal inow ski (1946) observed that societ-

ies

classify thei r surroundings according

to

thei r needs

and

interests ,

and

that

th is is done through language. F or example , in M al inowski ' s s tudy of

pr imit ive

l anguages ,

i t was

found that

the

indigen ous people

o f a

p r imi t ive

communi ty t ended

to

identify

and

different iate

the few

objects that were

use fu l

to them an d the rest were treated as an undifferen tiated heap . A p l an t

or a tree in a fo res t that was not connected to them t radi t ional ly or ri tually, o r

that

w as not usefu l to

t hem w ou ld

be

s im ply dismissed

as "a

bush."

A

bird

tha t p l ayed

no

part

in

the ir tradition

o r was not

part

o f

their diet w ou ld

be re-

ferred

to as "just a flying animal" (1946, p . 331). How ever, if an object w as

useful ,

it

w o u ld

be

n a me d

an d its

uses

and

propert ies described

in

detai l , that

is, it

w o u l d

be

dis t inct ly individua l ized.

T he fact

that trees

and

b i rds were



28

M A R T O N ,

R U N E S S O N , T S U I

not nam ed separately for their individual appearance s does not m ean that

the people o f th is com m uni ty could not see that th e trees o r b i rds were phys-

ical ly different . I t s im ply m eans that to them the di fferenc es were not so cr i t-

ical in

relat ion

to the

specif ic

contex t

o f

their everyday l ives

as to

warran t

m aking di s t inc t ions

b y

l inguis t i c m eans .

On e of the

m ost widely quoted examples

is

that Esk im os have seven wo rds

fo r

"snow,"

each of which m akes very fine distinctions between th e size of the

flakes of snow to indicate ho w heavy the snow is. Th e Sam i l anguage has al-

mos t 200 w ords for "snow," a nd each word indicates the con di tion of snow,

that is,

whether

one can

w a l k

on it, or ski on it,

w hat tem perature

it is,

whether

it

w i l l change quic kly

and how

(see V uolab, 2000). L angu age, therefore,

en-

codes

the

dist inctions m ade

and the

c ri tical features

of the

dist inctions;

th e

distinctions

are

app ropriated

and

m ain ta ined

so as to

ma k e

th e

di scernmen t

of

the cri t ical features possible.

Another example

is the

central i ty

of the fami ly and the

impor tance

o f

rank according to gen erat ion in the Chinese cu l tu re . This is ref lec ted in the

complex kinship terms that make very fine d i s t i nc t i ons be tween w he the r

one is

related

to the

fa the r ' s s ide

or the

m othe r ' s s ide,

and w ho is

related

to

w h o m

in the f ami ly

tree.

These

dis t inct ions

a re

cr i t ical

in

Ch inese cu l t u re

because they indicate the place that one occupies in the fami ly tree, and

hence

the

status

in the f ami ly ( in the

sense

of the

ex tended

fami ly) .

Because

of these dis t inct ions , it is possible to have a s i tua t ion w h e re a ve ry youn g

person has a h igher rank than somebody who i s con s iderab ly o lder, and

therefore the younger

person

i s addressed w i th a kinsh ip term that indicates

he or she is

zhang b e i ( P u t o n g h u a )

[ -^ j£ ],

t ha t

is, of a

m ore senior genera-

t ion

in the

extended family .

Dist inct ions that have been m ade

to

su it socia l purposes

a re not

only

e n-

coded

in the

l anguage

bu t

a lso ma in ta ined

b y

m e a ns

o f

l anguage .

I n

other

words,

th e

categories

se t up, and

hence

th e

di s t inc t ions m ade

by

language ,

no t

only express

the

social s tructure

but

also create

the

need

fo r

people

to

conform to the behavior a ssociated w i th these categories . The com plex kin-

ship term s

in

Chinese

a re a

real izat ion

a s

w e l l

as a

me a n s

o f

m a in t a in in g

the

hierarchical human relat ions

in

Chinese societ ies.

A s

Hal l iday (1978)

pointed out , "By thei r everyday a cts of m ean ing, people act out the social

structure, aff i rming thei r ow n statuses and roles, and es tabl ishing and trans-

mit t ing th e

shared system

of

value

a nd

know ledge"

(p. 8).

N ot

only

are

distinctions m ade

to

suit social

purposes,

they

a re

also m ade

to serve spe cific nee ds at par t icu lar m om ents in t im e . Let us use, for e x a m-

ple, color dist inc tions . Th e dist inction betwe en brigh t red and dark red is

commonp lace

and

mos t people w ould

be

able

to

di s t ingu ish

a

bright

red car

from a dark red car. Suppose you w i tnessed an acciden t between a dark blue

car and a br ight red car and you were asked by the pol ice to provide an eye-

witness account

of

w hat happened.

Y ou

probably w ould

say

som ething l ike

this:

"A red car was

going

a t full

speed when

a

b lue

car

c o mi n g

from the op-



1 . T H E

S P A C E

O F

L E A R N I N G

29

posite direct ion suddenly swerved into the opposite lane and coll ided

head-on wi th

the red

car."

Y ou

w o u ld

not

take

the

trouble

to say

"the bright

red car" and the "dark blue car" because the distinction between and bright

and

dark colors is not c ri t ical . How ever, if it w as a bright red car co l liding

wi th a dark red car, then the dist inction between dark red and bright red

w o u l d be cr i tical . Of cou rse, if there w as o nly one car , there w ou ld be no

nee d to

describe

the

color

at

al l .

For

exam ple,

i f you saw a car

crashing into

a

supermarket , your eyewitness account to the police would be something

l ike

th is : "I saw a car crashing into th e supermarket at 10:00 a.m . this m orn-

ing,"

but not "I saw a

bright

red car

crashing into

the

supermarket

at

10:00

a.m." be ca us e the co lor of the car is not c ri tical in relat ion to the e vent or the

contex t .

C ri t ical to the event or the con text is w ha t happe ned.

In

the contex t of a learning si tuation, such as the

classroom,

the lan-

g u a g e

th a t is use d by the t eache r and the s tude nts to m ake di s t inc t ions in

re la t ion

to the

ob j ec t

o f

learn ing

is

often

o f

cr i t ica l imp or tance .

L et us use

an e x a mp l e

f rom

a lesson tha t w i l l be repor ted in greater detai l in chap t e r

5.

A sc ienc e t eacher , in the contex t o f teach ing how a reed re lay

3

ope ra te s ,

asked the s tudents what happened to the electrical resistance va lue w hen

l i g h t w as shone o n a l ight-diode res is tor

4

( L D R ) . O n e s tudent rep l ied ,

"Sm al l. " W hen the s tudent used the adjec t ive

"small,"

she was m ak ing a

dis t inc t ion b e t w e e n th e size of the res i s tance in the LD R be fo re and af ter

the

l igh t

w as

shone

on the

L D R .

In

o ther w ords ,

she was

descr ib ing res is -

tance as a state. T he teacher, however, w as no t happy w i th the descript ion

b e c a u s e he r ques t i on was "What happened to the res i s tance?" In o ther

w o r d s , she w anted the s tuden ts to descr ibe the chang e of s t a te cause d by

l i gh t sh in ing on the LDR , and "small" was therefore no t an ap propr ia te an-

swer .

S he

ins i s ted tha t

the

s tudent

use the

verb

"decreases"

i n s t ead

of the

adjec t ive "small." This t eacher w as no t n i tp i ck ing , bu t was m a k in g an im-

por tan t

di s t inc t ion be tween a state

and

a c h a nge

o f

state.

In

o ther words ,

the two s ta tes were

c lass i f ied

as two dif ferent p h e n o m e n a . In o ther con -

t ex t s , such

a

di s t inc t ion

m a y n o t

have been imp or tan t

a t

a l l ,

but in the

c o n -

text

o f un der s tand ing a p h e n o me n o n in phys ics , spe c i f i ca l ly the ope ra t ion

of a ree d relay, th is w as an im portant dis tinct ion (see chap. 5 for a m ore de-

ta i led

exp l ica t ion of the reed re lay) .

Let us take another example from a classroom learning s i tuat ion. T w o

H o n g Kon g primary teachers were teaching lessons about festivals.

O ne o f

the

objects

o f

l earn ing

in

both lessons

w as to

he lp

the

s tudents

to

indicate

their p references for the festivals, usin g th e phrase

"like best."

Both teachers

gave thei r s tude nts the sam e l ist o f

festivals.

Teacher A asked the s tudents to

first indicate

the

festivals

that they l iked and then indica te w hich one they

l iked bes t .

B y

doing this ,

th e

teacher opened

up a

dim ension

o f

variat ion

in

indicat ing preferen ces that included "like"

an d

"like best,"

an d

p resupposed

th e

choice of "do not like." In other w ords, in the sem antic system of

"like,"

there we re three choices : "do not like,"

"like,"

and "like best." B y j ux t apos -




ing

"like" a nd

"like

best," the teacher w as able to help the students experi-

ence variation in their fee ling s towa rd these festivals an d thereby discern the

meaning

of

"like

best" as the

superlative form

of

"like."

B y

contrast ,

Teacher

B

made

no

such dist inction.

S he

sim ply asked

her

students

to

indi-

cate what they "liked best." Consequent ly , some of the s tudents in this class

took "like

best" a s

having

a

s imi lar m eaning

to "like."

La n gu a ge

an d

Structure

of

Awareness

In our discuss ion of s im ul tanei ty and aw areness, w e pointed out that aware-

ness is the total i ty of our experience of the w orld an d that w e experien ce ev-

ery

s i tuat ion against

th e

b a c k g r o u n d

o f a

vas t number

o f

p rev ious

experiences . W e fur ther pointed ou t that the c harac ter is t ic of hu m an aware-

ness is that only a limited num ber of thing s com e to the

fore

and becom e fo-

cused, whereas

the

rest recedes

to the

background.

W e

observed that

the

f igure-ground s tructure of awareness i s dyn am ic and ever ch an gin g.

In the discuss ion o f language and the const rual of experience, we pointed

out that the enc oding o f previous ex perience by l inguis t ic m eans enab les us

to m ake sense of w hat we are experiencing. W e w ish to further argue tha t

language also plays

an

im portant role

in not

only represe nt ing

the

structure

of

aw areness

but

also

in

changing

it . Let us

take

the

previou s ly c i t ed exam -

ple of the janitor locking the door of the computer laboratory. If we say.

"The janitor locked

the

door,"

the

jan i to r becom es

the

t hem e

or

sub jec t

o f

the clause and is the grounding for the rest of the clause . That is.

what

the

janitor d id w as the figu re. How ever, if w e say, "The door w as locke d by the

janitor," the

fact

that the door w as locked becom es the ground, and the ja n i-

to r becomes the f igure .

In classroom situations, it is very imp ortant

that

the teacher is able to bnng

critical fe ature s of the object of learning into s tuden ts'

focal

aw areness. That

is to

say,

it is

crucial that

th e

teacher

is

able

to

bring

out the figure and

ground

relationsh ip. This is often achieved through linguistic means, and m ost obvi-

ously through

the use of

questions because

th e

structure

of all

quest ions

in-

volves

a f igure-ground

relationship.

For

exam ple,

the

often ci ted question,

"Have you stopped beating your w ife?" presupposes that yo u have been beat-

in g

your wife

and

queries whe ther

y ou

have stopped

th e

action

or

no t .

In

other

words, "beating yo ur w ife"

is

ground,

a nd

"have

you stopped" is figure.

W h at

th e

teacher presents

as

ground

is

wha t

he

assumes

to be

shared knowledge,

and wh at he presents as f igure is w hat he w ants to be the focus o f the students '

attention. For exam ple, let us see how

different

questions asked by different

teachers can result in different learn ing experiences for students ( this exam ple

is presented in m ore detail in chap. 5). Tw o primary E ng lish teachers in Hong

Kong were teaching

the

determ iner "some"

to

indicate inexac t quanti ty. Both

teachers used O ld

M acDonald

's

Farm as the

context

for

teaching,

and

both

showed th e students a series of pictures with different kinds of animals and



T H E

S P A C E

O F L E A R N I N G

different

numbers of animals on the computer screen. Both teachers also

started by showing one anim al and asking the students w hat they c ould see so

as

to

elicit

th e

n a me

of the

anim al shown. After this,

the first

teacher repea t-

edly

asked

th e

students, "How many (name

of

animal)

can you

see?"

This

elicited exact num bers, such as

"three,"

"four," "five," and so on. The second

teacher, how ever, repeatedly asked the students, "What can you

see?"

and did

not ask

"How many?"

The

question "How m any cats

can you see?"

presup-

poses that the an ima ls that the students can see are cats and queries the exact

num ber of cats . Hence, the cats are the ground and the num ber of cats the fig-

ure.

This question focuses the students' attention on the exact number. The

question

"What can you see?" presupposes that the students can see some-

th ing

(on the

computer screen)

and

queries

"what"

it is

that they

can

see.

In

other

words,

the

exact number

of

animals they

can see is not the f igure.

Their

focus of

attention

is on

whether there

is

only

one or

more than

one

animal .

The students ' performance in a test administered at the end of the lesson

showed that

the

students taugh t

by the first

teache r

did

less we ll w hen u sing

the

determiner

"some"

to indicate inexact qu an tity than the students taug ht by

the

second teacher.

T H E

SEMANTIC DIME N SIO N

OF THE SPACE O F L EARNI NG

S o

far ,

w e

have focuse d

on the

necessary co ndi t ions

f o r

learning,

the

nec-

essary con di t ions being the discernm ent of cr it ical features of the objec t

o f

l earn ing th roug h expe r iencing dimens ions of var ia t ion re la t ing to th i s

speci f ic ob j ec t

o f

l earn ing bo th diachronica l ly

an d

synchronica l ly ,

and

h o l d i n g

these c r i t ica l fea tures

in

focal awareness s imul taneous ly . How-

ever , these necessary con di t ions

m ay no t be

suf f ic ien t

fo r

pow erfu l l earn-

ing to

t ake p l ace .

Let u s

take

fo r

exam ple some science lessons that

wi l l be

explained

in de-

tai l in chapter 6. Two science teachers e xplained the process o f

neutraliza-

tion to their students. Both explained that neutralization is a reaction

between acid

a nd

alkali that results

in a pH

value

of 7.

Both

o f the

teachers

used

laboratory demonstrat ions

to

show w hat

happens

when neutral izat ion

occurs , by us ing a chang e of the color of the solution as the m eans of m aking

the

process visible. Both varied

the

prop ort ion

of

acid

and

alkali ,

and the

chang e of pH

value

to

indicate

the

levels

of

acidity

and

alkalinity,

to

help

students understand the concept of neutral izat ion. However, one teacher

used many everyday examples that were familiar to the students to help

them make sense

of

neutral izat ion (e.g. ,

the use of

alkaline ointment

to

sooth the i tchiness caused by a cids injected into the skin by m osquitoes, a nd

the use o f alkaline toothpaste to neu tral ize the acidic sal iva w h e n cleaning

our

teeth) .

The

other teacher, however, dealt w ith neu tral ization very m uch

as

a proc ess of m ixing ac ids and alkalis in a laboratory experim ent. B y using



32 M A R I O N , R U N E S S O N , T S U I

examples that the students were able to relate to easily, the first teacher

m ade available possibili ties for students to assign a m u c h richer mean ing to

the object o f learning. F o r these students, neu tralization w as no longer ju s t a

process

that

took place

in the

laboratory,

b ut a

also

a

process

tha t

had a

p lace

in their daily lives.

T he

space

o f

learning

is

const i tuted therefore

no t

only

by the

possibi l i t ies

for discernmen t of cr it ica l features of the object of learnin g, of ten b rough t

about

by

l inguist ic means,

bu t

also

by the

examples

and

ana log ies tha t

the

teacher uses,

the

stories tha t

the

teacher tells,

the

contexts that

the

teacher

brings

in, and so o n. I t is

constituted

by the

me anin gs th at learners assign

to

these examples, analogies, stories,

and

contexts ,

as

w e ll

as by the

previous

experience that they bring

in as

they

try to

m ake sense

of the

object

of

learn-

ing. A ll of this const i tutes the sema ntic dimen sion o f the space of l ea rn ing in

w hich the cr i tica l features of the object of learning are interpreted and un-

derstood.

A

space

o f

learning that

is

semant ica l ly

rich

a l lows s tudents

to

come

to

grips wi th

th e

crit ical features

of the

object

o f

l ea rn ing m uch m ore

effectively

than one that is semantical ly impover ished.

T H E SHARED SPACE

O F

L E A R N I N G

In order for us to discern cr i t ica l features of the ob jec t in q u e s t i o n , w e need

to be able to make sense o f w h a t w e are exper ienc ing in re la t ion to w h a t we

have

experienced

before; this is the d iachronic d im ension o f our aw areness .

A s we poin ted out before , w e cannot ta lk about ta l lness un less w e have a lso

exper ienced shor tness; w e canno t say wh at br igh t red is un less w e have ex-

per ienced other shades of red. In other wo rds, w ha t learners have expe r i-

enced before

is

crucia l

to how

they m ake sense

o f

the i r cur rent expenen ce .

In

order

to

m a k e

i t

possible

fo r

learners

to

discern

cri t ical feature s

of the ob-

j e c t o f learning, teachers mu st be aware o f w hethe r lea rners c an make sense

of

these cr i t ica l features through their previous exper ience.

T he

teacher

m ust a lso be aware of how m u c h is shared be tween h im se l f and the learners.

In other words, w hat the teacher presents a s ground should b e shared com -

m on

ground between h im se l f

and the

s tudents ,

so

tha t w ha t

he

presents

as

f igure can be made sense of by the s tuden ts in re la t ion to the ground. In this

sense, the space o f learning is a shared space o f l e a rn ing .

Lan guag e is the key m eans by w hich th is shared space is con st i tuted. W e

have

i l lustra ted this poin t in the previous discussion on teach ers ' quest ion s.

The fo l lowing is a further exam ple . In a s tudy of some m athem at ics lessons

of Brazi l ian kindergar ten chi ldren, in wh ich the teacher was tea ch ing addi-

tion and the concepts

o f

m o r e and

less,

Cestan (2001)

found

that the use of

unclear deic tic reference and the lack of an explic i t indica t ion as to wh ich

rea lm the teacher was m oving in confused the s tudents and made them un-

able

to

answer

her

quest ions.



1 .

T HE S P A C E O F L E A R N I N G 33

The lesson was a mathematics lesson at kindergarten level and the stu-

dents w ere around 5 or 6 years old. T he teacher w as teaching addit ion and

v/as helping the s tudents to unders tand not only addi tion but also the m athe-

mat i ca l

concepts

o f

more

and

less.

T he

teacher

put

three boxes

on one

side

and tw o

boxes

on

another.

S he

then asked the s tudents whether there were the same number of boxes on

both s ides , w hich s ide had m ore, and wh ich s ide had less . The teacher had

no prob lem s get t ing the s tudents to indicate that the s ide wi th three box es

had m ore. However , w hen she asked the s tudents about the s ide w i th two

boxes , confus ion

set in. The fol lowing is an

excerpt

f rom the

lesson:

1.1

[Cestan,

2001]

5

T :

W hich s ide

has

m ore?

6 S: 3

7

T :

(The side)

of how

m a n y?

8 Ss :

O f 3

9

T :

Which

has 3. A nd

this side, w hich

has 2?

10 S: 2.

11

T:

H m m ?

12 S: 2.

13 T: This side has m ore or less? (po inting to the side with 2 boxes)

14 S: M o r e

15 T:

H m m ?

16 Ss:

M o r e

Ss:

Less

17

T : W hy

less?

It is

becau se there

are

only

.. .

18 Ss: M o r e

19

T: 2, and here there are m ore beca use there are . ..

20 Ss: Less

21 T: Here there are m ore becau se how m any are there?

22 So me

Ss: 3

23

T: 3, then 3 is bigge r than . . . ?

24 S: 2

In

line

9 ,

w h e n

the

teache r asked

the

que stion, "And this side, w hich

h as

2?" one s tudent s imply reported the num ber of boxes on the other s ide ( line

10), and the same answer w as given when the teacher asked for the answ er

again w ith an

interrogative

interjection

(line

11). The teacher then repeated

her

quest ion

in a

sl ightly fuller form that included

the

q uant i ta tive com para-

tive no t ion

"more

or

less."

She

also g ave

a

more expl icit indicat ion

of

w h ic h



34 M A R IO N , R U N E S S O N , T S U I

side she was referring to by point ing to the s ide w ith tw o boxes ( l ine 13).

This,

how ever, did not meet with m uch success. T he c lass w as sp l i t between

"more" an d "less" (see lin e 16). In line 1 7, even thou gh the teacher provided

the l inguist ic sc affoldin g to help the s tudents to

jus t i fy

why one s ide was

less than the other side, and tr ied to get them to fill in the b lank w i th

"two."

she still faile d to elicit the correct answ er. I t was not un t i l sh e made the j u s t i -

fication very explic i t by s ta t ing the qu anti ta t ive com parat ive no t ion "more"

and the number "how many are there" ( line 19 and line 21) tha t she

f inal ly

succeeded in get t ing th e correct answer.

Cestari (2001) ident i f ied the source of confus ion as em ana t ing from the

absence o f a

defini te

reference in the incom ple te in te rroga t ive in l ine 9, and

observed

that even tho ug h the teacher t r ied to repair the com m un icat io n gap

by

point ing

to the

s ide w ith

tw o

boxes

and

exp l i c i tly a sk ing wh e the r

i t had

more or less , the con fus ion rem ained. Th e confus ion has very m uc h to do

with the fact that the teacher was t rying to establ ish a correspondenc e be-

tween the n u m b e r o f boxes and the m a t h e m a t i c a l n o t io n o f "more" and

"less," and the fact there w as a lack of com m on ground, or m utu a l i ty , be-

tween her and the s tudents with regard to whether she was moving in the

realm of quant i ty of boxes, or in the rea lm of the m ath em at ica l no t ion of

"more" and "less." In line 9, w hen the teache r asked the cryp tic qu est io n

"And th is side , which h as 2?" she was m oving in the rea lm of the m athe m at-

ical notion

o f

"more"

and

"less,"

and

t rying

to ge t the

s tudents

to

ex t rapola te

f rom the ques tion w hat she wan ted them to te ll he r, w hich was w hether the

side with tw o boxes had more or less boxes than the s ide w ith three boxes.

The students , how ever, were m oving in the realm of the qua nti t y of box es.

W hen the teacher then tr ied to get the studen ts to ju s t i fy wh y one s ide had

less , she was m oving in the realm of the qua nti ty of boxes and w as t rying to

get the s tudents to com ple te the ju s t i f ica t ion by s u p p l y i n g the n u m b e r o f

boxes ( l ine

17 and

lin e 19). Yet,

the

s tudents were m oving

in the

r ea lm

of the

m athemat ica l not ion o f "more" or "less." I t was on ly when she m a d e the re-

la t ionship e xplic i t between the m a thema t ica l no t ion o f m o r e and the quan-

tity

of boxes ( l ine 21) and said,

"Here

there are m o r e because

ho w

m a n y are

there?" that

the

students w ere able

to

answer

the

ques t ion . This exam ple

il -

lustra tes nicely that unless the teacher and the learners share a common

ground in relation to the ob jec t o f lea rn ing , it is no t po ss ib le for the learners

to make sense of the object o f learning.

There

is a fur the r sense in wh ich the space of lea rnin g is a shared space.

W e have a lready pointed ou t th at previous exper ience is the f r ame o f refer-

ence against which current experience is interpreted or made sense of , but

that the current experience a lso mo dif ies the way in w hic h the previous ex-

perience

is construed. This is an ever-changing and interact ive process in

which

the

features that

w e

discern

in a

situation

and

w h a t

w e

discern

as

criti-

cal keep being revised.

O ne

crucia l mean s

in

wh ich th i s

is

done

is by

t a l k i n g

over events w ith people an d by ref lect ing on the events after they have oc-



T H E

S P A C E

O F L E A R N I N G

curred (B ritton, 1 970) . L angu age n o t only plays a crucial

role

in the m odif i-

cation

o f

each other 's un derstanding

and

perception

of the

world

bu t

also

becom es part of the exper ience itself. T he m odif ica t ion of the learners ' and

teacher 's un derstanding

of the

w orld

is

w hat c lassroom teaching

and

learn-

ing is all

about . This

process is

brough t about joint ly

by the

teacher

and the

learners through interaction in which meaning is neg otia ted and co-con-

structed. In this sense, th e space of learning is a shared sp ace of learning. In

chapter 6 , we see how the s tudents m odify each

other's

understanding of the

wor ld by engaging in collaborative talk. In chapter 7, we see how the teacher

and the students togeth er co-construct an understan ding of the funct ion of a

"clan"

(a

comm uni ty

in

w h i ch

a ll

m embers have

the

same surname)

in a

his-

tory lesson .

TOWARD A

P E D A G O G Y

O F

L E A RN I N G

The expression pedagogy o f learning may strike the reader as vaguely odd.

Pedagogy is about teaching and upbringing after all; and teaching and upbring-

ing is m uch about learning, so is the pedagogy of learning not a tautology?

Well ,

it could have been, but it is not . W e set out at the beginning of this

chapte r

by

poin t ing

to the

fact that discussions abo ut pedagogy are,

a s a

ru le ,

not

phrased in terms of learning but in term s o f the co ndit ions of learning ,

and that they of ten lack precise s ta tements about the ways in which those

condi t ions facili tate learning and what kind of learning they would

facil i-

ta te . It is of ten s imply assumed that t he condit ions argued for w o u l d facil i-

tate all kinds of learning.

W hen w e use the expression

pedagogy

of

learning,

we do not refer to the

process whereby the condit ions o f learning are taken as the poin t o f depar-

ture

an d it is

s imp ly assum ed that these condit ions embo dy " the

a rt of

teach-

ing

a l l thin gs to a l l men." T he pedagogy of learning m eans ta kin g learning

as

the po int of depar ture an d exploring the con dit ion s that m ight be condu -

cive to br ingin g that learning ab out .

As lea rn ing

is

a lw ays

th e

learning

of

som ething, there

are

severe lim its

to

discussing learning in gen eral , w ithou t reference to w hat is learned. W hat is

learned is the ob ject of learning and we argue that a pedagog y of learning

m u s t take as i ts poin t of departure the very o bject of learning .

Most

of the stu dies reported in this book

follow

the simple design of com-

paring how the same o bject of learning was dealt w ith in two or more

different

classrooms.

W e

have used this model because

w e

believe that

the way in

which

the obje ct of learning is dealt w ith in the classroom is of decisive im -

portance , and that w e can o nly f ind out how the object of learning is dealt w ith

in

the

classroom

by

com paring

it

with another

way of

deal ing w ith

the

same

object of learning (this follows from the theory of variation discuss ed in this

chapter) .

In this book, w e describe m uch of w hat we found about differences

in the w a y s in w hich the same objects of learning were dealt w ith.




In

all

studies reported

in

this book,

w e

t ranscr ibed verbat im everything

that w as said in the

classroom

and carried out our analyses on the t ran-

scripts.

W e

have also used som e

of the

transcripts

or

par ts the reof (w i tho ut

ident i fying

the school, class, or the teacher) in seminars and workshops .

Frequently we let the

workshop

par t ic ipants—educational researchers,

school administra tors , teacher educators , and teachers—read through the

transcripts

and

then address

our

in i t ia l ques t ion:

"W e

have here

tw o

classes

deal ing w ith the same top ic (content or obje ct of l ea rn ing) . W h a t w o u l d y o u

say you f ind the most s t r iking dif feren ce between the two?"

Very rarely

did we

hear comm ents

on the way in

w h i c h

th e

object

of

learning

w as handled in the two classes, that is, w h a t it was possible for the student to

leam

in one

case

and

wha t

it was

possible

for the

student

to

learn

in the

other.

M ost comm ents concerned w hether there was a case o f

wh ole-class

teaching o r

group work, w hether the teaching w as teacher-centered or student-centered,

whether

or not

audiovisual tools,

IT ,

m am pulatives were used,

and so on.

W e do no t

deny that

the way in

w h i ch

the

lea rn ing s i tua t io n

w as

a r ranged

in each c lass w as of impo rtance for the pos sibi l i ty to learn. For ins tan ce, w e

agree wi th the a rgument tha t the opportuni ty fo r c o m m u n i c a t i o n in the

classroom

is of

impor tance

fo r

s tudents ' lea rn ing ,

and w i t h the

a rg u m e n t

that

the wa y in

w h i ch

the

learners

are

able

to

par t ic ipa te

in the

cons t i tu t ion

of the ob jec t o f learning i s a lso imp ortant . How ever , w e c l a im that w h a t s t u -

dents a re com m unica t ing and w hat they a re in te rac t ing abou t i s ju s t as s ig-

n i f ican t

as how

they in te rac t

and

c o m m u n i c at e .

Le t us use an example

from

a s tudy of a m ath em atics lesson repor ted by

Voigt (1 995,

pp .

173-174)

to show that there can be features of the learning

si tuat ion other than interac t ion tha t are a lso impo r tant fo r s tuden t s ' l e a rn ing .

Voig t described

how two

students , Jack

and

Jamie , went about so lv ing

a

group o f ar i thmetic tasks:

1 .

5 0 - 9 = 41

2 . 60-9 = 51

3. 6 0 - 1 9 = 41

4. 41 + 19 = 60

5.

31+29

= 6 0

6. 31 + 19 = 50

7. 32 + 18 = _

L et us take a look at how problem 7 was ta lked about by the boys.

Jack: U h-huh, that 's

18, not 1 9.

Jamie: Yeah , but th at 's 32 no t 31.

Jack: Oh

yeah

Jamie:

They're the

same th ing .



1 .

T HE S P A C E O F

L E A R N I N G

Researcher: What's the

same thing?

Jam ie : These two. [He points to the 3 1 + 1 9 = 50 and 32 + 1 8 = _ ]

Researcher: Hang

on , I w as

asking Jack. Which

ones?

W e've

got 3 1

and 19.

Jack: Makes 50.

Researcher : Yeah.

Jack:

A nd

look,

32 and 18.

See,

its

jus t

one more

than that

[points to the task], and that 's one higher than that .

It can be

seen

f rom the

excerpt that

the

last task

w as

solved

by a

compen-

sation

s tra tegy, a s tra tegy that the boys actual ly had not u sed in the previou s

tasks.

S o,

this tas k

w as

handled differently from

the

previous ones.

In

other

w ords, the boys learned to handle the problem in a new w ay. V oigt (1 995)

used

the not ions "negotia t ion o f mathemat ica l meaning" and "meaning

taken as shared" (p. 174) for understanding and explaining students ' learn-

ing .

H e a rgu ed tha t wi thout the interact ion between the boys, this new

strat-

egy never would have emerged. Undoubtedly, th e interaction was o f

im po rtance for the s tud en ts ' learning . in this case . How ever, can this new

w ay of han dling the task, and hence the s tudents ' learning, be ex plained by

the interact ion and the negotia t ion of meaning

on ly?

W e be lieve we m ust

also

unde r s t and w ha t

it is

po ssible

to

learn

in the

s i tua t ion

in

order

to ac-

count

for

w h a t

the

participan ts actua lly learn.

If

w e

take

a

closer look

a t the

problem s,

it is

possible

to

look

at

this other

side of learning ; that i s , what i t w as possible to learn. To us as authors , it is

obv ious tha t

the way in

which this group

of

problems

w as

composed

af-

fected w h a t

i t was

possible

to

learn.

In

this group

of

problem s, there

was a

pa rticula r variation present. S om ething varied,

whereas other

things were

invar iant

be tween the problem s. Firs t o f all , there was a varia t ion between

addi t ion

and

subtract ion (problem

1

through

3 and 4

through

7,

respec-

t ively).

Further, if w e f irst an alyz e problem s 4 and 5 in detail , w e w ill find

another var ia tion , nam ely tha t

the

tenths chang ed both

in the f irst and the

second addend (from 41 to 3 1, and from 19 to 29, respectively). B oth these

addit ions have the same tota l sum ( i.e. , 60), bu t they have a different par t

par t -whole re la t ion .

Let us now

look

at

problem s

6 and 7.

Problem

6 in-

volves and

combines numbers

from

problems

4 and 5. Th e f irst

addend

is

the

sam e as the f irst adden d in prob lem 5 and the second a ddend is the sam e

as the second addend in problem 4. In problem 7,

there

is a change of the

one s in both the adden ds ( i .e ., increas ing from 3 1 to 32 and dec reasin g from

1

9 to 1 8, respect ively) . Obviously, there was a very system atic var ia tion in

the com posi tion

of the

problems.

W e

would

say

that

a

particular p attern

o f

var iat ion

w as

afforded

to the s tudents to exper ience. An d

from

the excerpt

ju st cited w e interpret that the students did discern a pattern of variation. For



38

M A R T O N ,


instance, one of the boys said: "See, it 's ju st o ne more than that [points to the

problem], and that 's one high er than that." So , we w a n t to co nc lude tha t th e

afforded varia tion w as a feature of the learning si tuat ion that w as a lso s ig-

n i f ican t

fo r

s tudents ' learning.

In

these exam ples, w e have tr ied to poin t out a varia t ion tha t w as presen t

in the learning environm ent , a var ia tion tha t i t was possible for the learners

to exper ience. What w e a rgue for in the

fo l lowing

chapters is that this a f-

forded

variation is a cr i t ica l feature in re la t ion to the way in w h i ch the in-

tended learning is brought about , as w e l l as be ing a cr i t ica l feature fo r

students ' learning. The thesis o f th is book is tha t the dif ferences in w h a t the

students leam is to a large extent a funct ion of w hat they can poss ib ly leam .

W h a t

they

can possibly

leam

is a space of

learning co nstituted

by

tha t which

it

is

possible

to

discern.

In

the aforementioned example , there is cer ta inly an interact ion taking

place tha t contr ibutes to const i tut in g the space of learn ing. But the ser ies of

problems a lso cont r ibutes to c on s t i tu t ing the space of lea rn ing . W itho ut the

pa rticula r pattern

o f

var ia t ion tha t

is

embo died

in the

p rob lem s ,

the

s tudents

w ould not have been ab le to com e u p w i th the idea of comp ensa t ion , not in

that par t icular s i tuat ion, at least. In several places in th is book, w e give ex-

amples

of how the

space

o f

learning

is

cons t i tu ted

in the

in te r ac t ion .

In

chapter 5, chapter 6, and ch apter 7, for instanc e, we see how the teacher and

the s tudents join t ly co nst i tute the space of learning as the teache r takes on

the s tudents ' responses and opens them up for inq uiry and further develop-

m ent . W e a lso see how s tudents in te rac t ing in groups , jo in t l y cons t i tu ted the

space of learning by b r inging in their own cu l tura l and

da i ly

exper iences to

m ake sense o f the object of learning . For exam ple , in chap ter 6, w he n stu-

dents discuss h ow the appearance of the s loth sh ou ld be descr ibed, several

of them th ink tha t a ll eyes are b lack and tha t the re fore there is no need to in-

clude the color of the s loth 's eyes. In other w ords, they are not able to dis-

cern the color o f i ts eyes as a crit ic al feature . H ow ever , one s tudent draw s the

group's

attention to the

fact

tha t a rabbit ' s eyes a re r ed, thu s show ing tha t no t

all eyes are black. A nother s tuden t agrees w ith his observat ion. The group

f inally agrees on inc lud ing the color of the s loth 's eyes in the descn ptio n.

W hat is happ ening here is that through col labo rat ive inte ract io n, the s tu-

dents are able to br ing in dime nsio ns of var ia t ion tha t m igh t otherw ise be

neglected if students are not afforded the oppor tuni ty to in te rac t am on g

themselves.

W e are not

denying tha t

the

space

of

learning

may in

part,

or

ent ire ly,

be

const i tuted in the interact ion between students . However , the point we

w ould l ike to m ake is that reference is f requent ly m ade to interact ion (s tu-

dent centeredness, activity approach, task-based learning, etc.)

as

some-

thing that is inherently conducive to learning, without relating the inter-

act ion to what is learned. And that the l ived object of learning is—as a

ru le—not expla ined in any precise way. Interact io n, s tude nt centeredness.




and so on, are assumed to be good for learning in

some

very general , but

rather vague sense,

and for

their

ow n

sake.

In this

book , we try to

establish

the precise

l ink between learning

and

condi t ions of learning.

This

link is established by m ean s of the relat ionsh ip

between the object of learning and the space o f learning, where the enac ted

object

of

learning

is

identical

to the

space

o f

learning, both

of

w hich refer

to

the ob jec t of learning as it real ized in the classroom . It is the ob jec t of learn-

ing that the studen ts encounter, and the ob ject of learning th at they ca n pos-

sibly

learn,

o r

learn about , making

it

into

a

part

of

themselves .

If we are

interested in how

students learn

to see

certain things

in

cer tain ways,

w e

m ust ask o urselves w hat c r i tical features of the ob jec t o f learning s tudents

can

possibly discern in a part icular classroom si tua tion . N obo dy can learn to

see

cer tain th ing s

in

cer tain w ays w i thout experiencing cer tain pat terns

o f

var iat ion. This s tatement is true in general as far as this kind of learning

( learning to see

som eth ing

in a

cer ta in wa y)

is

concerned,

and it

im pl ies that

very

specific

pat terns of variat ion are necessary condi t ions for the learning

o f—o r learning abou t— specif ic objects of learning.

Having

said that,

we do not

w ish

to

im ply that

i t

does

n ot

m at ter whether

th e

teaching

is

wh ole class,

or

whether students work

in

groups; w hether stu-

dents are engaged in task-based or problem-based learning, or in project

work;

whether teaching

is

student centered; w hether

IT is

used;

or

whether

there is a joy fu l atmosphere in the classroom or not . Differences in the way in

w hich the co nditions of learning are organized m ay u ndo ubtedly constrain or

facilitate the

constitution

of the

space

of

learning necessary

fo r the

develop-

m ent of a certain capab ility. But in order to understand how these differences

inhibit or facilitate the developm ent of a certain cap ability, w e have to under-

stand h ow

they con strain

or

facilitate

th e

constitution

of the

specific space

o f

learning necessary

for

developing that specific capability.

A nd

this under-

standing

can

never

be

derived

from

a

general

way of

organizing

the

condi-

t ions of

learning.

F or

this reason,

we can

never

truthfully

argue that

one way

of

organizing

th e

con ditions

of

learning

is, in

gen eral , bet ter than another w ay.

In

this book we try to develop a theore tical perspective and a conceptua l

f ramework

for

unders tanding learning

in

schools

in

t e rm s

of

w h a t

it is

poss i-

ble to

learn

in

schools.

I f we

know w ha t

the

studen ts shou ld learn,

and if we

know w hat condi tions a re necessary fo r them to learn , then w e co uld rea-

sonab ly

work toward creating those necessary condit ions. I t must be re-

m em bered, however , that

for

each

specific

capabil i ty

(of

seeing something

in a certain w ay ), there are necessary, specific con dit ions. Even i f w e know

in general that there m ust

be a

certain space

of

learning that

com prises di-

mens ions

o f

variation th at correspond

to the

cri t ical features defining th is

specific way of seeing a specific p h e n o m e n o n , we do not know w hat these

crit ical

features

are in

every specific case.

This "blessed

ignoranc e" is a

w eakness that

can be

turned into

a

strength

by en gag ing the teachers themselves in finding the missing insights that are



40

M A R T O N ,


needed fo r achieving

different

par t icu lar educat ional a im s , and for develop-

ing speci f ic capabi l i ties an d par t i cu lar ly pow erfu l w ays of seeing part icu lar

phenom ena. Teachers focu s ing

on the

same ob jec t

o f

learning

can do so to-

gether by f inding the cr i t ical features in each case, creat ing what are be-

l ieved to be the necessary condi t ions fo r develop ing tha t capab i l i ty ,

check ing wha t

th e

stude nts leam

an d

w h e t h er

th e

co n jec tures were ju s t i f ied ,

revising th e fr amew ork if neces sa ry, check ing aga in , docu m en t ing th e pro-

cess as we l l as the ou t com es , and sharing it

w i th

o ther t eachers .

Teachers could

in

th is

w ay

par t i c ipa te

in the

co l lec t ive cons t ruc t ion

o f

professional knowledge , not on ly a s a par t of t he i r ow n profe ss ional devel -

opmen t but also as scientif ic research that m ay y ie ld new ins igh t s . Severa l

examples

o f

such

an

enterprise

are

ou t l i ned

in

c h a p t e r

8 of

th is

book .

E N D N O T E S

'T o be

fu l l y a ccu r a t e ,

o f

cour se ,

w e

shou ld say , "deve lop ce r t a in capab i l i t i e s

and values However , a l though

not

w i s h i n g

to

p l ace m o r e i m p o r t an ce

on one

r a ther than

th e

other,

th e

f o c u s

o f

th i s book

i s on the

d e v e lo p m e n t

o f

c ap ab i l i ti e s

r a ther than va lues ,

a s

th is

h a s

been

th e

f o c u s

o f o u r

s t u d i e s .

2

The pron oun "he" is used in a sex n e u t r a l s en se to a v o id a w k w a r d use o f "he o r

she."

3

A

reed re lay

is a device th a t w i l l cha nge a weak e lec t r i ca l cu r r en t in to a very

st rong cur rent when it is connec ted to e l e c t ri c c i r cu i t s . R eed r e l ay s a re u sed in

m any e lec tr ica l a pp l i ances tha t r equ i r e l a rge cur r en t s fo r o p e r a t io n , su ch a s e l eva -

tors, motors, and so on.

4

A light

d iode

resistor ( L D R ) ca n p r even t a n e l ec t r i c cu r r en t f rom pass ing

th rough a n e l ec tr i c c i r cu i t becau se of i t s g rea t res i s t a nc e . L ig h t d iode r es i s to r s a re

sensi t ive to ligh t . W hen exposed to b r i g h t l i g h t , th e r e s i s t an c e r edu ces , t h u s a l l o w -

in g the e lect r ic cur rent to pass th rough .



O n

Learning



2

Variation

and the Secret

of the

Virtuoso

Po

Yuk Ko

Ference Marton

MAKING

SYSTEMATIC USE OF

VARIATION

In chapter

1 , we

argued that whatever object

of

learning learners,

try to ap-

prop r iate , cer tain cr i t ical features

o f

that objec t have

to be

d iscerned, that

is ,

learners must learn to see cer tain s i tuat ions in cer tain ways. B u t learners

can

never discern anyth ing w ithout expe r iencing var iat ion. T he exper ience

of

pat terns

o f

var iat ion

specif ic

fo r different

objects

of

learning

is a

neces-

sary condi t ion for appropr iat ing those objects o f learning. If this is true,

then

success fu l

teachers mus t

b e

good

a t

con st i tu t ing such necessary con di-

t ions

in the

classroom, that

is, the

specif ic

pat terns

o f

var iat ion.

One of the

m am

po in ts o f th is book is tha t w e have m anaged to identify a cr i t ical factor

in

teach ing , a

factor

tha t d is t inguishes

be tween

teach ing tha t

m a k es

a cer-

ta in

learning possib le and teach ing that

fails

to achieve this . Th e em pir ical

compar i sons in chap ter 3 and chapter 4 demonstrate th is in greater detai l .

In

any

ins tance

o f

teach ing ,

there are

th ings that

are

repeated

and

there

are

thing s that vary.

On e of the

fea tures

of

good pract ice

and

pow er fu l peda-

gogy is the

eff ic ient

use of var iat ion and repet i t ion, whether i t be con-

sciously

or

less consciou sly .

Let us

look

a t an

example .

K w a n ,

Ng, and

C hik (2002)

offered a

por trayal

of an

innovat ive teache r 's

w ay of t r ansform ing the intended object of learning into an enacted ob jec t

of learning in the course of a double lesson in Chinese ( the class was a pri-

mary Grade

2

class

in

Hong Kong) .

T he intended object o f learning could be split into tw o in ter twined as-

pec ts that were n ot to be dealt with sepa rately, but at the same t im e. T he s tu-

43



4 4 K O A N D

M A R T O N

dents were expected to become better at the fo l low ing sk i ll s : (a ) describing

animals , and (b) using the four language ski l l s in an in tegra t ive manner .

T he doub le

lesson

b u i l t on the previous lesson in w h i c h th e s tudents h ad

learned to discern

di f fe rent

aspects o f a pan da, such as i t s app earanc e (body,

head, four l im bs, color) and its movement . A s the po in t o f departure fo r the

double lesson, a 3-m inute film sequence w as shown to the c lass . In th e f i lm

sequence , th e s tudents s aw a young s lo th , w h o according to the na r ra to r h ad

lost

its

m other.

T he

s tudents

saw the

s loth c l im b down

f rom a

tree

in

search

of a new home, swim

across

a nearby river, and c l im b u p ano ther tree w here

it encountered

another sloth—which w as luck i ly f r iend ly—and t hus the

young s lo th found a new home.

The s tudents f i rs t watched the v ideo wi th the narra t ion, then watched i t

a ga i n wi t hou t

th e

na r ra t ive ( see ing , l i s t en ing ) . N ext they foc used

on the

sloth ' s appearance by discu ssin g it s var ious fea ture s (body, he ad, four

l imbs,

color) and its movement

(speaking, l i s tening) .

Then the

s tudents

w rote down th e i r descr ipt ions

on

overhead t ranspa rencies

and

showed them

to the re st o f the c l a ss (w r i t ing , r ead ing) . F ina l ly they appo in ted a m em ber

of the

group

w ho

c a me

to the f ront of the

c lass

a n d

ac ted

a s

na r ra to r

a n d

read

a loud the i r desc rip tion w hi l e the m uted f ilm seque nce w as rep layed on the

video (speaking, l istening ).

Dur ing

th e

lesson,

a

h igh ly co m plex pa t te rn

o f

va r i a t ion

w as

j o i n t l y c o n-

st itu ted by the teache r and the s tu den ts . Let us look a t some inte res t ing pa t-

terns o f var ia t ion and invar i ance .

To begin w i th , the s tudents were expected to

sh i f t

the i r a t t en t ion be tween

tw o

aspects

of the

an imal :

its appearance and its

m ovement.

W e

cannot

say

t h a t these

tw o

aspects var ied ,

but the

s tudents them se lves were a sked

t o

vary

the foc us of the i r a t ten t ion between the two

di f fe rent

aspects and the four

di f ferent par ts of the animal . This show s tha t va r ia t ion can th us be exper i -

enced by exp er i enc ing va r i a tion genera ted by the env i ron m ent ( e .g . ,

focus-

ing on

d i f ferent animals)

or by

varying

one's

at tent ion

o r

imaginat ion (e .g . ,

f oc us ing

o n d i f ferent a spec t s of the same a n im al ) . Fur the rm ore , va r i a t ion is

a lway s exper ienced aga ins t the backgro und of wh a t i s invar i an t . So the re -

fore w e

speak

o f "patterns o f

va r i a t ion

and

invar iance ."

In our

spec i f ic case

w e have th e fo l lowing :

Variation Invariance

di f ferent

a spec ts same an im al

and

Variation

Invariance

di f ferent par ts same aspect (app earance )

B y genera t ing two k inds of varia tion in re la t ion to the same an im al ,

differ-

en t

aspects

and

different parts

can be

discerne d.

B ut is

th is specif ic

to

th is ani-



2.

V A R I A T I O N A N D T H E S E C R E T O F T H E V I R T U O S O 45

m al? In order to generalize the acts of discernm ent, they have to be applied to

m ore than

o ne

an imal .

As the

same exercise

w as

also carried

out in

relation

to

a

pa nda dur ing the previous lesson, th is condi t ion w as ac tual ly m et .

Variation Invar iance

dif fe rent

an im als same ac ts o f d iscernm ent

(panda and s lo th) (be tween aspects , and between par t s )

So fa r w e

have been dea l ing w i th

t he first of the two

in tende d ob je c ts

of

l ea rn ing :

be ing ca pab le o f describ ing an an im al . W hat about the second in-

tended object

of

learning, using

the four language

skills

in an

mtegrative

m a n n e r ? A s a m a t te r o f

fact ,

the two in tended ob jec ts o f learn ing can be

b r o u g h t

toge the r

b y

app ly ing them

to the

same task : tha t

is ,

desc r ib ing an i -

m als in

speech

a nd in

w ritten

fo rm, and

tak ing par t

in the

desc r ip tion

by

l i s -

t e n i n g a n d r e a d i n g . T h e s t u d e n t s t a l k e d a b o u t t h e a p p e a r a n c e a n d

m ovem ent o f the s lo th , they wro te down the ir observat ions , they read eac h

other s ' observat ions , they com m ented on the fi lm sequence wh en the sou nd

w as

o f f ,

and they

l i s tened

to

each others' c o m m e n ts .

Variation

Invar iance

different same thing

described

com m unica t ive ac ts ( the s lo th)

W e can see here the double funct ions o f var iat ion, that is, tha t d i f ferences

between the

different

ac t s can be d iscerned when the i r

objec t

i s the same .

This

is

w h a t

w e

refer red

to as separa t ion in the

previous chap ter .

It is the di-

m e n s i o n o f co m m unica t iv e ac ts t ha t is be ing separa ted from other aspects o f

the relat ionship between the descr iber and the descr ibed, that is , between

the

s tudents and the s tory about the s loth . But because the object of these

ac ts is the sam e, com m onal i t ies a re b rought ou t as wel l : w ords , express ions ,

and sen tences .

Dif ferent

acts are d iscerned and broug ht together at the sam e

t ime. A

th ird pat tern

o f

var iation presen t

in the

lesson m akes

it

possib le

fo r

the

s tuden ts to ar r ive at the ins igh t that the sam e task can be c ar r ied out in

dif fe rent bu t

e qual ly correc t w ays . However,

th e

different w a y s

o f

d o ing

som eth ing on ly becom e v is ib le

if

they

a re

perceived

as

being

different

w a y s

of doing

t he

same

thing

(otherwise

different

acts and

different

tasks co-vary

and can not be separa ted from each o ther).

This

is exa ct ly the c ase in the les-

son

d iscussed here ;

the

sloth

i s

described

in

different w ays , t ha t

is, by

m e a n s

o f d i f ferent communica t ive ac ts .

The teacher in th is example is a Chinese teacher from Hong Kong . I n

fact,

a lmos t

all of the

examp les

in

this

book are

abou t Ch inese teachers ,

and

m ost o f them are

from

Hong Kong. St igler and Hieber t (1999) emphasized

that

teach ing is a cu l tural act iv ity a nd argued tha t teachers in different cu l -



46 KO AND M A R T O N

tures follow different scripts. If so , is it the case that there is a spe cific Chi-

nese pedagogy, a Chinese script that is characterized, among other things,

by

an elaborate use of patterns of variation and invariance?

Is it reasonable at all to expect a speci f ic Ch inese pedagogy? Trying to

find

out

whe ther there

is one or not

wou ld

be an

im possibly large undertak-

ing because

of the

sheer vastness

and

va riabil i ty

of the

Chinese cu l ture.

A n

easier question to address—and one tha t for our purposes is ac tua l ly more

interes t ing— is this : W hat

are the

pedagog ical pract ices considered

to be ex-

emplary

in

C hina? This

was the

question addressed

by one

me mb e r

of our

team (Ko, 2002),

and the

fo l low ing sect ion bu i lds

on her

work .

A

L E S S O N

O N

S E M A N T I C S

In th is sect ion, we present a lesson tau gh t by an expert teach er in the Peo-

ple ' s Re publ ic of Ch ina (PR C; the lesson w as referred to br ief ly in cha p. 1) .

The t eacher is a "Special Rank Teacher," and the w inner of a pres t ig ious

s tate-granted tea chin g aw ard.

T he

do uble lesson

is a

dem onstrat ion lesson

that

w as

audiotaped, t ranscr ibed,

and

pu bl i shed (Qian , 1985) ,

in

order

to

dissem inate the teac hing expert ise of the teac her as a m odel lesson for his

counterpar t s

to follow. It

a l low s

us to see

w h a t

is

considered

to be

good ped-

agogy

in the

P R C .

The sample lesson is a reading lesson based on a prescribed text ca l led

"Semantics ," wh ich is a piece of exposi tory w ri t ing abou t the lexical m ean -

ings of w ords. In the lesson, the teacher a im ed to introd uc e several

l inguis t ic

concepts on semant ics , including th e

scope

of m e a n in g o f words; the level

of

generali ty

of

words ; homonym s, synonyms,

and

an tonym s,

and

thei r

us-

age. In the fol lo w ing , w e first describe the lesson and then a na lyze the varia-

t ional pattern.

S u m m a r y of the L e s s o n

Instead

of

in t roducing

th e

l inguis t ic know ledge direct ly ,

the

teacher started

w ith a s tory aim ing to i l lus t ra te that the m ean ing of words can vary a ccord-

ing to the co ntex t , and that i t is im portan t to be aware o f the co m plexity of

the me a n i n g o f words .

Afan t i

was a

hairdresser. There

was one

cus tomer ,

A h u n g ,

w ho

a l w a y s w e n t

to

A f a n t i ' s

p lace

to

have

his ha ir cut but

never paid

for the

service.

It

made

Afan t i

very

angry.

He

wan ted

to

p lay

a

t r ick

o n A h u n g . One day A h u n g

c a m e

t o Afan t i ' s aga in .

Afan t i f i r s t cu t

A h u n g ' s

hair .

T h e n

he

began

to

s h a v e A h u n g ' s

face, and

asked,

"Do

you w a n t

you r

eyebrows?"

A h u n g

rep l i ed ,

"O f

course

W hy

ask " Then,

qu ick

as a

flash, Afan t i

shaved

off

A hu ng 's eyebrows and said, "You wan ted your eyebrows, so I

w i l l

g ive them

to

you "

A h u n g was too m ad to say

any th ing ;

because

he had

indeed

said

he

"wanted"

his

eyebrows.

M e a n w h i le Afan t i

asked,

"Do you

w an t your

beard?"



2.

V A R I A T I O N

AND

THE

S E C R E T

OF THE V I R T U O

A h u n g

had a

beau t i fu l

beard , and he imm ed ia te ly sa id , "M y beard? No, no I d o n ' t

w a n t my beard " B u t aga in

Afan t i

proceeded to shave off his beard .

A h u n g

s tood up

and saw an egg- l ike head in the m ir ror . [Both the teacher and

s tuden ts

l augh . ] Fur i -

ously, A h u n g reproved Afan t i , " W h y did you shave of f my e y e b r o w s and beard?" "I

w as on l y

fo l lowing

y o u r

orders, s ir "

Afan t i

a n s w e r e d calmly. There w as

no t h i ng

A h u n g cou ld

say to

tha t

After tel l ing the story, the teacher asked questions to help the studen ts to

unravel

the

ambivalence

of the

mean ing

o f

"want"

( in

Chinese,

y a o

(Pu tonghua)

2.1

T :

Af ter

l is tening to this story, do you know what kind of tr ick

Afant i

played on

Ahung?

Ss: Afan t i played a trick using the word "want."

T :

W hat did A fanti m ean by asking "Do you

'want'

your eyebrows?"

Ss: It

meant

"to give."

T :

Exact ly

It

mean t

"to

give."

You

w ant them, then

I

shave them

off

and

give them to you. Then what i s the meaning of the word

"want"

in "Do you

w ant your

beard?"

Ss:

"T o

keep."

T :

Yes,

it

me a n s

"to keep." But how did

A hung interpret

th e

w ord?

H e

st il l though t

i t was to

"give"

h im h i s

beard.

That's w hy he im -

media te ly answe red, "I don ' t wa nt it." A nd he fell in to the t rap.

S o you

see,

the

word

"want" has tw o

meanings .

It can

mean this ,

or it can

mean tha t. Afant i exploited

the

am bigui ty

of the

m e a n-

ing of "want" to trap A hun g. This story tel ls us i t is im portant to

master the m ean ing of a word a nd its scope of m eaning [Teacher

writes o n the blackboard: meaning, scope of m ean ing ] .

In the

story,

the

word

"want" (yao

(Putonghua) [-lc])

had two

mean-

ings

— ei ther "to keep" (liu (Pu tonghua) [ ̂ ]) or "to give" (gei (P u tonghua)

[ £«•]) acc ording to different contexts. Afant i exploited the am bigui ty of the

mean ing

o f "want"

(homonyms)

to

t rap Ahung. When Ahung interpreted

"want" as meaning "to keep," A fan ti deliberately interpreted the

"want"

as

m ean ing "to give," and vice versa. A s a result , Ah ung lost his eyebrow s and

his beard. In the teache r-led discussion that im m ediately fo l low ed the read -

ing, the teacher did not u se m etalan gu ag e (i .e., the term

hom on y m s )

to illus-

trate the semantics concept, but simply highlighted the complexity of the

mean ing

of

words .

Nex t ,

the

teacher showed

the

class some books

and

asked students

to

name them.



4 8 K O A N D M A R T O N

2 2

T : . . . I first

w a n t

you to

look

at

some th ings

a nd

nam e them

[holding

up a

book] . W hat

is

this?

Ss: A Chinese book.

T :

[hold ing

u p

another book] W hat

is

th is?

Ss : An E ng l i sh book .

T :

[holding

up two

books tog ether]

I f w e put

them toge ther, wh a t

do

w e cal l them?

Ss: Books .

T: Narrow down th e scope.

Ss:

Textbooks.

T: [holding up a dic t ion ary] W hat is this?

Ss: A dic t ionary.

T: Is i t a book ?

Ss: Yes, it is.

T: W hat k ind

o f

book?

S s:

Re fe rence

book?

T: W hat are these three a l l togeth er?

Ss: Books.

T :

That's

right. Chinese book, textbook, book, the scope of the

meanings becomes b igger an d b igge r .. .

In this excerpt, we see that the teacher started with specif ic k inds of

books and

then asked

the

students

to

provide

a

general w ord that could cover

both kinds o f books. B u t w e also see tha t the teacher tried to he lp the s tu-

dents

to see the

differenc e

in

scope

o f

m e a n in g

b y

showing

how one

k ind

o f

book subsum es an other kind of book, such that lan gu ag e books are a kind of

textbook and textbooks are in turn a kind of book, jus t as a reference book is

also a kind o f book.

On one

hand,

th e

teacher cleverly juxtap osed books

at the

same level

of

specificity—a

Chinese languag e book

and an

English language book—and

showed that it is only necessary to go one level up in order to su bsum e both

books,

name ly

by

us ing

th e

word

"textbook."

Hen ce, there

is no

need

to

sub-

sume them both under th e very general term

books .

T he teacher then jux ta-

posed textbook and reference book, which are also at the same level of

specificity, and showed that the next level up to subsume both would be

"books." T he

class were therefore presented w ith three levels

o f

generality,

and the relationship between the examples w as a hierarch ical structure, that

is, with one subsum ing the other.



2 . V A R I A T I O N A N D T H E S E C R E T O F T H E V I R T U O S O 49

In order to help the students see the relat ionship b etwe en w ords of differ-

en t levels of generality, which is denoted by the word relat ion known as

h y p ony m s , the teach er varied the com bination of the spe cifics and the levels

of ge nerali ty. A s pointed out , th e com bination of the Chinese l anguage book

and the

Engl ish language book

can be

subsumed precisely under " text-

books," w hich is at a m ore gene ral level , but less precisely under

"books,"

w hich is a t a yet

more general level . However, when

the

co m bination

is of

var ious

types

of

books (i .e. , text books

and

reference books) ,

the use of the

word

"books"

is the m ost app ropriate.

The teacher helped the s tudents unders tand the semant ic features of a

book by con sidering w hat i s not a book ( i .e ., by us ing

con tras ts,

m en t ioned

in

chap .

1 ):

2 3

T :

...

[holding

up

pieces

o f

new spaper]

Is

this

a

book?

S s: N o ,

that ' s newspaper .

T: W hy is i t not a

book?

S s:

B ecause there 's

no t

enough [pages] .

S :

Eve n a pi le of new spaper ca n ' t be cal led a book. A book has a

cover,

a

new spaper do esn ' t .

S: N ot exactly. If I have a book, and I tear off the cover, the book is

still

a

bo ok. Pictorials also have covers,

b ut

they aren't c alled books.

S: A

book

is a

com pos i tion boun d

by a

cover.

T :

[ho lding

up an

exercise book] This also

has a

cover , hasn ' t

it?

B ut

w e

do n ' t c al l that

a

book .

A

book

is a

l iterary com posi t ion

bound by a

cover.

You can see

that w i th dict ionaries , r ight? [s tu-

dents nodded thei r heads]

T o be a

book,

it has to be

bound

by a

cover, and a t the

same t ime

it ha s to

fulfi l another requi rem ent :

that

o f be ing a compos i t ion . Books are bound compos i t ions .

This

is the

definit ion

of the

word.

Now can you

give

me the

defi-

ni t ion of a

textbook ?

S : A

textboo k

is a

composi t ion used

for

t each ing , bound

in a

cover .

T :

R ight Then please give

me the

definit ion

o f

th is C hinese book .

S:

A

com pos i tion used

for

teaching Chinese, bound

by a

cover.

T :

V ery good

W e put in

m ore l im i ts here. From

the

exam ple above

w e

can see that , from "book" to "textbook" to "Chinese book,"

w h a t

happe ns to the scope of m eaning?

Ss: I t

becomes narrower.

T :

Then

how

abou t

the

m eaning? Does

it

become m ore

specif ic , or

m ore genera l?




Ss: Specif ic

T: A gain , you have discovered a rule: the sm aller the scope of the

mean ing ,

the . . .

w h a t

. . . the

mean ing becomes?

Ss : The

m ore specif ic

the

m ean ing becomes .

T :

Then

how

about ,

th e

b igger

th e

scope?

Ss: The more general the meaning becomes .

The teacher varied the examples of "not a

book"

and looked at the fea-

tures they had in comm on and those that

differed.

Having a cover, for exam-

ple,

is

c er tainly

not a

cr i t ical feature becau se a l thou gh

a

m agaz ine

and an

exercise book both ha ve covers

an d a

new spaper does no t ,

a ll

three

o f

them

are not books. The defini t ion of the sem ant ic features of a book paved the

way for def ining

more

specif ic

k inds

o f

books,

fo r

example ,

the

l anguage

textbook. B y getting students to def ine what a language textbook is, the

teacher demonstrated tha t

as the

scope

o f

m ean ing ge ts narrower ,

t he

m e a n-

ings

of the

words

get

m ore specif ic .

The teacher also t ried to relate scope of m ean ing to levels of gen eral i ty .

From book to textbook to langua ge book, the scope becom es sm al ler and

smaller. From

book to

textbook

to

langua ge book,

the

level

o f

gene rality

be-

comes m ore

and

m o re speci f ic .

T he

teach er used several

d i f ferent

contex t s

to

i l lus t rate

how

words

a t

d i f -

ferent levels

of

generali ty should

be

used

in

relat ion

to d i f ferent

contex t s :

2.4

T : S o, I 'd

l ike

to

ask, should

we be

more speci f ic

or

more genera l

w h e n w e

make choices

o f

words

in

w ri ting

an

essay?

S :

Somet imes

it is

better

to be

specif ic ,

bu t

somet imes

it is

better

to

be general .

T : A ny

examples?

S: I f

somebody asks , "How m any books

do you

have?"

A nd you an-

swer, "I have one m a th , one Chinese, one Engl ish , one phys ics

and on e chem istry book, so five book s in total ." That w ou ld be

very clumsy.

W e

w ould just say,

"I

have

five

books."

T :

Any o ther com m ents?

S : Sometimes w e should be more sp ecific. For exam ple, if that is a

rabbi t ,

w e

should

no t

ju s t g ive

a

general answer

and

only

say

tha t

it is an a n i ma l .

T:

V ery good.

In

w riting

and

speaking,

how

should

w e

choose

our

words? More specific ones

or

more general ones?

It

depends

on

th e need of individual expressions. B e specific when necessary.

T he same applies to being general. Your b iggest problem w hen



2.

V A R I A T I O N A N D T H E SECRET O F T H E V I R T U O S O 5_[

choosing words

is

that

you

tend

to be too

general

and

vague when

you

need

to be specific. You saw a

rabbit,

but you say you saw an

animal .

S o

people don't know what

y ou

actually saw. Could

you

give m e

some examples

of us ing

words with vague meanings?

...

Afte r

dealing with levels o f generality, th e teacher dealt with another

type

of

word

relation:

synonyms.

To bring out

this kind

of

word relation,

the

teacher contrasted

it

with homonyms, which

had

already been covered

in the story of

A fan t i.

Although

homonyms

are

words

with two meanings,

synonyms

are the opposite; that is , the same meaning denoted b y

d i f f e ren t

words.

In

other

words,

synonyms

are

understood

in the

context

of the

rela-

t ion

between meaning

an d

word; synonyms being

o n e

kind

o f

meaning

word relationship

and

homonyms being another kind

of

meaning word

re-

l a t i onsh ip .

2.5

T :

. .. So , now w e come to another question. In the story w e men-

tioned, the word "want" used by Afanti has two meanings. But

there

are

other situations where

one

meaning

can be

expressed

by

a

number

of

words.

Can you

give

me

some examples?

S : For example "see," we sometimes use d i f ferent words like look

up

at, glance at,

"look

down, etc. All these basically mean

th e same as

"see."

T:

Very good. These

are the d i f ferent

interpretations

of the

word

"see." Now, I'd like you to find some

more

examples of different

words representing the same meaning.

S :

Father, daddy, papa.

T:

Y ou

learned

a

noun

in the

Poem

of

Mulan recently. What

was i t?

S:

Pater.

T: Father, daddy, papa,

and

pater

are a ll in the

same semantic scope.

L et

u s illustrate the scope o f meaning by circles. F o r example,

book, textbook,

a nd

Chinese book [teacher draws

a

circle

on the

bo ard] . If this circle indicates

"book,"

then where should w e p u t

the word textbook?

Ss:

Inside

the

circle.

T :

[drawing another circle] Then,

h ow

about

the

circles

o f

pater,

f a-

ther , daddy, and papa?

Ss:

They

are of the

same size.

T: Al l

these four circles

are

overlapping.

W e

call these four words

synonyms.

W e

also consider them equivalent

as

they share

the

same meaning....




Because

the

teacher contrasted these different examples,

the

students

be-

came aware of the two different re la t ionsh ips be tween w ords and m eanings ,

that

is, the

dif ference be tween hom onym s

and

synonyms.

Follow ing th is , the teac her drew the stude nts ' at tention to the use of syn-

onyms . Different examples were used

to

i l lustrate t ha t

d i f ferent

synony-

mo u s

words

should

be

used

in

differen t contexts

for

exam ple: form al versus

informal ("father" vs. "daddy" or

"papa");

t echnica l versus nontechnica l

("sodium

chloride"

vs. "salt"); and different degrees of politeness ("wrinkly

old fel low" vs. "Grandpa").

The teacher then revisi ted the

different

levels of gen eral i ty.

2 6

T: S , please read out the first and second paragraph. [The student

reads

it

ou t ] W hich sen tences have

you

m a r k e d?

S :

I

have m arked

the

las t sentence

in

bo th paragraphs .

The two

tha t

talk abou t the concepts of "ship" and "paper."*

[*The last sentenc es

in the two

paragrap hs are : "The conce pt

tha t

'ship'

as a kind o f marine transportat ion vehicle is generalized

from the comm on propert ies tha t all sh ips share," and "The c on-

cept of

'paper'

is a lso ge nera l ized

from

the com m on proper t ies

shared by all paper."]

T: Now I ask you, how does the general concept of "book" come about?

S: I t c o me s f rom the com m on proper ti es tha t are shared by d i f ferent

kinds of books .

T :

Then w ha t a re the com m on proper t ies o f books?

Ss:

They

are

b o u n d

by a

cover.

T :

A n d . . . ?

Ss: They are com posi t ions bou nd by a cover.

T: These

are the

com m on properties that every book has . W ith these,

w e can generate the concept of book. The con cepts of

"ship"

and

"paper" a re also g enerated l ike this . Thu s, we can unders tand the

creation

of a

concept.

S ,

could

you

please read

th e

following para-

graph? [co nt inues to read, from "Comrade M ao Zedong" to

"these tw o books"] W hat sentences have y ou m arked?

Ss: [most s tuden ts] This one: "In select ion of w ords , one m us t be

clear about the meaning and the scope of meaning in order to

choose

an

accu ra t e

and

sui tab le word."

T :

Have

you

no t iced wha t Com rade

M ao

said? This rem ark

is

in ter-

est ing. A ccording to our theory, have you

seen

th e word "men?"

S s:

[some] Yes,

w e

have, [some]

N o , we

h a ve n ' t,

no t

acco rd ing

to

the

book .



2.

V A R I A T I O N

A N D T H E S E C R E T O F T H E V I R T U O S O 53

T : N o n e of you have seen the word

"men."

"Men" is an abs t rac t

concept . W hat we see are Cheung , Lee , W ong, Ch iu , and so on .

They are concrete , real people. W hat i s the relation between the

concept "men"

and all

real people?

S: A ll

real people have general propert ies .

T :

— The com m on proper ti es genera te a concept . Have you seen

the word "building?"

Ss:

N o.

T: W e see the

words "teaching block,"

"classroom," and

"our

ow n

flats," w hich are our

"homes."

A ll these are the solid "bu ildings"

that

w e can rea lly touch .

In

t h i s exce rp t , t he t eache r r e f e r r ed back t o t he d i s cus s ion abou t

"books"

a n d

a sked s tuden t s

to

n a m e

th e

c o mm o n p r o p e r t ie s

o f

d i f fe ren t

kin ds of book s . Then the teac her gave a

fu r ther

i l lu s t r a t ion o f the con cep t

of the

d i f fe ren t

l evel o f ge nera l i ty o f w ords . For exam ple , "bu i ld ing" i s a t

a h ighe r l evel o f ge ne ra l i ty o r abs t rac t ion than "teaching block," w h i ch

r e fe r s to a s p e c i f ic b u i l d i n g .

Af te r c la r i fy ing

th e c o n c e p t , th e t e a c h e r

g u i d e d

the s tudents to apply the knowledge to an exerc i se in the t ex t -

b o o k .

In

the

las t par t

o f the

lesson,

the

teacher in t roduced another w ord re la-

t ion

in

semant ics , tha t

is ,

antonyms.

H e

first asked s tudents

to

s u g g e s t

w ords w i th cont ras tive m ean ings (em inent -m ediocre , c lever-stup id , a r -

rogant-modest). B y

search ing

fo r

examples

to

e xem pl i fy an tony m s , s t u -

dents foc used on the cr i t i ca l fea ture s o f these types o f wo rds— con t ras t in

m e a n i n g .

2.7

T: Now we w i ll d i scuss another phenom enon in semant ics— con-

trast

in

m eaning . Could

you

please tel l

m e,

w h a t

is the

term

for

words wi th contras t ive meaning?

Ss: [all ] A ntonym s.

T : Can you g ive m e some examples o f an tonym s?

S: Em inent and m ediocre .

S:

Clever and s tupid.

S: Arrogant and m odest .

T: I t seems qui te easy for you to give examples for an tonym s . W ha t

I real ly want you to focus on i s how m uch un ders tanding an t-

onyms

can

help

in presenting our ideas? For

example,

when we

grasp the pair "arrogant" and "modest," h o w c a n we present our

unders tanding o f these antonyms? Comrade M a o h a s stated ...



5 4 K O A N D M A R T O N

S :

"Modesty helps

you

improve, arrogance makes

you

decline."

T: Y ou see, w e express our ideas from both the posit ive and neg a-

tive p oint of view. W hat is the advantage of doing this?

S: W e can present our ideas com prehensively.

S:

Thoroughly.

T: Co m prehensive, thorough, are both correct . A n addi t ional point

I

w a n t to m ake : L anguage presented in a thorough w ay requires

our own

thorough th inking.

It is

better

to

consider

a

problem

from both the posit ive and negative sides. Thu s, ma stering rich

antonym s can a lso help us to consider a problem thoroug hly. I

wil l

w ri te som e w ords below

and I

w a n t

you to

tell

m e

their ant-

onym s. Then, please use these antonym s to com pose a sentence

in

order to show th e meaning of these words.

[Teacher writes praise, arrogant , good . Students state the ant-

onyms:

condem n, modes ty , bad ,

and the teacher w rites them down

on

th e

board.]

T : Now , please use these words to make sentences. Remember,

present them

in a

thorough way.

S:

It is

good

to be

praised. How ever,

it

wo u l d

be bad if we

became

arrogant .

T: Good Then w hat should w e do after being pra ised?

S:

The

m ore praise

w e

receive,

th e

more mo dest

w e

should

be . W e

not

only learn

from

criticism,

w e also

appreciate praise.

T: You see,

after

learning these anton ym s, we can tackle a problem

thoroughly, and present our ideas met icu lous ly . OK, we wi l l stop

here . I hope w e have a good com m and of

an tonyms— help ing

u s

toward a deta i led presenta t ion; the more antonyms we master ,

the more complete will be our meaning. After school, please

read the rest of this intellectual short essay, "S em antics 1 ," and

m ark the im portant sentences.

T h e Sys tema t i c

Us e o f

V a r i a t i o n

in the

Lesson

A t the beginning of this chapter, w e proposed that a systematic use of varia-

t ion m ight

be a

specific

feature

of

Ch inese pedagogy,

o r at

least

o f

wh a t

is re-

garded as good teach ing in Ch ina. The lesson "Sem antics," w hich was taught

by a state-selected expert teacher, exem plified that the teac her use d variation

system atically to create an optimal space of learning for the students.

There

are several

different patterns

of

variation-invariance

in the

lesson.

For example, the story of Afanti highlighted a variation between w ord and

m eaning: tha t is , the concept tha t one word ("want") s ignif ies t wo m e a n -



2.

V A R I A T I O N A N D T H E S EC R ET OF T H E V I R T U O S O 55

ings

("keep" and "give") was

illustrated

by

making

the

word

("want")

invari-

ant while varying the meanings ("keep" and

"give").

This allowed students to

discern

a split between word and meaning (cf.

"separation,"

mentioned in

chap.

1).

When introducing

the

concept

of

synonyms,

the

variation

of

word

and meaning

w as

used again.

T he

concept

of synonyms w as

highlighted

b y

keeping

the

meaning (e.g., "see") invariant

and

varying

the

words used

to re-

fer to this meaning (e.g., "see," "look up, glance at, "look down ), which

al lowed students to see that th e same meaning could be represented by differ-

ent

words. B y varying the relationship between word and meaning, students

were guided

to

discern

the

complex relationship

a nd

also

to

discern

th e differ-

ence between homonyms and synonyms.

Homonyms:


meaning word

Synonyms:


word meaning

T h e

awareness

of the

level

o f

generality

o f

words

w as

highlighted

b y

another

set of

variation, namely "books"

as a

category,

and

d i f ferent types

o f books (e.g., Chinese book, reference book, and textbook). When the

teacher guided students to compare the lexical meaning of "book" with

categories that were within

the

scope

of

meaning

of "book,"

students dis-

cerned that there were d i f ferent levels o f generality within th e same cate-

gor y o f words.

Variation

Invariance

level of generality category ("books")

Another pattern

of

variation

was

used

to

illustrate

the

relationship

be-

tween words an d contexts. T h e teacher drew students' attention to d i f fer-

en t synonyms

and

their level

of

generality. This

was

done

by

keeping

the

words (the

d i f fe ren t

synonyms) invariant a n d varying th e contexts. Stu-

dents' attention

was

drawn

to

focus

on the

match

or

mismatch between

words

and the

d i f ferent contexts,

an d

they were also made aware

o f the im -

portance

of the

usage

of

words

in

relation

to the

contexts. What

is

interest-

in g i s the w ay in which th e teacher tried to simultaneously bring into th e

students' awareness what

was

covered

in the

previous episode, that

is, a

k ind

of

word relation that pertained

to

levels

of

generality,

and the

critical

semantic features of a word or a phrase.



5 6 K O A N D

M A R T O N

Variation

Invar iance

con text synonym s ( i .e ., one synonym at a t im e)

When

the

dist inct ion between

the

synonyms

w as

clar if ied

by

m e a n s

o f

showing their appropriateness to one context but not to another, the teacher

also dem onstra ted that the appropria te synon ym s var ied w ith con text . This

is an example o f "fusion" as described in chapte r 1

(i .e., fusion

between syn-

onym and context ) .

T he

teacher constructed

the

lesson coherent ly

by

m e a n s

o f

correlated

var ia t ion. The l inguist ic concepts in this lesson were not introduced dis-

cretely; but were closely linked together by the teacher's use of the same

word

as

example

or

coun te r example .

F or

ins t ance ,

the

word

"books"

w as

used

to

i l lustra te concep ts th at have d i f ferent

bu t

re la ted m e a n i n g s .

I t w as

also used to il lustrate the difference be tween nar row and wide scope of

meaning (Chinese book, reference book, and books, respect ively) . And in

the la t ter par t of the lesson co ncerning synonym s, the exam ples book,

text-

book, and Chinese book were referred to again, a s a contrast to a new set of

exam ples, pater , father, daddy, and papa , in order to

i l lustrate

tha t the latter

shared the same scope of m ean ing. Likew ise the w ord "want" w as used in

the

story

o f

Afan t i

to

i l lu stra te that

th e

w ord mean ing r e l a tion

can be

a m b i g -

uous , and was la te r used aga in as a coun te rexam ple of synonym s.

This

analysis shows that

the

teacher used var ia t ion constant ly

and

sys-

tematically to raise students' awareness of the

richness

of the meaning of

words,

as

w e l l

as the

higher order structure

o f

words, such

as

h o m o n y m s ,

narrow-wide scope o f m eaning, spec if ic -genera l m ean ing, synonyms, ge-

neric and

specific

re fe rence , and antonym s.

A N O T H E R

TH E O RY

OF VARIATION

In chapte r

1 , we

presented

a

theory

o f

learning tha t revolves aroun d

the

con-

cept of

var iat ion.

In this chapter, we described two d i f ferent examples of

teaching carried

out by

Chinese teachers

w ho

bo th made pedagog ica l ly

so -

phist icated use of varia t ion. B asing our assessment on the a fo rement ioned

theory, both teach ers are doing a good job and can be expected to m a k e u se

of var ia t ion in pedag ogical ly po w erful way s. I t shou ld be noted that another

theory

o f

learning based

on

variation

w as

presented long before

our

own,

b y

a mathemat ics educa tor

from

Shan ghai , Gu Lin gy uan (Gu, 1 991) . Interest-

ingly, unl ike our theory, which was der ived from our character izat ion of

learning in the edu cat iona l context , Gu developed his theory indu ctively by

observing cases o f good practice, that is, cases o f teach ing tha t resul ted in

good learning. So , in a way, Gu 's theory o f variation is itself a depict ion of

features o f good

Chinese

pedagogy.

Gu's theory

is

more psychological ly or iented than ours (which

is an ex-

per ient ia l theory) , insofar as Gu is character izing learning—notably the



2 . V A R I A T I O N

A N D T H E S E C R E T O F T H E V I R T U O S O 5 7

learning o f m athem at ics in term s of

three

consecutive, h ierarchically orga-

nized levels of functioning, or educational goals. The following brief ac-

count

of som e parts of his theory is adm ittedly colored by the

fact

that one

theory (Gu's) is here seen through the lenses of another theory (our own).

W hat fo l low s is our understanding of Gu 's theory on the way in w hich the

m astery of the levels of m athem atical insights can be achieved by m eans of

consti tuting different patterns

of

variation.

1 .

U n d e r s t a n d i n g

th e P r o c e d u r e s o r

Pri nc i p l es

This section

is

about

th e

ways

in

w hich

it can be

m ade possible

for

students

to

discern

th e

critical features

of a

certain concept

or

principle.

Due to the

fact

that Gu developed his theory within the field of geometry and only subse-

quently

gen eralized it to other fields of m athem atics and to other school sub-

jects ,

w e use the geom etrical i llustrations from G u's original pu blication.

a. Widening of the concept , b y blocking o ut eatures erroneously assumed

by s tudents to be cri t ical features of the concept . For

instance, s tudents

most ly think in terms of s tandard f igures , tac i tly (and erron eously) assum -

ing that th e difference s between s tandard a nd nonstandard figures represent

critical

feature s (see F ig. 2.1) .

In th is case, the variation builds on the teacher ' s understan ding of the s tu-

den ts ' understanding of the concept prior to the inst ruct ional sequen ce.

b. M a k in g

it

possible

for the

s tudents

to

discern what

is

taci t ly under-

s tood, by

me a n s

o f

contrast ing noninstances.

F igure 2.2 is an example .

c. M aking i t possible or the s tudents to m ake d is t inct ions be tween cases

that they t reat

as

m e m b e rs

of the

same se t .

Here , contrast ing cases

are

intro-

FIG. 2 . 1 . Dist inguishing b etween essential an d nonessen t ial features by contrasting

standard

and nonstandard

figures. From

L . Gu (1991) , Xuehui Jiaoxue

[Learning

to

teach],

p. 68.

Beij ing, PRC : Peop le 's Educat ion Press .

Copy right ©

1991

by Gu

L ing

Yuan.

Reprinted with perm iss ion.



58 K O A N D M A R T O N

duced

in

order

to

make

the

dist inctions

possible. T w o

examp les

are

shown

in Fig. 2.3.

A ll three of these different ways of contributing to make i t possible for

the students to discern the cri t ical features of the concept or principle in

quest ion,

presuppose

that

the

teacher

has a

good unders tanding

of the

stu-

dents 'preconce ived ideas and of their hab itual w ays of deal ing w i th the con-

cept. T he first pattern of variation corresponds to gen eralizat ion and the two

other patterns to

contrast

as defined in chapter 1 .

2.


the

Process

of

Fo rmi ng

the

Procedures

or

Pri nc i p l es

This

sect ion h as to do w ith Gu 's observation tha t s tudents

f requent ly

have

difficulties discerning the figure-ground structure o f geom etric form s, that

is, w ith the qu est ion of discernm ent of wh oles and parts of pa rt icular in-

stances ra ther than the discernment of features across instances. This is

very m uch l ike the discernm ent (or del im ita t io n) of the deer and i ts parts

discussed

in

chapte r

1 .

The dis tinct ion between the discernm ent of

features

and the discernm ent

(o r

de l imi ta t ion)

o f

parts

and

wholes reminds

us

that

the

lat ter

w as

intro-

duced

b y

Svensson (1976)

to

characterize

differences

in the

unders tanding

of the

sam e text. (Svensso n arg ued tha t readers differ

as to how

they de l imi t

the

w holes

a nd

parts

a nd

therefore ma k e different senses

of the

same text.)

FIG. 2.2. D i s t i ngu i sh i ng be tween

the

presence

and

absence

o f

essent ia l f ea tures

by

contras t ing conceptua l and n o n c o n c e p t u a l

f igures .

From L . Gu ( 1 9 9 1 ) ,

Xuehui

Jiaoxue [Learning to teach] , p . 69. Be i j in g , PR C: People ' s Edu ca t ion Press . Copy-

r igh t © 1991 by Gu L i n g Y u a n . R e p r i n t e d w i t h pe rmiss ion .



2 . V A R I A T I O N A N D T H E S E C R E T O F T H E V I R T U O S O

59

F IG. 2 .3 . Foc us ing

on

e s se n t i a l f e a t u r e s

by

om i t t ing t he m . F r om

L. Gu

( 1 9 9 1 ) ,

Xuehui

Jiaoxue [Lea rn ing to teach] , p. 70. B e i j i ng , PR C : P e op l e 's E du c a t i on P r e s s .

C o p y r i g h t

©

1991

by Gu

L i ng Y ua n . R e p r i n te d w i t h pe r m i s s i on .

This dis t inct ion between the tw o form s of discernm ent i s discussed in m ore

detail in chapter 3.

T he

k ind

of

variat ion th at

Gu

proposes

to

make

i t

po ssible

for the

s tudents

to

discern the

part-whole

(and figure-ground) structure, is the trans form a-

t ion o f the

same

figure

through rotat ion

and

otherwise (see F ig. 2.4).

The s tudents can in th is w ay discern how com plex f igures are com prised

of s imple f igures. Another example can be seen in F ig. 2.5.

FIG. 2.4. Se para t ing geom etr ica l ta rgets f rom c om p l e x b a c kg r ounds b y va r i a t i on .

F r o m L .

G u

( 1 9 9

\) ,

Xuehui

Jiaoxue

[Lea rn ing

t o

t each] ,

p . 73.

B e i j i ng , PR C : P e op l e ' s

E duc a t i on P r e s s . Copy r i gh t © 1991 by Gu L i ng Yua n . R e p r i n t e d w i t h p e r m i s s io n .



60

K O A N D

M A R T O N

F I G . 2.5. Sep ara t ing com po nen t par ts o f geom et r i ca l f igures b y

s tr u c tu r a l \ a n a t i o n .

F r o m L . G u (199 ) ,X u e h u i J i a o x u e [ L e a r n i n g to teach] , p. 74.

B e i j in g ,

P R C : P e o p l e ' s

Educa t ion

Press . Copyr igh t

©

1991

by Gu

L i ng Y ua n .

Rep r i n t ed

w i t h p e r m i s s i o n .

3. D i s c o v e r i n g New

Procedures

and

P r in c ip l e s

by t h e S t u d e n t s Themselves

This is the third form of variation in the sense that here th e students produce

variation,

or

open their m inds

to

variation (rather than enc oun tering va riation),

within constrains

posed by

questions. This type

of

variation

is

illustrated

in

chapter

3,

when

w e

look

at the

open-ended problem

of

"the p ostm an's route."

VARIATION

W I T H

REPET I TI ON — TH E

F E A T U R E

O F G O O D TE AC HIN G IN CH I N A

Unti l

recently,

teaching

in

m ainland China

w as

m ostly described

as

conser-

vative,

textbook -oriented,

and

charac ter ized

by

teache r-centered rote learn -

ing

(e.g. , Cleve rley, 1985; Se ybolt , 1973). Som e resea rch ers, su ch

as

L e u n g

(1991), claimed that the conservat ive features mainly s temmed from tw o

tradit ions: the C onfu cian pedagogica l t radi tion , and the Sovie t m ode of in-

struction. This resulted in a hybrid pattern of

t each ing

and l e a r n i n g

tha t

w as

more

or less textbook-based, teacher-centered, and

con ten t -over loaded .

T he

predominance

of

drilling

and

repet i t ion

in

Chinese c lass rooms sug-

gested

that Chinese teachers believed that repeti tion skil l dev elo pm en t

should precede interpretat ion (Gardner 1989).



2.

V A R I A T I O N

A N D T H E

S E C R E T

O F T H E

V I R T U O S O

6 ^

Som e studies, as represented by Pa ine's (1 990) work, described the dis-

t inctive

teaching pract ice

in

modern China

as

being

a "virtuoso model"—

hen ce the t i t le of this chapter. In Ch ina, direct w hole-group instruction an d

teacher ta lk were found to be prevalent in classrooms. Paine (1990) ob-

served that

"It is

this f lair—a special t iming,

an

elegance

of

language ,

a

power

of

expression— that dis tinguishes

the

great teach er

from the

ordinary

one '

1

(p. 69).

S he

recognized

the

shortcomings

of

this model

in the

sense that

the

teacher plays an active role whereas the students have a passive role; the

teacher i s the actor, the s tudents the audienc e. She com m ents that

A l t h o u g h t e ache r s in C h i n a f r equen t ly v o iced conce rn abou t r e ach ing th e s tud en t s ac -

ademica l ly , t h e

l i te ra ture

and in te rv iews w i t h t e ache r s sugges t tha t th e m a i n i n t e l l ec-

t u a l

th rus t

o f t each ing c e n t e r s on the t e a c h e r s ' p e r f o r m a n c e an d m i n i m i z e s o r

i nadver t en t ly neg lec t s

th e

in t e rac tiona l p o t e n t i a l

o f

c l a s s room expe r i ence . A da p t i ng

t e ach in g to par t i cu la r aud iences , t hou gh c l ea r ly th e m a r k of a good teach er , is no t a

necessa ry r e qu i r e m e n t of the f ine c l a ss room pe r fo rm er , given the d o m i n a n t co n c e p -

t ion

o f the

t e ache r ' s

role .

( Pa in e , 1990,

p. 6 8)

However, Paine admits that despite

the

negat ive impl icat ion

o f

th is

mo de l , the emphasis on teaching as a vir tuoso performance incorporated

both a

recognition

o f the importance of

know ledge

and an

acknowledgment

of the role of personal , humanis t ic qual i t ies o f aesthetics, af fect ion , and

com m itm ent in t each ing .

Cheng (1 992)

had

similar view s

on the

pract ice

o f

t each ing

in

China ,

and

used the metaphor of "drama" to describe it:

So m e t im es , I t h i n k , to t e ach a lesson in C h i n a is to be l ike an a c t o r p e r f o r m i n g a

dr a ma . E v e r y t h i n g s h o u l d be p l a n n e d in deta i l ; ev e ry ac t ion shou ld fol low the scr ipt .

T h e r e

is no

room

for any

m i s ta k e s .

T he

lesson plan

is

j u s t

l ike

the scrip t of a

d r a m a ,

(p .

107,

in

C h in es e ,

ou r

t rans la t ion )

Cheng (1992) believed that the emphasis on strict lesson planning may

have

an

undesirable

effect , as it

reduces

the

opportunit ies

for

students

to

contribute to the plan ning o f the lesson. H ow ever, Cheng points out that the

emphas i s

on

serious lesson planning reflects

the

conscientious at t i tude

of

teache rs in China that contributes to m aintainin g the quali ty of the teac hing

profess ion

in the

country .

It

sho uld be noted th at there is also other— m ostly more recent— litera-

ture that portrays

the

Chinese classroom

as

interactive

and effective.

These

works argue that

the

whole-class ins t ruct ion method commonly

found in

Chinese classrooms al low s each chi ld to have the m axim um opportunity to

benef i t

from the

teacher,

an d to

enhance conceptual unders tanding;

and

tha t

it is this that contributes to the excellent perform ance of Chinese students in

international academic campaigns (Stevenson & Lee, 1997). These re-



62 KO AND M A R I O N

searchers have also found that Chinese classrooms are active, and that stu-

dents participate in though t-provoking tasks o r ques t ion ing (Co rtazzi 1998;

Cortazzi

&

Jin, 2001). Some researchers

are

also interested

in

t racing

the

historical origin

o f

some

of the

dist inct ive perceptions

o f

t e ach ing

and

learning in Chinese c lassrooms. They ident i fy the impact of Conf uc i a n

views of teaching and learning on educat ion in C hin a and some o ther East

A sian coun tr ies , as the C onfuc ian-her i t age-cu l tu re (CH C) l ea rne r phenom -

enon (e.g., Biggs, 1996;

Ho,

1991).

These

researchers

try to

associa te som e

of the dom inan t learning approaches adopted by studen ts in the East A sian

countr ies w ith the C onf uc i an cul ture . They p oin t out tha t a l th ou gh Ch inese

classrooms

are

apparently

full o f

rote learning,

the

repetit ion

is

used

by the

learners

as a

means

to

enhance unders tan ding. These researchers a rgue tha t

the emphas is on repe t i t ion and memor iza t ion should not s imply be d is-

m issed as conservative , as Ch inese teachers a lso em ph asize reci ta t ion w ith

ref lect ion,

and

m em orizat ion w ith un derstan ding (B iggs, 1 996; Lee , 1996) .

B y

us ing

a

combina t ion

of the

variation theory

o f

lea rn ing presented

in

chapte r 1 , and Gu 's theory o f variation as a con cep tua l f ram ew ork , Hu ang

(2002) recently character ized mathematics teaching in China (more pre-

c ise ly in S hangha i ) as be ing both h ig hly teacher -cente red and h igh ly s tu-

dent-centered ( if we use "teacher-centered" in the sense of the enacted

object

of

learning

being close to the

intended object

of

learning,

and

"stu-

dent-centered" in the sense of the s tudents owning the space of learning,

that is , tha t they par t ic ipate in br inging it abou t) . Those lessons

tha t

a re con-

sidered

to be

good

in

China

are

p lanned, cho reographed,

and

w e l l t h o u g h t -

out lessons. B ut their e laborate design never theless stil l offers p lenty o f

space for the s tuden t s ' ow n independen t and spon taneou s ideas . T he s tu-

dents

a re

h ighly ac t ive

and

they

pay

a t tent ion

to the

teacher .

In a

s imi la r way .

the teacher, having thoroughly orchestrated the lesson, can fully focus on

the var ious ideas the s tudents com e up w ith. B y usin g her previou s exper i-

ences

and her

know ledge

o f the

w ays tha t

the

s tudents often th ink a b o u t

the

specific objects o f learning, the teacher is able to ant ic ipa te wh at the stu-

dents

are

going

to

come

up

wi th spontaneously .

T he

m a them a t ic s le sson

from

a Shanghai c lassroom descr ibed in chapte r 3. is ano the r example o f

this

way o f

teaching.

A s w e

a l ready m ent ioned , Pa ine (1 990) a rgued tha t

in

the Chinese c lassroom , the teacher is the perform ing actor w hereas the s tu-

dents m ake up the pass ive audience . A more accu ra te m etaphor w ou ld be ,

w e believe, to see the teacher as the director, and the s tudents as the actors

playing

in accordance

w i th

a

script that they ha ve never seen.



3

D i s c e r n m e n t

an d th e Question,

W h a t

Can Be

L e a r n e d ?

U l l a Runesson

I d a A. C. Mok

In

chapter 2, the pr imary focus was on variat ion. In this cha pter, th e

focus

is

m ain ly on

d iscernm ent .

In

accordance w i th

the

theory

p ut

forward

in

chap-

ter 1 , we argue that a cer tain w ay of learning, of unders tand ing or "seeing" a

part icular phenomenon, means that certain cri t ical features must be dis-

cerned a nd held in our awareness s imul taneous ly . Hence , the possib il i ty for

the

learner

to

discern

o r

focus

on

these

features is a

necessary c ondi t ion

fo r

lea rn ing som eth ing in a cer tain w ay. W e i l lus t rate th is theory us ing different

examples

from

mathematics lessons.

DISCERNMENT, E X P E R I E N C E ,

AN D

M E A N I N G

In

chapter 1 , exam ples w ere given that i l lus t rated how different profess ion-

als m ust pay at tent ion or mu st be sensit ive to cer tain aspects o f a s i tuat ion in

order

to

handle

the

s i tuat ion

in a

cer tain w ay.

T he

ability

to

handle

a

si tua-

t ion

c ou ld be descr ibed in terms o f the w ay in wh ich the s i tuat ion is seen or

exp erienced ; in other wo rds, the origin of

pow erfu l

w ays of ac ting is power-

fu l w a y s o f seeing.

The w ay in w hich a s i tuat ion is seen or experienced depends on the fea-

tures of the situation that are discerned. In every situation, we can attend to

all

the

different aspects

of the

si tuation . How ever, this

is not

wh at happens .

W e

do not at tend to al l these asp ects and w e do not at tend to them at the sam e

t ime . Ins tead, we pay part icular a t tent ion to some aspects—that i s , some

63



64 R U N E S S O N AND MOK

features

of the si tuation are discerned, w herea s othe rs are not . Th e features

that w e discern are in the fore of our at tent ion, or put differently, they are

held

in our

focal

awareness; and

they

are

held

in our

awareness

at the

same

t ime.

W e can say

therefore, tha t

a

certain

w ay of

exp er iencing could

be

cha r -

acterized in term s o f the aspects that a re discerned s im ul tane ous ly .

T he

par t icular

way in

w h i c h

the individual

experiences

a

s itua t ion— or

a

phenomenon—is

the way the

individual unders tands

it.

E x p e r i e n c in g

im -

plies experiencing the object as som eth ing , t hus experiencing a m e a n in g .

When

we use the

concept

a way o f exper ienc ing someth ing and

describe

how

som eth ing

is

experienced,

w e

describe

the

m ean ing t ha t t h i s som eth ing

has for the individual. That w hich appears to be the same thing could have a

different

mean ing

for

different

individual s .

It

could also have

different

mean ings for the same individua l at different t im es . W ha t m ean ing it has for

the individual cou ld be unders tood in terms of wh ich aspects of the object

are

discerned

and

held

in the

focal awareness s im u l t aneous ly .

One way of

experiencing impl ies the s imu l t aneous d i s ce rnmen t o f cer tain features ,

w hereas another w a y o f exper iencing im pl ies th e s imu l t an eo u s d i s c e rn m e n t

of

other features .

W e

leam to experience by discerning aspects of the object to w h i ch w e

direct

o u r

aw areness.

In

order

to

gain

a

cer ta in un ders tan ding

o f a

p h e n o me -

non ,

w e

m u s t

be

able

to

discern cer tain cr i t ical features . Fo l low ing this l ine

of reasoning, if w e, as educators, w ant our students to gain a p ar t icular w ay

of unders tanding, o r to develop a par t icular ca pabi l i ty , w e m u s t m a k e it pos-

sible

f o r

them

to

discern feature s that

are

cr i t ical

fo r

tha t par t i cu lar l earn ing .

D I S C E R N I N G C R I T I C A L F E A T U R E S

O F WHAT IS TAUG H T

Wh a t

do we

me a n

by

crit ical features '?

And how can d i f ferent

w a y s

of

h a n -

dling

these cr i t ical feature s

in the

l earn ing s i tua t ion provide

d i f ferent

possi-

bilities

for

learning? Learning what

a

square is—and what

it is

no t—for

instance, takes

the

di scernment

o f the

cr i t ical featu res

o f

that geom etr ical

shape. Consequent ly , if the teacher a im s a t m a k in g the learner un ders tan d

wha t

a square is, he o r she

mu s t start wi th w hat

it

takes

to

know

and recog-

nize

the

cri t ical features

o f a

square,

in

order

to

m ake learn ing poss ib le .

In

this case,

the

cri t ical fea tures

are the

size

of the

angles ,

th e

n u m b e r

o f

sides,

and the relat ions betw een them , and i t m ust be possible for the learners to

discern these features . How ever , s im ply po int ing

ou t

these cr i t ica l features

to the learners is not enough .

W e i llus t rate th is po int w i th a t hou gh t experimen t . Le t us i ma g i n e tw o

dif ferent c lass rooms wi th

tw o dif ferent

t eachers , bo th in tending

t o

he lp

their students learn w h a t a square is. They both ta lk about the characteris-

t ics of a square and refe r to a pictu re of a square. In that respect the lessons

a re

s imi lar .

But le t us

im ag ine t ha t

th e first

t eache r s im p ly po in t s

to the an -

gles, stating that they are four righ t angles; po ints to the fou r sides, show-



3. D I S C E R N M E N T

A N D

" W H A T

C A N B E

L E A R N E D ? "

6 5

ing the

relat ion be t w e e n

th e

sides ( i .e. , equal);

an d

f inal ly g ives

a

defin i t ion o f a

square .

T he

second teacher s imi lar ly points out—or

fo-

cuses on—the ang les ,

th e

sides

and the

re la tion be tween them,

b u t

also

in -

t roduces a variat ion of these aspects . F or ins tance, she draws a pictu re of a

rhombus bes ide

the

square

an d

draw s

th e

s tuden ts ' a ttent ion

to the differ-

ence be tween th e angles o f the square and the angles o f the r h o mb u s re -

spect ively. Next she compares the number o f s ides in a square wi th the

number of ' s ides

in a

t r i ang le .

In the

same way,

she

con tras ts

the

re la t ion

betw een the opposi te s ides of a square and a rectan gle. F inal ly , the teac he r

points to squares of d i f ferent sizes.

I f w e

take

a

closer look

a t how

that w hich

w as

t augh t

w as

handled,

and

w h a t

i t was

po ssible

to

learn,

w e

find

that

the

same cr i t ical features

of the

square w ere fo cuse d on in both lessons (ang les , num ber of s ides , and the re-

lat ion

betw een them ). How ever, w hereas

the

second teacher indica ted that

the

size of the angles, the num ber of sides, and the relat ion betwee n the sides

cou ld be different be tween what is a square and w h a t is not a square, her

counterpart

did

not .

In

th is way,

a

variat ion

of the

cr i t ical features

w as

broug ht to the at tent ion of the s tudents by m eans of contras ts . The teache r

also gave exam ples

o f

different squares ( i .e., squares with different area) .

In

this

way ,

the

geometrical shape

w as

con stant,

but the

size

of the

shape

w as

varied. In the lesson taugh t by the

first

teacher, how ever, such variation w as

no t in t roduced. I t w as not possible for the learners to experience the fact that

the

size

of an

angle c ou ld vary. N either

was i t

possible

for

them

to

experi-

ence the

fact

tha t the same shape could have

different

sizes, but still be

cal led

a square .

Accord ing

to the

theoret ical f ramework laid down

in

chapter

1 , tha t

w h i c h varies

is

likely

to be

discerned.

F or

ins tance ,

it is

necessary

to

know

w h a t

a

right angle

is

no t ,

in

order

to

learn w hat

i t

ac tua l ly

is. And it

takes

the

experience

of (at

leas t )

tw o

different

examples

of

squ ares ( i .e. , variat ion

of

the area)

to

unders tand what

a

square

is. So, in

other words ,

the

space

of

var iat ion

afforded

o r

const i tu ted—part ly wi th

the

learners—is cr i t ical

fo r

the po ssibil i ty to discern these cri t ical fe ature s. A certain pattern o f varia-

t ion is

necessary

fo r a

certain learning

to

happen .

So , in

answer

to the

ques-

t ion , "How can learning best be promoted for m y studen ts?," w e w ould say ,

"Take

as yo ur point of departure the ca pab i l it ies you wa nt them to develop.

W hat do you w ant you r students to learn? W hat is cri t ical for th is learnin g

and fo r

this

way o f

u nders tanding? Make

it

po ssible

for the

learners

to

dis-

cern those features that

are

cri t ical

for

that learning."

However , we

must s t ress that

we a r e no t

say ing tha t what

is

t a u g h t

is

necessa r i ly w hat i s learned by the s tuden ts . From our point of view, there

is no

cau sa l i t y be tween t each ing

an d

l earn ing . That

is ,

there

is no

gua ran-

tee

t ha t a par t i cu lar l earn ing w i l l t ake p lace s imply beca use t eachers ac t in

a ce r ta in way , o r s t ructure th e learning s i tuat ion in a par t icu lar w ay . B ut ,

w h a t

t eache r s

can

accom pl i sh

is to

create

t h e

pos s ib i l i ty

o f

learn ing som e-




thing in a cer ta in w ay. It is not

possible

to say co nc lus ive ly how the t e ache r

af fects what s tudents

leam

s imply by looking a t the way in which the

teacher teaches th e

lesson.

How ever , it is po ss ib le to say w ha t s tuden t s are

afforded

to learn in that pa r t icula r learning si tuat io n to acc ou nt for

d i f fer-

ences in pos sibi l i ties for learning , and to show h ow th ese are ref lec ted in

what s tudents ac tua l ly lea rn .

STUDENTS'

A C H I E V E M E N T S

AN D POSSIBILITIES FO R L E A RN I N G

In 1992, Stevenson and St igler published some rem arkable findings in their

book, The

Learning

G a p.

These findings indicated more or less tha t previ-

ous

specula t ions— tha t

is ,

tha t

a

lea rner 's achievem ent

is af fected by differ-

ences

in

w h a t

it is possible to

discern—seem ed

to be

correct .

In tw o

studies,

Stevenson and St igler (1992) com pared achievem ent in m ath em atics in pr i-

m ary Grade 1 and pr imary Grade 5 s tudents from a num ber of schools in

Sendai, Taipei,

and

M inneapolis ;

and in

Sen dai , Taipei , B e i j ing ,

and

Chi -

cago, respec t ive ly . Al though the Amer ican s tudents a l ready se r ious ly

lagged behind the Asian s tudents in pr imary Grade 1 , by the t ime they

reached primary Grade

5, the gap had

w idened

so

m u c h

tha t

there

w as

bas i -

cal ly no overlap; the per form ance in the bes t A m er ican schools w as w e a k er

than the perform ance in the w eakest o f the A sian sch ools .

Several other comparative studies (e.g. , the Third In te rna t iona l M athe-

ma t i c s and Science Study [TIMSS], 1999; see M u l l i s et al , 2000) hav e

demon stra ted that Japanese s tudents ,

and

Chinese s tudents

from

H o n g

Kong and Ta iwan, do m uch be t te r in m athe m at ics than Am er ican s tudents .

There

were ser ious a t tem pts to acco un t for such dif ferences . On e of these

was the TIMS S-video s tudy, in w hich a great nu m ber of ma them at ics les-

sons in Germany, Japa n, and the Un ited Sta tes were recorded and in tense ly

scrutinized. Stigler and Hiebert followed up The Learn ing G ap (Stevenson

&

Stigler, 1992)

by

publishing their book, The Teach ing Gap,

in

1999

(Stigler

&

Hie bert, 1999). Th eir

w a y o f

describing

the

typic al Japan ese les-

son and the typical A m erican lesson offers a potent ia l exp lana t ion of the ob-

se rved d i f f e r ences in ach ievement be tween Japanese and Amer ican

students.

In a typical Japanese lesson,

af ter

having reviewed the previo us lesson,

the

teacher introdu ces

the

problem

of the

day:

a

p rob lem comp lex enough

to

be used as a f ramework for the entire lesson and for e labora t ing d i f ferent

ideas and procedures. A s a rule, the students first work on the problem indi-

vidual ly

and in a num ber of different w ays , and then cont in ue the wo rk in

groups. Eventual ly different groups present their solut ions

and

these

are

compared . T he t e ache r—and the s tudents as w e l l — c o m m e n t on the

strength an d weakn esses of dif ferent approaches. Final ly , the teacher sum-



3.


A N D

" W H A T

C A N B E

L E A R N E D ? "

6 7

m arizes the work and points to the most pow erfu l ideas that have come up

during the lesson.

In a

typical Am erican lesson,

the

teac her also starts

by

review ing

the

pre-

vious

lesson.

Then

the teacher m ay int roduce

definit ions,

term s and, above

all , a method for solving a certain k ind of problem . Af ter the dem ons t ra tion ,

the

s tudents are given a relat ively large num ber of problem s of the same

kind

to pract ice on. After they have prac ticed these, another type o f pro blem

m ay

be

in t roduce d.

T he

m ethod

fo r

solving this kind

of

problem

is

demon-

strated

by the teacher, and the students are given a further set of problem s of

this

other kind

to

pract ice

on .

M a t h e m a t i c s lessons

in

China have been described

in

s imi lar terms

as

Stigler

and

Hiebert

described

the

Japanese lesson

(see

Stevenson

&

Stigler,

1992).

An d to a

certain extent ,

it

wou ld

be

true

to say

that

th e difference s

j u s t

i l lustrated could potent ial ly provide an explanation of the differences in

achievement

between Asian

and

American s tudents .

If w e

s impl i fy th ings somewhat ,

we can

argue that

an

im por tan t differ-

ence betw een Chinese an d Japanese m athem at ics lessons on one hand, and

Amer ican

lessons

on the

other,

is

that

in the

former,

the

s tudents most ly

face

one

problem

to

w hich they

are

asked

to f ind different

solut ions , w hereas

in

the latter, the students are presented wi th one method fo r solving one kind of

p rob lem,

which they then prac t i ce

by

solving

different

problems

of the

same kind.

In

each case ,

t he

s tudents were af forded dif ferent poss ib i l i t ies

fo r

w h a t

cou ld b e

learned.

In one

type

o f

lesson, s tuden ts w ere given

the

poss ibi l i ty

to

learn

how to f ind

solut ions

to a

p rob lem , w hereas

in the

other , they w ere

af forded the po ss ib i l i ty to learn ho w to m ake use of a pa r t icula r solut io n.

In

these s tudies , comparisons were made using lessons wi th

different

mathemat i ca l

co ntents . Thus, the comparison w as m ade o n a general

level.

In

the

fo l lowing

example ,

tw o

lessons tha t aim ed

to

teach

the

same

specific

conten t are

com pared

in

relat ion

to

w h a t

w as

possible

to

learn.

L E A R N I N G

TH E OPERATOR

ASPECT

O F TH E FRACTION AL

C O N C E PT

R une sson (1999) s tudied f ive m a them at i c s le s sons , a ll t each ing f rac t iona l

num bers an d percen tages . In many respect s , the l essons w ere very s imi lar .

F o r

i n s t ance ,

four o f

them used

the

same textbook,

and the

c lass room

w ork was orga n ized in a very s imi lar way . The a im of Ru nesso n ' s s tudy

w as to

invest igate

th e

var ious ways

in

which teachers handle conten t ,

in

th is case, f ract ional n u mb e r s

an d

percen tages .

Le t us

take

a

closer loo k

a t

tw o of the

teachers.

In both lessons, the content being taught was the operator aspect o f the

fract ional co ncept (e.g. , how to f ind 1 /3 of 12). In both cases, the discussio n



68

R U N E S S O N

A N D M O K

took place

in a

whole-class

setting. The lessons were audiorecorded and

transcribed verbatim.

T he

d ia logue

is

p resen ted a longs ide

o ur

analys i s :

3.1

[Mathematics

Lesson

/

F ract ions/

Secondary Grade

1 ]

Teacher

A

T: OK. Here I have a piece of

string. It's

90

cent imeters long.

[Teacher holds up a piece of

string] Three people have

to

share that equally. How do you

go about that? Fair share? Tell

m e,

Sylvia .

S 1 :

Wel l ... divide by three.

T :

Yeah, each

o ne

w i ll

get a

th ird .

B ut let's say one of them wants

to have more than the others .

The str ing is

stil l

90 cen t ime-

ters long and I want 2/3. H ow

cou ld we f igure tha t out? 2/3 of

a

piec e of str ing tha t is 90 cen-

timeters long?

Thomas?

S 2:

[ inaud ib le]

T:

R ight. First

you

f igure

out the

length

o f a

third

and

then take

another

one . . . and

together

that makes

... ?

W h a t

d id you

say?

60

cen t im eter s? Yes.

So,

first you

have

to figure out the

length of 1/3. Measure that,

an d

then t ake ano the r one .

[The teacher

first

marks 1/3 ,

then 2/3 of the whole length o f

the str ing] .

T: OK.

Let ' s take

a

look

a t

th is

piece

of

string. [The teacher

is

hold ing up a

shorter piece

o f

str ing] This is on ly 40 cent i-

meters long. I would l ike to

have

one fifth of 40

cen t ime-

ters . [Wri t ing on the b l ack -

board: 1/5 of 40 cm]

The teacher introduces the

problem.

A man ipulative aid is

used.

A

s trategy

fo r

solving

the

p r ob l e m (1/3

of 90) is

intro-

duced.

The

nom inator is changed; 1/3

is changed to 2/3 (2/3 o f 90).

The

teacher elucidates the

strategy an d illustrates with

the manipulative aid. (1/3 o f

90 = 90/3 = 30)

A

ne\v

problem

(1/5

of 40) is

introduced. A manipulative

aid is

used.

Writ ten

representation



D I S C E R N M E N T A N D " W H A T C A N B E L E A R NE D ' . ' "

69

S 2: 8 cen t im eter s .

T :

Yes, each fifth is 8 cen t ime-

ters .

B u t le t 's s ay we wan t 3/5.

How do you f igu re that out?

Tell m e, L i s a .

S 3: Th r ee t imes 8.

T : O K . Firs t w e m u s t f igure out

how m u c h 1/5 is. So, you di-

vide 40 by 5, and you get 8.

A n d

three f i f ths m ust be three

t i m e s

a s m u c h .

Three

s u c h

p i e c e s . Th at ' s 24. B ut le t 's say

t ha t the piece of str ing is 60

c e n t i m e t e r s in s t ead . [Wr i t e s

60 cm on the board] . One of

y ou

should have 3/5,

and an-

other o n e

2/5.

H o w m u c h w i l l

the person w h o gets 3/5 have?

...

O K . H o w d o w e g o abou t

th is? T h e w ho le p iece o f string

is

60.1 shou ld have 3/5, then

I

m u s t

f i g u r e s o m e t h i n g

o u t

f i rs t , w h a t .. . ? M ar tin .

S4: 5 d ivided by 60

T : Wel l , now you said it the other

w ay

around— 60 d iv ided by 5.

W hat ' s t ha t?

S5: 12

T : OK. 12 . So now we know tha t

1 /5 is 12. Then how m u c h is

3/5?

The

n o m i n a to r is changed (3/5

of 40). The

teacher asks

for an

appropriate

s t ra tegy.

The teacher elucidates

the

s tra tegy .

The

who le

is

changed

(3/5 o f

60).

W ri tt en represen ta tion

The

teacher asks

for the ap-

propria te s t ra tegy.

I f we

an alyze this data

in

term s

o f the

aspects focus ed

on , it is

apparent

tha t

the

focus

was on the

strategy

fo r

solving

the

problem ( i .e . , calc ulat ing

the

length of a fractional part of a piece of str ing) .

This

is the aspect that the

teach er tr ied to draw the students ' at tention to. B ut only one strategy or proce-

dure

wa s presen ted, and hence the strategy w as not varied. This particular as-

pec t was foc use d on, but w as kept invariant. However, the teacher did chang e

the param eters in the problem . After introducing the first problem and pre-

senting an appropriate solving strategy, the teacher ch anged the length of the

piece of siring (i .e. , the wh ole) a s we ll as the size of the fractional part (1/5 o f



7

R U N E S S O N

A N D M O K

40).

In the fo l lowing

example ,

the

num era to r

w as

changed (3/5

o f

40),

an d fi-

nally in the last example, the who le ( i .e ., the length of the string) w as changed .

Thus, the

strategy

w as

invariant , while

the

numbers var ied

in a

sys tema t ic

way.

(1 /3

of 90, 2/3 of 90, 1 /5 of 40, 3/5 of 40, 3/5 of 60)

Let us now contrast th is approach w i th that o f Teacher B , wh o se t each in g

also deal t wi th

th e

operator aspect

o f f rac t ional

n u m b e r s .

Th e day

be fo re

this lesson, the

students

had been working on a

p ar t icu lar

problem in

w h i ch

they had to mark 3/7 of a recta ng le w i th a size of 7 x 8 squares , as shown in

Fig. 3.1 .

3.2 [Ma them at ics /Frac tions /Pr im ary Grade 6 ]

Teacher B

The

rectangle

is

shown

on an

O H T T o

begin w i th

the

teacher

asks Lena to

tell

the class how

she

marked

3/7 of the

rectangle.

SI: If you just take seven squares

from the

whole,

and

then take

three of those ... If you count

"one, two, three,"

and

mark them.

T:

W h y ?

SI: Well it is 3/7 of the small pile.

And then

I

continue: one, two,

three, four,

five,

six, seven,

go on

like that.

I

keep counting

to

seven

and

m arking three of them .

A

manipulat ive

aid is

used .

In each group of seven squares ,

three are m arked .

The teacher asks

fo r an

argu-

ment.

The s tudent i s explaining her

s tra tegy .

FI G. 3 . 1 . T he grid fo r m a r k i n g 3/7 of 56.



3. D I S C E R N M E N T A N D

" W H A T

C A N B E

L E A R N E D ?"

71

T: Oh yeah . I unders tand You

counted one, two, three,

four,

five six, seven, and then you

marked th ree

o f

t h e m.

A n d

t hen one , two , t h ree , fou r ,

f i v e ,

s i x , s e v e n , a n d y o u

m arked them . In o ther words ,

you do it

l ike this [pointing

a t

the pro jec t ion on the board]

one, two, three, four, five, six,

seven.

You can

ma r k

the

las t

ones l ike tha t . How do you go

on? In the same w ay?

S I: Yes .

T: Wel l did anyone do it differ-

ently?

Did you all do it like

that?

Ss: N o.

T :

Well what about you ...

Sophie?

S 2:

We l l ,

I

j u s t d iv ided

it

in to

seven parts .

T: OK. You

jus t counted

all the

squares and divided them into

seven. OK, Maria what about

you?

S 3: Wel l I tried

different

numbers

like that unt i l I got seven parts .

The teacher e lucidates Lena 's

s tra tegy.

A manipula t ive aid is used .

The

teache r asks for a l terna-

t ive s tra tegies .

Another

s tudent expla ins

her

strategy, which

is

different

f rom the

previous

o n e .

The

teacher asks for a l terna-

t ive s tra tegies .

Yet

another s tudent exp la ins

her

s tra teg y, which

is different

f rom the prev ious one .

Here, Teacher

B

focused

on the

solving strategy

in a

s imi lar

way to

Teacher A. Thus, the foc used aspects w ere the same in both lessons . B ut , w e

can

observe that Teacher B asked the students to come up with

different

solving strategies to the sam e problem (3/7 of 56). The variation in the stu-

den ts ' solving s t rategies was m ade exp l ici t w hen the teacher asked: "Did

you al l do i t

l ike that?"

T he

studen ts ' responses show ed that they

h ad

c o me

up w i th different w ays of solving the problem. Lena solved the problem by

count ing seven squares in each column and then marking three of them.

So phie divided the 56 squares into seven parts (and m ult ipl ied six by three ).

A nd f inal ly,

M aria tried

different

num bers, which m ul tip l ied

by

three equ als



72 R U N E S S O N A N D M O K

56. So, in B 's lesson, the solving strategy varied, w hereas the param eters o f

the problem were the

sam e

(i.e., 3/7 of 56), and hence were invar iant .

T he

different w a y s

in

w h i c h

the

studen ts chose

to

solve

the

problem

im -

ply

that

they had

differe nt interpretations

of the

operator aspect

of fractional

num bers. Th e way tha t Lena solved the problem im plie s that she interpreted

3/7 of 56 squares by a rranging the 56 squares in to groups of seven an d then

taking three ou t of seven in each group (s tre tcher /shr inker interp reta t ion ;

B ehr, Harel, Post, & L esh, 1993) as i l lus trate d in Fig. 3.2.

The other two stra tegies both imp ly another interpreta tion, na m ely divid-

ing 56 squares in to seven group s and then tak ing three groups out of the seven

groups (dup licator/partit ion -reducer interpretatio n) as

illustrate d

in F ig. 3.3.

In

Lesson

B , the

var ia t ion

in

so lving stra tegies that were presented

by and

to the

s tudents a lso in volved

a

var ia t ion

in the

sem ant ic in te rpre ta tion

of the

operator aspect o f f ract ional num ber s . Thus , in th is s i tua t ion , a var ia t ion o f

the semantic interpreta t ion of the concept was introduced.

N ow le t us take a c lose look a t the two lessons. W hat is the m ain differ-

ence be tween the two teachers ' w ays of dea l ing wi th the same conten t ( a

FI G. 3.2. Le na 's strategy for f ind ing 3/7 of 56.

F I G .

3 .3 . A no the r s tud e n t ' s s t ra t egy fo r f i n d i n g 3/7 of 56.



3 . D I S C E R N M E N T AND "WHAT CAN BE L E A R N E D ? " 73

strategy

for

solving a/b

of c)?

Teacher

A

introduced

a

m e thod

for

com put ing

the fraction of an integer that basically involved dividing the integer by the

denomina tor

and

m ult iplying

the

quot ient

by the

nominator . This method

w as

first

applied

to one

problem, then

to

another,

and

finally

to a

th ird, tha t

is, the method w as the same but the problem s

differed.

Teacher B offered the students one problem only but invited them to find

different ways of solving i t . Three different students found three different

w ays of solving the same p roblem. Hence, the problem w as invariant but the

solving strategy varied. This w as the oppo site of w ha t w e observed in the

case of teacher A , w here the me thod w as invariant and the problem varied.

A com parison of the tw o lessons is i l lustrated in Table 3.1.

From Table 3.1,

it is

apparent that there

is a

system atic

difference

in the

aspects that the two teach ers varied and those they kep t invariant. Som e as-

pect s varied in one lesson, w hereas they w ere invariant in the o ther and vice

versa.

In the first case (T eacher A ), w e find a variation in the a lgo rithm ic so-

lu t ion,

w hereas

in the

second case (Teacher

B ),

there

is a

variation

in the se-

mant ic interpreta tions o f fraction numbers as operator.

Seeing

the two

lessons

in

terms

o f

possibi l i t ies

for

d iscernment (i .e.,

w h a t m i g h t be discerned), the two lessons are also different; different n u m -

bers are plugg ed into the formula in one lesson, and different wa y s o f inter-

preting and solving the problem, in the other lesson.

Focused Aspects an d D i m e n s i o n s of V a r i at io n

For every aspect of the ob jec t o f learning , there is a corresponding dimen -

sion of

varia t ion.

B y

that

w e

mean tha t

a

part icular aspect co uld

b e

some-

th ing

different . For instance, in the exam ples ju s t c i ted , the calcula t ion

a /b

o fc could be done in different ways , and thus the ca lcula t ion corresponds to

a dimension of variation in the solving strategies. One way of solving the

problem is a

"value"

in the dimension of solving s t ra tegies , whereas an-

other way of solving is another

"value"

in the same d imens ion. When

TABLE 3 .1

The Space of V a r i a ti o n

Constituted

in Lesson A and

Lesson

B,

R e s p e c t i v e l y

S o l v i n g

s t ra tegy

Paramete rs o f ope ra t ion

Rep r e s en t a t i o n

S t ude n t s ' unde r s t a nd i ng

Semant i c in t e rpre ta t ion

Teacher A

Inva r i an t

Var i ed

Var i ed

Invar ian t

Invar ian t

Teacher B

Var i ed

Inva r i an t

Inva r i an t

Var i ed

Var i ed



74

R U N E S S O N

A N D M O K

studying the lessons f rom the po in t of view of how the "enacted object of

learning" is con stituted, w e find that the aspect focus ed on in each lesson is

varied

and we

describe tha t

in

term s

of the

opening

o f a

d imens ion

of

varia-

tion

o f

that par t icular aspect .

F o r

instance,

in

Lesson

B ,

w he re

the

focus

w as

on the solving strategy, and different solving stra tegies w ere dem on stra ted,

a

dimension

o f

tha t aspect ( i .e ., m etho ds

o f

so lv ing)

w as

opened.

In

addi-

t ion ,

we saw

that

the

teacher presented different in te rpre ta t ions

of the

con-

cept and different w ays of un derstan ding , and thu s that these aspects were

also opened

as

d im ensions

o f

var ia t ion.

In

other wo rds,

the

solving strate-

gies , the interpreta t ion of the concept , an d the s tudents ' unders tan ding were

dimensions of var ia t ion that were a l l opened in Lesson B. In Lesson A,

other

aspects

varied (i.e. ,

the

parameters

o f

op era t ion

and

representa t ion) ,

and therefore other dimensions

o f

var ia t ion were opened (see Table 3.1) .

Thu s, the spaces of var ia t ion con st i tuted in the lessons w ere di f fe rent .

DISCERNING PARTS

AN D

W H O L E S

So far in

this chap ter ,

w e

have discuss ed

how dif ferent

aspects

o r

fea tures

of

an object of learning are discerned. B ut the ob ject of learning is a lw ay s s i tu-

ated in a context , a nd it has to be discerned

from

tha t par t icu la r context in

order to re la te i t to other con texts and to other instan ces and by doin g so dis-

cern

its

fea tures . Fur therm ore ,

the

ob jec t

o f

l e a rn ing

is a

whole and .

as a

rule , dis t inct par ts within i t can be discerned.

These

par ts can also be de-

scribed in te rms o f their features, their re la t ions to each o ther and to the

whole , and in term s o f their parts.

In chapter 1 , re fe rence w as made to Svensson (1 976) who s ta ted that the

ent it ies , or the phenomenon (we w ould say the ob jec t of lea rn ing ) w e en-

counter m ust be del im ited ( i .e . , d iscerned) by the sub ject and they can be de-

l imited (or

discerned)

in

different

w ays . Such

d i f ferences

accou nt par t ly

fo r

the reason wh y we al l see t h i n g s

differently.

T he exam ple g iven in chapte r 1

w as the

deer

in the

forest ,

bu t

these dif ferences

are

present

in all

cases wh en

somebody is learn ing something . In the exam ple s g iven in th is chapte r , w e

can a lso see tha t m athem at ica l problems in the c lassroom have to be d is-

cerned f rom the con text . At very least , the s tuden ts m us t be able to dist in-

gu i sh be tween wh en the pa r t i cu la r p rob lem i s d i scussed and w hen

something e lse is ta lked about . Fur thermore, if the problem is the w h o l e,

there a re generally also parts that can be

identif ied,

such as separate ar i th-

metic operat ions,

and the

m eaning s tha t derive from

the

p rob lem .

Let us look again a t the c i ted exam ple , in w h i ch tw o dist inct ively

differ-

ent way s of dealing w ith the operator asp ect of the

f ract ional

concept were

described. According

to the

m e thods used

in the

first example (Lesson

A )

the s tudents cou ld ident i fy and learn to use an a lgor i thm for the ca lcu la t ion

a/b of c, by

carrying

ou t the

division c /b

and

thus ob ta in ing lib

of c, and

then

mul t ip ly ing

by b to obta in

a/b.

There w ere four subprob lems :




A N D " W H A T C A N B E

L E A R N E D ? "

75

Answer

1. 2/3 of 90 30

2. 1/5 of 40 8

3.

3/5 of 40 24

4. 3/5 of 60 36

W hen deal ing with this part icular kind

of

problem ,

the

students

had to

del imit this sequence from the context of the lesson. By doing so, they be-

came poten t ia lly capable of relating it to sim ilar kinds of problem s in the fu -

ture.

The

sequence could then

be

considered

as a

part

of the

lesson,

but

also

as

a whole in which the

four

subproblems could be discerned as parts.

Within the subproblems, the three kinds of components—numerator , de-

nominator , and the whole—could be discerned and re la ted to each other

within the

same subproblem,

or to

corresponding par t s wi th in o ther

subproblems.

A s

w e

show

in the first

example

in

chapter

4,

this process

of

del im ita tion

also

appl ies

to the

process

o f

reading

a

text . W hen reading texts ,

the way in

which the

reader

delimits the whole and the

parts,

and

relates

them to each

other is of vital importance for unders tanding.

L E A R N I N G

A B O U T

P R O B L E M

S O L V I N G —

T H E

POSTMAN'S ROUTE

Th e secon d ma in data set to be used in this chapter is "the p ostm an 's route,"

which gives

a

further i l lustration

of the

thesis presented

in

chapter

2. In the

Ch inese

lesson that we describe, the teacher carefu l ly planned the lesson

and

fo l low ed th e lesson p lan accordingly. W e f irs t present a summ ary of the

lesson fo l low ed

by an

an a lys i s.

S u m m a r y of the Les s on

This lesson w as a demon stra tion lesson con ducted a t the N at ional C onfe r-

ence

for

Open-Ended

Que stions

held

in

Shanghai

in

N ovem ber, 1998 (the

data w as d iscussed in M ok, 2000, 2002). Dem onstra t ion lessons, in w h i ch

an

expert teacher is invited to teach a class in front of an audience , are a

com m on prac t ice in schools in the

Peo ple 's

R epu bl ic of China. The c lass-

room w as a room m uch la rger than a normal c lass room. The front section o f

the room had the normal c lassroom set ting w ith a teach er ' s po dium , and the

back section

w as

l ined w ith about

50

chairs

fo r the

audience.

For the

dem -

onstrat ion lesson u nder discussion here , the audience w as made u p of par-

t ic ipants

of the N at ional Con ference. Despi te the demonstra t ion natu re of

the lesson, i t w as a real 40-min . prim ary Grade 4 lesson, co ndu cted during

the norm al school t imetab le . There were 28 studen ts and they sat in g roups




of four. B efore the lesson, the teacher gave the au dienc e a one-page lesson

plan . It w as s ta ted in the plan tha t the obje ct ives of the lesson w ere to de-

velop students ' problem-solving stra tegies by so lv ing a pos tman 's prob-

lem, and to develop stude nts ' creat ivi ty and divergent th ink ing via problem

solv ing.

In the

lesson plan ,

i t w as

exp l ic i t ly s ta ted tha t

the

t e ache r wo u ld

ap -

proach the problem by asking students to design rou tes for the postm an in a

real-l i fe context . Fol lowing th is , the t e ache r wou ld he lp s tuden t s to con-

sider th e problem in a m athematical context , by asking them to look for reg-

ular i t ies exhibi ted in the routes th at they had com e up w ith , and to thin k

about the possible transform ation of the

shapes.

(The routes becam e shapes

once the direct ion arrows w ere taken aw ay.) To beg in wit h, the teache r ex-

plained

the

problem

by

holding

up a

sample worksheet (see Fig. 3.4). Here

is a transla t ion of the problem sta teme nt that w as show n on the black bo ard

and explained by the teacher verbal ly:

There are nine dots on the paper. The dot surroun ded by a t r iangle in

the left u pper comer represents the post off ice. The pos tman needs to

start at the post

office

deliver a letter to each of the e igh t p lace s , and re-

turn to the post off ice . W hat could be the po s tm an 's route?

T he

lesson consisted

o f

four phases

in

w h i c h

the

teach er he lped

the

s tu-

dents to tackle the problem according to the lesson p lan . Th e

four

p arts are

now illustrated:

Part

1:

Students Designing Their

O w n Routes .

The

teacher asked

th e

students to work in groups an d exper iment w ith as m any routes as possible .

Each student designed his/her ow n route o n the pieces of paper provided by

the

teacher,

and the

designs

o f all

group m embers w ere

put in a

p i l e .

T he

s tu-

den ts w ere very

eff ic ient

and

only ta lked w i th the i r ne ighbors occas iona l ly .

W hen they h ad f in ished al l the papers o n the i r desks , they ra ised the i r han ds

for more . T he act ivi ty lasted about 1 0 m i n .

F IG .

3.4.

T he workshee t .



3.


A N D " W H A T C A N B E L E A R N E D ? "

77

Part 2:

Evaluating

Their O wn D es igns Selectively. During this phase, th e

teacher resumed the at tention of the whole class. She posted some of their

designs

on the

blackboard

and

asked

the

class

to

j udge

whether the

designs

w ere correct . One group produ ced 18 designs and the teache r asked the stu-

dents to discuss with their group members whether this group's designs

were correct (see Fig. 3.5).

After the discussion, the whole class agreed that a ll of the designs were

correct . Then the teacher pointed to a faulty design produced by another

group,

and

asked whether

i t w as

correct (see Fig. 3.6).

Th e s tudents pointed o ut that the arrows w ere m iss ing from this design,

and that there w as no indicat ion of how the postm an cou ld return to the post

office .

Fol lowing this,

the

teache r asked

the

class

to

think

o f

w a y s

t o

deter-

m ine wh ich design w as the best . After a few exchanges of ideas between the

class and the teacher, they agreed that the shortest route w as the best . Then

the

teacher guided

the

class

to

compare

the

n u mb e r

of

straight

a nd

d i agona l

F I G .

3.5. The 18 rou te s .

FI G. 3 .6 . The w rong route .



78

R U N E S S O N A N D M O K

segments

in the

designs,

an d to

determine

the

shortest rou te based

on

this

in-

formation

(see Fig. 3.7).

The teacher removed the longer routes, leaving

seven

on the

board.

Part

3:

Group Interchange

in

Order

to

Supplement Additional Best Routes

After

this, the teacher asked the students to supply more of the shortest

routes f rom their own piles of designs. They handed in 5 m ore, w hich made

a tota l of 12 on the blackb oa rd. The teacher g uided the class to remove the

repe titions and to disregard the arrows. E ven tua lly only 8 designs rem ained

on

the

board (see Fig. 3.8).

Stra ight

segments

Diagona l

segments

F IG . 3.7.

T h e

four pat terns

and the

n u m b e r

o f

l ine segments .

F I G . 3.8. The 8 pat terns

after

neg lec t ing the a rrows . N ote tha t (1 ) has the m iss in g

part fac ing left

w he r e a s ( 2) has the m i s s ing pa rt

fac ing

up .



3.

D I S C E R N M E N T A N D "W H A T C A N B E L E A R N E D ? "

79

Part 4: Converting a Practical

Problem

Into the

Mathematical Problem

of

Categorizing th e Routes

A ccording

to

Th eir

Shapes.

Once th e arrows were

discarded, the designs of the routes becam e geom etric shapes. In this part of

the

lesson,

the

teache r asked

the

students

to

catego rize

the

shapes acco rding

to the way

they

saw the

relationship between them. There w ere very l ively

class discussions, and the students gave a lot of suggestions, such as how to

rotate

the

shapes (see Fig. 3.9)

or

flip them over (see Fig. 3.10).

Consequently, the students had different ideas about the number of cate-

gories, for example, infinity, 2, 8, and 16.

Toward the end of the lesson, the teache r invited the class to th ink abo ut a

related problem, which

had the

addit iona l constraint suggested earl ier

b y a

student, that

is,

wha t

the

postman would

do if

there

w as an

urgen t letter.

Ana l ys i s of the

L e s s o n :

T h e P oss ib i li ty of D i s c e r n m e n t

i f f e r e n t Solutions to the Same Problem. At the outset, the teach er asked

th e students

to

work

in

groups

and

experiment w ith

as

many po ssible rou tes

as

they

cou ld think

of. It is

significant that

th e

teacher asked

for as

m any routes

as possible instead of the best route. This demand for as many solutions as

possible created

a

dimension

of

variation

in the

possible routes. W hen

the de-

signs were pu t on the board, the oppo rtunities for discerning alternative rou tes

became m anifold because each student had to consider not only th e routes

proposed

by

their group m em bers,

but

also those suggested

by

mem bers

of

other groups.

F I G.

3.9.

A

ro ta t ion .

F IG . 3.10. Ref l ec t ions .




Possible

Versus Impossible Routes .

In order to help students discern the

critical features of a possible rou te, the teacher del iberately focused the stu-

dents' attention o n a faulty design

(i.e.,

an

im possible route),

and

asked

the

class wh ether this design

w as

correct (see F ig. 3.6).

In the

di scussion about

w hether the route was correct or not , one s tudent pointed out that the arrow s

were missing, and another student pointed out that the route did not lead

back to the post

off ice.

In other w ords,

by

juxta po sing poss ib le rou tes wi th

an

im possible route,

the

teacher

w as

able

to

help stu den ts discern

tw o

cri t ical features

of a

possi-

ble route. One is tha t to con st i tu te a route, there has to be an indic at ion of the

direction of the route, and using an arrow to indicate direction is im portant.

T he

other

is

tha t

the

rou te needs

to

reach

a

pa r t i cu l a r des t ina t i on .

In

th is

case, the pos tm an needed to be able to go back to the post office

af ter

del iv-

ering the letters. Discerning these tw o critical features helped the class to

cons ider

t he

designs th at they

had

come

up

w i th

and

e l imina te

the

imp oss i-

b le

rou tes .

Possible

Routes Versus

Bes t

Rou tes.

Af ter

this , the teacher raised th e

quest ion

of how to

dec ide wh ich design

w as

best .

T he

fol lowing

is an ex-

cerpt from

the

di scuss ion .

3.3. [Math Lesson/Primary Grade

4]

T: How

should

w e

decide wh ich design

can be

called

th e

best design?

S3: Use the

shortest route?

T: "Use the shortest route," goo d. A ny others?

S 4:

Do n ' t repea t

the

rou te .

T :

Good,

"Don't

repeat the route." A ny others?

S5: If

there

is an

urgen t le t ter that needs

to be

del ivered

first,

w h a t

should we do?

T: Goo d, "If there is an urg ent let ter." V ery good. An y others?

[N o

m ore su ggest ions . ]

T :

Let ' s

first put S5 s

problem aside

an d

assum e tha t there

are no ur-

gent letters.

A ll

let ters

are

eq ual ly im por tan t. Then , w hich

is the

best design?

S6: The shortes t route.

B y

asking the s tudents to th ink about w ha t const i tu ted a

"best

route," the

teacher w as trying to ge t the students to revis i t the routes that they had de-

signed

f rom a

different perspective: that

is,

w h a t

is

possible versus what

is

best. The s tuden ts 'judg m ent of the best route w as at f irs t s imp ly an intui t ive

judgm ent w i th re ference to the postman's prob lem . The c ri teria for the best

route were

no t

form al ized. Subsequent ly ,

the

teacher g uided

the

students

to




A N D

" W H A T

C A N B E

L E A R N E D ? "

8J_

coun t the

number

of

straight line segments (horizontal, vertical,

and

diago-

na l ;

see Fig. 3.7). A t this point, the teacher w as in fact guiding the students to

scrutinize

the

routes from

a

m athem at ical perspective.

U p to this poin t in the lesson, the teacher had taken an open problem , p re-

sented at a level very close to the students' everyday experience (design ing as

many paths as possible from the postman's perspective), and deliberately

guided

the students to twice revisit the designs that they prop osed: first to pick

the correct routes a nd then to pick the best rou te. In this way, the students not

only had the

chance

to see

that

the

problem

w as

open,

b ut

also

to see

that there

w ere m any possible solutions. In other words, the problem w as the invariant

in

the

lesson, w hereas

a

dimension

of

variation

w as

created

in the

m ethods

of

solving th e problem . Because of the variation created, students were

given

oppo rtunit ies to see various aspects of the problem— the m any po ssible solu-

t ions to the same problem; the difference between possible and impossible

solutions; the difference between possible and best solutions; and that th e cri-

teria used

m ay

vary between

an

intuitive choice

and a

mathemat ica l ly

grounded ch oice.

Categorization

of

Shapes:

Rotat ions and Reflections. In the

fourth par t

of

the lesson, the tea che r asked the class to discern the regu lari t ies exh ibited

in the eight shapes that rem ained on the board, an d to catego rize the shapes

(see F ig. 3.8). This task gene rated

a

very l ively wh ole-class discuss ion.

T he

fo l lowing

is an

excerp t from

the

discuss ion:

3.4 [M ath Le sson/Prim ary Grade 4]

T: N o w ,

we are not

going

to

consider di rect ion anymore. Look

at

these shapes . I w ould l ike you to use different m e thods to ca tego-

r ize

them. [Referr ing

to

Fig. 3.8.]

S 1 1 :

There are eight

shapes.

A ccording to the direction in w hich the

miss ing part

is

fac ing, there

are four

categories. There

are two

shapes for each category. Eight altogether.

S I 2 : Move

the

second shape [referring

to

shape

6 in

Fig. 3.8]

on the

second

row

aro und, then

i t

becomes

th e

third shape [shape

7] on

th e second row. [The teacher then moved the shape acc ording to

th e

student 's instruction.]

T: Very

good.

S he

found

tha t

af ter

ro tat ing, these

tw o

shapes

[6 and

7],

become the same. Any m ore sugges t ions?

S12 : M o v e

the

third shape

[7] on the

second row,

it

then becom es

the

third shape

[3] on the first

row.

T :

Let m e f irs t label these patterns. One, two, .. . eight [Students

said

the num bers aloud and the teacher wrote the num bers under

the patterns.]

SI 3 : [ inaudible]



82

R U N E S S O N

AND MOK

T: S13

said that rotating

the

sixth shape

[6]

w i l l resul t

in the

eighth

shape [8]. What next?

SI 4:

[ inaudible]

T: S1 4 said that rotat in g the eighth shape [8] w il l aga in resu lt in the

seventh shape [7]. [The teacher wrote "6-8-7" on the board.]

S15: Turn the f i f t h shape [5], and turn again . It

wi l l

resul t in the eighth

shape [8]. Turn

the

third shape

[3]

upward.

No, flipping it

over

wil l resul t

in the fifth

shape [5]. [Flipp ing

the

shape w i l l produce

an image by ref lec t ion; see Fig . 3.10.]

T: W e started by sugg esting rotat ion . No w S1 5 sugg ested flipping

over

the

shapes.

A re

there

any

more suggestions? [The teacher

recorded the fl ipping in another row on the boa rd; see Fig. 3.1 1 .]

After

labeling the shapes 1 to 8, students became very active in pu tt ing

forward

thei r ideas for rotat ing them . The teacher put down a record of the

rotat ions

(6, 8, 7, and

later

5)

that

th e

students suggested (see Fig. 3.11).

How ever, rotation wa s not the only w ay to move the shapes a bou t . Som e s tu-

dents

found that they could also

obtain

matching images

by flipping

over

the shapes vert ical ly or ho rizontal ly ( i .e . , by r ef lec t ion; see Fig . 3.10) . The

students suggested altogether 1 8 rotations and seven reflections.

Let us exam ine w hat happ ened in th is excerpt . The f i rs t student (SI 1)

suggested that the eight different shapes could be put in to four

categories

according

to the

direct ion

in

w h i c h

the

"miss ing

part" w as fac ing,

t ha t

is ,

whether it faced

left

or right , up or down. This s tudent w as looking at the

shapes as static

f igures.

Af ter th is , ano ther s tudent ( S I2 ) sugges ted tha t

moving

the

second

on e on the

second

row

(i .e. ,

6 in

F ig. 3.8) wo uld resul t

in

the third one in the second row (i .e. , 7). This app roach sug ges ted seeing the

shapes as dynam ic by m oving them and looking for a m atch ing image by ro-

tat ion.

In

other words ,

in

th is exam ple ,

the

seve nth shape could

be

seen

as an

image of the sixth shape af ter a c lockwise ro ta t ion . In a s im i lar way , ano ther

FI G.

3 .1 1 .

T he

t e ache r ' s symbo l ic

r epresen ta tions .



3. D I S C E R N M E N T AND " W H A T CAN BE L E A R N E D ? " 83

student (S14)

saw the

eighth

and

seventh shapes (i.e.,

8 and 7) as

images

of

the sixth shape after consecutive rotat ions. By doing this , the shapes were

no

longer

different,

they were s imply

different

orientat ions

of the

same

shape resul t ing f rom rotations and ref lect ions . In other words , the shapes

con sti tuted a dim ension of variat ion in the orientat ion of an invariant shap e.

The discernm ent of the equivalence between the shape an d i ts m atching im -

age was m ade poss ib le w hen the teacher rotated and f l ipped over the shapes

on

the

board fol low ing

the

students ' suggestion (see Fig. 3.9).

It

is clear that th e students' focus , in this p art of the lesson, was on the

t ransformation

( rotat ion and ref lect ion) of the shapes . They im agined the

shape turning in thei r mind s and m ade suggest ions to the teacher . W ith trial

and error, it was no t

difficult

for some students to see that there were two

possible m eans of t ransform at ion, that i s , ro tat ion and ref lect ion , and that

the rotat ional im ages could

be

categorized into

tw o

types . This categoriza-

tion

becam e ex pl icit w hen the teacher asked a new quest ion, near the end of

the

lesson, tha t requ ired the s tuden ts to think abou t their obse rvations at a

higher level o f ab straction. The fol low ing is an excerpt from th e discussion:

3.5

[Math lesson/Primary Grade 4]

T :

Let's

first

look at 1 ,2 ,3 ,4 , these

four

shapes . W hat do w e not ice?

[Referring to Fig. 3.8.]

S33: [If we] keep rotating [the shape], eventually it wi l l becom e the

first again .

T:

How abou t 5, 6, 7, 8? Does the sam e ru le app ly?

Ss:

[ inaudible]

T : Now , can we tel l how m any categories there are al l together?

S33:

E igh t .

S34: Infinitely many .

T: "Infinitely

many"

refers to the designs. Bu t we said at the begin-

ning there are eight best des igns . I f w e go back to the problem of

the postma n del ivering let ters , how m any categories of bes t de-

signs are there?

S35:

Infinitely

many .

S36: Two.

S37: Eigh t .

S38: 16.

T: W h y ?

S36: B ecau se there

are

eight shapes.

Af ter

changing

the

directions

(of

the routes), there wil l be 16.

T: Good. Then, how did S36's suggestion of " two" come up?



84

R U N E S S O N

AND MOK

S38: Because all these shapes can be obtained by rotating tw o

differ-

ent

shapes.

T : Good.

These

are the different w a y s o f categor izat ion. Here , w e

conclude

f rom the

simple problem

of the

postman.

There

were

1 6 best routes. In the earlier part of the lesson, S5 suggested th e

problem of an urgen t letter . Teacher gave yo u this to think about

as a postlesson problem. If we

need

to

send

an

urgent

letter to the

third

poin t , how m any types o f best design are there? Don't for-

get to

tell

the

teacher you r

findings.

This

is the end of the

lesson.

Bye, c lass [Class dismissed] .

In the above excerpt, the teache r requested the studen ts to

ref lect

o n the

rela t ionship between shapes,

and

asked

for the

n u m b e r

o f

categor ies

o f the

shapes. When the s tudents were u nable to come up wi th the correct answ er,

the

teacher brought

the

c lass back

to the

everyday context

of the

pos tman .

A s we can see, this con textual

shif t

enabled som e s tuden ts to come up w ith

the correct an sw er. It is hig hly likely that as soon as these sh apes w ere seen

as

the postman's routes , the cr i t ica l features of possible routes and best

routes th at were discussed ear l ier in the lesson, that is, the

indica t ion

o f di-

rect ion and shortest distance respectively, came to the

fore

of the s tudents '

awareness. The fact that there were eight shortest routes and tha t the post-

m an cou ld e i ther go c lockw ise or cou nterc lock w ise , as po inted out by S38,

led to the answ er of 16 routes . Here w e see tha t the s tude nts ' answ ers w ere

once again focused on the

postman's

routes, bu t that this t im e the answers

were enr iched wi th

a n

u nde r s t and ing

of the

m a t h em a t ic a l m e a n i n g s .

Contextual

Variation. When w e look back at the lesson as a w h o l e , it is

no t di ff icul t to see tha t th e problem w ent through a shi f t o f context from real

life

to ma the m atica l , and vice versa (see Fig. 3 .12) . Th e problem w as f i rs t

introduced in a real-l i fe context tha t w as eas i ly access ib le to the s tudents .

T he

different solut ion s were exam ined

in

te rm s

of

fea s ibi l i ty ( w h e t h e r

the

routes were correct

o r

not )

and the

o p t im u m r e q u ir e m e n t ( w h i c h

one was

the best) . In both cases, the use of the postman's route as a con text for under-

standing

possible rou tes a nd best rou tes was a

power fu l

one . I t was easy f o r

students

to

re la te

to the

possible routes

and the

best routes

from the

post-

m an's perspect ive: that is , he m us t be ab le to re turn to the s tar t ing po int , the

post

office,

and he

should

be

able

to finish his

m ail delivery

a s

eff iciently

as

F I G . 3 .1 2 . C o n t e x t u a l

va r i a t ion .



3 . D I S C E R N M E N T A N D

" W H A T

C A N B E L E A R N E D ? " 8 )

possible, that

is, no

part

of the

rou te should

be

repeated unne cessari ly.

T he

teacher shifted into

a

mathem at ica l con tex t

b y

invit ing

th e

students

to

cate-

gorize the routes . The s tudents then examined the

different

solutions and

thei r

relat ion s, using rotation and reflect ion. W hat is interest ing is the way

in w h i c h

the

teacher exploited

the

contextual shift back

to the

pos tman ' s

rou te when

the

students

h ad diff icult ies

coming

up

w i th

the

correct answ ers

fo r

c atego rizing the routes. Even m ore im portant , the teach er referred to the

postm an's problem again at the end of the lesson, and co ncluded the discus-

sion by

aff i rming that there were

1 6

best ro utes.

This

conc lusion

w as

buil t

on the comparison between the m any po ss ibil it ies , different rotat ions and

ref lect ions , an d the

directions

of the

routes .

A t the end o f the

lesson,

after the

various stages of explorat ion, the way in which the students discerned the

postman's problem

w as

u ndoubtedly different from thei r unders tanding

o f

this

problem at the outse t of the lesson. T he lesson provided a rich ex peri-

ence o f problem solving reinforced by the teacher wi th

careful

p l ann ing .

However ,

the

s tudents also played

a

cru cial role

in the

con st rual

o f the

ob jec t

of

learning. For exam ple, when the class wa s discuss ing the best route, one

s tudent

imagined the si tuation of an urgent letter. This show ed tha t the stu-

den t 's reflec t ions on the solution

were

very m uch in areal- l i fe context a t th is

stage.

T he

teacher skillfully kept

the

s tudents ' focus according

to her

or igi-

nal

p lan ,

and put

this nove l idea aside

fo r

that par t icular m om ent . However ,

after

examining

t he

solutions

of the

problem

f rom a

m athem at ica l perspec-

t ive, the idea of "an urgent letter" became a m ean in g fu l al ternat ive problem .

T he

problem

was the

same type

of

problem

as the

original one,

bu t

w i th

a

var iat ion,

and as such, it w as an opp ortunity for the students to put w h a t they

h ad

ju s t experienced into pract ice.

This example provides

a wonderfu l

illustration

of the way in

w h i ch

a

t eacher

can

provide studen ts w ith

a

rich un ders tanding

of the

ma n y

facets o f

problem solving even with the use of one single problem. The lesson also

suppor ted th e teacher 's lesson objective "to enhance s tudents ' p rob-

lem-solving abil i ty

and

strategies"

in an efficient and

s t im ulat ing wa y.

WHAT

C O UL D BE L EARNE D?

W e

s tar ted this chapter by saying that unders tanding something as some-

th ing

im pl ies discerning features ,

o r

aspects,

o f

that which

is

experienced.

Certain learning takes the s im ul taneous di scernm ent o f certain c ri t ical a s-

pec ts of the o bjec t of learning . That is , the cri t ical asp ects are held in the fo-

cal aw areness a t the sam e t im e. How ever, an aspect can on ly be discern ed if

it

is expe rienced as a dime nsion of variation. From this assum ption, we ar-

gue that those dim ensions of variat ion that are presen t in the learning en vi-

ronm ent are cri tical for learning w ha t is possible to learn . In other words, i f

an

aspect is presented as a dim ension of variat ion to the learners, i t m ake s i t

poss ib le

fo r the

learners

to

discern tha t pa rt icular aspe ct .

And i f

several

di-



86

R U N E S S O N

A N D M O K

mens ions

o f

variat ion

are

open s imul taneous ly ,

it

ma k e s

it

poss ib le

for the

learners to discern al l of these aspects s im ul tan eo usly . So, wh at i s varying,

w h a t

is

invariant,

and

w h a t

is

varying

at the

same t ime

are

impor tan t

fo r

w h a t

is

po ssible

to le a m .

W e

have an alyzed three m athem at ics lessons f rom the point of view of

the pattern of variat ion that was consti tuted during the lesson, and have

identif ied the pattern of variant and invariant aspec ts in the three lessons re-

spectively.

From this w e can draw

some

co nclusio ns about the poss ib i l i t ies

to leam that were provided for the learners.

In the f irst tw o

exam ple lessons ,

in

w h i c h

th e

object

o f

learning

w as f rac-

t ional

n u m b e rs

as

operator,

w e can see

tha t there

was a dif ference in

w h a t

it

w as possible to learn . Teacher A provided the learners w ith the possibili ty to

leam

to

solve

different

p rob lem s w i th

the

sam e strategy, w hereas T eacher

B

provided the learners w ith the possibil i ty to leam to solve the same p roblem

wi th different strategies. In Teacher A 's lesson the chang ing of the parame-

ters

in the

operat ion opened

a

variat ion

of different

examples , whereas

in

Teacher B 's lesson, the param eters were invarian t and the s t rategy varied

(F ig . 3 .1 ) . In addi t ion , in Teacher B 's lesson, the learners had the po ss ib i l i ty

to

discern

a

semant ic aspect

of fractional

numbers ; th i s

did not

occur

in

Teacher

A 's

lesson.

On the

o ther hand,

the

s tudents

in

Teacher

A 's

lesson

were presented w i th

a

variat ion

of how a f ract ional

num ber cou ld

be

repre-

sented,

and

thus

the

possibil i ty

to

discern this pa r t icula r aspect .

It

is

obvious that these

tw o

lessons were very s im i lar

on one

level ,

for in-

stance in the t each ing me thods and the a r r angem en t of the l earn ing s i tua-

t ion.

How ever,

o n

an other rather m ore su bt le level (but

one

t ha t

is

im por tan t

from

the

po in t

of

view

of the

s t uden t s ' po t en t i a l

fo r

l earn ing) , they were very

different. W hen com par ing tw o lessons as we ha ve done here, i t seems na tu-

ra l

to ask, "W hich one is the best?" However, there can be no gen eral answ er

to

tha t ques t ion .

T he

answer

to any

assessm ent

o f

th i s k ind

wi l l

a lw ays need

to take into con siderat ion th e ca pab i l i t ies the t eache r wan ted th e s tudents to

develop,

and

t hus

the

in ten ded object

o f

learning .

The lesson on the postman's routes showed how the teacher very

though t fu l ly , and j o in t l y w i th her s tuden ts , con st i tu ted a pa t tern of variation

that w as

very

rich in

several aspects.

T he

learners ,

in the

s ame

way a s

those

in Teacher B 's lesson, were

afforded

the opportunity to discern that there

can

be

many poss ible solut ions ( routes)

to the

s ame p rob lem .

A s

we l l

as

this ,

they were provided

the

opportunity

to

evalua te ( scru t in ize)

th e

so lu-

t ions

in different

w a y s ,

in an

everyday contex t

and a

m a them at i ca l con t ex t ,

and

in

term s

of

w he ther

the

solut ion s were feas ib le (poss ib le

o r

impo ss ib le)

and

optimal (best) . They were also required to discern the character of a

shape

by the

variat ion

in the

o r ientation

of the

sam e shape

af ter

rotat ion

and

ref lect ion. Tha t is ,

w i thin

th e

m athem at ica l con tex t ,

th e

same shape

c an

pro-

duce many different possible routes by rotat ion o r ref lec t ion. Rotat ion and

reflection were tw o

w a y s

b y

w h i c h

the

s tudents cou ld

see

os tens ib ly differ-



3.


A N D

" W H A T

C A N B E

L E A R N E D ? "

87

ent shapes

a s the

same. Fu rther,

th e

students w ere able

to see the

sam e prob-

lem a nd its solutions differently, before and af ter scrutinizing the solut ions

in

a m athem at ical context.

A l though our

focus

has been o n the impo rtance of the ob ject of learning,

w e do not wish to imply that c lassroom arrangemen ts are unim portant . A s

w e have seen in two o f the examples (Teacher B 's lesson and the Chinese

demonstrat ion lesson)

the

students contributed very much

to the

co nst i tu-

t ion and the widenin g of the space of variat ion. It is reasonable to assum e

that

this variation

w as a

resul t

of the

group discussions that took place

b e-

fore the w hole-class sessions. In both of these lessons, the studen ts w ere al-

lowed, and even enc oura ged, to discuss the problem w ith their peers. Th us a

certain

arrangement (group work)

facilitated

th e

opening

of

variation. How -

ever, w ha t w e w ant to stress is that i t is not a certain arrangem ent in i tself that

m ake s a certain learning possible, but rather that the possibil i ty to learn is

provided

by

w h a t

it is

possible

to

discern.

In th is chapter w e have fo cu sed on the poss ib i l i t ies to learn, rather than

w hat the s tudents actua l ly learned. W e have also descr ibed the en acted ob-

j e c t

o f

learning

as a

po ten t ia l

fo r

s tudent learning seen

from the

po in t

o f

view

o f the researcher. How ever, we w ould no t a rgue tha t what w as poss i -

ble

to

experience

w as

indeed wh at

th e

s tudents actual ly experienced.

It is

l ikely tha t

th e

s tuden ts learned d i f ferent t h ings . W ha t

w e do

argue

is

tha t

is

l ikely that the s tudents learned cer tain th ings in one lesson, and other

th ings in another .



4

Simultaneity and the Enacted

Object of Learning

P a k e y

P . M . C h i k

M u n L i n g L o

In the

three previous chapters,

the

im portant role

of

variation

in

opening

up

possibil i t ies for a

particular learn ing

(or the

deve lopmen t

o f

certain cap abil-

i t ies) to

take place

w as

described

and

exem pl i f ied .

W e

also i l lustrated tha t

the way in

which

w e

experience

or

understand som ething depends

on

which fea tures of it we are aware of and can discern s im ultaneously. Thu s,

w h e n different

aspects

of the

same th ing

are

discerned

and

focused

on ,

d i f -

ferent

ways of understanding wil l resul t . More powerful ways of under-

standing a m o u n t

to a

s imul taneous awareness

of

those fea tures tha t

are

crit ical to

ac hieving certa in a ims.

In

this chapter ,

we

pr im ar ily focu s

on

describing

one of the two

fo rm s

of s im ul t ane i ty d i scussed

in

chapte r

1 :

synchron ic s imul tane i t y , w h i c h

r e fe r s

to

expe r i enc ing d i sce rned fea tu re s

at the

sam e time , w he re

th e

dis-

cerned features

may be

he ld

in two

differe nt types

of

re la tionship. W hen

th e

d isce rned fea tu re s a re seen a s aspec ts o f s o m e t h in g , w e r e f e r to re l a -

t i onsh ips

o f

th i s k ind

a s aspect-aspect re lat ionships. F o r

e x a m p l e , w h e n

we see a person

w ri ting

an

essay

on a

com pute r,

we may

exp erience

it as

som eone eng aged in an ac t of essay w ri t ing as we l l a s an ac t of word pro-

ces s ing .

T h e other re la t ionsh ip invo lves see ing t h e discerne d parts of the

wh o l e ,

and the

whole tha t

is

del imited from

a

context ,

at the

same t ime .

For exam ple , one may d isce rn the eyes , m uzz le , and l im bs a s d i f fe ren t

p a r t s

of the

body

o f a

deer , which

is in

turn de l imi ted f rom

th e

w o o d s

(Mar ton & B ooth, 1997). The kind of l inkag es

established

between an

ob jec t or a phen om enon and it s pa r t s be ing d iscerned a re re fe r red to as

part-whole re lat ionships.

89



90 C H I K A N D L O

Things m ight or migh t not be experienced s im ul tane ou sly , and in teach -

ing, various things

m ay o r m ay not

come

to the

fore s imu l taneo usly .

In

this

chapter,

w e

compare lessons that

differ in

this respect; th at

is, the

in tended

object

o f

learning

is the

same,

but the

enacted object

differs,

as

does

w h a t

the students leam (i.e., the

l ived object o f learning) .

Let us, however, start with a study in which th e learners were facing the

sam e situation, but the w ay they discerned and experienced the relation s be-

tween

parts, an d

wholes

differe d. Saljo

(1982)

carried out a study to investi-

g a t e t h e d i f f e r e n t w a y s i n w h i c h u n i v e r s i t y s t u d e n t s i n S w e d e n

comprehended the same text . He

found

tha t a l though these s tudents were

reading

the

same text (w hich was,

by the

w ay, about

different

perspectives

of

learning),

the

students

saw

different

meanings

in it. Tw o

dis t inct w ays

of un-

derstanding

the

text were identif ied.

In the first

way ,

th e

students

saw the

text

as

having

a

sequential s tructure, with

different

perspectives

o f

learning being

described,

but

bearing

no

relationship

to

each other.

In the

second way,

the

students discerned

a mam

t hem e

(the

f o r m s of learning) i l lustrated

b y a

n u m -

ber of

subthemes ( d i f f e r e n t

perspect ives o f learning) .

They

saw the

text

as

having a

hierarchical structure w ith clear

part-part

relat ionships (between

the

subthemes) and part-whole relationships (between th e subthemes and the

m ain theme).

In

both w ays

o f

com prehending

the

text ,

all the

parts contained

in the text were distinguished, but these

parts

w ere seen as occupying differ-

ent structural positions. S aljo (1982) also found that th e students w ho under-

stood

th e text in the hierarchical way had a

more

organized and m ean ing fu l

understanding, and were better able to grasp the mam idea of the text than the

students

w ho

understood

the

text

in the

sequent ial way.

It is not

diff icul t , therefore,

to

i ma g i n e

w hy i t is

tha t

in any one

par t i cu lar

classroom si tuat ion, d i f ferent s tudents w i l l have

d i f ferent

levels o f under-

s tanding even thou gh they all are given the sam e presen ta t ion by the teacher .

W hat s tudents

gam

from

a

lesson,

and how

w el l they unders tand tha t l esson ,

depends

on the w ay

they com prehend

the

s t ructure

of the

presen ta t ion ; th i s

in turn dep ends on w ha t t hey focus on and w hat recedes to the background

(or is

taken

fo r

granted) w hen they

try to

unders tand

the

lesson. Some s tu-

dents w i l l

see no

relat ionsh ip between

the

different par ts

of the

p resen ta tion ,

whereas others w i ll be able to comprehend the presentation in m ore power-

fu l

ways (especial ly

if

they

can

s im u l taneous ly

see

c lear re la tionsh ips

be -

tween the parts and the way in which these parts are related to the

presentat ion

as a

w h o l e ).

It

then fo l low s tha t s tudents wi l l leam m ore

effec-

tively if the teacher is able to consciously structure the presen tat ion in such a

w ay as to

bring

out

clear ly

the


of the

ob jec t

o f

learn ing ,

as

w ell as

thei r relationships

to the

object

o f

learning

and to

each o ther.

In

other

words , the way the lesson is structured w il l have a n impor tan t inf luence on

s tudent learning .

W e

now

provide three sets

o f

c lass room data—compri s ing

six

pa i rs

of

lessons—to i l lus t rate th e w a y s in w hich teachers can s t ructure the i r lessons



4.

S I M U L T A N E I T Y

A N D T H E

E N A C T E D O B J E C T

O F L E A R N I N G 9 ±

to

enable their students

to

discern

the

aspect-aspect

( or part-part) and part-

w hole relat ionships of various fe atures o f the object o f learning. I n par t icu-

lar,

we look at w hat i t is possible to learn regarding

specific

obje cts of learn-

ing

(i.e.,

enacted objects of learning) and w h a t is actual ly learned by

studen ts ( i .e. , l ived objects o f learning ).

The

first pair

of

mathemat ics lessons

is

drawn

from

Runesson 's (1999)

study

and is

used

to

i l lustrate

the

aspect-aspect relat ionship.

The

second

and the

third pairs

o f

lessons

are

taken from

a

2-year research p roject un der-

taken

by a research team in Hong Kong,

1

and involve a pair of primary

Grade

2

Chinese language lessons

and a

pai r

of

pr imary Grade

1

E ngl i sh

l anguage lessons , respect ively ( for detai led informat ion and discuss ions

abo ut other aspects

o f

these

tw o

pairs

o f

lessons,

see

C hik, 2002;

L o &

Ch ik ,

2000, and M ok et al ., 1 999). These three p airs of lessons wil l be m ain ly used

to

i l lus t rate part-whole and

aspect-aspect

relat ionships . Each pai r o f les-

sons was o n the same topic, but taug ht by two different t eachers .

The

analysis

is

based

on the

audio

o r

video recordings

of the

lessons

and

the subsequent transcript ions. In order to explore the impact of the struc-

tural

difference s

between the lessons on s tudent learning outcom es, the les-

son

analyses

of the

second

and

thi rd pai rs were also com pared against

the

student data , w hich include the w orksheets c om pleted by the s tudents im -

media te ly

after

each lesson.

A P A I R O F

MATHEMATICS LESSONS

The two m athem at ics l essons focused on teach ing two

different

aspects of

fractional numbers : the part-whole aspect and the division-quotient as-

pec t , where

the

former aspect involves adding

up

parts

to a

w hole (e .g . ,

1 2

qua rters add up to 3) and the lat ter involves dividin g up a who le in to par ts

(e.g. , 1 2 divided by 4 is equal to 3). The different w ays in w hich these two

aspects and thei r relat ionsh ip are s im ul taneo usly brough t to the s tuden ts

1

focal

awareness

are

com pared .

Des cr i p t i o n

of L e s s o n A

This lesson con sists of three main e pisodes. In Episode 1, the teacher drew

the

students ' at tention

to the

part-whole

aspect

of

fractional

numbers .

S he

used an ico nic represe ntat ion to show six pieces of 1 /3 of a pizza and invited

the s tudents to represent th is wi th mathemat ical symbols

2

( i .e. , symbolic

represen tat ion) . The fol low ing suggest ion was arr ived at by the s tudents :

— or 2

3

(6 pieces

of

pizza, each

1/3 of a

whole, equal

2

whole p izzas)



92 C H 1 K A N D L O

In Episode

2, the

teacher focused

on the

division-quo tient aspect

of frac-

tional

numbers

(6 divided by 3), and asked the students, "How can this be

represented by (mathem at ica l ) sym bols?" The same represen tat ion w as ar-

rived

a t

again

by the

students:

— = 2 (6

divided

by 3

equa l s

2)

T he teacher further illustrated this with an example of dividing 6 by 3

(e.g., 6 p ieces of pizza are divided am ong 3 persons) :

In

Ep isode 3, the teacher broug ht the two aspects together by ex pla inin g

to the

class:

T: ... the resu l t is the same, but it is said

differently.

Somet imes I

will say. "20 divided by 4" and som etimes I w ill say, "20 quar-

ters"

. . . the resul t i s 5 anyway. But you should know that a l -

thoug h these are actual ly qu i te different [concepts] , the r e su l t is

th e same.

Des cr i p t i o n o f L es s o n B

This

lesson can also be divided into three m ain episodes. In Episod e 1, the

teacher drew a picture of 12 apples on the b lackboard. H e sa id that 3 per-

sons were to share them equ al ly ( the divis ion-quot ient aspect of f ract ional

num bers w as fo cuse d on) , and asked the class to th ink in s i lence how m an y

apples each person would get .

Meanwhile ,

he

drew

a new

picture—a bowl with

a lot of

triangles

in it

(where each triangle was supposed to be 1/3 of an app le)— and asked the class:

...

If you

have

to

pick

up as

man y p ieces

o f

apple

from the

bowl

as you

have there (m eaning the same as the total of the problem ju s t g iven) ,

how

many p ieces

of

apple

do you

have

to

p ick

up?

Again ,

the

students were instructed

to

th ink abo ut

the

answer

in

si lence.

In th is way, the teacher in t roduced both the divis ion-quo t ient aspect and

the

part-whole

aspect

by

usin g icon s ( i.e.,

the

p ic tures

of

apples)

a nd

m a d e

the difference

between

the two aspects visible by asking the students to

m ental ly solve two p roblems that resul ted in the sam e num ber ( i .e . , 4) .

In Episode 2, the teacher referred back to the first example (12 apples

shared

equally

by 3 persons) and

asked

h is

s tudents

to

represent

it

u s ing

mathemat ical symbols . He also asked for the resul t of the operat ion. The

teacher then wrote

the

student 's suggestion

on the

b lackboard:



4.


A N D T H E

E N A C T E D O B J EC T

O F

L E A R N I N G

93

12

— =4 (apples)

N e x t ,

the teacher referred to the second example ( th i rds of apples) and

asked , "How m any thi rds

of an

apple

did w e

need

to

pick

u p, and how

could

that

be wri t ten w i th symbols?" T he teache r wrote dow n wh at the s tudents

sugges ted :

12

— (i.e., 12 x 1/3 apple)

A g a i n , both aspects w ere focu sed on s imu l taneously in th is episode.

In

Ep isode 3, the teach er asked the stu den ts to consider and com pare the

tw o

examples . After

som e

questions

and

comments f rom

the

students,

the

teacher

f inal ly conc luded:

.. .

1 2 divided by 3, and 12 thirds, the resu l t is the same. So w h e th e r

you have 1 2 apples shared by 3 or you have 1 2 thirds, you w i ll get the

same resu l t .

Aga in , the teacher l inked the two aspects of fract ional num bers by con c lud-

ing tha t they corresponded to the same nu m ber (4).

Thus,

thro ugh out this lesson,

the

teacher

ha d

kept

the two

aspects toge ther.

Aspect-Aspect R e l a t i o n s h i p

S h o w n

in D i f f e r e n t L e s s o n

O r g a n i z a t i o n s

A lthough bo th lessons were teaching the same content , the part-whole as-

pect

and the

divis ion-quot ient aspect

of

fract ional

num bers , t hey

differed

signif icantly in term s o f wha t

aspects w ere

kept in focu s, w hat varied, and

whethe r

the aspec ts were varied at the sam e t im e (see Fig . 4 .1) .

In Lesson

A, the tw o

aspects

of fractional

num bers were b rough t

up one

after

the o ther ( i .e. , f i rst, the

part-whole

aspect and then the division-quo -

t ient

aspect ) . I t was only in the last episode that the two aspects were

b r ough t together

as two

aspects

of a fractional

num ber . Thus ,

a

consc ious

effort

to set up the

condi t ion

for the

s tudents

to

discern

th e

a spect-aspect

re-

la t ionship

betw een the two aspects s im ul tane ously was observed in the f inal

F I G .

4 . 1 .

The focused

a spec t ( s )

i n

d i f f e ren t e p i sode s

o f

Lesson

A and

Lesson

B .



94 C H I K AND LO

episode of Lesson A. In comparison, the teacher of Lesson B

focused

on

both aspects in each of the three episodes. He

first

asked the class to men -

tally

work

o ut the

solutions

of tw o

problems, each po int ing

to one of the as-

pects

o f

fractiona l

num bers and resul t ing in the same n um ber (4) . Then, he

asked the students to represent their solutions in term s of m ath em atic al

symbols.

He

concluded tha t

the

same num ber could

be

arrived

at by

m e th -

ods

that reflected

the different

aspects

of

fractional num ber s.

In

th is way .

the

relationship between the two

aspects

perm eated the who le lesson and the

condition for the exp erience of the relations hip w as co nsciou sly created all

through the lesson. This is an exam ple of the pat tern of variation refe rred to

as

us ion

in

chapter

1 : The two

aspects vary together

to

br ing abo ut

a

s imu l -

taneous awareness

of

both

in the

learners.

The two lessons il lustrate how two aspects o f the sam e direct object of

learning

(fractional

num bers )

can be

brou ght in to students '

focal

awareness

simultaneously .

In the

fol lowing sect ions,

we try to

invest igate

how

stu-

dents ' learning outcom es are affected by the w ay in w h i ch a lesson is struc-

tured—from

the point of view of the part-whole relationship s.

A P A I R O F PRIMARY GRADE 2

C H I N E S E L A N G UAG E

L ES S O N S

Tw o pr imary Grade 2 Chinese langu age lessons tau gh t by two different

teachers from

the

same school were selected

for the

study. B oth lessons

were th e first of a senes o f lessons dealing w ith th e teach ing of vocabulary

in a

text. Both classes

(2 A and 2B)

consisted

o f

s tudents

w i th

s imi lar

abili-

ties.

T he

title

of the

text

was "A

polite l i t t le guest."

T he

com ple te tex t

is

translated into E nglish and reproduced in Table 4.1 .

Description of Lesson 2A

The lesson can be roughly divided into

four

episodes. In Episode 1, the

teacher introduced

the

main them e

of the

text

as

"being polite." This

w as

TABLE 4.1

The

Text Used

in

Both

Lesson 2 A a nd Lesson 2 B

Lesson

10: A

Pol i te Li t t le Guest

Father intended

to

visi t

a

fr iend w i t h

us. He

asked , " W h a t m u s t

on e do to be a

pol i te

little guest?"

M y

y o u n g e r sister said, "When

we are

ea t ing,

w e

should

no t

turn food over

again and again to select food in the dish." M y elder sister said, "W e should look at the

person

we are

ta lk ing

to, no t

look from side

to

side.

W h e n

other people

are

t a lk ing ,

w e

should not

interrupt ."

I

said,

"On

leaving,

we must say

goodbye." Father

w as

very

pleased after

hea r ing these , he prom ised to give us the c ha nc e to show ourse lves to be a

pol i te guest .



4 . S I M U L T A N E I T Y

A N D T H E


O F

L E A R N I N G

95

done by asking the students to first nom inate the classmates that they con-

sidered

to be

poli te,

to

give their

reasons, and

then

to

read

the

text

in

si lence

to f ind out w h a t w as mean t by being poli te.

In

Episode 2, the teacher taught the at tributes (e.g. , forms, pronuncia-

t ions,

and me anings) of seven words

3

that had been p re-iden tif ied

from

th e

text. M any teaching aids were used to show the m eaning of each word (e.g. ,

drawings

and

real objects) . References were also made

to

show

how the

mean ings

o f

these wo rds con tributed

to the

t hem e

of the

text— being pol i te .

With each word they studied, the teacher posted up on the b lackboard the

corresponding word card.

In E pisode 3, the teacher asked the students to f ind the sen tence in the text

where

each word that

they

had

studied

w as

used,

and to

read

the

sentence

out loud.

The

sentences were then p osted

up .

W hen

all the

sentences (each

involving on e or tw o of the

w ords) were found,

the

teacher told

the

students

that

if

they

did all of the

th ings that were described

in the

sentences, they

wou ld

be

po l i te chi ldren. The phrase "polite children" [ ^ = f ̂ |^ ^j ̂ -f- ]

w as

a l so pos ted

up . The

s tudents

w ere

then asked

to read the

text together .

In th is way, the teacher focused the s tudents ' a t tent ion on the words as

parts

o f the

sen tences , w hich were

in

turn parts

of the

text

an d i ts

them e

of

"being poli te."

In Episode 4, the teacher taught the students how to write some of the

characters .

4

Des cr i p t i o n

o f L e s s o n 2 B

There are five m ain episodes in the lesson. In Episode 1, the teac her gave

the stud en ts an overall idea of w hat the text w as abou t by asking a few ques-

t ions

to

in t roduce

the

content

of the

text .

In E pisode 2, the teacher foc used on teaching the form s of a num ber of

charac ters that she thoug ht her s tudents migh t f ind

difficult.

Individua l stu-

dents were invited

to

come

o ut and try to

w ri te each character

o n the

b lack-

board.

T he

other students were required

to pay

at tention

and to

j u dg e

whe the r the character was correc tly writ ten or no t . I f not , the teacher w ould

invite othe r studen ts to try unti l the charac ter was co rrectly writ ten. In some

cases, the

teacher also posted

up a

word card highlighting

the

structure

of

the character.

In E pisode 3, the teach er identified a set of w ords

from

the text and taug ht

the m e a n in g

of

each wo rd. From t im e

to

t im e,

the

studen ts w ere invited

to

give a verbal explanation of a certain w ord o r to act out i ts me an ing.

In

Episode 4, the teacher focused on teaching the pronunciat ion of the

words in the text. This w as done b y asking different groups of students to

take

turns reading them. Ins tant feedback

w as

given when

the

students

could not pronounce the w ords correctly.



96

C H I K . A N D L O

In

Ep isode 5, the teacher introduced a m a tch ing game . In th i s gam e, the

teacher showed the students three phrases one by one and asked them, in

grou ps, to m atch the phrases by finding a w ord in the text tha t convey ed the

same meaning.

Part-Whole

R e l a t i o n s h i p i n t h e H i era rch i ca l S tructure

of Lesson

2A

Lesson

2A was

structured

in a

hierarchical

w ay

that showed clear

part-

whole re la t ionships between the word a t t r ibutes (each as an aspect of a

charac ter), the ch aracters (each as part of a wo rd), the w ords (ea ch as part of

a

sentence),

th e

sentences

(each

as

part

of the

text)

and the

text

(a s

con tribut-

ing to the u nderstanding of i ts them e). Figure 4.2 i l lust ra tes the part-who le

re la t ionships in the hierarch ical organ izat ion o f Lesson A .

For

example,

th e

character that

has the

meaning

o f "insert"

[}ff

] w as first

learned on i ts own wi th a part icular form, pronuncia t ion, a nd m e a n i n g . It

w as

then referred

to in the

context

of the

word "interrupt"

[} §

* % ] , which

is

m ade up of two characters ,

"insert"

[}fj] and "m outh" [°%]. The charac te rs

now took on a different m e a n i n g in com bina tion . In th is wa y , their re la t ion

w as

such that they were

no

long er

tw o

separate p arts

pu t

together,

bu t

con-

stituted a

who le,

in

w hich each

was a

part . Hence, w hen

the

wo rd "interrupt"

[ t§ "H ] was focused on, the characters "insert" [ ̂ ] and "mouth" [ °% ], as

w ell as their relatio n to each other , w ere broug ht

s imul taneous ly

to the s tu-

FIG. 4.2.

A n

i l lus t ra t ion

of the

part-whole re la t ionship shown

in the

h ie r a r ch ica l

structure

of Lesson 2A .



H H

den t s ' focal awareness . Nex t , the word was seen again in a sentence, "W hen

others

are

ta lk ing

to

each other,

w e

should

n ot interrupt"

[}fj

*$].

Here

the

word, w hich com pr ises tw o ch aracters , becomes part of a sentence on po-

l i teness

th at contributes

to the

learning

of

poli tene ss. Thus,

the

part-whole

relat ionships between the characters and the word, as w e l l as the word and

the

sen tence, become clear . Fina l ly

the

sentence, which involved

the

word

as a part, wa s seen in the con text of a text . Together w ith al l the other sen-

tences

identified from the text , i t also con tributed to the und erstan ding of the

theme of the text. A gain , w hi le focu sing on the text , the sentence, the w ord,

and the charac ters were s imul taneous ly focused on to

facili tate

the discern-

m e n t of the

par t -w hole

relat ionships as we l l as the relat ionships betw een

each par t .

In this w ay, Lesson 2A dem onstrated h ow the parts (e.g., different attrib-

utes of a charac ter , an d

different

characters that m ake up a word) were em -

bedded in the wholes (e.g. , a character is embedded in a word; a word is

embedded

in a

sentence) . Therefore

it

provided

the

s tudents w i th

a

s imu l ta -

neous

experience (and hence, discernment)

of

these

par t -w hole

relat ion-

ships throu gh ou t the lesson. The s tudents cou ld refer to the word ca rds, the

sentence

stops,

and the text throughou t the lesson, thus making

possible

the

discernment

through synchronic s im ul taneity .

Part -Whole

R e l a t i o n s h i p

i n t h e

Seq uent i a l S truc ture

of L es s o n 2 B

T he teacher of Lesson 2B spent m ost of the

class

t im e o n vocabulary teach -

ing,

w hic h she organized unde r the three at t r ibutes of w ords ( form , pron un -

cia t ion, and m eaning ) and presented in a sequ ent ial m anner (see Fig . 4 .3) .

In this lesson, the

different

attributes of a character were taugh t in differ-

ent episodes, but no at tempt was made to relate the different at tributes of

each character

to one

another ( the aspect-aspect relat ionships) .

A s a

resul t ,

some s tudents m ay have unders tood the characters as to tal ly discrete ent i -

t ies.

Let us take fo r exam ple, the word "interrup t" [$| °^], which consists o f

two cha racters , the first one m eaning "insert" [ j j ] , and the second m eaning

"mouth" [°^]. Instead

o f

teaching

the

form s

of

these

tw o

characters

at the

F IG . 4.3.

T he

se quentia l organizat ion

of

Lesson

2B .



98

C H I K A N D L O

TABLE

4.2

A

Comparison of the Structures of Lessons

2A

a n d 2B

Lesson

2A

Lesson

2B

Word 1 -»

form;

p ro n u n c i a t i o n ;

m e a n i n g

Word 2 -»

fo rm;

p ro n u n c i a t i o n ;

m e a n i n g

Word

3 -» ...

form;

p r onunc i a t i on ;

m e a n i n g

Form •>

w or d 1 ;

word 2;

word 3;

P r o n u n c i a t i o n ->

w or d 1 ;

w o r d 2;

w or d

3;

M e a n i n g

w or d 1 ;

word 2 ;

w o r d

3;

same t im e

as

teaching

the way in

w hich they combine

to

form

the

wo rd ' 'in-

terrupt" (as the teacher in Lesson 2A did) th e teacher of Lesson 2B taught

the

form s

of the first

character

on i ts ow n in

Episode

2, and the

p r o n u n c i a -

tion

of

this character

as part of the

word

"interrupt" in

Episode

4.

F urther-

m ore in Episode 5, the word "interrup t" w as given a

defini t ion

(" joining in

others ' conversation" [fa ̂ #J A ^ |£ f£ ]) tha t was ne i ther s i tuated in

the

con text of being po li te, nor re lated to the text .

Thus,

in

each

of the

three con secutive episodes

of

Les?on

2B, one o f the

word at t r ibutes ( form, pronunciat ion,

or

m e a n i n g )

w as

kept invariant ,

and

thus became superordinate , whi le the characters /words tha t varied were

used to illustrate the attribute. B y con trast, the words were the focus of Les-

son 2A, and each w ord becam e supe rordinate w hi le the three at t r ibutes (or

aspects) varied at the sam e t im e, in order to enhance th e s imul taneou s expe-

rience of the w ord at tributes. This is ano ther exa m ple of the pattern of varia-

t ion called

fusion.

A m a jo r

difference

be tween the two classes is w h e t h e r

at tr ibutes or w ords were supe rordinate , as determ ined by the different w a y s

in

w h ich

th e

lesson

w as

structured (see Table 4.2).

The

quest ion

w e

need

to ask is,

does th is

difference

have

an

i mp a c t

on

students ' learning outcomes?

Des cr i b i ng L ea rn i ng Outcomes

Af te r each lesson,

the

s tudents

in

bo th c lasses w ere reques ted

to

com ple te

a worksheet . Thi r ty worksheet s were co l lec ted from Class 2A. and 31

from

Class

2B. The

workshee t con t a ined

tw o

par t s .

In the first

par t ,

the

s tudents were asked

to put

down w ha t they thoug h t

w as the

mos t impor -

tan t th ing tau gh t and/or l earned in the l esson . The second pa r t requ i red the

students to

com ple te

a text by fil l ing in b lanks wi th ap propriate words tha t

had

been t augh t

in the

lesson (see Table

4.4 for the t ex t ) .



4. S I M U L T A N E I T Y

AND THE


OF L E A R N I N G 99

What W as

Taught

and Learned From the S tuden t s '

Perspective?

In an-

sw er ing the first par t of the quest ion, some s tudents put down m ore tha n one

response . A s shown in Table 4 .3 , the responses of both c lasses fel l in to two

m ain ca tegor ies . Som e s tudents r eported tha t they w ere taug ht the them e

(e .g . , "how to be poli te," "being a pol i te guest") and sub them es o f the tex t

(e.g.,

"When others are

talking

to

each other,

we

should

not

interrupt."),

and

som e repor ted that they were tau gh t vocabulary. How ever,

dif ference s

wer e

observed in their pat tern of responses .

More students from Class 2A reported the main theme of the text or the

subthem es as the

mo st important thing taught.

In

co ntrast,

a

higher prop ortion

o f

Class 2B considered vocabulary th e m ost important thing taugh t in the lesson.

W hen w e look a t the b reakdown of the s tuden ts ' r esponses , we can see

tha t

the answers of the students in

Class

2A covered all subthemes of the

text , w hereas the answ ers o f the s tudents in Class 2B o nly covered two of the

sub themes .

With

regard

to the

learning

o f

vocabulary,

th e

students

of

C lass

2B

m os tly

descr ibed w ha t they had learned in m ore general terms (e .g ., "using w ords to

m a k e

sentence s," "reading w ords," etc.) . B y co ntrast , a high er proportion of

the

s tudents

in

Class

2A

wrote down specific wo rds tha t they

h ad

learned .

What

Were

the

L ea r n i n g O u t c o mes ?

T he

r esu l t

of the

secon d par t

of the

w orksh eet is shown in Table 4 .4 . To assess the ap propr iate use of wo rds, the

s tudents ' answe rs w ere m arked cor rec t even i f they had ma de m inor mis-

takes in the w r i tten form of the words. W ith respe ct to the w ords " inter rupt"

and

"pol i te ," wh ich

had

been g iven specia l emp has is dur ing teac h ing

in

bo th

c lasses , we can see tha t Class 2A per formed much bet te r in us ing these

words

to

com ple te

the

given text

(30 out of 30

correct

for

C lass

2 A, and

only

9

out of 31 for C las s 2B ) . Rega r d ing the ch arac ters

("insert"

[^|] and "ap-

p e a r a n c e "

[ f f e ] )

w hose form s bo th teachers h ad spen t time teach ing , again

th e

s tuden ts o f C lass 2 A were be t te r ab le to w r i te these charac ter s than the

s tudent s

f rom C lass 2B . Only one m is take (on "insert") was m ad e in C las s

T A B L E 4.3

The

S t u d e n t s '

Responses

S h o w n

in the

First Part

of the

Workshee t*

What is the

mos t impor tan t th ing

Genera l Ques t ion:

Class

(N - t o t a l n u mber of r e sponse s )

1

. The m a i n t h em e a nd s u b t h e m e s of the text

2. V o c a b u la r y

3.

I r re l evan t

r e sponses

taught/ learned

in the

le s son?

2 A ( W = 3 5 ) 2 E ( W = 3 9 )

18 10

5 22

12 7

*Some students

put down

more than

one response.



TABLE 4.4

Th e Students Performances as S h o w n in the Second Part of the W orksheet

Second Par t : Complete

th e

fo l low ing tex t wi th appropr ia te words /phrases

y ou

ha ve

learned in the lesson.

O u r teacher often te l ls u s t ha t w he n w e mee t teache rs an d c la ssmates in school , w e have

to greet

3

t h e m . In the c la ss room, when th e teache r is t a l k i ng w i t h other c lassmates , do

not in te r rup t a s one l ikes ; w hen the teac he r ta lks to you , do no t look from s ide to s ide .

c

Afte r

school , we have to say goodbye to our teachers and c lassm ates . Then we can be

counted

as

good students

who a re

po l i t e .

d

[English translation]

2A 2E

1 . Use of words

1

. 1

A ppropr ia te

for all

b lanks

30 9

1 .2 One to t h r e e b l a nks m i s s ing / ina pp r op r i a t e — 22

2. Form

of

cha rac te r s

W r o n g l y w r i t t e n

N ot t a ugh t in the le sson :

T a ugh t in the lesson:

" M o u t h "

"Wave"

"Watch"

"West"

"Insert"

"Appearance"

8 4

1

1 —

— 1

1 7

—

4

Note .

a

T he

word

"greet" [^J

% Q °^-]

i s m ade up of

three Chinese characters , "beat"

T ], "wave" [ j£ ], and "ca l l" [ *f-].

word " in te r rup t" [ | j |

° ^]

is ma de up o f two C hin ese cha rac te r s , " inse r t" \ f f i j

]

and

" mou th"

°The word

" look

f rom s ide to s ide" [ Jt ^ \3j St ] '

s

rnade up of four Ch ine se c ha r a c t e r s ,

"east" [ Jt ],

"open"

[ ̂ ],

"west"

[ gj ], and "watch" [ 5t ]•

d

The word

"pol i te" [^ffe]

is

ma de

up of two

Ch ines e cha rac te r s , "po l ite"

[^] and

"appearance

100



4.


A N D T H E E N A C T E D O B J E C T O F L E A R N I N G 1 01

2A ,

w hereas

1 1

m istakes w ere noted

in

Class

2B (7 on

"insert";

4 on

"ap-

pearance") .

Simultaneity

and the

Possibility

fo r

Learning.

In

order

for the

s tudents

to

be ab le to use the w ords learned in the lesson to f i l l in the blank s o f a given

text,

i t w as not enough for them simply to know how to w ri te the form of the

characters that made up that wo rd. T he students also had to understand the

meaning of the words, and be able to use them in an appropr ia te context .

That

is,

they

had to be

able

to

discern simu ltaneously

the

form ,

th e

meaning,

and the usage of the w ord. Lesson 2 A w as s tructured in such a w ay as to a l-

lo w

the

students

to be

simultaneously aware

of the

w ord attributes (form

and

m e a n i n g )

that are cr i t ica l to the words being used appropr ia te ly. Corre-

spondingly,

w e

fo und that

the

students

in Class 2A

were better able

to

dis-

cern these a t t ributes s im ultan eou sly than the s tude nts of Class 2B.

In Lesson

2B ,

a l thoug h

the

s tudents were a lso taugh t

the

same w ords ,

the

cr i t ical a t t r ibutes o f each word were taug ht in different episodes, and there

w as no a t tem pt to he lp the s tudents link these aspects together . A lthou gh the

form of the charac te r meaning "insert" was taught in Episode 2, and the

m ean ing of the word " interrupt" (w hich consists of the two ch aracters " in-

sert"

and

"mouth")

w as

t a u g h t

in

Episode

3, the

s tudents were

no t

m a d e

aware s imul taneous ly

of

these

tw o

attr ibutes (form

and

m e a n i n g )

of the

character "insert,"

and may

have considered them

as two

different, unre-

la ted ent i t ies . In oth er wo rds, even if only three words were taug ht in the les-

son, if the three different attr ibutes of each word were taught as unrelated

en t i t i es—ins tead

of

present ing them

as

three attr ibutes

o f

three words—

some students m ay perceive these attributes as nine unrelated e ntit ies to be

learned. The l a rge numb er o f un re la ted ent i t ies m ight cause some s tudents

to be

confused, whereas others m ight

not be

able

to

cope w ith

so

m a n y

n ew

th ings in a

shor t t ime . This

m ay

accoun t

for the

fact

th a t a l thoug h

the

teacher

of Lesson 2B spent mu ch t ime teaching the s tudents how to cor rec t ly w r ite

the forms of the words "insert" and "appearance," many students still got

them w rong. Of course , some s tudents m ight still be able to exper ience the

at t r ibutes s imul taneously

because o f p rev ious exper iences . How ever, the si-

m u l t a n e o u s exper ience

o f different

a t t r ibutes

was no t

b rough t abou t

by the

co n sc io u s effort of the teacher , un l ike in Lesson 2A , whe re the teacher con-

sc ious ly s t ruc tured the learning exper ience s to facil i tate such an exp er ience .

A P A I R O F P R I M A R Y G R A D E 1

E N G L I S H

L A N G U A G E

L E S S O N S

In this section, w e further i l lustrate o u r point by looking at two double peri-

ods of E ng l ish languag e lessons taken from tw o pr im ary G rade 1 c lasses

(Class IB and Class IE ) that were taught by two dif ferent teachers in the

same schoo l . B oth lessons w ere

on e of a

series

of

lessons

on

"Food

in the



1 02 CHIK A N D L O

superm arket ." B efore this lesson, both c lasses of s tud en ts had a lready

learned the n a m e s o f several i tem s o f food a nd d r ink . Bu i ld in g o n th i s

pnor

knowledge , the teachers a im ed to develop the s tu dents ' abi l i ty to use differ-

ent langu age i tems to describe food and drink (n oun s: e .g., c r isps , m ilk;

partitives: e.g., a bottle of, a pa cke t of; and adjectives describin g size: e .g. ,

large, small), as wel l as their ability to extract spec if ic inform ation (prices

of food and drink) through the use of d ia logue ("How much is it?" "It is

dollars.").

The two

classes

were of similar ability and most of the students were

quite good

at

E ngl ish

as far as

speaking

and

listening were concerned.

Des cr i p t i o n

o f

Lesson

1 B

This lesson consisted

of four

m ain episodes, each

focus ing on an

objec t

of

learning.

In

Ep isode

1, the

teache r revised

th e

names

of

e igh t kinds

o f

food

and

drink that

the

students

had

learned

in

previous lessons. Pictures

and

word cards were shown.

In Episode 2, the teacher introduced th e phrases "a bottle of and "a packet

of to describe th e attributes of some of the food and drink item s shown in Ep-

isode

1. She

explained

to the

class that there were some

food

i tems that

needed

a

partitive

and

some that

did

not .

She

represented

th e

phrases

in

pic to-

rial, spoken, a nd written fo rm s. A lso, w hen she exp la ined the wo rd "packet,"

which was new to the students, the teacher made re fe rence to the more

famil-

iar

word "bag" that earned the sam e mea ning as "packet."

In Episode 3, the teacher expla ined the use of the words "large" and

"small" to

describe

different

sizes

of the

sam e kin d

of food/drink for ident i -

f icat ion purposes—in

her

words ,

"so

that peop le know w hich

one yo u are

ta lking about ." A gain, pic tures

and

word cards were used .

The

m e a n in g

of

the word

"large"

was also exp la ined in term s of another word ,

"big,"

w h i ch

w as

more fam iliar

and has a

s imilar mean ing

to "large."

Finally in Episode 4, the teacher used the context of a supermarket to in-

troduce

the

dialogue, "How m uch

is

it?"

" It is

dollars," w hich

w as

then

posted

on the

blackboard.

T he

students practiced

the

dia logu e

in tw o

differ-

ent

tasks:

guessing the prices of different food and drink i tems, and

role-playing the act of buy ing in a superm arke t. In both tasks, the teacher

did the ques t ioning w hi le the s tudents w ere invi ted to respond by g iv ing the

"i t is" s ta tem ent e ither on a w ho le-class or individual bas i s .

Descript ion

o f

Lesson

1 E

This

lesson

comprised

three interrelated

episodes. In

Episode

1, the

teacher

introduced

the

m ain theme

of the

lesson, "Buying food

in a

supermarket."

Specifical ly,

the

teacher focused

on two

ma in aspects , nam ely

the

food

and

drink tha t could be fo un d in the superm arket, and the dialo gu e used to ask

for the prices of food and drink.



4.


A N D T H E


O F L E A R N I N G 1 0 3

In

Ep isode 2, the teach er began by asking , "What kinds of food a nd dr ink

can

we find in a

superm arket?"

Then, the

teacher used pictures

to

in troduce

eight pairs

o f

food

and

drink i tem s

one by

one. Each pair consis ted

o f two

dif ferent-s ized

vers ions of the same kind of food/dr ink (e .g ., one large and

one

sm all bot t le

of

w ater ).

The

teacher required

the

s tudents

to

n a m e e a ch

pai r of i tem s (e .g . , "a large bo ttle of water" and "a sm all bot t le of water"). In

th is way,

the

wo rds describ ing s ize,

the

p arti tives,

a nd the

n a m e s

o f

par t icu-

lar k inds of food and dr ink were presented to the class s imultaneously .

In Episode 3, the teacher to ld the class, "Well , here are some k inds o f

food and dr ink tha t we can f ind in a supermarket . I f we w ant to buy them ,

w h a t

should

we say?"

Then ,

she

pos ted

up the

d ia logue "How m uch

is

it?"

"It is dollars," and in t roduced i t as a way of f inding out the

price

o f

food and dr ink i tem s in a superm arket . T he s tu dents then pract iced the d ia-

l o g u e

by engaging in

different

tasks , such as gue ssing the pr ice of cer tain

i t ems of food and/or drink and pretending to buy thing s in the sup erm arket .

Part-Whole R e l a t io n s h i p s in D i ff e r e n t

Lesson

O r g a n i z a t i o n s

A l t h o u g h

the lessons bo th deal t wi th s imi lar teach ing conten ts , the two

teache rs used

d i f ferent

w ays of s t ruc tur ing the i r l essons , and henc e the re la-

t ionsh ips es tab l i shed s im ul tane ou s ly be tween

the

ob jec ts

o f

learn ing w ere

also d i f ferent . In Lesson IB , the teach er p resen ted the ob jec ts o f learn ing

( n o u n s

fo r

descr ib ing food

and

dr ink; adjec t ives descr ib ing s ize; par t i t ives

used

in con junc t ion w i th uncoun tab le nouns ; and a d i a logue pa t te r n ) in a se-

quent i a l w ay (see F ig . 4 .4) . For ins tan ce, in order to foc us on "small," the

t eacher

showed many exam ples

o f

sm al l i tem s

of food and

dr ink. Then ,

in

order to foc us on "large," she showed m any ex am ples o f la rge item s of food

and

dr ink.

A s a

resu l t , despi te

th e

fact tha t

th e

s ame examples

o f

food

and

dr ink

were used th roughout the lesson , on ly one ob jec t o f learn ing was

b r o u g h t to the fore in each ep isode . This ob jec t o f learn ing w as then left in

the

backg round in the nex t ep isode w hi le som eth ing e lse w as

h i gh l igh t e d .

Episode 1

Introduction

of

the nouns

for different

foods

and

drinks

b,

Episode 2

Introduction

of partitives:

"A

bottle of

and

"A

packet of

^

Episode 3

Introduction

of

adjectives

fo r describing

size:

"Large" an d

"Small"

Episode 4

Introduction

of

a dialogue

used to elicit

prices:

"Dollars"

"How much

is

it?"

FIG. 4.4. T he

sequent ial s t ructure

of Lesson IB .



1 4

C H I K A N D L O

In comparison, the teacher of Lesson IE focused on each kind of

food/drink as an object that had different attributes (nam e, size, packaging,

and price), and set up the l earn ing wi th the them e o f buy ing in a supermar-

ket . For ins tance, the food and drink i tems (which have thei r own name,

size, and packag ing) were presented a s the th ing s tha t can be found in a su-

permarket (whole)

and

also

as the

objects being referred

to in the

b u y i n g

ac-

tivity. In

th i s way ,

th e

same

set of

nouns , adjectives, par t i t ives ,

and

d i a logu e

were organized in a m anner tha t re la ted them to each other as a t tr ibutes of

certain food/drink i tems,

a s

w e ll

as to the

them e

o f

buy ing

in the

superm ar-

ket as a

w hole . Lesson

IE can

t hus

be

described

as

h a v i n g

a

h i e ra rch i ca l

o r-

ganization (see Fig. 4.5) that ma de

it

possible

for the

students

to

experience

both the

part-whole

relat ionsh ips between thin gs and the aspect-aspect re-

lationships betw een at tributes sim ultaneo usly (see also Table 4.5).

E

pisode 1 : Introduction of the theme, "Buying in a supermarket"

Episode 2: Introduction of food an d drink that can be foun d in

su

dr

pennarket [name, size, and packaging of a certain kind of food and/or

ink]

Episode

3 : Introduction of the buying activity in supermarket

["Dollars,"

"How mu ch is it?" " It is dollars."]

FIG.

4.5.

The

hierarchica l s tructure

of

Lesson

1 E .

TABLE

4.5

A C omparison o f the Structures o f Lesson IB and L esson IE

Lesson

IB

Lesson IE

N o u n s

Adject ives

descr ib ing

size •> Partitives

Type

of

food/

Type

of food/

Type

of

food/

dr ink

1 -> d r ink 2 -> dr ink 3 -^ ...

food/drink 1 ;

food/dr ink

2;

food/dr ink 3;

food/drink 1 ;

food/drink 2;

food/dr ink 3;

food/drink 1 ;

food/drink

2;

food/dr ink 3

n o u n ;

adjectives

descr ib ing

size; w i t h

or

w i t hou t

part i t ive

n o u n ;

adject ives

desc r ib ing

size;

wi th

or

w i t h o u t

par t i t ive

n o u n ;

adjectives

descr ib ing

size;

w i t h

or w i t h o u t

parti t ive



4. S I M U L T A N E I T Y A N D T H E


O F L E A R N I N G

105

Because of the

different foci

and organization of the lessons, the two

classes also

differed in

what came

to be

superordinate.

In

Lesson

IB, the

no un s, adjectives, and part i t ives tha t described food and drink i tem s becam e

superordinate,

as

each

w as

focused

on and

i llustrated w ith varied exam ples

of food/drink i tems, whereas

in

Lesson

IE, the

food/drink became super-

ordinate

as the

teacher focused

on each of the

food

a nd

drink

i tem s and

var-

ied the nouns and adjectives used to describe them (see Table 4.5).

In Lesson IE , how ever, w e find another example of "fusion," tha t is, di f -

ferent aspe cts (size, parti t ives) varying together. W hat is the im pac t of th is

structural difference on student learning?

D e s c r i b i n g L e a r n i n g Outcomes

To investigate the impact of structural difference on student learning, 43

students in

C lass

IB an d 45

s tudents

in

Class

IE

w ere invi ted

to

com ple te

a

worksheet immedia te ly after

the

lesson.

T he

worksheet consis ted

of two

questions. T he

first

question required the students to put down what they

perceived

as the

m ost imp ortant th ing taugh t and/or learned

in the

lesson.

The second question required them to fi l l in blanks in a dialogue (see Fig.

4.6

w here

the

expected answers

are

underl ined) .

F I G .

4.6.

T he

second ques t ion

of the

workshee t .



1 06

C H I K A N D L O

T he Students Un ders tanding

of

W h a t

They

Learned

in the

Lesson. A s

shown in Table 4.6, nearly a ll the students in Class 1 B reported that the most

important things taught in the lesson were some language items (e.g.,

names, adjectives describing size, partitives,

and the

dialogue). Only

o ne

student mentioned that they

had

learned how

to find the

prices,"

a

concept

that should have been one of the main foci of the lesson.

T A B L E 4.6

Th e

Students Responses

to the

First General Question

of the

Written Task

1 . 1

1 .2

1 .3

1 .4

1 .5

1 .6

1 .7

1 .8

1 .9

1 . 1 0

2.1

2.2

3.1

3.2

T he

first

que s t i on :

(N =

total number o f

re sponses;

some students

gave more than o n e response)

]

.

Language items

S om e food

and

dr ink i t ems

Good s

o the r than

1 . 1

Size

Part i t ives

Size

and

par t i t ives

Dol l a r

Pr ices

of d i f f e ren t

food

and

dr ink i t ems

Pr ices

o f goods

other than food

and

d r i n k

T h e

How m u c h ?"

d i a l ogue

Learn ing Engl i sh in genera l

terms (e.g.

r e a d i ng ,

w r i t i n g

E n g l i s h ;

some

E ng l i sh w or ds )

2.

Theme

How to find the pr ices

C o n d u c t i n g

th e

d i a l ogue

o r

a sk ing

the how

m u c h ? "

ques t ion or buy ing food and dr in k in the

contex t o f supermarke t o r t e a c h i ng s i tua t i on

3.

Others

I r re levant

M i s s i n g

W h a t

was the

most

important

t h i n g

t aught / l ea rned in the

lesson?

Class

IB Class IE

(N = 50) (N = 48)

48 40

26 —

— 4

4 8

1

—

3 —

10

6

3 —

— 4

1 1 4

— 4

8

1 —

— 8

I Q

1

—

— —



4.

S I M U L T A N E I T Y A N D T HE E N A C T E D O B J E C T O F L E A R N I N G 1 07

There were relatively fewer responses in C lass IE (40 out of 48) indicating

language

i tem s

as the

most imp ortant thing taught.

O ne

sixth

o f the

students

actually

quo ted som e exam ples from their ow n personal experience

of buying

goods

at a

supermarket; these exam ples included i tem s men tioned

in the

les-

son

(e.g.,

food or

drink)

as

w ell

a s

some

not

m ent ioned

in the

lesson (e.g.,

ap-

ples, m elons, a teddy bear). N one of the students from the other class did so.

Also ,

regarding those responses that m ent ioned the them e of buy ing

th ings

in a

superm arket,

the

responses

from

Class

IE

w ere m ost ly related

to

the context of buying in a superm arket, con duct ing the dialogue, and asking

the "How much?" quest ion, whereas , the responses

from

Class IB were

main ly abo ut el ic i t ing prices , an d the context w as seldom ment ioned.

What

Are the

Learning Ou tcomes?

The second quest ion required th e

s tudents

to first fill in appropriate words to indicate the different sizes of two

bags pr inted

on the

worksheet ,

and

then

to fill in the

m iss ing blanks

in a

s im -

u la ted d i a logue

on

buying

and

sel l ing.

In

order

to be

able

to fill in the

appro-

pr iate

w ords in the f irst section, the s tudents had to be able to different iate

large and

sm al l objects

and to use the

correct vocabulary.

In

order

to fill in

the b lanks

of the

dia logue ,

the

students

had to be

able

to

recognize

the

sen-

t ences

as par ts o f a dialogu e carr ied ou t in a buy ing and sel l ing context be-

fore

they cou ld choose

the

most appropriate words

to fill in the

b lanks .

A s

shown

in

T able 4.7, nearly

all of the

s tudents

in

both classes were able

to descr ibe the two bags w i th appropriate w ords that indicated their s ize.

This

show s that both classes

had a

good m astery

of the

words descr ib ing

size

as t a ugh t in the lesson. However, a differenc e w as observed in the two

c la sse s 'pe r fo rma nce in answer ing the second part o f the que s t ion . W hereas

m ost of the

s tudents

in

Class

IE

w ere able

to

un ders tand

the

dia logue

as be-

long ing

to a

buy ing

a nd

sel l ing context ,

a nd

comple ted

it in a

me a n i ng f u l

way,

only

o ne

third

o f

C lass

IB

could

do so.

Many s tudents

in

C lass

IB did

no t

recognize

the two

sentences

a s

cons t i tu t ing

a

dia logue ,

and

took them

as

single sentences unrelated to one another . F or ins tance, some s tudents u n-

derstood

the first

inco m plete sentence, "Good a f te rnoo n .

,

please."

in a

c lass room

context ,

and f il led in the

wo rds "sit dow n," even thou gh they

m ade sense

of the

second sen tenc e," dol lars , p lease."

in the

buying

and

se l l ing contex t ,

and f il led in the

word

"ten."

Simultaneity

and the

Possibility

for

Learning.

One

possible

way to ac-

coun t

fo r

these d i f ferences

in

learning

is the

structural difference observed

in

the tw o

t eachers ' ways

o f

handl ing

the

objects

of

learning.

T he

t eacher

of

Lesson IE

organized

the

direct objects

o f

learning

in a

hierarch ical s truc-

ture,

us ing "buying

in a

supermarket"

as a

theme. Different at tributes

( n a m e ,

s ize, pack aging, and price) o f each food/drink we re focus ed on at the

same t ime, w hich

afforded the

po ssibil i ty

of the

s im ul taneous experience

o f

those

at tributes. A s a resu lt , m ore o f the students in Lesson IE expressed



TABLE

4.7

Th e

S t u d e n t s'

Answers to the

Sp ecif ic Quest ion

of the Worksheet

Second part :

F i l l in the blanks

(A ) A

large/big bag.

A

small bag.

IB

IE

Class

(N = 43) (N = 45)

1 Use of words to indic ate s ize:

1 . 1 Appropr ia te 39 45

1 .2

One to t h ree b l an k s m i s s i n g / inappropr ia te 4 —

(e.g.

"a

large

of

bag,"

"a

smal l

of

bag")

2.

W r o ng

spel l ing

o f

words ( large, smal l , bag)

6 1 1

(B) SI :

Good af ternoon,

a

large/big bag/any

goods.

please.

S 2: Here you are.

S3: How m u c h is it?

S4: Ten dol lars , p lease.

1. Fil l in bo th b lanks appropr ia te ly

( e i t h e r

u s i n g the 15 37

i n format ion

from

the

lesson, i .e.

the

e igh t k inds

o f

food

and

d r ink i t ems ,

o r

that provided

in the

worksheet , i .e . two bags of

different

s izes )

2. Fi l l in one of the blanks appropriately

2.1

,

please.

— 2

2.2

dollar s, please.

1 8

a

4

3. Inappro priate answers to

3.1 both

2.1 and 2.2 2

b

—

3 . 2 2 . 1

a n d

l eav in g

2 .2

b l an k

l

c

—

3.3 2.2 and

l e av in g

2.1

b l an k

2

d

—

4. Did not

respond

5 2

N o t e . I nappropr i a t e answers to 2 .1 , fo r example, "si t down," "Miss W ." " H a v e a b i scu i t . " "many

in," "you are," "teacher and,"

"good

night ," " thank you."

Inappropr iate answers to, for exam pl e , 2.1 "you," "teacher and"; 2.2 "here." "it is"

Inappropr i a t e

answers to, for example, 2.1 and leaving 2.2 blank ("many in") .

Inappropr iate answers to, for example, 2.2 and leaving 2.1 blank ("it," "it is").

1 8



4 . S I M U L T A N E I T Y

A N D T H E


O F

L E A R N I N G

1 09

w hat they h ad learned in a contextual and organized w ay. In this lesson , be-

cause

th e

food

and

drink items were superordinate

to

their attributes,

it

seems that

the

students cou ld relate mo re readily

to the

fact that

the

objects

of learning w ere

the

food

and

drink items that

can be

purchased

in a

super-

market , and that the "How

much? "

dialogue w as used to inquire about price

in a supermarket . The students could hence see the relevance of wh at they

learned, because i t w as fam iliar to their daily experience. In Lesson IB ,

however , because

the

words and/or adjectives describing

the

attributes

of

food and drink were su perordinate to the food and drink i tem s, it seem s that

mos t

of the

students

not

only

had

difficulties relating these attributes (the

languag e i tem s)

and the use o f the

dialogue

to the

t hem e

of

"buying

in a su-

permarket,"

but also in

relating

them to

their

ow n

daily

experiences.

A l-

though some s tudents might have been able

to

recognize

the

relat ionship

betw een the two by draw ing on their ow n past experiences, this had been

left

to c han ce, ins tead

o f

being co nsciou sly structured

by the

teacher.

In

Lesson

1E,

on the o ther hand, the consciou s effort of the teache r to structure the les-

son using the theme of buying in a superm arket

afforded

the stude nts the si-

m ul taneou s experience of context , w hole and parts .

Because l anguage i t ems such

as

part i t ives were highlighted

and

kept

superordinate

in Lesson IB and not in Lesson IE, we w ould expect to see

some difference between Lesson IB and Lesson IE w i th respect to the s tu-

dents ' unders tanding of these langu age i tem s. That i s, we should see that

some studen ts in C lass IB should be able to

identify

these i tems as the mo st

imp ortant th ing taught

in the

lesson. This

w as

indeed borne

out by the

stu-

dent da ta: Four s tudents in Class IB m ent ioned part it ives as being the m ost

impor tan t

thing being taug ht , w hereas none

of the

students

from

Class

1 E

mentioned part i t ives (see Table 4.6).

C O N C L U S I O N S

So far, we have discussed the possible effect of lesson structures on stu-

dents ' learning outcomes. This effect might be unders tood in terms of

whe the r

aspect-aspect

and/or

part-whole

relat ionships could

be

experi-

enced s imul taneous ly

by the

learner. Usin g

th e

example

o f the

pai r

o f

m a th -

emat ics lessons ,

w e

i l lustrated

the

different w a y s

in

wh ich

the

teachers

created the con di t ions for the s im ul taneo us experience o f the two aspec ts of

fract ional

numbers . We then gave examples of two Chinese language les-

sons

and tw o

E ngl ish lang uag e lessons

to

i l lustrate

how the

teachers w ere

able

to structure their lessons to facilitate the s tude nts ' s im ul taneou s experi-

ence o f parts and w holes, and aspects versus aspects.

In the ana lysis of these tw o pairs of langu age lessons, i t w as also shown

that

the

differences

in

students' learning outcomes

are

related

to the

struc-

tural

differences in the way s in w hic h the teachers organized the objects of

learning, tha t is, to the differences in the enacted object o f learning. The in-



1 1 0 CHIK A N D L Q

teresting fact is tha t in the case o f these tw o pairs o f lessons, the two teachers

used the same teaching material, subscribed to the same intended object o f

learning, and almost certainly believed tha t they carried out the sam e lesson

as

w el l.

W e c an

presum e that both teachers w ould have said that

the

enacted

object o f learning was, o f course, the same in both classes.

How ever, this w as not the ca se— as w e have seen. T he enacted o bject o f

lea rn ing differed sub s tant ia l ly in both ins tanc es . This i s because w ha t stu-

dents learn is not a

func t ion

of the in tended ob jec t of lea rn in g , but of the

enacted ob jec t o f l e a rn ing , and w h a t the s tudents in these tw o c lasses

learned c lear ly d i f fered . The teachers were f ound to have directed stu-

dents' a t tent ion to par t icu la r aspec ts o f w h a t w as t o be learned by s tructur-

ing the

lesson

in

such

a way

tha t

th e

chosen aspec ts were kept invar iant

and

superordinate to those aspects that var ied. B u t w h a t w as invar iant an d

superord ina te m ade a d i f fe ren ce to how w el l the s tude nts achieved the ex-

pected l e a rn ing ou tcomes .

This has s igni f icant imp l ica tions for w ays of im proving the qu a l i ty of the

teaching-learning cyc le . It is l ikely that s tuden ts w il l learn bet ter if teachers

can structure their lessons in such a way tha t s tudents are able to discern and

exper ience s im ultan eou sly par ts and w holes, and aspects versus aspects .

E N D N O T E S

'For the backg round o f th is research p roject , see the E p i lo g u e .

2

It i s impor tan t to no te tha t accord ing to the no ta t ion sys tem used in S w eden ,

6/3 has dual meanings: "s ix th i rds" and "six divided b y three."

3

W e use

"word"

here to refer to a m ean ing fu l en t i ty in the C hinese l anguage . A

m e a n i n g f u l

ent i ty

can be

s ing le -sy l labic (cons i s t ing

of one

cha r ac t e r )

o r

mu l t i -

syllabic (comprising two o r more characters) .

4

W e

u se "characters" to

re fer

to the w r i t ten fo rm s o f m o r p h e m e s in the Chinese

language. Some characters are m ean ing f u l on their ow n (s ingle-syl labic en t i t ies)

and

some need

to be

co up led w i th o the r cha rac te r s

so as to

m a k e

a

mean in g fu l

en-

t i ty (m ul t isyl labic ent i t ies) . B ecau se a l l the s in gle-sy l labic ent i t ies referred to in

this chapter have thei r ow n m eaning s , and bec ause very

of ten

the i r fo rm s o f w r i t-

ing

were deal t w i th

in the

lesson,

w e

sha l l refer

to

these

a s

"characters,"

and

re fe r

t o

mult isyl labic ent i t ies

as

"words"

fo r

easy re fe rence .



O n

Language



5

Questions

and the Space of Learning

Amy B M

Tsui

Ference

Marton

I d a A. C. Mok

Dorothy

F P Ng

Q U E S T I O N S

Quest ions is perhaps the most thoroughly researched area of classroom

learning.

This is probably because it is the most distinctive feature of

class-

room

discourse .

A

lesson

is a

speech event w here people com e together

and

engage in an

activity referred

to as

"learning." Lessons

are

organized

in

such a way

tha t there

is at

leas t

one

person

in the

classroom

who is the

"pri-

mary knower" (Berry, 1987) and who is responsible for d i s s e m i n a ti n g

knowledge

to the others. ' The knowledge gap between the "pr imary

knower"—that

is, the

t eache r— and

the

"secondary know er"— that

is, the

s tudents—vests

author i ty

in the

fo rm er

in

de termin ing

the

direct ion that

the

lesson

wi l l take ,

th e

act ivi t ies that w il l

be

conducted,

the

quest ions that w il l

be

asked,

and

what constitutes appropriate answers

to

these questions.

W h e n

a

teacher asks

a

que st ion,

the

purpose

is not to

obtain inform ation

that

the teacher does n ot have, but to check whether the students have the

m issing inform ation indicated

in the

quest ion. W hen

a

teacher asks, "W hat

t ime

is it,

Johnny?"

Johnny know s that he is supposed to tell the teacher the

t ime even tho ugh there is a big clock on the w all that everybody can see. If

Johnn y says, "W ell, look

at the

clock

on the

w all,"

or if he

pu ts

th e

question

back

to the teacher,

"What

does the clock

say?"

the class knows that John ny

is head ing

for

t rouble.

1 1 3



1 1 4 T S U I E T A L .

Students also know that questions are not asked for their ow n sake, but that

they have

a

pedagog ical m otivation behind them , even thoug h

i t m ay no t be

clear

to the

students exactly what that motivation

is.

Therefore, when

a

teacher asks a series of qu estions, the students are supposed to try and answ er

each one as best they can. They are not supposed to query the purpose of those

questions

by

asking, "W hat

are you

trying

to get

at?"

or

"What

has

this ques-

t ion got to do w ith the preceding question?" at least not in A sian classroom s.

Qu estions serve a num ber of other purposes in the classroom besides know l-

edge checking. For example, questions can be used for classroom manage-

m ent purposes such as preventing th e students cha tting, getting the students to

focus

on the

lesson rather than daydreaming,

and so on

(see Tsui, 1995).

In

this chapter,

we are not

interested

in

classroom questions

per se, but in the

way the space of learning is c onsti tuted l ingu ist ical ly by the quest ion s asked

by the teacher, tha t is, the responses that can be

el ici ted,

and those that are ac-

tually elicited, and wha t th e teacher accepts as appropriate.

Q U E S TIO N S AN D FOCAL AWARENESS

Qu es t ions asked a t cruc ial stages of a lesson can focus s t uden t s ' at tent ion

on the

critical aspects

of the

object

o f

learning, c reate

the

con text that w i l l

help

students

to

make

sense

of the

object

of

learning,

and

open

up the

space

for explorat ion of an answer .

The

data that

we

look

a t in

this chapter co nsists

of

data sets

from

science

and

En glish classroom s

in

Hong Kong. Prior

to

presenting e ach data set,

w e

provide

a brief sum m ary of the classroom contexts and the objects of learning.

Physics

Lessons:

The Reed Relay

T he data set w e look at in this section con sists of two ph ys ics l essons taug ht

by the same teacher, one taught in Engl ish , w hich is a second language for

the students (referred to as EM I, Engl ish as a medium of instruction), and

one in the

s tudents ' m other tongu e, Ca ntonese ( referred

to as

CM I, Chinese

as a m edium of ins t ruct ion) . The di rect object of learning in both lessons is

the sam e: the function of a reed relay an d how it operates. (F or a deta i led de-

scription of the background of these two lessons, see Ng, Tsui , & M ar ton ,

2001.)

A

brief explanation

of the

direct objec t

of

learning

is in

order here.

T he

funct ion

of a

reed relay

is to

enable

a

w eak electric current

in an

elec-

tric c ircuit to start a m uc h stronger c urre nt in anoth er electric c ircuit by con-

nect ing the tw o w i th a reed sw i tch (see Fig . 5.1 for a picture of a reed relay) .

When a w eak electric current in one circuit

passes

through the reed relay,

a m agnet ic field is produced and the coil becomes an electromag net, caus-

in g

the two

ends

of the reed sw itch to touch one another. O nce the two ends

of the

reed swi tch touch

one

another,

th e

c ircu it that carries

a

very large elec-

tric curre nt is closed a nd the electric curre nt w i ll pass throug h and operate



Q U E S T I O N S A N D T H E

S P A C E

O F L E A R N I N G

1 1 5

FIG.

5 . 1 .

A

reed relay.

the device tha t is connected to it (see Fig. 5.2b and Fig. 5.3b). In the ex am ple

l e s s o n s , th e t e a c h e r u s e d a d e v i c e c a l l e d a l i g h t - e m i t t i n g d i o d e

(LED)—which requires only a weak cur rent to operate (see Fig. 5.2a)— and

a motor— w hich requires a very large current to operate (see Fig. 5.3b)—to

i l lustrate

how the use of a

reed relay enables

a

weak cur rent

to

activate

a

very

large current ,

an d

cause

the

motor

to

rota te .

T he s tructures of the two lessons are a lmost iden tical . In both lessons, the

teacher

first

explained the structure of a reed relay by showing that i t con-

sists o f a reed sw itch w ith coi ls wrapped round it (see Fig. 5.1) . S he then ex-

plained

the

con f igura t ion

o f a

simple circuit connected

to an LED

(see Fig.

5.2a),

and the

conf igurat ion

of a

complicated circuit also connected

to an

L E D (see Fig. 5.2b).

Th e teacher asked the s tudents to condu c t tw o exper imen ts . In the

f i rst

expe r imen t , s tudents w ere asked

to

connec t

tw o

c i rcui t s .

O ne

c i r cu i t

w as

cont ro l led by a push bu t ton sw i tch an d conn ec ted to an L E D , and w as re-

F IG .

5.2. (a) A s imple ci rcui t , (b) A compl ica ted c i rcu i t w i t h a reed relay.



1 1 6

T S U I

E T A L .

F I G . 5.3. (a) A s i m p l e c i rcu i t , (b) A c o m p l i c a te d

c i r c u i t

w i t h reed

relay .

ferred

to as the

s imple circuit (see Fig. 5.2a).

T he

o ther c i rcui t

w as

a lso

control led by a p u s h b u t t o n , and had a reed re lay con nec ted to it as w e l l as

an L E D .

This

c ircui t w as referred to as the

com plicated circuit

(see Fig.

5 .2b) . Th e teacher asked the s tudents to press the pu sh but ton sw i tch for

both c i rcui t s . In both c i rcui t s , the LED glowed when the c i rcui t s were

closed by pressing the push bu t ton swi tch , w h ich a l lowed an e lectric cu r-

rent to pass thro ug h. In the second ex per im ent , the teach er asked the s tu-

den t s to r ep lace the LE D w i th a mo to r, and the push bu t ton sw i tch w i th an

L D R

( l ight-d iode res is tor )

2

fo r

both

th e

s i m p l e

and the

c o m p l i c a t e d c i r-

cu i t s (see Fi g. 5.3a and F ig. 5.3b) . An L DR i s a l ig ht sens i t ive device t ha t

stops an

electric

cur rent f rom pass ing through. When l ight shines on an

L D R , its resis tance drops an d e lec t r ic i ty can pa ss th rough . T h e t e a c h e r

asked the s tuden ts to sh ine a torch on the LD R and w atch wh at hap pen ed.

T he students found tha t th e motor in the s imple c i rcui t (wi thout the

reed

r e l ay )

d id no t

move , whereas

th e

motor

in the

c o m p l i c a te d c i r cu i t ( w i t h

th e

reed re lay) did. Th i s i s beca use the e lec tr ic cur rent tha t passed thro ug h the

s imple c i rcu i t w as not b ig eno ugh to caus e the mo tor to ro ta te . By cont ras t ,

in the

c o m p l ic a t e d c i r c u i t ,

th e

cu r r en t became m uc h la rger

a f te r

p a s s i n g

throu gh the reed relay , and hence a l low ed the m otor to ro ta te .

After

the s tudents had per formed the two ex per iments , the teacher w ent

over w hat they had experienced w ith the wh ole c lass . She asked them to

tell

her w h a t happened to the LED when they

pressed

the push button switch

and they repor ted that the L ED in both c ircu i ts glo w ed. On h ear ing the s tu-

dents ' reports, the teacher posed the fo l lowing q u e s t i o n :



5.

Q U E S T I O N S

A N D T H E

S P A C E

O F

L E A R N I N G

1 1 7

5.1 [Physics Lesson/CMI]

3

T : It

seems tha t

if

this

is the

case,

w e do no t

need

to use the

reed

re-

lay.

W hy use the com plicated ci rcui t wh en the s im ple ci rcui t can

do

the

job?

Do you

agree?

T he

teacher problematized

the

students' observation

by

pu t ting

a

hypo-

thet ical s tatem ent to them : "If this is the case, w e do not need to use the reed

relay." Here , "this

is the case"

refers

to the fact

that

the LE D

glow ed

in

both

circui ts ,

sug gest ing that there w as no difference between the two ci rcui ts .

However ,

the

teacher signaled that this hypothesis

m ay or m ay not be

con-

firmed, by

prefacing

the

statement with

"it

seems

that." This

prepared

the

ground

fo r the

fo l low ing quest ion: "W hy

use the

com plicated ci rcui t w hen

the

sim ple circuit can do the

job?"

Th e presuppo sition of this que stion is tha t

the

sim ple circuit

can do the job in the

same

w ay as the

com plicated circuit .

W hat is quest ioned is the reason for us ing the co m plicated ci rcui t . The q ues-

t ioned element focused

the


on the

com pl ica ted circuit ,

and the

reason

fo r

us ing

it . Th e

jux tapo s i tion

of the fact

that

the

s imple

and

com plicated ci rcui ts could both l ight

up the L ED

created

the

need

for an ex-

planat ion (see Ogborn, K ress , M art ins , & M cGil l icuddy, 1996) and opened

up the

space

for

exp loring

the

function

o f a

reed relay.

T he

qu est ion created

th e

context

for

making sense

of the

ou tcome

of the

second experiment .

T o

put i t another way, the quest ion created the need to look for the answer in the

second experiment .

As already described, in the second experiment, the teacher asked the

s tudents to replace the push but ton swi tch w i th an LDR and the LE D w ith a

m otor in both ci rcui ts . She asked them to shine a torch on the LDR and see

whe the r

the

motor moved

in

each

of the

circuits (see Fig.

3a and

F ig. 3b).

After

the

experiment ,

the

teacher w ent over wh at

the

students

h ad

experi-

enced.

S he

asked

the

s tudents w hat

had

happened

to the

m otor

in the

c o m-

plicated circuit . The students reported that the motor rotated. She then

cont inued

as

follows:

5.2

[Physics Lesson

/

CM I ]

T :

Yes ,

h o w

about th i s s ide? [The teacher po in t s

at the

s i mp l e

c i rcu i t ] This s ide is even s impler . Now, here w e g o . S t r o n g

l i g h t sh i n e s

on the LD R, e l ec t ri c r e s i s t anc e va lue dec rea ses .

W e expec t t ha t there's an e lec t r i c cur ren t , a s t ronger e lec t r i c

cu r ren t , pas s in g th ro ug h the c i r cu i t and t he m o to r shou ld ro -

ta te , r igh t?

But i t i s

ve ry unhappy .

I t does n o t r e s p o n d . W e

n e e d

to exp l a in t h i s .

This tim e, the teach er drew the studen ts ' at tention to the sim ple c ircuit by

asking , "How about this

side?"

S he problem at ized the experience by po in t -



1 1 8 TSUI E T A L .

ing ou t that the failure o f the m otor to respond, even tho ug h a stronger elec-

tric current

passed

through

the

circuit,

w as

contrary

to

w hat they expected.

Again she created a need for an explanation.

Let us

pause here

and

look

at why the

teacher

did not

focus

on the

reason

for

the

m otor rotat ing

in the

com plicated ci rcui t ,

bu t

ins tead focused

the

stu-

dents'

attention

on the reason fo r the m otor in the sim ple circuit no t rotating,

even tho ugh the electric resistance value decreased and the electric curre nt

became stronger.

W hy did the

teacher

do

that?

In

the first experiment, the LED worked in both circuits . If the teacher

had drawn the students ' at tention to the complicated circuit , the students

w ould have not been able to discern the

differenc e

between the two ci rcu i ts

because

in the

co m plicated ci rcu i t both devices ( the

LED and the

m o to r)

worked. B y jux tapos ing a c i rcu i t in w h i ch the motor worked (a com pl ica ted

circui t)

wi th another ci rcui t

in

w h ic h

it did no t

work

(a

s im ple ci rcui t ) ,

the

teacher brought into the students '

focal

aw areness different respon ses of the

same device, and opened up the space for exp loring the answer in the differ-

ent configurations of the two circuits.

Sub sequently, the t eacher put an a mm e te r in each c i rcui t to m easu re the

strength of its electric current. T he readings showed that the electric curre nt

in the

s imple c i rcui t

w as

m uch sm al ler than tha t

in the

com pl ica ted c i rcu i t .

T he teacher then guided the students through each circuit and helped them

to formula te the reason w hy the m otor did not rotate in the s imple c i rcui t ;

that is,

that a l thoug h

the

elect r ic current became s t ronger when

the

resis-

tance value decreased,

i t w as not

s trong enoug h

to

cause

the

m o to r

to

rotate.

The teacher did not s top here, how ever. She then w en t back to the s imp le

circui t

w i th

the LE D in

Fig .

2a and

posed

the fo l lowing

ques t ion :

5.3 [Physics Lesson/CMI/T8]

T: W hy is i t

that this circuit [ the simple

c i rcui t

connected

to an

LED ] worked?

Why was i t

[LED]

so

w el l -behaved?

W hy did i t

[LED] l igh t

up?

B y

asking these quest ions ,

th e

t eacher

w as

j ux t apos ing

the

s im ple c i rcui t

connected to an LED w ith the s imple ci rcu i t conne cted to a m otor. In other

words ,

she now

held

the

ci rcu i t constant,

and

varied

the

device,

the

motor ,

and the

LED.

T he

questions

she

asked brought into

the

students '

focal

awareness the

different

responses of the two devices, and opened up the

space for exploring the reasons. A correct unde rstanding of the reasons w as

achieved w hen o ne student explained that th e c i rcu i t w i th the LE D l i t up be-

cause the electr ic current needed by the L ED w as sm al ler than the curren t

needed

by the

m otor. This

is the

corollary

of w hy the

m o to r

did not

rotate .

Let us recapi tulate the wa y in w h ic h the teacher structured the l earn ing

experience.



5. Q U E S T I O N S A N D T H E S P A C E O F L E A R N I N G 1 1 9

First of all, in the

first

experiment , the teacher varied the con f igura tions

of the tw o circuits so that there wa s on e w ithout a reed relay (i .e . , a sim ple

circuit [Cl]),

and one

with

a

reed relay (i.e.,

a

complicated circuit [C2]),

w hereas the device that the s tudents operated was invariant ( the LE D [D l]) .

In both cases, the LED li t up.

In the

second experiment,

the

teacher changed

the

device

from the LED

( D 1 ) in the first exper im ent to the motor (D2) for both c i rcui ts . This t im e, it

w as also the device that w as invariant (the m otor [D2]), and the circuit that

varied (the

one

w ith

a reed

relay

[C1 ] and the one

without

a reed

relay [C2]).

W hat the

teacher

did is

represented diagrammatical ly

in

F ig. 5.4a .

How ever, in the second experiment , the variation tha t th e teacher wanted

the

students

to experience was not the

variation between

the two

circuits,

but

the varia t ion between w hat they experienced in the previous

conf igura -

tion (the first experiment) an d the present

configurat ion

( the second experi-

ment) , which

was due to the use of

different devices:

Dl in the first

exper iment

and D 2 in the

second experiment .

T he

teac her ' s exho rta t ion

for

an ex planat ion in the second ex cerpt (5.2) and the question in the third e x-

cerpt (5.3) foc use d precisely

on the different responses of the LE D (D 1) and

the motor (D2) . In other words, the teacher was now construct ing the s tu-

den ts ' total experience (of the two experiments) as a wh ole. S he held the cir-

cui t conf igura t ions cons tant

(in

both exper iments ,

a

s imple

and a

compl ica ted circuit w ere involved), and w hat varied w ere th e devices ( in the

first experim ent an LED was involved, w herea s in the second experim ent a

motor

was

involved).

The

structure

of the

potential learning experience

can

be represented by Fig. 5.4b, where the bolded parts represent the aspects

that

w ere held constant

in the first and

second experim ents ,

and the

unde r -

lined p arts represent

the

aspects that varied.

This structure of variation brought the

responses

of the devices into the

students '

focal

aw areness

in

relation

to tw o

contexts:

why the

m otor rota ted

in the co m plicated circuit but did not in the simp le circuit , and w hy the LE D

worked in the simple circuit but the m otor did not. If, in the second experi-

men t ,

the

teacher

had

replaced

the LED

w i th

a

motor only

in the

com pl i-

First E xpe r ime n t Cl -^ Dl C2 -»• Dl

Second E xpe r ime n t C l -*-> D2 C2

-*•

D2

C l = s im p le c i r cu i t D l = LE D ( l ight-emit t ing d iode)

C 2 = com pl i ca t ed c i rcui t D2 = m o t o r

- * • caused

device

to opera te

-*r>

fai led to

ca use device

to

opera te

F IG .

5 .4a . S t ruc tur ing learning.



120

T S U I

ET AL.

First E x p e r i m e n t Second Expe r imen t

Cl •* D_L

C l -x->

D2

C2

•* Dl C2 •* D2

FIG. 5.4b. Stru cturin g of learning; first experim ent versus second experim ent.

cated circuit (as shown in Fig. 5.4c) both devices would have worked and

the

s tudents ' a t tent ion w ould

n o t

have been

so

sharply focu sed

o n

w h a t

it is

that

a

ci rcu i t w i th

the

reed relay

can do

tha t

one

w i thou t canno t .

C onversely, if the teache r ha d started off by us ing the m otor as the device

for

both ci rcui ts

in the

first

experiment , then

all the

s tudents w ould have

seen w as that the

m o to r

w orked only in the c i rcu i t w i th the reed relay. They

wou ld n ot have been able to see tha t the electric curren t in the s im ple c i rcu i t

w as a weak current w hich could operate an L ED , but not s trong enoug h to

operate the motor. Consequently, the main characterist ic of the reed relay

( that

it uses a smal l current to swi tch on a s t rong current) would n ot have

been so

effectively h igh l igh ted.

Wh a t

is

even more interest ing

is the w ay the

t eacher m ade

the

s tudents

see the interrelat ionsh ip betwee n the first exp erim ent and the second experi-

ment : that

the LED

needs only

a

smal l current

to

operate (w hich

is w hy i t

worked

in the

s imple ci rcui t ) , whereas

the

motor needs

a

large current

(which is why it did not w ork). In order to ma k e the mo tor wo rk , a reed relay

is

needed becau se

it can u se a

smal l current

to

start

a

very large curre nt .

The

teacher ' s e xplanat ion can be represented on fo l low ing pa ge (see Fig. 5.4d).

T h e w a y tha t the teacher s t ructured th e learning experience by posing

questions

a t

cri t ical points

in the

lesson brou ght in to s tuden ts '

focal

aware-

ness cri t ical aspects

of the

exper im ent

and

opened

up the

space

fo r

explor-

ing the

answers

to the

quest ions .

This w as

cruc ia l

in

b r ing ing about

the

s imu l taneo us aw areness of the three phenom ena ( i .e ., the sm al l current re-

quired

to operate the

LED,

the

very large cu rrent needed

to

operate

t he mo-

tor, as we l l as the w ay in w h ich t hey are re la ted) , w hich w as necessary for

the

students

to

unders tand

the funct ion of the

reed relay.

S o

far,

w e

have i l lus t rated

h ow

quest ions

can be a

pow er fu l m eans

for

bring ing cri t ical aspects

o f the

ob jec t

o f

l earn ing in to s tudents ' focal aware-

ness,

and

opening

up the

space

for further

enqui ry .

W e

have also seen

how

Fi rs t E x p e r i m e n t S e c on d E x p e r i m e n t

C 1 - D 1 C 1 - * D 1

C2-"D1 C 2 - D 1

F I G .

5.4c.

A l t e rn a t iv e s t ru c tu r i n g o f

l e a r n i n g .



5. Q U E S T I O N S A N D T H E S P A C E O F L E A R N I N G 1 21

Cl <C2

Dl

<D2

C l

- * D 1

C l -x->D2

C2-*D2

F I G . 5 .4d . Teacher ' s exp lana t io n.

the teacher skillfully structured the learning experience by posing que stions

at cri tica l junc tures

in the

lesson.

In the

follow ing section,

w e see how

different questions asked

by the

teacher

can bring different aspects of a phenom enon into students' focal awareness.

E ng l i s h Lessons:

O ld M a c D o n a l d ' s F ar m

The

data that

is

discussed

in

this section consist

of two

primary Grade

1

En gl ish lessons (Class ID and Class IE) tau gh t by two teachers w ho used

very similar materials and whose lesson object ives were the same. T he

topic o f the lessons w as "Old MacDonald 's Farm," a n Engl ish song about

farm an imals that

is

fam iliar

to

ch ildren

o f

many

different

na t ional i t ies .

O ne

of the ob jectives of the lesson w as to teach the determ iner "some" to signify

inexact

quantity.

In the

song,

the

word

"some"

appears many t imes

in the

lyrics, and for this reason, the teachers used the song as a vehicle for teach-

ing this determ iner

to the ch ildren.

B oth teachers used com puter-generated

im age s to revise

farm

anim al vocabulary and su bsequ ent ly to teach

"some."

(For a deta i led description of the backgroun d of these two lessons, see M ok,

R unesso n, Tsui , W ong, Chik, & Pow, 2002.)

Teaching "Some."

B oth teachers began

by

revising

th e

vocabulary

for

farm anim als by asking the quest ion, "W hat can you

see?"

In each case, the

pic ture

of a single anim al was presented on the com puter, and the respo nses

solicited

w ere "I can see a [name of animal]." The

focus

at this stage o f the

lesson w as the nam es of the anim als , ra ther than the num ber. The imp ortant

difference between the two lessons l ies in the subsequent episodes where

both teachers dealt with the teaching of "some."

After

the

vocabulary revis ion,

the

teacher

in ID

asked

the

students

to

guess the number of

different

kinds o f animals o n a farm. She

fol lowed

this

by showing the students different kinds of farm animals and asking how

ma n y

animals there were in each pic ture . The fol low ing is an excerpt of

w h a t

took place in the lesson im m ediately

after

the vocabu lary revision. To



122 T S U I ET AL.

make

it

easier

for the

reader

to

fol low

the subsequent

discussion

of the

data,

the

parts

that will be

discussed

are underlined.

5.4 [English

Lesson/Old MacDonald's

Farm/Primary Grade

I / I D ]

4

11 9 T: . .. Do you know how many cows o r hens? O r how m any ho r ses ,

120 how many hens , how m any p igs a re ( there) in a

fa rm?

Do you

1 21 know? D o you k n o w ?

122 Ss: No.

123 T: OK,

let's

see

wh a t 's

in the

farm.

A ll

r ight ,

O K ,

w h i ch

one do you

1 24 w a n t to see first?

125

Ss:

Cow.

126 T : OK. you w a n t to see cows. Righ t . Guess how many cows a re there

127 in the

f a rm ?

128 S :

[ shout ing

from his

seat] Four.

129 T: How many cows?

130 S:

[shout ing

from his

seat] Four.

131 T: Yes, Leo.

132 S:

Four .

133 T:

W h a t

do you

think, Louise?

134 S: Three.

135 T: W h a t do you think, H o Seng?

136 S:

Six.

137 T:

W h a t

do you

think Elaine?

138 S: F ive .

139 T: OK , Elaine. Do you wa nt to find out? OK, come here. Let 's find

140 out how

many.

OK,

cows. [Speaking

to

Elaine] Press

the

button

141 please. [Elaine com es up to the f ront and cl icks the m ouse. A n

142

image

of a cow appears on the screen.] All right, OK. Le t 's see

143 how

many cows

in the

fa rm.

W h at

can you see

here? [Teacher

1 44

points

at the

screen. ] What

can you see

here?

145 Ss: I can see a cow.

146 T :

Good.

N ow

let's

f ind out how

m any cow s there are? [Teacher

1 47 clicks the m ouse and four more cows appear on the screen. ] H ow

1 48 many cows are there?



5. Q U ES TI O N S

A N D TH E SPACE O F L E A R N I N G 1 23

149 Ss: Five.

150 T: Four?

151

Ss:

Five.

152 T: 10?

153 Five.

154 T: . I can s e e . . . ?

155 Ss: ... five cows .

156 T: Righ t . Or you may say ... ?

1 57 Ss: I can see f ive

cows .

158 Ss: I can see a

cow.

159 T:

W h a t ?

16 0 Ss : I can see . ..

161

T: Some

162 Ss:

Some cows .

163 T :

Some cows. Yes. There

are

some cow s here .

Is it

only one?

164

[Point ing

at the

screen.]

165 Ss: No.

166 T: There are four

cows.

You may

say,

I can see some

cows.

OK,

167

wh ole c lass.

168 Ss: I can see some cows.

169 T : A l l r ight , le t ' s con t in ue . . . . [Teacher c l icks the m ouse several times

170 and six

different

types

of

animals appear

on the

screen]

OK, do

17 1 you w a n t to f ind out how many [point ing to the pic ture o f a

1 72 duck] ducks there [are] in the fa rm? ...

In

this excerpt , the teache r started w ith the qu estion , "Do y ou know how

m any cows

or

hens?

O r how

m any horses,

how

m any hens,

how

many p igs

are [ there] in a farm?" The quest ioned elem ent i s the numbe r o f anim als ,

and it w as repeated four t im es . A s w e have pointed out previously , it is the

ques t ioned

e lement tha t

focuses

the

students ' at tention.

T he

focus

on the

n u m b e r o f

an imals

w as

reinforced when

the

teacher asked

the

s tudents

to

guess "how m any" cows there were on the farm (see l ines 126-127). A s w e

can

see

from

the stude nts ' responses, they did indeed focus o n the num ber,

and

proffered

"four,"

"three," "six,"

and "five" as answers. Af ter th is , the

teacher asked

the

students

to f ind out the

answer

for

them selves

b y

invit ing

one of them to c o me up to the com pu te r at the front of the class . The s tudent



1 24

TS U I

E T A L .

cl icked the m o u s e and one cow appeared. T he teacher asked the s tudent

w h a t

she

cou ld see,

and the

student said that

she

cou ld

see a

cow. This

w as

fol lowed

by the

teacher showing four more cows

on the

screen

and

once

again posing

the

ques t ion , "How m any cows

are

there?"

B y

doing th is ,

the

teacher

w as

con trast ing "one" w ith "more than one." M oreover,

by

repeat-

edly asking the s tudents "how m any cows" there were , the teacher w as con-

trasting "one" with

"other

num bers," that is , w i th a va lue o f more than one ,

hence opening up a dime nsion of var ia tion in num ber . In other words, w ha t

w as brought in to the s tudents ' focal awareness was exac t num bers , w hereas

the object ive of the lesson w as to teach

"some,"

w hich i s an inexac t num ber

rather than an exact number .

T he

focus

on exac t numb er w as re inforced by the teacher sub sequ ent ly

get t ing four s tudents to guess the exact nu m ber of cows ( l ines 1 3 1 , 1 3 3 ,1 3 5 ,

and 137) . W hen the cow s were shown on the screen, the teacher

offered

d i f -

ferent n u m b e r s

to

tease

th e

s tudents

an d

de l ibera te ly suspended

th e

evaluative feedback

on the

exac t num ber tha t

the

s tude nts provided.

I t was

no t unt i l l ine 156 that the teacher t r ied to e l ic i t the determ iner "some" from

the students

b y

us ing

th e b lank -f i l ling

ques t ion :

"Or you may say . .. ?" Th e

students ' responses to this b lank-f i l l ing ques t ion were te l l ing. Some s tu-

dents sa id, "There are five cows," an d some said, "I can see a cow." Bo th a n-

swers provided exac t num bers , w hich sugges ts tha t exac t nu m ber

w as

stil l

very m uch in their focal aw areness. Th e determiner "some" was supp l ied by

the teacher and the s tudents were m ade to repeat it after her. Bu t i t is doub t -

fu l

if the

s tudents

ful ly

unders tood what

"some"

m ean t . W hen

the

teacher

m oved on to the next episode ( l ine 170), w here she showed the pic ture of a

duck, she aga in asked the s tudents whether they w anted to f ind how m any

ducks there were on the farm.

The focus on exact num ber w as a lso re inforced by the way in w hic h the

teacher introduced

the

determ iner

"some."

I n

both cases,

the

word

"some"

w as

in t roduced

a t the

very

end o f the

episode,

by

presenting

it as an

a l te rna-

tive

s ta tem ent

to an

exac t num ber,

fo r

examp le, "There

are

four cows .

Y ou

m ay say, I can see som e cow s," "There are seven d uc ks , or you m ay tell m e, I

can see

some ducks."

In

both cases

the

exact number preceded

the

inexac t

number s igni f ied b y

"some."

Le t us com pare the ju st c i ted discourse w ith the fo l low ing excerpt that

shows w hat took place in the lesson of Class IE after the teacher had fin-

ished vocabulary revision.

5 .5 [Engl ish Lesson/Old M cDonald 's Farm/Pr imary Grade I / I E ]

70 T: [Teacher cl ick s the m ouse ] A dog. [Teacher cl icks the m ouse

71

aga in ] ano ther

dog

[Teacher cl icks

the

m ouse ag a in ] ano ther dog .

72 W o w , w h a t can you see? Al ice?




73 S: I can see three dogs.

74 T: V ery goo d, three dogs. There are three dogs. Thank yo u. And you

75 can say that, in other w ords, w e can say that . ..

76 Ss: We can see

dogs.

77 T: Remember the word "some"?

78 Ss:

Yes .

79 T:

Thank you , very w el l .

I can see

some dogs.

Do you

remember

th e

80 word "some"?

81 Ss :

Yes.

82 T: Yes, a l l r ight . Now , another one. [Teacher cl icks the m ouse] A no ther

83 p ig . OK. Now, so we have a pig, w e' l l see OK. C o m e and press the

84

but ton.

[A

student comes out.]

85 T: Is he

finished?

Is there another pig there? Press the but ton. W ow,

86

ano ther p ig? W ha t

can you see

then?

87 S: I can see some pigs.

88 T:

V ery good

To

begin w ith, the teacher in IE showed the picture of a single an im al, a

dog , ju s t

as the

teacher

in 1D had

done. However, before

she

showed

the

p ic-

ture,

the

teacher asked,

"What can you see?"

rather than "How m any dogs

can

you

see?"

T he quest ioned element is

"what"

and not "how many."

Asking "What

can you

see?"

did not

focus

the

stude nts ' at tention

on the ex-

act

num ber. I t w as open to the students to give ex act or inexact num bers as

answers .

W h e n

the

teache r asked

the

students

to

offer

an

al ternative

fo r

see-

ing

three dog s, the studen ts said, "W e can see dogs." In other w ords, conc ep-

tually, the students were aware that one alternative was to leave out

speci fying

the

exact number ,

and to

s imply

use the

p lura l form

to

indicate

that there

w as

more than

o ne

dog.

A t

this point ,

the

teache r provided

the

l in-

guistic

support

to the

students

by

reminding them that

the

word

"some" had

been in troduced before .

In the

subsequent episodes ,

the

teacher showed

three

different

kinds o f farm anim als : p igs , duc ks and cats . In each episode,

she

varied

o ne

w i th

more

than one,

and

posed

th e

same question, "What

can

you see?"

T he

students

had no

problems responding wi th ,

"I can see

some

p igs

[some ducks , some cats]." In other words , the quest ioned element ,

"what," opened up a dimension of variation in inexact number, that is, on e

versus

some.

Af ter

successfu l ly soliciting the determiner

"some"

from the students,

the teach er w ent on to pose the quest ion, "How m any [anim als] are there?"

in the

third episode.

L e t us

consider

the fo l lowing

excerpt:



126 T S U I ET AL.

5.6 [English Lesson/Old MacDonald 's Farm/Primary Grade I / IE ]

103 S: I can see some cats .

1 04

T :

V ery good.

O K.

W a it

a

m inu te .

How

many ca ts

are

there?

1 05 How m any ca ts a re there?

106 S: Four cats .

107 T: Is he correct?

108 S: Yes.

1 09

T :

V ery good.

Thank

you .

OK, how

about this picture? A lright.

1 1 0 [Teacher clicks the m ouse.] H o Ming, would you come ou t

111

and

press

i t for me to see

what p ic ture comes o ut?

[Ho

M in g

1 1 2 c l icks the m ouse .]

11 3

T :

W h a t

is it?

1 1 4 Ss : Ducks , ducks .

115 T: V ery good. Thanks. [Teacher asks Ho M ing to c l ick the

1 1 6

m ouse . ] A ny more ducks? [S tudent c l icks the m ouse and

11 7 some duck s appear.]

118

T : Any

more?

[Student clicks

th e

mouse again

and

some more

1 1 9 duck s appear .] A ny m ore? [Student c l ic ks the m ouse

1 20 aga in . ] No more . OK , w hat can you see now ? Hold the m ike

1 21

and

te l l yo ur c lassm ates,

O K?

122

S: I can see some duc k.

123

T:

D u c k s .

124 S:

Ducks .

125 T : Ducks .

126 S: Ducks.

127 T: OK. V ery good. How m any ducks a re there? How m any

1 28

duck s are there?

1 29 S: [same student] Five duck s.

1 30 T: Five duck s. Thank you very m uc h. Five duck s. Yes. you can

1 31

see some duck s, you can see some pigs, you can see some

132 cats,

and you can see

some

...

133

Ss: Dogs.

1 34 T : Dogs. O K . . . .



5.

Q U E S T I O N S

A N D T H E

S P A C E

O F L E A R N I N G 1 27

Let us consider the sequence o f quest ioning

from

the p erspect ive o f the

logical relationship between inexact

and

exact numbers.

The

determiner

"some" signif ies a range of num bers or qua nt i t ies and is inclus ive of exact

num bers such as 3 ,4 ,5 ,1 0 , and so on . The teacher in Class IE

first

posed the

ques t ion ,

"What

can you see?"

fo l low ed

by

"How m any?" This

is a logical

sequence—when reques t ing in format ion ,

one

often goes

from

general

to

speci f ic—and the exact num ber is seen in relat ion to the inexact num ber. B y

contrast ,

the teacher in Class ID s tar ted wi th , "How many cows can you

see?" which is already very sp ecific, and therefore renders the use of the de-

te rminer

"some"

to describe an inexact num ber su perf luou s . Thus the pro-

duct ion

o f

"some"

becom es contrived.

W hat both teache rs tr ied to teach w as how to express inexact nu m bers

that

are

more than one. However,

the

different quest ions that

the

teachers

asked,

and the way

they sequen ced

the

questions, focused

the

students '

at-

tent ion o n

different w a y s

of

express ing nu m bers that

ar e

m ore than

o ne

( that

is , exact num ber and inexact num ber), and opened up different dim ensions

of variat ion. The enacted object of learning in one case w as an inexact nu m -

ber, wherea s

in the

other case,

i t w as an

exact number , which

w as not an in-

tended ob jec t of learning.

In post lesson interviews con ducted wi th hal f

of the

s tudents

from

each

class ,

a task w as given to solici t the use of "some" to describe a selection of

pic tures . The results showed th at students in Class IE perform ed bet ter than

students in

Class

ID .

QUESTION

TYPES,

QUESTION S EQU EN C ES ,

A N D T H E

SPACE

O F

L EARNI NG

Quest ion Types

Many studies have focused on the cognit ive aspect of questions, and vari-

ous

t axonom ies

o f

question types ha ve been proposed,

for

example ,

the

sys-

tem

of

classifying questions according

to

whether they require

higher or

lower order thinking skil ls . Our concern in this chapter is not to examine

que stion types per se. W e are interested in those qu estions tha t have been re-

ferred

to as

"open"

and

"closed"

que stions, and the oppo rtunities for learn-

ing that are afforded by these qu estions. In part icular, we are interested in

the w ays in wh ich teachers m odify and sequen ce their qu est ions in order to

el ici t

responses from s tudents ,

and

hence

how

teach ers shape their s tud en ts '

learning experiences.

In classroom research l i terature, dist inctions have been made between

closed

a nd

open qu estions. However, there

a re different

criteria

for

identify-

ing

these q uestion s. In education research l i terature, a

c losed ques t ion

has



128 T S U I ET AL.

been un ders tood as having only one r ight answer, whe reas an open ques t ion

is one

that

has a

n u mb e r

of right

answ ers.

In

th i s vo lum e,

we use

c losed

ques t ions

to m ean qu estions w here there is only one acceptable answer, and

open

ques t ions to mean quest ions where there is a range of poss ib le an-

swers,

or a

range

of

poss ib le w ays

of

present ing

the

answer.

For

exam ple,

"Why does this motor work?" is an open ques t ion , w hereas "W hat is the

nam e given to th is m agnet?" is a closed q uest ion . W hen the teache r asks an

open question,

the

space

of

learning

is

w idened because

the

question chal-

lenges the s tudents to consider a num ber of

poss ib i l i ties ,

and to formulate a n

answer that makes sense no t only to them selves but also to the res t of the

class.

T he

formulat ion

of an

answer

is a

process

in

w h ich

the

students clar-

ify

thei r th inking

a nd

the i r unders tanding

of the

ob jec t

o f

learning.

On the

other hand, closed que st ions narrow down the poss ib le an swers to only one

choice,

or a

l imi ted number

of

choices,

and

hence al low l i t t le room

for

learners to explore answ ers .

In classrooms, it is very common for teachers to decompose a complex

open question into

a

series

o f

simpler questions

in

order

to

help students

to ar-

rive

at

an

appropriate answer. This

is

referred

to as

"piloting"

by

Lundgren

(1977). Studies

of

classroom questions have identified different sequences

of

questions u sed by teache rs, and ana lyzed them as to whe ther they were suc-

cessful

or not in

term s

of

helping students

to

answer

the

que st ion.

For

exam-

ple, among th e sequences of questions that Brown and Edmondson (1984)

identified w ere these

tw o

sequences , w hich they referred

to as

" funne lm g"

(p .

114): an open que stion follow ed by spec ific quest ions; and an open quest ion

followed by a narrowing down of this que stion to recal l facts and s imple de -

ductions.

"Funneling" is mos t com m only found w h e n the teacher has failed

to elicit a response from students w ith the ini t ial open que stion.

In c la s s room s w here a l angu age o the r than th e m o t h e r t o n g u e is used a s

a

m e d iu m

o f

teach ing

and

l earn ing (e .g . ,

in

E n g l i sh

as a

s ec o n d l a n g u a g e

classrooms), we typical ly find modi f ica t ion of wh-ques t ions ( i . e . , from

w hy ques t ions

to

what ques t i ons ) ,

and

c h a n g e s

in

ques t i on

fo rmat

(e .g . ,

f rom wh-ques t i ons to yes-no ques t i ons ) . Th i s is p r imar i l y because re -

sponding to why-ques t ions is l inguis t i ca l ly more demanding than re-

sponding

to

w h a t -qu e s t io n s ( w h i c h of ten r equ i re answers cons i s t i ng

o f

only on e or two w ords o r a phrase) . A nd responding to yes-no ques t i ons

(or a l t e rna t ive que s t ions ) i s leas t dem and ing becau se i t genera l ly involves

the

product ion

o f

ei ther

a

"yes"

o r a

"no" answ er

(o r in

some cases, m ak in g

a choice among the al ternatives provided). "Blank-fi l l ing" questions

(where

th e

t eache r p rov ides pa r t

of the

sen tence

an d

b l a n k s

out the key

word( s ) for the s tudents to f il l in) are a l so typ ica l ly found becau se t hey

lessen

the

l ingu ist ic

burden of the

students (see Tsui, 1995).

Let us

return

to the

physics lesson

on the

reed relay

a nd

consider

the

fo l -

lowing extract :




5.7 [Phys ics Lesson/Reed R elay /EM I/S2/T8]

1 T: . .. Oh

then surely ,

n ow

girls,

can you

explain

to m e, why

doesn ' t

2

th is m otor work?

3 Ss: [silent]

4 T : W hy does n ' t th is m otor work? Jus t because m otor m ust use ?

5 Ss:

[silent]

6 T: The current tha t is ? Large or small ?

7 S: Large .

8 T:

Large .

W e can see that the teacher asked an open quest ion and no response was

fo r thcoming .

Then the teach er provided some l ingu is tic scaffolding in the

form

of filling in the

b lanks . W hen th i s failed

to

el ic i t

a

response,

she

pro-

vided

m ore l inguis t ic help and a gain invi ted the s tudents to f i l l in the b lank .

W hen a response w as not imm ediately for thco m ing, she provided a choice

for them . This kind

of

sequen ce res t r ic ts wha t counts

as an

acceptable

an-

swer; the answer n ot only has to be appropriate in term s o f the content , but

also

has to f i t into the l ingu ist ic structure provided. In order to an swe r the

teacher ' s

ques t ion , th e s tudents had to shift their focus o f at tent ion

from

the

substantive pa rt (i .e.,

the

reason

why the

motor

did not

work),

to an

answer

tha t w ou ld fi t the syn tax given by the teacher . W hen the teacher provided

tw o

choices

to the

s tudents ,

the

cogni t ive deman d

w as

m in im al . This k ind

of

funnel ing effect reduces th e space in w h ich the students can explore variou s

possible answers for them selves , and formula te the appropriate answer. It

a lso has the de t r im enta l effect o f encouraging s tudents to gues s wha t the

teacher has in

m i n d ,

and to try to

produce

an

answer tha t wi l l meet

the

teacher's approval. T he fol low ing is

another

excerpt

from

th e

physics

lesson

on

the

reed relay taug ht through E ngl ish (EM I).

5.8 [Physics Lesson/Reed Relay/EMI/S2/T8]

T he teache r asked the students to compare the electric current re-

quired

to

operate

a

motor

and the

electric current required

for an

LED to

light

up .

1 7 T: . .. W hy

does

the LE D

work here? [Nom inate]

1 8 S :

[silent]

1 9

T: The LE D w orks, but it [Teacher points at the m otor] does not

20 rotate . It 's [a] sim ilar construction. [N om inate] Tell m e, how

21

m uch cu r ren t

is

needed

to

operate

a

motor?

22 S: [silent]



1 30 T S U I E T A L .

23 T: How much cu r ren t is needed? It should be very ?

24 S: 200mA.

25 T : A h ,

nearly 200mA, very good, very large current .

B ut can you

26 t e ll m e how m uch curren t i s needed to opera te a L ED ?

27 S:

V ery smal l cur ren t .

28 T:

Yes, very sma ll current

is enough all

r ight . Then

can you

explain

29 to me, why does this LED light?

30 S: [si lent]

In

th i s excerpt ,

th e

t e ach e r posed

an

o p e n q u e s t i o n

in

l ine

1 7:

" W h y

does the LED

work?"

W h en the s tudent had d i f f i cu l t i e s responding to the

ques t ion ,

th e

t e a c h e r m o d i f i e d

th e

q u e s t i o n i n t o

a

m o r e

spec i f i c o n e

a b o u t

th e

a m o u n t

o f

e l ect ri c cu r ren t r equ i red

to

o p e ra te

a

motor , "How

m uch cur ren t is needed to

operate

a

motor?"

( l ines

20-21).

She then na r -

ro we d d o wn th e ques t ion fu r the r by t u rn i n g it in to a b l a nk- f i l l i ng q u e s -

tion

in

line

23, "It

shou ld

be

very

?"

w h i c h p ro v i de d

th e

s t u d e n t s

wi th the l inguist ic s t ructure of the first par t of the answer , and on ly re-

qui red them

to f i l l in the ke y

w o rd ( s ).

A s

p o i n t ed

o u t

be fo re , t h i s k ind

o f

funne l ing o f ten h a p p e n s

in

c l a s s ro o m s wh e re

th e

s t u d e n t s ' l a n g u a g e

ability

is

we a k because

i t

lessens

the

l ing uis t ic burden

on the

s tudents

to

f o r m u l a t e

the re sponse .

The use of this type of quest ioning sequence focuses the studen ts ' attention

on how they can finish the sentence in a w ay that w ill fit into the syn tax of the

partial

sentence provided, and, very

of ten, in a way

that

wi l l

also correspond

with

th e

answer

the

teacher

has in

m i n d.

In the

ju st c i ted excerpt ,

the

teach er 's

subsequent question "How m uch current is

needed?"

focused the students' at-

tention on the

size

of the

current .

The

l inguist ic

scaffolding

that

the

teacher

provided

required

the

students

to put in an

adjective rather than

an

exact

figure

(see line 23). Th e student, however, attended to the "how m uch " qu estion and

provided

the

ex act size

of the

current. Al thou gh this answer

was

accepted

by

th e teacher, she rephrased it as "very large current." W e can assum e that the

students then realized th at the teacher was loo king for a general description of

th e

size rather than

the

exa ct size

of the

current ,

if w e

look

at the

subsequent

exchange.

W h en

th e

teacher asked, "How m uch current

is

needed

to

operate

an

LED?"

(line 26), a student this tim e replied, "a very sm all current" instead

of

giving

the

ex act size

of the

current (see l ine 27).

From this discussion,

we can see

tha t

th e

types

o f

qu est ions asked

by the

teacher can

either o pen

up the space of

learning

by

encou raging students

to

explore possible answers

an d to

form ula te the i r

ow n

answers ,

or

reduce

the

space o f learning by conf in ing students to only a rest r ic ted num ber of possi-

bilities

and

even

by

encouraging them

to

engage

in

guesswork.



5. Q U E S T I O N S AND THE S P A C E OF L E A R N I N G 131

Question Sequence

and

Focal Awareness

So

far, w e have seen that questions play a very im portant role in constituting

th e

space of learning in the classroom . They structure the learning experience

and they focus th e students' attention on

different

aspects of the object of

learning, w hether wit tingly,

or

unw ittingly,

on the

part

o f the

teacher.

In

dis-

cussing th e data from the E nglish lesson on O ld M acDonald 's Farm, we have

seen that different sequences of questions can fo cus the learners' attention on

quite different

things.

W e

also men tioned that teachers

often

decompose

a

complex question into simpler questions,

and we

focused

on the

ways

in

which such sequences could reduce the space o f learning. In this section, we

draw

the

reader's attention

to the

fact

that such sequenc es som etim es lead

to a

shift in focus, with the result

that

the intended object of learning is lost.

Let

u s

take

for

example

th e

fol lowing

tw o

paral le l excerpts

from the EM I

and the CM I

phy sics lessons, w here

the

teachers exp lained exa ctly

the

same

phenom enon : why the m otor does not rotate in the simple

ci rcui t .

5.9 [Physics Lesson/Reed relay/EM I/S2/T8]

1

T: . .. O h

then surely,

n ow

girls,

can you

expla in

to m e, why

d oesn ' t

2 th i s m otor wo rk?

3 Ss: [silent]

4 T: Why doesn't

this

motor

work? Just because motor m u s t

use ?

5 S s: [silent]

6 T : The cu r ren t tha t is ? Large o r small?

7 S:

Large.

8 T:

La rge .

1 7 T: . .. W hy does the LE D work here? [Nom inate]

18 S : [silent]

1 9 T: The LED works, but it [Teacher points at the

motor]

does not

20

rotate . I t ' s

[a]

similar con struct ion. [No m inate] Tell

m e, how

21 m uch cur rent i s needed to opera te a m otor?

22 Ss:

[silent]

23 T: How m uch current is needed? I t should be very ?

24 S:

200mA.

25 T: A h, nea r ly 200m A , very good, very large current . B ut can you

26

tell

me how

m uch current

is

needed

to

operate

a

LED?

27 S: V ery sma ll current .

28 T:

Yes, very sm all current

is

enough.

A ll

right. Then

can you

29 exp lain to m e, w hy does this LE D l ight [up]?



1 32 T S U I E T A L .

30 Ss: [si lent]

31 T : I t [ re fer r ing to the m otor] does not ro ta t e , j u s t beca use the re ' s

32 no

large current .

The LED

wo rks jus t because

?

33 S: Because the L E D —

34 T:

U s e —

35 S: Use

smal l current

and the

m o to r

use

very large current .

36 T: All r ight , yes, your answer is so impressive. Would you please

37

repea t

it

once . I t ' s cor rec t , repea t

it

o n c e .

38 S: The LED use[s] smal l current w hi le the motor use[s] very large

39

current .

40 T : Yes , very goo d , t he L E D u s e [ s ] [a ] s m a l l c u r r e n t w h i le the m o to r

41

use[ s ] very l a rge curre n t .

A ll

r igh t ,

O K .

Here the teacher asked two open quest ions: "Why doesn' t this motor

work?"

and

"Why does

the LED

l ight

[up]?" These

qu est ions opened

up a

num ber of possible answ ers , as pointed out before . However, because the

teacher used

b lank-f i l ling

quest ions to help the s tudents to provide an an-

swer

to the

open quest ions,

th e

s tudents '

focus o f

awareness shifted from

the

reasons w hy the m otor did not rota te , and why the LE D l i t up, to the am ou nt

of cu rrent needed

by the

m otor

and the

L E D .

F or

exam ple,

in

l ines

20 and

23,

the

teacher repeated

the

ques t ion , "How m uch current

is

needed

[ to op-

erate a

motor]?"

In line 26, she asked the same q uest ion abou t the L E D . A l-

though

the

students were able

to

tell

the

teacher tha t

the LE D

needed

a

very

sm all current , w hen the teacher posed the quest ion about w hy the L ED did

not l ight up in l ine 29, there w as no response from the c lass

unt i l

she gave

them some help.

In

other w ords,

the


w as

focused

on the

size of the current bu t they w ere u nab le to relate the size of the cu rren t to the

reason w hy the m otor did not rota te w hereas the LE D did l ight up .

Let us

com pare

the

a foremen t ioned exam ple w i th

the fo l lowing

excerpt

taken

from

the CM I c lass room .

5.10 [Physics Lesson/Reed re lay/CM I/S2/T8]

1 T: We find

that even thou gh

we

shone

a

strong l ight

on the

L D R ,

2

yes,

its

electric resistance value decreased.

But in fact th e

electric

3 curren t tha t w i l l pass through i s and the e l ec t r ic cu rren t neede d

4 to by the motor is . Do you kn o w w h a t I wo uld l ike you to

5

answ er? [ N omi na te ]

Y o u

try,

you t ry to

exp l a i n

w hy

n o t h i n g

6 happ ens here . N ow I sh ine a s trong l igh t on the L DR . r igh t? I ts



5.

Q U E S T I O N S

A N D T H E

S P A C E


7

res is tance

is ?

8 S: Smal l .

9 T : Yes, sm all. So there w ill naturally be an electric current com ing

10 in . Can you guess w hat the

difference

is between this electric

11 current

and the

electric current

it

ac tua l ly needs?

1 2

S : The

resistor 's electric current

is

smal ler than

the

motor ' s .

1 3 T : This means the motor needs an electric current that is ?

14 S:

L a rge .

1 5 T: N ot only large, but very large. Yes, and so . . . thank yo u, you

16 have answ ered correctly. An d so, even thoug h w e shine a strong

17 l ight on the LD R , i ts resistan ce value drops, and the so-ca lled

1 8 larger electric curren t

f lows

through the c i rcu i t . The m otor needs

19 a

very large electric current

to

rotate,

and so

this

is the difference

20

betw een th is c i rcui t

and the

other c i rcui t .

In this excerpt,

the

teac her also asked

the

s tudents

to

exp la in "why n o th-

ing

happens

here,"

m eaning

w hy the

m otor

did not

rotate ( l ines

5 and 6). She

also provided l ingu is t ic

scaffolding

to help the s tudents to provide the an-

swer ,

by ask ing them what k ind of cur ren t would pass th rough and what

kind

of

cur ren t

w as

needed ( l ines

3, 4, and 7).

However ,

after the

s tudents

had fi l led in the blanks, she posed an open que st ion once ag ain ( l ines 1 0 and

11 ) .

All the t ime, the

teacher

focused the

s tudents '

attention on the

differ-

ence be tween

the

current

needed

and the

cur ren t tha t ac tua l ly passed

th r ough

th e

c i r cu i t .

T he

mo di f ica t ions

of the

open que st ion

and the

s e q u e n c -

ing of the

closed quest ions

did not shift the

s tudents ' focal awar enes s away

from the

or iginal open quest ion.

Final ly, compare the fol lowing paral lel excerpts from the EMI and the

C M I

physics lessons where again

the

s ame phenomenon

w as

be ing

deal t

wi th ;

that is , w hat happene d w hen the l ight shines on the L DR .

5 . 1 1

[Phys ics Lesson/Reed Relay /CM I/S2/T8]

1

T: OK. [Teacher points to the com plicated c i rcui t ] W e love

2

shining

a

strong l ight

on the

LD R. Now , he re

it

conies, strong

3 l ight shines on the LD R . [Teacher shines the torch on the LD R ]

4 I' ll ask you questions step by step. For the circuit on the left side,

5

th is c i rcui t ,

the

largest

ef fect is the

e lec t r ic res is tance value ,

6 right? Strong light shines on the LDR, I 've told you before , a nd



134

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

S:

T:

S:

T:

S:

T:

Ss:

T:

Ss:

T:

S:

T:

Ss:

T:

S:

T:

S:

T:

T S U I E T A L .

the

electric resistance value drops.

O K,

w h a t

effect

wi l l

it

have

on the electric current on this side of the c i rcu i t ? [nominate]

Electric resistance

drops.

Electric resistance

drops, the

electr ic curre nt

?

Increases.

Yes, th e

electric

current

increases,

th e electric current

becomes

larger,

r ight?

W h e n

an

electric current

f lows

through

the

c i rcui t ,

this coil

is no

longer s imply

a

coil ,

it

becomes

an

e l ec t romagne t .

E lec t romagnet s can p rod uce ?

Magnet i c f i e lds .

Yes, they produce magnet ic f ie lds. When

it

produces

an

electromagnetic field, it has a series of effects on this side [of the

circuit]. Then what? [nominate], you try and con tinue. [Pointing

to the

com pl ica ted c i rcu i t ]

[si lent]

N o w .

the

coi l

has a

m agne t ic

f ield, and the

reed swi tch

? The

reed swi tch

?

[silent]

The reed switch, the two ends do not touch each other originally,

but

now w hat happens to these tw o ends?

Touch each other .

Yes, the two ends touch each other . I f the two ends touch each

other ,

how do w e

describe this swi tch?

[silent]

The two

ends touch each other,

how do I

describe this sw itch?

Closed .

Close d, very good. Yes, thank y ou . No w, i f

this switch

closes,

then

the

elect r ic current

can

pass through th i s

c i rcui t .

Thi s motor

9

Rotates .

Rotates .

Is

tha t

O K?

Here the teacher asked four "open" quest ions (see l in es 7, 8, 1 9, 26, 28,

and 29) and four "closed" ques tion s (l ines 10, 1 5, 22, 23, 34. and 35). If we



136

T S U I

ET AL.

1 3

T :

Should work ,

but it

does

not

rotate th is t ime .

How

a bout th is

1 4 ci rcu i t? [Teacher goes to the com plicated ci rcu i t ] Now once

15

again l ight shines

on the

L D R ,

its

res is tance dec reas efs] .

So,

1 6

cur ren t f lows through th i s c i rcu i t . N ow it's no t only a coi l

17 but a ?

18

Ss: [silent]

19

T: Now

this question again, [nominate]

N ow

th is t im e

it is not

20 mere ly a coil but a ?

21

S s: [silent]

22

T :

Artif icial

magne t , all r igh t . Do you still rem em ber [ the]

23 name?

24 S: E l ec t romagne t .

25

T : Once again .

26 S: Elec t romagnet .

27 T : Electromagnet , thank you, it becam e an electrom agnet, and

28 it produced a mag net ic field. So the sw i tch here

wi l l

close

29 and a

current [will]

pass

through this circuit ,

so the

m otor

30 rotate[s]. There is a sequence of processes] [that] occur here an d

31 i t m ake[s] the m otor rotate .

Here th e teach er asked an open question (lines 6 and 7):

"What

happens to

it [resistance] when light shine[s] on the LDR?" This q uestion, in a sim ilar

way to the qu estion posed in excerpt 5.11 , asked for a description o f the pro-

cess. W hen

the

teacher failed

to elicit a

response

from the

students,

she

posed

three blank-filling ques tions , one of which i s a repe t it ion (lines 10 ,1 1 ,1 6 ,1 7,

19, and 20), w hereas the others were c losed question s ( l ines 22 and 23) . How -

ever, in the course of

modify ing

the open question into

blank-fi l ling

ques-

tions, the blank-filling quest ions became focused on the devices and the

labels

( an

artificial

magnet

and an

electrom agnet) ,

and the

description

of the

process

w as

lost.

On the

basis

of our

observation that questions

focus

stu-

den ts ' awareness on the aspect of the phenom enon that was q uestione d, w e

can reasonably conclude that

the

consequence

of

asking quest ions about

the

devices,

rather tha n the processes, wo uld

result

in the devices being brough t

to the fore of the students ' aw areness and the processes rece ding to the back -

ground. A nd yet , it is the processes and not the devices

that

are cri t ical to the

understanding

of the

operation

o f the

reed relay.

C O N C L U S I O N

In chapter 1 , M arton, R une sson, and Tsui demon strated the central role

played by langua ge in con st i tu t ing the space of learning, and discussed at

length the im portance o f l anguage as a m e a n s o f en capsu la t ing experience ,

m aking di s tinc t ions , and m odi fy in g one an other 's und ers tandin g of the




world. They a lso

observed

the

function

of language in representing and

shaping

the

structure

o f

awareness

o f

participants

in a

d iscourse .

In

this

chapter , w e have foc use d

specifical ly

on the s tructure of que st ions and how

they impinge on the s tructure of awareness of par t ic ipants in a discourse .

Throughou t the lesson on the reed relay, w e demonstra ted how a teacher

w as able to help her s tudents discern the cr i t ica l features of a reed re lay a t

cr i t ical

points in the lesson, by asking qu est ions tha t focused their a t tent io n

on aspects that var ied. Throughout the English lesson, w e demonst ra ted

how the different quest ions asked by the teacher co uld resul t in s tudents fo-

cus ing on very

different

aspects of the object of learning. W e also showed

that

the way in wh ich the teacher sequen ced the quest ions co uld resu l t in a

shif t

of the

learners '

focal

awareness

from

the

crit ical aspects

of the object

o f

learning

to

aspects that

are not

crit ical.

In

other words,

the

teacher ' s

awareness

of how

ques t ions

can

shape

the

space

o f

learning ( i .e . ,

the en-

ac ted ob jec t of learning) is essential if our effort in br inging abou t power fu l

l earn ing in the c lassroom is to resul t in the convergence between the in-

t ended ,

the enacted, an d the l ived object of learning.

E N D N O T E S

'The term d issemina t ion is used in a neutral sense; it does not imply a

t ransmiss ive view o f t each ing .

2

F or an exp lana t ion of the L D R , see chap te r 1 , endnote 4.

3

In

this chap ter, data from the lesson taught in Can tonese w i l l be coded as CM I,

and data from the lesson taug ht in Engl ish wi l l be coded as E M I. T he data from the

CMI lesson is t ransla ted semant ica l ly , keeping as m uch as po ss ib le to verba t im

transla t ion.

4

A1 1 s tuden ts ' nam es

are

f ic t i t ious .



6

The Semantic Enrichment

of the

Space

of

Learning

Amy B. M. T s u i

TH E SEMANTIC

D I M E N S I O N

OF THE SPACE O F

LEARNING

In chapter 1 , M ar ton , Runesson , and Tsui proposed that learning is the

proces s

o f

develop ing

a

cer tain

w a y o f

seeing,

an d

po in ted

o u t

tha t

d i f fer-

en t

w a y s

o f

seeing al low

fo r dif ferent

w a y s

o f

ac t ing . They a l so po in ted

ou t

t ha t in order to he lp l earners to develop a ca pab i l i ty fo r seeing things

in a

p o w e r fu l w a y ,

w e

need

to

focus

on

w h a t

is

being learned

and

he lp

learners d i scern c r i t ica l fea ture s

of the

object

o f

l earn ing .

In

o ther words ,

inves t iga t ions o f l earn ing involve s tudying h o w learners experience th e

o b j ec t

o f

l earn ing ,

and

inves t iga t ions

o f

c lass room learn ing involve anal -

yses o f the opportunit ies to experience the object o f

learning

that are af-

forded to learners . In th is sense, the space of learning is an exper ient ia l

space.

A n exp erient ial space is not an ins tan t iat ion, but rather a po tent ial

for unders tanding, seeing, and act ing in the world (see Hal l iday &

M a t t h i e s s e n ,

1999). It is in re la t ion to th is potent ial th at learners can m a k e

sense of a pa r t icu lar objec t of learning . As su ch, the exp erient ial space is

e las t i c . The tea che r can e ither widen th i s space by af fording learners op-

por tun i t i e s

to

explore

the

o b j ec t

o f

learning

in a

variety

o f

w a y s ,

o r

nar row

this space

by

depriving them

o f

such opportunities.

In

the

preceding ch apters,

w e

have seen that

the w ay in

wh ich

the

object

of

learn ing is experienced by learners depends on w hich aspects of the ob-

ject of learning are

being

focused on and discerned as critical. In this chap-

ter, it is

proposed that experiencing

an

object

of

learning—in

the

sense

of

discerning i ts cri tical aspects and experiencing the patterns o f variation—

13 9



140

T S U I

necessar ily involves ass igning a m ean ing (or me anin gs) to i t. For exa m ple,

for a youn g learner w ho lives in a country w here high-rise b uilding s do not

exist , a "house" m e a ns a p lace where people live, as opposed to p l aces

w here a nim als live, such as

"stables."

A ho use is therefo re a choice in the se-

mantic system of accom m oda tion for different k inds of l iving th ings . How-

ever, to a you ng learner who l ives in a ci ty w here th ere are high -r ises as wel l

as houses, a house means something

different.

In this instance, "house" is a

choice in the seman t ic sys tem of accom m odat ion for people, wh ere houses

and

apar tments

are

choices .

A

house m eans

not an

apar tmen t : tha t

is. it is a

two- or three-story building, rather than a single unit within a m ul t i-s tory

building com pr is ing m any un i t s .

T he

meanings that learners assign

to the

object

of

learning depend

on a

host of th ings . The teacher can affect these m ean ings t h rough examples and

analogies , throu gh

the

stories th at

he

tel ls ,

and the

contex t s tha t

he

br ings

in .

The m ean ings wi l l also depend o n the persona l experiences that the learners

bring to bear o n the object of lear ning . Together , a l l of these m ea nin gs con-

stitute the semantic dimension of the space of learning, o f which language

plays a central role.

In this chap ter, exam ples from a variety of classroom s are ci ted to

i l lus-

t rate wha t is mean t by the sem antic dimension of the space of learning, and

the way s in whic h the learners ' experience of the object of learn ing is en-

riched semantically are discussed. T he central role played by language in

the

const i tu t ion

of the

seman t ic d im ens ion

of the

space

of

learn ing

is i l lus-

t ra ted by com paring classrooms w here r ich

l inguis t ic

resources were avail-

able, with those w here the l inguist ic resources were l imited.

CONTEXTUAL

VARIATION AND THE

SEMAN TIC

E N R I C H M E N T OF THE

SPACE

O F L E A R N I N G

It is c o m m o n pract ice among teachers , no matter what subject matter they

are dea l i ng wi th , to

shif t

f rom the c lass room c ontex t to co ntex t s ou t s ide the

classroom

(ranging

from

contemporary contexts

to

historical contexts)

in

the course of thei r explan at ions . How ever , few teachers ask why they are

doing this , and w h a t effect th i s k in d of con tex tua l var ia t ion has on l earn ing .

In this chapter, it is proposed that contextual var iat ion is a very im por tan t

and

co m m only used pract ice that help s learners to ma ke sense of and to re-

late

to the

object

of

learning.

M a t h e m a t i c s Lesson: Th e P o s t m a n ' s Ro ute

Let us t ake , fo r exam ple , the ma the m at ics l esson on the pos tm an ' s rou te

discussed

in chapter 3. To help the s tudents to see the relat ionships be-

tween pa t te rns ( as seen th rough ro ta t ion an d r e f l ec t i on ) , th e t eache r

started

by

asking

th e

s t uden t s

to

c o m e

up

w i th

a s

m a n y p a t t e rn s

as

poss i -



6 . S E M A N T I C E N R I C H M E N T O F TH E

S P A C E


ble , by c on nec t ing the dots that s tood for delivery po ints . In order to

faci l i-

tate task com ple t ion , the teacher provided the context of a pos tm an h aving

to deliver let ters to eight d ifferent places and then re turn to the post off ice.

W h e n the s tudents h ad com ple ted the task, the teach er asked the s tudents

to f igure ou t wh a t w as

wrong

with one particular design that he [the

teacher] ident i f ied , and then to dec ide wh at cons t i tu ted the best route . The

s tudents had no diff icul ty

po in t ing

o u t

tha t

the

design

in

ques t ion

fai led to

show the direct ion of the route , and fa i led to show h ow the po stm an c ou ld

get back to the pos t of f ice . They a lso had no d i f f icul ty dec id ing tha t the

best

route

w as the

shortest route.

T he tasks were n o t diff icul t for the

stu-

dents becau se the con text of a pos tm an de l iver ing mai l w as very

famil iar ,

and i t w as

easy

fo r

them

to

ident i fy

the

routes

in

re la t ion

to

w h a t

a

pos t -

m a n ' s

job

involved. On ce

the

e ight

bes t

rou te s we re

identif ied, th e

t e ache r

swi tched from the everyday context to a m athem at ica l context , so tha t the

designs took on a different meaning.

They were

no longer

routes

but pat-

terns .

T h e

c o n c e p t

o f

rou tes nece ssari ly involved having

a

d i rec t ion

a nd

being able to re turn to the s tar t ing point , w hich m ade i t very easy fo r the

s tudents to think of the cri ter ion for the best route . If the teacher had

started

the lesson by present ing the pa tte rns in a mathem at ica l con text , the

students would have ha d to think in sym bolic and abstract te rms and the

t a sk wo uld have been m ore dif f icu l t .

W hat is

interesting

is

tha t when

the

students failed

to see the

re la tionsh ip

between the e ight pat terns and hence were unable to categorize them , the

teacher switched back to the context of the po stm an's route , wh ich im m edi-

ately m ade

the

task easier.

The

students were then able

to see

that

th e

eight

routes w ere re la ted in two different ways: rota t ion and ref lect ion. In other

words,

the

studen ts w ere able

to

draw

on

their everyday kno w ledge

to

m a k e

sense of what the pat terns m eant .

E ng l i s h as a Second L a n g u a g e ( E S L )

Lessons:

W e a t h e r

an d Seasons

In a

s tudy

o f p r imary E S L teaching, Chan (2002) s tudied the p r imary

Grade 4 lessons taug ht by two teachers , in which the d i rec t ob jec t of lea rn-

ing

w as weather, c lothing, and

seasons.

In the first

part

of an 80-minute

lesson, both teachers used p ic tures

to

e l ic i t

th e

vocabula ry

fo r

w ea the r

a n d

c lo th ing .

Hav ing establ ished that there

w as

shared kno w ledge

o f

di f ferent

w e a t h e r con di t ion s and the corresponding types of c lo th ing , both teachers

in t roduced "seasons" and asked s tudents to deduce the season from the

clothing that they showed them .

In so

doing , both

teachers

w ere trying

to

he lp the i r s tudents see tha t w ea ther and c lo th in g w ere re la ted in m eaning-

ful wa y s . W e cou ld say tha t the teachers were t rying to establ ish a s e m a n -

tic

f ie ld w i th two sem ant ic dom ains : wea ther and c lo th ing . Su bsequen t ly ,

both teachers in t roduc ed a fur ther semant ic domain of

"seasons,"

h e n c e



1H42

T S U I

wea the r , an d c lo th ing ) w ere unders tood no t on ly o n the i r own , b u t also in

relation to

each other.

In the

latter part

o f

each lesson,

th e

teachers used

a

story

a s the

context

fo r

recycling the vocabulary i tem s introduced, a nd for reinfo rcing the students '

unders tanding of

wea the r

and

seasons.

T he

stories that

the two

teachers

told, however, were very different.

Teacher A to ld a s tory abou t a poor little gir l , M ary, w h o w a s driven o u t

of the house by her

s tepmother

in the

w inte r wh en

i t w as

cold

a nd

snowing.

T he s tepmother sa id tha t she w o u l d not le t Ma ry b a c k in un le s s she

brought back some beau t i fu l f lowers . Mary walked up the h i l l and

fell

as leep wi th ex hau s t ion . Four brothers ,

th e

four

sea sons , c am e

to her

res-

cue. Brother Spring waved

a

mag ic w and

and the

w ea ther became w arm

an d

ra iny . M ary

w as

then able

to ge t

f lowers

for her

s tepm othe r .

B u t

w h e n

Mary brought

the

f lowers home,

h er

s tepmother would

no t le t her in and

told

her to ge t

some app le s . Th i s t ime Bro the r Su m m er cam e

to her

re scue ,

and the w ea ther becam e h ot and sunny so tha t M ary could p ick some ap-

ples . T h e

s to ry con t inued

and a l l four

b ro the rs cam e

to her

re scue

in

tu rn ,

each t ime

the

greedy s tepmother m ade unreasonable dem ands

fo r

some-

th ing tha t cou ld not be f ound in tha t pa r t i cu l a r sea son .

L e t us

c o n s i d e r

the

s e m a n t i c d i m e n s i o n

of the

s p a c e

of

l e a r n i n g

t h a t w a s

o p e n e d

u p

w i t h t h i s s t o ry . P r i o r

to

t e l l i n g

th e

s t o r y ,

th e

t e a c h e r had a l ready e s t ab l i shed the r e l a t i o n b e t w e e n two s e m a n t ic do-

m a i n s ( s e a s o n s

a n d

w e a t h e r )

b y

s h o w i n g

h o w o n e i s

r e l a t e d

t o t he

other . The story p ro v i d e d the c o n t e x t not o n l y for m a k in g

sense

of the

r e l a t i o n s h i p b e t w e e n w e a th e r a n d s e a s o n s , b u t a l so fo r i n t r o d u c i n g

a n o t h e r s e m a n t i c d o m a i n r e l a te d

to

w e a th e r

a n d

sea son , t ha t

i s ,

p l a n t s

a n d

f r u i t s .

W h i l e p l a n t s a n d f r u i t s w e r e p a r t o f t h e s t u d e n t s '

e x i s t i n g

k n o w l e dg e , i t w a s th e t e a c h e r w h o b r o u g h t th e r e l a t i o n s h i p o f t h i s d o -

m a i n w i t h s e a s o n s

a n d

w e a t h e r i n t o

th e

s t u d e n t s '

f o c a l

a w a r e n e s s .

W h a t

is

i n t e r e s t i n g

is the way the

t e ach e r va r i ed

the

r e l a t io n s h i p s

be-

t w e e n s e a s o n s , w e a t h e r , an d p l a n t s an d f r u i t s . S h e s t a r t e d w i th a n e g a -

t ive re l a t ionsh ip b e twe en them

by

g e t t i n g

the

s t u d e n t s

to see \vhat

could n o t b e found i n a p a r t i c u l a r s e a s o n , a n d s h e h e l p e d t h e s t u d e n t s

to make

sense

of t h i s n e g a t i v e r e l a t i o n s h i p t h ro u g h the c h a r a c t e r of

th e s te p m o t h e r , w h o m a d e im p o s s i b le d e m a n d s o n l i t t l e M a r y . L a t e r , a

p o s i t i v e r e l a t i o n s h i p b e t we e n t h e s e d o m a i n s

was

e s t a b l is h e d w h e n

e a c h

o f t h e f o u r

b r o t h e r s c a m e

to

M a r y ' s r e s c u e

b y

c h a n g i n g

th e

sea-

son and the w e a t h e r so t h a t the p l a n t or the f r u i t d e m a n d e d by the s t ep-

m o t h e r c o u l d b e

f o u n d .

As the lesson progressed, there was a

gradua l w idening

of the

semant ic

f ield f rom w e a th e r an d c lo th ing , to inc lude sea sons , p l an t s , an d fruits . T he

fol lowing

excerpt

is an

example

of how the

teacher related

one

semant ic

do ma i n

w i th ano the r.

H

idening the semantic field so that the three semantic domains seasons,



6.

S E M A N T I C E N R I C H M E N T O F T H E S P A C E O F L E A R N I N G 1 43

6.1 [English Lesson/P4/Weather and Season]

T :

Mary's mother

says, "No.

I don't

want you.

Go away." Her

m other says, "Okay,

you ask me to let you

come back,

b ut

unless

you get me some

beau tiful flowers

(I

won't)."

Can you get some

beaut i ful

f lowers

in

w inter?

Ss: N o.

T: Outside it is .

Ss :

Cold

and

snowy.

T :

Can M ary get some f low ers?

Ss : [loudly] N o

T he readiness w ith

w hich

the students

responded

to the teacher

when

she

asked if M ary co uld get flow ers in the w inter when i t w as cold and snowy

show ed that they w ere able to make sense of the story an d see the relation

be tween the semant ic domains.

Teacher B also told a story

after

introducing all the vocabulary i tem s for

w eather, clothing,

and

seasons.

T he

story

w as

about

a

little boy, B illy,

and

w h a t he did on each of the seven da ys of a w eek and wh at the we ather w as

like. For

example,

on M onday,

when

it w as

raining,

Billy watched televi-

sion;

on

Tu esday, when

i t was

sunny, B illy play ed basketball ;

and so

forth.

The students were asked to learn the days of the w eek, and to say w hat B i l ly

did

and wh at the weather w as l ike . The w ay in w hich the teacher tr ied to re-

late the three sem antic doma ins was largely arbitrary. A ltho ug h certain ac-

tivities w ere logically related to the w eather co nditions (e.g. , "swimm ing"

and

"sunny w eather"), there were others that w ere not (e.g. , "w atching tele-

vision" and

"rainy

w eather").

A ctivities

and

days

of the

week

are of

them -

selves

no t

log ically related either. When

the

three sem ant ic dom ains w ere

taken

together, they

did not

form

a

sem ant ic

field. T he

story therefore

did

not serve as a

meaningfu l

context to w hich the stude nts could easily relate,

nor did it

help

th e

students

to

make sense

o f

each

of the

sem antic dom ains

in

relation to the other two . In other w ords, the s tuden ts ' un derstanding of the

relat ionship

betw een the three dom ains was not enriched sem antical ly by

the story.

If

anything,

the

story confused

the s tudents '

u nderstanding

be-

cause of the

arbit rary re la t ionsh ip that

the

teacher

had

tried

to

establ ish.

S c i e n c e L e s s o n : N e u t r a l i z a t i o n

To further i l lustrate what

can be

achieved

by

contextual variation,

let us

take a look at an example of a secondary Grade 2 level science lesson

(Hoare ,

2003). The object of learning in the lesson was "neutralization."

The teacher first introduced the concepts

o f acidi ty , alkal ini ty ,

an d the use

of the/?// value s cale to measu re the strength of acids and alkalis. Sh e also

asked

the

students

to find ou t the

acidity

and

alkalinity

o f

som e acids

an d al-



144 T S U I

kalis

by

using

pH

paper .

Af te r

this,

she

asked

the

students

to

test

the pH

value of several h ouseh old substances , su ch as lem on ju ice , vinegar , tooth-

paste , baking soda, b leach ing ag ent , and a canned soft dr ink. The fo l lowing

is

an excerpt

from

the classroom.

6.2 [Science lesson/S/Neutral izat ion/EMI]

T: . . .

Okay, now,

in our

dai ly l i fe

w e

have ,

um, we

com e in to con-

tact

wi th many things , r ight? For example, toothpaste , lemon

juice, e tc . . Do you k n o w w h a t is the pH va lue o f th i s? I s th is a

strong ac id?

Is it a

weak ac id?

Is it a

strong

a lka l i o r

weak a lka l i?

W e

don ' t know. S o in the fol low ing I w a n t you to do [the] experi-

m e n t

on

page

.

S:

167, 167.

T :

167,

is

th at right?

A nd

then

w e

have

to

test

the pH

va lue

of

lem on

juice, bleaching agent, baking soda, detergent, glass cleaner,

toothpaste , 7-Up™, but don' t drink it [s tudents laugh ] , m i lk o f

magnes ia ,

sea

w a te r

.. .

S : I[ ' l l] drink it .

T : Do n' t dr ink it.

S:

Why?

T: I [wi l l] have to call the am bulan ce. So, you do the same. Use the

pH

paper.

H ow

ma n y

o f

t hem?

S: Those 7-Up, change [them]

to

Coca-Cola™

ah

[Meaning

re-

place 7-Up with Coca-Cola]

T:

Yes.

S :

Ten...

S: Those 7-Up chang e [ them]

to

C oca-Cola .

T: Yes, you know that there is C oca-Co la there.

S: [inaudible]

T: Yes, sorry, ah, maybe 7-Up w as

diff icult

to buy.

S: A h I don ' t . .. I can go to the 7-11 ™ to buy i t.

T :

Okay , after this lesson. Okay

w e

change [ them]

to

Coca-Cola.

B ut

don't

drink

it.

Remember.

[Students co nduc ted the experiment and recorded the pH values

of the

substances.]

T: Now

okay look here. Lemon juice

is of pH ...

S: Three.

T: So we

cal l

it .

Ss: Strongly acidic, strongly, strongly acidic.

T: How do we describe it?



6.

S E M A N T I C E N R I C H M E N T OF THE S P A C E OF L E A R N I N G 145

Ss:

[silent]

T : Yes, it is a strong acid, so it is s t rongly ac idic . . . .

Prior

to

this experiment, al though

the

s tudents were famil iar wi th

th e

household substances listed

by the

teacher, these substances m eant n othing

more than things that they found

in

supermarkets

and

k i t chens .

In

other

words , the meanings of these substances were interpreted in the semant ic

domain

of the

supermarket

or the

ki tchen,

an d the

level

at

w h ich

the

students

were operat ing when they thought about these objects was the level of ev-

eryday knowledge. However, when the teacher asked the students to do an

exper iment

on

hou sehold substances ( i .e., w hen

the

s tudents w ere engaged

in

f inding

o ut their pH values and using tech nical langu age, su ch as "acid,"

"alkali ," and "strongly acidic" or "weakly acidic" to describe these sub-

stances),

the

household substances were recon strued,

not in the

semantic

dom ain of everyday items, but in the dom ain o f chem icals . A t th is point , the

level at w hich th e students were operating changed from the level of every-

day

know ledge

to the

level

o f

scientific

(or

technical ) knowledge. What

is

interesting

in the

jus t m entioned excerpt

is

that

w e can see the

students

and

teachers operat ing at both know ledge levels and in both sem ant ic dom ains .

In

other words ,

we may say

that

the

semant ic dimension

is

enriched

in the

sense that there

is an

addi t ional layer

of

mean ing .

Having established the con cep ts of alkalinity and acidity, the teach er in-

t roduced the

concept

o f neutralization by

asking

the

students

to mix an

acid

(hydrochlor ic

acid) with a n alkal i (sodium hydrox ide) unt i l they obtained a

pH value o f seven, a point a t wh ich t he so lut ion becom es nei ther acidic nor

alka l ine .

T he teacher explained that neutral izat ion is a process by w hich an

acid is added to an alkali unti l the result ing solution is salt a nd water . A f te r

the s tudents had done the experim ent , the teacher t r ied to help them to m ake

sense

of

neu tralization

by

shifting

from

the

science laboratory context

to an

everyday context . She used a num ber o f exam ples to explain the app l ica-

tions

of

neutralization.

O ne

example

w as

that

of

using toothpaste

to

brush

our

t ee th .

S he

explained that

the

ac id produced

after

eat ing food causes

o ur

teeth to decay, and that toothpaste neutralizes the acid. Another example

was the use of

m i lk

o f

magn esia

to

neutral ize excessive acid produced

by

food

in the stomach, and thus al leviate stomachache. Yet another example

w as the use of ointm ent con taining alkal i to neutral ize the acid produc ed by

m osqu i to b i tes .

In

this section

of the

lesson,

w e see the

reverse process

of

contextualizat ion happening. Previously, neutral izat ion

w as

m ere ly

a

labo-

ratory process in w hich ch em icals were m ixed together . Here, neu tral iza-

t ion

w as presented as a process that takes place frequen tly in our everyday

lives. Ac ids

and

alkalis were

no

longer un derstood on ly

a s

chem icals

in

sci-

ence laboratories

but as

chemicals that could

be

found

in

ma n y

different

substances outside the laboratories. Once again, there were two levels of

knowledge

operating, and also tw o

semantic domains

in

wh ich neutral iza-



146 TSUI

t ion w as unders tood: a scien t if ic process dom ain, and a dai ly life process

domain. The fol lowing excerpt shows that as soon as the teacher explained

the toothpaste as an example of neutral izat ion, the s tudents were able to

make sense of neutral izat ion in another daily

life

contex t— the use of m ag-

nesia to neutral ize ac ids in the s tomach.

6.3 [Science lesson/N eutralization/S2/EM I]

T:

A h, toothpaste is alkaline, and it neutralizes the acid in our

mo u t h af ter w e have taken some

food

. . . . A nd n eu t ra l iza tion

takes place there so that we can ha ve hea l thy teeth . Okay. Sec-

ond,

I

know some, m any, people w ould like

to

have m any— a full

lunch . . . . W hen

you

have taken

a lot of

food,

and

som etimes

you

find

that this part

is not

okay . S tom ach

?

S : S tomachache .

T: You have s tom achache . Oka y . . . . W hen you have taken a lot of

food, yo ur s tomach w i l l g ive

out

acid

to

m a k e

the food

in to sm al l

pieces so that you can take in the food, okay? . . . So at that t im e

w hen your stom ach gives out a lot of acid, you find that it is pa in-

f u l . . . . S o what should you do a t

that

t im e? Some peop l e w ou ld

like to

take some tablets. O kay this

is one of the

tablets .

W e call it

m ilk of m agnes ia . . . . H as anybody taken th is before? W hen you

have s tomachache, you can take one . . .

. .. W hy do w e have to take one?

S: Neut ra l ize .

T : Y e s , . . . the reason is tha t it ne u t ra l izes the acid f rom o ur s tom ach

so

tha t

y o u

becom e peace fu l . . . .

A s in the previou s excerpt (6.2), we may say that by varying the con text,

the sem ant ic dim ension w as enriched and the teacher w as able to help s tu-

dents ass ign an addi t iona l layer of m ean ing to the ob ject of learning .

COLLABORATIVE E N RI CH M E N T O F TH E SE MANTIC

D I M E N S I O N

BY

LEARN ERS

So

far,

the

exam ples examined w ere classroom exam ples w here

the

teacher

enriched

the

sem ant ic d imen s ion

by

br inging

in

stories

o r

con texts outs ide

the classroom and the laboratory to help learners to m ake sense o f the object

of learning. In this section, w e look at examples in w h i c h the learners

brought

in

their

own

experience

to

assign m eanings

to the

object

of

learning

and

see how the space of learning w as enriched se m ant ical ly by the collab-

orat ive construction o f m ean ing among the learners.



6 . S E M A N T IC E N R I C H M E N T

O F T H E

S P A C E


C h i n e s e

L e s s o n :

The S lo th

The data presented here com e from a prim ary Grade 3 Chinese langua ge les-

son, "The

Sloth,"

th e

background

of

which

has

already been introduced

in

chapter

2. W e

shall

now see how the

learners assigned meanings

to a

video

that they watched together,

how

they collaboratively constructed

a

written

representation

of the

video,

and how the

space

of

learning

w as

enriched.

In

th e

lesson

on the

sloth,

the

object

of

learning

w as to

w rite

a

descript ion

of the appearance of a youn g s loth , and a story about its search for a new

h o me

af ter

it lost its m other and had ea ten all the leaves on the tree where i t

lived.

T he

teacher provided

a f ram ework for

describing

an

animal that

w as

based

o n the

de script ion

of a

panda that they

had

studied

in the

previous les-

son.

The

teacher used

the

word "appearance"

as a

hyponym

for

body

or

t runk, head (brain),

four

l im bs and color (of the

fur

or skin). Then he po inted

out to the class that it w as also necessary to describe w hat the anim al was

like wh en i t was in m ot ion. For example, the movem ent of a panda is very

c lumsy. He also pointed o ut that i t w as necessary to describe the slo th 's eat-

ing h abi ts and character. After p roviding the f rame wo rk, he showed a video

of the

story

of a

sloth.

O ne

striking featu re

o f

this lesson

is the w ay in

w h i c h

the

teacher repeatedly showed

the

video,

at

first with narrat ion

and

later

wi thou t

narration, each t im e showing a

different

segment of the tape w ith a

different

focus.

This repeti t ion not only rei terated the content , but also

opened up the space for students to explore the ways in which they could

m ake sense

of the

features

of the

sloth. Students w ere then asked

to

work

in

groups

and

produce

a

writ ten text

to

describe what they

had

seen.

In the

fo l low ing di scuss ion ,

w e

exam ine some

of the

t ex t s p rodu ced

b y

the s tudents , and the discuss ion data that led to the product ion o f these

texts .

W e see how the

s tude nts ass igned m eanings

to the

video,

and how

their

cons t rua l

of

wha t they

had

seen enriched

the

semant ic aspect

o f the

space of l earn ing .

Sloth s Head a n d

Body. The fol lowing is a w ritten descript ion produ ced

by Group 2: '

It is a

s lo th ,

it s

head

is

l ike

a

b ig

chicken egg, it s

body

is l ike a

b ig

os tr ich

e gg ,

very

long , and the

th ree c laws

on its

fo r e l imb s

are

pa r t icu la r ly long .

Its

co lor

is

b l a c k ,

wh i t e , gray, brown. Very

short

tai l . T o

look

for food and a

home ,

the s loth

s low ly

c l i m b e d

d o w n the tree, and swam frees ty le . It crawled to the shore . A s soon as it

r eached

th e

shore ,

it

g lanced

to the

east

and the

west . V ery

soon,

it found a

tree.

It fi-

nal ly found

a new home .

Let u s

focus

for the

m o me nt

on the

s tudents ' desc ription

of the

head

and

body

of the

sloth. Although most groups s im ply m ade

u se of the

teache r's

suggestion that the sloth 's head w as like a m onkey 's head, this group felt



148 T S U I

tha t us ing another an im al

to

describe

the

sloth

w as no t

adequate ,

and

tha t

they ought to use something else for comparison. T he fol lowing excerpt

shows

how the

students explored

the

descript ion

of the

s loth ' s hea d.

6.4 [Chinese lesson/P3/The Sloth/Group Discuss ion/Group 2]

296 S: W ha t 's i t [ the hea d] l ike?

297 S:

Like

a

monkey ' s head .

298 S* This is not s ay ing any th ing .

299 S: They are both an im als .

300 S : I ts h e a d . . .

301 S: Is l ike a chicke n egg.

302 S: Is l ike an oval chick en egg .

303 S:

Ju st l ike

a

ch icken

egg is

okay.

304 S: No need to say tha t it is oval as w e l l.

305 S:

Just [put t ing dow n] chicken

egg is

o k a y ?

306 S:

Like

a

ch icken

egg is

okay.

307 S:

Ch icken eggs

are

a lway s oval .

308 S:

It 's

got to be

b igger than

an

egg. It ' s

no t

t ha t sm a l l .

309 S: Th at 's r ight , chick en eggs are very sm al l .

310 S: That's right .

3 11 S :

Wha t ' s

it

l ike again?

312 S: Like a big chicken egg.

313 S: A big

ch icken

egg is not

tha t b ig .

314 S:

That's

okay.

Y ou

describe

the

head

...

315 S: A big goose egg .

316 S: A big goose egg is fine.

31 7 S: A big

ch icken

egg is f ine.

318 S: How do I

w rite

the

word "egg"?

319 [The studen ts helpe d each other w rite the word

"egg"]

320 S: Le t 's see, w ha t 's a big ostrich egg like. L et 's say a big ostrich

321

egg,

is

that okay?

322 S:

Okay, ostrich egg .

323 S: Ostr ich eggs are very big?

324 S: Okay, let's describe the body.

325 S: [ reminding the s tudent who i s w r it ing] B ig ostrich egg.

326 S: Ostr ich egg.



6. S E M A N T I C

E N R I C H M E N T O F TH E S P A C E O F

L E A R N I N G

1 49

From this discuss ion (6.4),

we can see

that

tw o

cri tical features w ere

be-

ing

explored by the students: name ly, shape an d size. Of part icular interest

is the

ini t ial com parison

of the

sloth's head w ith

the monkey's

head

by one

student

(line 297), the reject ion of this com parison by another student ( l ine

298),

and the just if icat ion of the reject ion by a third ( l ine 299). What was

happening in that section of discourse? Why did the second student say,

"This is not saying anything," m eaning tha t com paring the s loth 's h ead wi th

a m onke y 's head w as not informa t ive at a ll? For the f i rst s tudent , w hat cam e

to

the fore of his awareness w as the comparison of the sloth with other an i-

mals .

T he

dimension

of

variation

w as

"heads

o f

anima ls" (wh ich

w as

also

w h a t the teacher had previously i l lustrated). However, for the second and

th i rd s tudents , w hat cam e to the

fore

o f their aw areness w as not to compare

the

sloth w ith other anim als, as can be seen from line 299. Their subsequent

discourse shows that it w as the shape that was in their

focal

awareness , and

t hus

they acce pted the analogy of a chicken egg that m ade the shape im m e-

diately

apparent .

"Oval" was a

shape tha t

w as

considered

by the

group

to be

a critical feature o f the shape of the sloth 's hea d. The s tuden ts w ere trying to

decide

w h ich

w as the

best a nalogy

to use to

describe

the sloth 's

head

a nd i ts

body. The de bate about whe ther i t w as necessary to specify oval when u sing

a chicken

egg as an

analogy

is

interesting both

at the

conceptual level

and

the l inguist ic level . Conceptually, oval

can be a

feature that

is

qu i te inde-

pende nt of an object . For exam ple, a table can be oval , roun d, or square.

Specify ing

the shape of an object presupposes that there are shapes other

than

that which

is

specified.

From the

discuss ion,

it is

clear that

for

some

students , oval was considered to be an inherent feature of a chicken egg,

w h i c h

rendered

the use of the

adjective

"oval" to

describe

the egg

redun-

dant . This is a fairly sophist icated level of unders tanding that the s tudents

w ere able to reach throug h col laborat ive ta lk . Lingu is t ical ly , "chicken egg"

w as

used to describe the shape, and "chicken egg" took on a m ean ing

that

w as

synonym ous w i th oval.

T he

other feature

is

size,

bu t

here

we see the

opposi te happening.

A l-

though

there

are

chicken egg s that

are b ig and

those that

are

sm al l,

th e

varia-

t ion

implied by describing the sloth 's body as a "big chicken egg" (as

opposed to "chicken egg" for its

head)

w as considered inadequate because

even b ig

chicken eggs were thought

to be too

small . Instead,

the

s tudents

proposed the

k ind

of egg as a dimension of variat ion. Thus they proposed

goose egg an d ostrich egg as a variat ion in size, and finally dec ided on os-

tr ich

eg g. Here

w e can see

three term s

in the

students ' semantic system

of

size:

chicken eggs , which are smal l ; goose eggs , which are b igger than

ch icken

eg gs; and o strich eggs, w hich are biggest of al l three. In the final

draf t tha t the students produced, they added the adjective "big" in front of

ostrich

eg g to describe the

size

of the

body.

B y

doing this ,

the

students have

added o ne m ore term to thei r sem ant ic sys tem of s ize to m ake f iner dis tinc-

t ions in

size.



150

T S U I

Th e collaborative co nstrual of the appe arance of the sloth is evide nt in the

way the

students questioned each other 's contribution

and

then cam e

to a

consensus on the most appropriate descript ion.

Sloth s Eyes. Le t us now cons ide r th e desc r ip t i on p roduced by an-

other g roup , Group 4. When desc r ib ing th e a p p e a r a n c e o f the s lo th , o n e

s tudent in Group 4 said that the

sloth's

eyes were b lack . However , the

o ther g roup me m bers im m edia t e ly po in t ed ou t t ha t eve rybody knew eyes

were black, imp ly ing t ha t this

piece

of i n fo rmat ion was supe r f l uous .

How ever , ano the r s tuden t po in ted ou t tha t the eyes o f a rabb i t were spe-

c ia l , and ano the r s t ud en t ch ipped i n and sa id t ha t r ab b i t s ' eyes w ere r ed .

In

t h i s d i s cus s ion ,

w e can see

t ha t i n i t i a l l y

for th e

s t u de n t s ,

a ll

eyes were

b l a c k and t he re fo re t he re was on ly one t erm in t he sys t em o f m ea n in g o f

color

of eyes.

How ever ,

as

soon

as the

color

of

rabbits' eyes

was

b rough t

in , t he mean ing o f t he co lo r o f eyes changed . B l ack was no l onger a

given, but a

choice

in the system of c o l o r— w h i c h at tha t par t icu lar po in t

in

th e

d i scou r se cons i s t ed

o f

b l a c k

and no t

b l a c k ,

t h a t is ,

red .

In

o t h e r

w ords , we co uld say tha t the co lor o f the eyes was an aspe ct t h a t w a s n o t

d i s ce rned

in i t i a l ly

(a t l eas t b y s o me of the s t u de n t s ) . I t was t a k e n fo r

gran t ed . How ever , w hen

a n

a l t e rna t ive

ey e

co lo r

w a s

e xp l i c i t l y b r o u g h t

u p , a d imens ion o f var ia t ion in co lor w as o p e n e d u p . Di sce rn ing t ha t th e

co lo r o f the s l o th ' s ey es i s b l ac k imp l i e s a d im ens io n o f v a r i a t ion w i t h a t

least

tw o

poss ib le value s : b lack

an d no t

b lack . De scr ib ing

th e

eyes

of the

s lo th a s b l ack m ean t t ha t co lo r was i n t he f oc a l aw aren es s o f one o f t he

s tuden ts . I t w as by

va r y i n g

th e

co lo r

o f a

s l o th ' s eyes ( and

a

r a b b i t ' s e y e s )

t ha t s t uden t s w ere ab l e

to

d i s ce rn t ha t ha v in g b l a ck eyes

w a s a c r i t i c a l

fea tu re o f t he s l o th ' s appea rance .

Sloth s

Body.

A l thou gh m ost groups described

the

body

of the

sloth

a s

"roundish,"

p lu m p , o r like a big ostrich egg (as Group 2 did), Group 5 de-

scribed the slo th 's body as very thin . Th e fo l lowing excerp t shows the m ean-

ing that Group 5 a t t ached to th is descr ipt ion.

6 .5 [Chinese Lesson/P3/The Sloth/Group Discuss ion/G roup 5]

S : Now , i t ' s bod y [shape]

...

S: I t 's body [shape] , i t 's body is qui te b ig , huh ?

S:

Thin

S :

Thinnish

...

Looks l ike

he is

un dernour i shed.

S: N o

S:

Thin

He is

very thin

S : H is body shape ...

S: In fact, it was his fur that covered it up.



6. S E M A N T I C E N R I C H M E N T O F T H E S P A C E O F L E A R N I N G 1 51

S: Oh no

S:

The fur

covered

it up

S : His body shape . . .

S:

Yeah

S:

In fact he is

very plump

S:

He is

very thin.

S : Yeah, th ink about th is . Plum p because o f the fur, his fur covered

up his body.

S:

Because

his fur is

long

This debate wen t on for quite a w hi le and finally the students agreed to put

down "thin." What happened here was that this

group's

construal of the

sloth's

appearan ce w as m ade in the con text of the narration that said that the

sloth's mo ther ha d died, that it w as alone, and tha t the leaves on the tree w here

it lived had all been eaten up. For this reason one of the studen ts said that the

sloth

was "undernourished." In order to reconcile the discrepancy between

what they saw on the video and

their

understanding of what his

appearance

should

be,

they cam e

u p

w i th

an

interesting explana tion: that

th e

sloth looke d

plum p only because

of its

fur. This suggests that

the

meanings that

are as-

signed by the students to the phenom enon under discussion m ay lead to a di f-

ferent construal of the object of learning.

Sloth's

Diet .

Let us

take

a

look

at an

excerpt from

the

discuss ion

in

Group 4 on the s loth ' s diet . The video narration only provided the inform a-

t ion

that

the

sloth

ate

leaves

from one

par t icular t ree:

I t [ the sloth] looks around and tries t o find a t ree wh ere i t wo uld l ike to live. The tree

should

be o f the same spec ies as the one that i t

lived

on before because wh en a

sloth

gets

used

to the taste of the leaves of a certain

k ind

of tree, it w i l l not change what i t eats .

6.6

[C hinese Lesson/The

S

loth/PS /Group Discuss ion/Grou p

4]

S :

It

eats

... it

only eats leaves.

S:

It

does

not eat

anything else,

it

only eats leaves.

S:

Ea ts leaves.

S :

E a t s le aves , i f . . . i f . . .

S: Like a big bear, it's pin sihk

2

(C antonese) [ $| ^ ] ("a

fussy

eater").

Like

the

panda ,

it's

p in

sihk.

S : He y . .. there's m ore

S:

It ' s

a.pin sihk

an imal .

S: It

does

not eat

me a t

and . . .



1 52 T S U I

S: I t

does

not eat

meat

and

does

not eat fish.

Does

it eat fish?

Ss:

N o

S: N o, i t also says . ..

S :

When

it

gets used

to the

taste

of one

k ind

of

leaf ,

it

wi l l

not

e a t . . .

S: That 's why [ I said]

ii'spin

s ihk .

In the or iginal n arrat ion , the narrator ex plain ed that the s loth had to f ind

a

tree

of the

same spec ies because

of its

p re fe rence

for a

cer tain type

of

leaves.

T he

students

in

Group

4,

however, ass igned fur ther m ean ing

to the

s lo th ' s p reference fo r l eaves . They used a s i n g l e e x p r e s si o n ,

p in

sihk

( Ca n t o n e s e )

[ ̂ ^ ], an

ad jec t iva l

ph rase

for

de s c r ib i n g s o m e o n e

who

is

a fussy eater, to describe the eat ing habits of the sloth. T he s tudents were

br ing ing in the i r own exp er ience of be ing to ld by th e i r pare n t s tha t they

should eat everything and not be

fussy

abou t the i r food ( a com m on exhor -

tat ion made by parents to their children ). T he phrase p in sihk is at a h ighe r

level of abst ract ion and general izat ion than the descr ipt ion given in the

video. Moreover ,

the

s tudents were also able

to

re la te

th e

s lo th ' s ea t ing

habits

to the

eat ing habits

o f the

panda, something that they

had

learned

about

in the

previou s lesson.

T he phrase

p in

sihk

proposed

by the

s t uden t s

has the fol lowing semant ic features : does not eat meat or f i sh , and eats

only one kind of leaves. There are at least tw o an im al m embers be longing

to

th i s ca tegory : panda s

an d

s loths .

T he

question

is, how

were

the

s tudents able

to

co l labora t ive ly cons t ruc t

such a rich text, both spoken and writ ten? How is i t that the same video

could be const rued in such a sem ant ical ly rich m anne r? How did the teacher

bring this about?

It seems

that there were tw o th ings that the teacher did that were qu i te

crucial .

The first has to do

w i th

the w ay he

varied

the

showing

of the

video

with and

w i th o u t

the

narrat ion.

Variation: Video With and Without Narration.

Wh e n

th e

teach er showed

the video for the f irs t t ime, the narrat ion w as given. B ut whe n he showed

segments of the video, he took away the n arration. The purpose of m ak ing

the video soundless w as, as the teacher told the studen ts, tha t if he pla ye d the

narrat ion as we l l , then there w ould be no thing for the s tu dents to talk about .

In

other

wo rds,

th e

narration

in the first

viewing gave

the

students

an

idea

o f

w hat the s tory w as abo ut . In a way, one c ould say tha t the narrat ion provided

the

context

in

wh ich

the

appearance

and the

m o veme n t

of the

s lo th cou ld

be

interpreted. This is most evident in the description made by one group of

students w ho described the sloth 's eyes as look ing l ike tw o teardrops. Th is

construal w as obvious ly made in l ight of the fact that the sloth h ad lost its

mother and had to struggle for survival.



6 . S E M A N T I C E N R I C H M E N T

O F T H E

S P A CE

O F

L E A R N I N G

1 53

For the second viewing, the narrat ion w as removed in order to allow the

students to interpret what they saw in their own ways. By doing this , the

teacher opened

up the

space

of

learning.

T he

students

were free to

bring

in

their

o w n

experience

and

previous learning

to

make

sense

of

what they

s aw

on the video without being constrained by wha t w as said in the narration.

In

other words, what

the

teacher varied

was the

n arration

and

wha t

he

kept

co nstant w as the visual im ages . B y so doing, the s tudents becam e very

m u c h aw are of the lack of narrat ion, an d the fact th at they ha d to write the

narra t ion

them selves .

In

order

to fulfill the

task, they nee ded

to focus

thei r

at tent ion on the

visua l images , especial ly

the

appearance

and the

mo ve me n t

of the

sloth.

Let

u s im agine that the teacher asked the students to do the same task, bu t

re ta ined the

narrat ion w hen showing

the

video

th e

second time. W hat w ould

have happened? A s the students had been given the task of w riting a narra-

tion of the story, it is likely tha t the structure of their

awareness

would have

changed. What would have come to the fore of their awareness, or wha t

w o u l d

have been f igural , w ould be the narrat ion; wha t the narrator actu al ly

said. T he

actual

appearance and the m ovem ent of the s loth w ould have re-

ceded

to the

ground. What

the

teacher w ould very l ikely have achieved

is

tha t the s tudents wou ld have t ried to regurgitate the narrat ion rather than

c o m i n g up

w i th thei r

ow n

descript ions.

Variat ion:

Teacher-Led D iscuss ion and S tudent -Led D i scus s ion .

R e-

searchers have pointed out that wo rking in groups is natu ral ly con ducive to

making

use of

variation (see W istedt

& Martinsson's

w ork, 1994,

on

inexac t

decimal representation

of the

fraction "one third," cited

in

M arton

&

Booth,

1 997). How ever, this does no t m ean that group work w il l necessarily lead to

successful

learning. W hether succ essful learning

is

achieved

or not

depends

on

whe the r

the

teacher

has

exploited

the

conduciveness

to

variation

in the

group wo rk. Ci t ing the wo rk of Lybeck (1 981) on group w ork ( in wh ich the

t eacher

conf ron ted

the

students with variat ions

in the

concept

o f densi ty

proposed by other students, and put the variat ions und er scru tiny), M arton

(1986) observed that the teacher "funct ioned as the arch i tect of the peda-

gogical mi l ieu,

the

midwi fe

of

experience

and the

sculptor

of

thought"

(cited in M arton & B ooth, 1997, p . 69).

In the lesson on the sloth, the teacher focused the studen ts ' at tention on

th e


o f the

sloth, such

as its

appearance

(which

is

stat ic),

and

its

m ovem ents (w hich

a re

dynam ic). This teacher-led discus sion pro-

vided the

sca f fo ld ing

for the

subsequen t s tudent - led di scuss ion

i n

groups .

The teach er a l so emph as ized the co l labora t ive na ture o f g roup w ork , and

to ld th e

s tudents tha t

i t w as

im por tan t

fo r

them

to pay

at tent ion

to the

con-

t r ibut ions of other group m em bers , to th ink about these con tr ibut ions , and

to

t ry to im prove on them . These are the ins t ruct ions he gave to the s tu-



154

T S U I

dents after

h e had put the

s truc tura l com pon ents

o f the

descr ipt ion

of the

sloth on the board.

6.7

[Chinese Lesson/PS/The Sloth]

T: A fter w atching th e video,

each

group wil l discuss among them-

selves...

. You

have

to

collaborate. D on ' t jus t write

it all by

your-

self. Y ou mu st work together and contr ibute your opinion. You

have to see whether w hat

another

member has said is right or not,

and

whether

it is

good

or

not . Af ter

a

mem ber

has offered a

[de-

scriptive] sentence, you can add you r opinion. L ike, "It w ou ld be

better

to

w rite

it

this

way

...,"

"It

w ould

be better to say it

that

way

. . . ," or "No, I disagree, I saw it [the sloth] making this kind of

movement." and you can give your own account [of what you

saw].

If everybody agrees, then y ou write it down.

B y providing the students with a detailed explanation of w h a t w as ex-

pected of them w hen they engaged in group w ork, the teacher was opening

up the

space

fo r

variat ion

in

discerning

the

c r i t ical features

of the

s lo th .

T he

data from the group discussions show tha t each group was able to bring their

ow n experience to bear on the descript ion, a nd

different

d imens ions of vari-

at ion w ere opened up .

A lthou gh the in i t i a l d i scuss ion w as t eacher- led , the l earn in g space w as

jo in t ly cons t i tu ted by the t eache r and the s tude nts in the sense tha t th e s tu-

dents offered descriptions of the cri t ical features o f appearance, such as

the hea d, the body, the color, and the four l im bs of the s loth , as w el l as it s

mo ve me n t s .

T he teacher also provided scaffolding for the group discussions by re-

m inding s tudents w hich aspects they should

be

focus ing

on in the

course

o f

the

discuss ion.

F o r

exam ple,

he

reminded

the

s tudents tha t they shou ld have

finished discussing the appearance and should be m oving on to the descrip-

t ion o f m ovem ent . A s the s tudents w ere discu ss ing the movem ents , he re-

m inded them of the various m ovem ents they should be descr ib ing, such as

sw im m ing, crawling up the r iver bank, c l imb ing up the t ree, and so on.

Table 6 .1 summarizes the contr ibut ions made by the s tudents in the

teacher-led discussion

and the

student-led discussion

in

four groups

out of

six.

T he

features

in the

s tudent- led discuss ions that were

no t

found

in

teacher-led discussion s are in i tal ics.

When the groups had finished drafting their

descriptions,

the teacher

asked each group

to

present their descript ions

as the

na rrat ion

as he

p layed

the video again. Here the teacher was further w idening the space of varia-

tion

b y

gett ing students

to

listen

to the

descriptions w ritten

by

other grou ps.

T he different

descript ions showed that

different

aspects

of the

sloth were

in

th e

focal awareness

of

each group.



TABLE 6. 1

D escr i p t i on o f t he S lo t h i n Teacher-Led an d S t u d en t -Led D i scu ss i on s

Teacher-Led Discussion

T

M o v e m e n t

Appearance

Colo r

Head:

l ike

m o n k e y ' s

head

Ss

Slow, s lowly

c l i m b i n g

up a tree.

Furry

B r o w n ,

w h i t e

Head very ro und, very

s mal l ,

neck

is

very

long, l i m b s

ar e

very

long

Student-Led Discussion

Gro up

1

Mouth (beak)

— very

f lat,

like a duck,

very shor t

Gro up

2

Very short tai l

Grayish, whi t ish,

brownish and whit ish,

black, brown

Looks l ike a m o n k e y ' s

head , ch icken egg ,

b ig

goose

egg , b ig duck egg ,

big ostrich egg

Gro up

4

Nose: b lack , body: black,

eyes: black

(a s

op p osed

to red) , mouth: f lat ,

protruding,

b lun t

Head

is l ike a

m o n k e y 's ,

head can turn 36 0 degrees

Gro up 5

Face: whi te, eyebrows:

brown, eyes: triangular,

l i ke m onkey

's

eyes , body:

l ike a

hum an be ing , very

small , only half a year

old, like

th e

thigh

of a

baby, l ike a b ig winter

m elon

R o u n d ,

ova l

tn

in

(cont inued on next page)



l/l

Os

TABLE 6. 1 (cont inued)

Teacher-Led Discussion

T

Four

l i m b s ,

f inge r s ,

p a w s

M o v e m e n t :

c r a w l i n g

S w i m m i n g

Diet

&

Paws, c laws, three

s harp

c l a w s

V e r y

s l o w , s lowly

c l i m b s

u p a tree

l o o k i n g

a r o u n d

Student-Led Discussion

Gro up I Gro up 2

Very l o n g ,

especially

th e

claws of

the for

climbs,

th ree c laws

V e r y s l o w , s l o w l y c l i m b s

d o w n

the tree ,

exhausted,

l o o k i n g

a r o u n d

a s

soon

as

i t r e a c h e d

t he

b a n k ,

c l i m b e d

up the

t r ee ,

it

f i na l l y

fo u n d a new h o m e

Free s ty le

Gro up

4

H a n d s

an d

legs

ar e

very

l ong , nai l s are very

pointed

(sharp) , four l imbs are very

l o n g an d sma l l , claws ar e

very long and razor sharp

Puppy

style, frog style

(breast stroke), free style

O nly

eats leaves, l ike

th e

panda, it is pin

sihk (fussy

eater) , does no t ea t meat or

fish

Gro up 5

Eats on ly leaves, any k ind

of

leaves that it likes.

Note . T he fea tures in the s tuden t - led d i s c u s s i o n s tha t

w ere

n ot f o u n d in teache r - led

d i s c u s s i o n s

are given in i t a l i c s .



6.

S E M A N T I C E N R I C H M E N T

OF T H E SPACE O F L E A R N I N G 1 57

L I N G U I S T I C

RESOURCES AN D

SEMANTIC

E N R I C H M E N T

In th is sect ion, we look at the w ay in w h i ch the same object of learning w as

construed semantically in very

different

ways in tw o classroom s because of

the

different l ingu ist ic resources avai lable

to the

teacher

and the

learners,

that is , one of the classes w as taught through the medium o f Chinese, w hich

w as the mother tongue for al l students (CM I), and the other through the me-

dium

of Eng lish, wh ich wa s a second language for all students (EM I).

The history lessons used as examples in this section further i l lustrate

w h a t w e mean by the

seman t ic d imens ion

of the learning space. (For the

background of

these lessons,

see

Tsui , Aldred, M arton, Kan ,

&

Runesson ,

2001.)

The

extracts

are f rom two

secondary Grade

2

(S2) (i.e., Grade

8)

c lass room s in w h i c h the sam e topic w as taught , and il lustra te the

difference

in the sem antic space opened up because of the different linguistic resources

avai lable to the s tudents .

H i s to r y L e s so n s : T h e M a r k e t in Early

Rural

C o m m u n i t i e s

In these tw o history lessons, the objec t of learning was the concept o f

m ar -

ket

in early rural com m unities in Hong Kong. The critical features that dis-

t ingu ish

this market (which perhaps t ranslates more accurately as "fair")

from

the market in modern societies, are the differen t func tions. In i ts his-

tor ical

contex t ,

th e

m arke t

was a

p lace w here people would come both

to

buy produce and to sell their ow n produce, or sometimes even to exchange

goods. The m arket w as also a p lace for social in teract ion, and w as loca ted

in a

particular place that

w as

accessible

to

man y villagers

and

clans. How -

ever, due to poor t ransportat ion markets w ere no t h eld every day but at r egu-

lar intervals.

The

fo l lowing

is an

excerpt

from

the EMI

lesson

in

w h ic h

th e

teacher

tried to elicit from the students the critical fe atures of the m arket in its his-

tor ical

con tex t .

6.8

[History Lesson/S2/EM I]

1

T : Do you think th e m arket at that time is the same as you[ V e ] go t n o w?

2

Ss: No.

3 T: How

[was

it]

d i f fe ren t?

4 Ss: [silent]

5 T:

H u h ?

6 Ss: [silent]

7 T: How [was it] different? Can you imagine? In the past,

market

[writing

8 the word "market" on the board]. Y ou[ Ve] got a m arket, there,

isn't

it?



158

T S U I

9 Is it a market there? [Points to the market next to the school. ] Have you

10

been there?

11 S:

Yes.

12 T:

Yes.

But in the

past

we

call[ed]

it

heui. (Cantonese)

[ ̂ ]

[Writes

the

13 Chinese

character heui (Cantonese) [J^]

on the

blackboard.] Chan

14 heui.

(Cantonese) [ ̂ ̂ ] And then at hat time people going to

15 market, we call[ed] it chan heui.

16 Ss: [laughter]

17

T: [writes the words chan heui (Cantonese) [ ̂ 4sj|

]on

the blackboard]

18 And then what does it mean? At that time the people—you find out that

19 for the

market ...?

20 S: [silent]

21 T: The market opens every day? Is it? There? [Pointing at the market outside

22 the

window]

23 Ss: Yes.

24 T: But at that time the market [did] not open every day. They

w i ll

fix some

2 5 day, for example,

for

each month, [on the] fifteen[th] and thirtieth], they

2 6 will have [the] market. And then people go there, and then to sell...

w h a t

2 7

they produce.

For

example,

you

look

at

him,

he

go[es] there

to

sell

his

pigs

2 8 and cocks, and at the same time by making money he can buy something

29

that

he d id not

produce

by

himself. Understand?

So i t is

dif ferent

from

3 0 your market, isn't it? And at the same time, at

that

time the market has a

31

function. First

of

all,

it is

selling

and at

same

t ime you buy

something.

A nd

32

also

you f ind out

that,

in the

second paragraph, what

did he

say?

33 [referring to the diary of Tang Tai Man.]

34 Ss: [silent]

35 T:

What

did he

say?

36 Ss:

[silent]

37 T: What did he say?

38 Ss:

[silent]

39 T: Huh? [Nominate], what did he say in the second paragraph?

45 S: [reading from the second paragraph of the diary of Tang Tai Man]



6. S E M A N T I C E N R I C H M E N T O F T H E S P A C E O F L E A R N I N G 1 59

46

"Today

I

also

met my f r iends

coming

f rom another village, we

47

chat[ted]."

48 T: Okay,

okay,

so what

did,

what

did he do in the

second paragraph?

49 S: [silent]

50 T:

What

is happening to

him?

51 S: He met his f r iends.

52 T: He met his

f r iends.

Okay, sit

down.

You

f ound

out

tha t then,

for the

5 3 market at that time, it also provides a chance for them to meet their

5 4

f r i ends . . . .

You

found

out

that

at

that

time [there

was]

no

transport,

you

5 5 can

only

?

56 S:

Walk.

57 T:

Walk.

Then sometimes it is

difficult

for you to find

your

friends, is it? So

58 the market provide[d] a place for them to

meet

their friends.... You think

59

about now,

is it

very easy

for you to see

your friends?

60 T: ... So you find out that here this is the function of the m arket [referring to

61 the

handou t ]

...

Here the t eacher w as t rying to br ing ou t the difference s be tween the mar -

ket in the past an d the m arket in the present, and its funct ions in early ru ral

c o m m u n i t i e s

in Hong Kong . S he started w ith a n open quest ion of how the

m arket in the old days w as different from the m arket nowadays (see l ine 3,

"How [was

it] different?").

W h e n

she failed to get an

answer ,

s he

na r rowed

down the question to specific features. First , she tried to draw on the stu-

dents ' m other tongue resources by invoking the exp ress ion chan heui ( Ca n -

tonese) [^^],

an

expression that

all

students were familiar with

as

evi-

denced by the l aughter . S he asked them to extrapolate one of the fea tures of

the m arket from

the

m eaning

of

this expression. (The word chan (Canton-

ese) [^ ] m e a ns to take the opportunity, and he word

heui

(Cantonese) [ ̂ ]

w as

used

by the

teacher

as an

equivalent

of the

market

in the

past . T herefore,

chan heui imp l ies tha t the market was not open every day, and t ha t w hen it

w as, people took the oppo rtunity to get what they wanted from the m arket .)

This

t e c h n i qu e

did n ot

m ee t w i th m uch succes s because unpack ing

a

Ch i -

nese expression in E ngl ish was far too difficult for the students. Failing to

get a response , the teacher s im ply pointed o u t tha t un l ike the m arke t nex t to

their school, m arkets in the old days were not open every day.

Af ter dea l ing wi th the first cr i t ical feature, the t eache r w en t on in the

same turn

to

provide

the

second critical feature

of the

m arket: U nl ike today,

peop le w e n t

to the

m arket

n o t

only

to

sel l their pro duc e

or to buy

som eth ing

they needed, but to do both at once. From lines 32 to 58, the teach er tried to



160

T S U I

elicit

a

third critical fea ture

of the

m arket

f rom the

s tudents ,

by

ask ing them

to

look

at the second paragraph of the diary that she had been referr ing to

earlier. One of the s tudents , after s t ruggl ing w i th th e t each er ' s ins t ruc t ions ,

sim ply read

out the

second paragraph instead

of

inferring

from

th e

t ex t w hat

the th i rd cr i t ical feature wa s, as the t eacher h ad w a n t e d. A l th o u g h the stu-

dent w as able to provide an appropriate answer

after

several prompts from

the teache r (see l ine 51 ) , the conn ect ion be tw een w hat appeared in the t ex t

and the third cri t ical feature of the m arket ( i .e ., that the m arke t p rov ided a

place for people to meet thei r f r iends) had to be m ade by the teache r . The

connect ion between the funct ion of the ma r k e t fo r soc ia l in terac t ion and

poor t ransp ortat ion w as also made by the teache r .

W e

can see in the

ju s t c i ted excerpt that

th e

teach er tried

to

focus

the

s tu-

dents ' at tention on the cr i t ica l fea tures of the m a r ke t in old r u ra l c o m m u n i -

ties

by

varying

the

contex t s

of

pas t

and

p resen t . However , because

of the

s tudents ' l im i ted l in gu is t ic resources in En gl ish , the teache r h ad p rob lem s

engaging the s tudents in m ak ing s ense of the contex t s in w h ich t hese f ea -

tures were to be understood.

Let us compare this lesson wi th an excerpt below f rom a CMI lesson,

where the same concepts were being explicated.

6.9

[History Lesson/S2/CM I]

[The teacher asks the students to identify on the m ap place s that con-

tain the word

heui

(C antonese) [

̂ ]

[standing for "market."] The n he

con t inues to ask the s tudents the

funct ions

of a "market."]

1 T : Nex t I wan t to ask you , what are the funct ions o f a heui?

2 S :

[cheeki ly]

N o

use .

3 T :

W h a t? W h a t

are the funct ions

of

heui . H as

anybody heard

the

4 saying "Three, w ha t , make a

heui?"

5 Ss: Three w om en

6 T : Wha t does that m ean? N ow w e a re not discriminating against fe-

7 ma l e

students.

W e are not saying that female

students

are talkative. So

8 what is the function [of a

heui]?

In fact, how can three people m ake

9 a

heui? W h at

is the

characterist ic

of a

heui?

10

S:

V ery noisv.

11 T :

V ery noisy. M aybe

w e

should

not use

[ the w ord] noisy.

12

S:

Busy .

13 T : Busy A lot of fun . Other than this? W hat else?

14

S : Lots of th ings for sale.

15

T :

W h a t funct ion does

th e

m arket have?



6 . S E M A N T I C E N R I C H M E N T O F T HE

S P A C E

O F

L E A R N I N G _

16 S: Transact ions .

17

Co nducting transactions, that's right. W hat kinds of things

for

us to

18 T: buy? In earlier

societies?

19 S: Jewelry.

20 T: Jewelry . A nything else?

21

22 T : That is, the market has the

function

of [conducting] transactions.

23 Where is it?

24 S: "Open air

n ightclub"

3

25

T :

"Open

air

nightclub

."That's

right . U sua lly

it is on a

piece

of

flat

2 6 land. W hereabouts? Is it near the village? Inside th e village ? N o.

27 Usual ly . . . c an you

imagine?

28 S: N e a r the vi l lage s .

29

T :

H m m ,

any

other suggestions?

30

S: Where there are lots of people.

31 T: W here there are lo ts of peo ple. An y other suggest ions?

32 S :

W here lo ts

of

people

can get to it.

33 T: W here lots of people can get to it. Is it a

place

only where people

34

w i th the surname "Tang" can go?

35

S: No.

36 T: The place is a piece of flat land where u sually other villagers can get

37 to as w ell . That is where th e m arket was loca ted. A lso, in the old

3

8 days, there w ere no buses, no subw ay, so it w asn 't so conven ient.

39 So w ou ld there be a m arket every day? W ould people go to

40 the

m arket every day?

41 S: No.

42 T: That seldom happen ed. U sua lly there was a

fixed

t im e, usual ly

43

several t im es a m on th, or once a w eek. B esides being a place

44 for co nd uc ting transactions, w hat other function did it have?

45

Jus t

n o w w e

said that three w om en m ake

a

m arket,

very

busy,

46

[people] cha t t ing

to

each other . W hat funct ion

[of the

m arket]

47 can you

deduce

from this? A h,

"You come from

the

nearby

48 vil lage , how is so and so?"

49 S: So cial interaction activit ies.

50 T : W hat kind of funct ion did it have?



1 6 2 TSUI

51 S : Social

interaction activities.

52

T: That's right. Yo u are

correct.

It

actually

had a

kind

of

interactive

5

3

function,

the

interaction between villages, am ong people

from

54 differen t clans.

W e

can see from this excerpt that in the CMI c lassroom, the lea rn ing

space in wh ich the features of the market w as understood w as jo in t ly con s t i-

tuted by the

teacher

and the students. I t was

also

semant ical ly m uch richer

than that const i tuted in the E M I c lassroom.

Firstly,

by a l luding to the C hinese co l loquia l expression, "Three w o m e n

make

a

m arket,"

the

teacher

w as

im m ediate ly able

to g et the

students

to as-

sociate

th e expression

wi th

"very noisy" and "busy"

(l ines

10 and

12).

W hen he asked the s tudents w here the market w ou ld no rm ally be located,

they used the ana logy "open-air n igh tclu b" (l ine 24). (The

"open

a ir n igh t -

club" was a large , w el l-kno w n, open-air nig ht m arket in Hong Kong , that

besides

having

a

variety

of

things

for

sale, also

had

entertainment shows,

fortune-telling,

and

haw ker stalls. People w ent there

no t

j u s t

to buy and

sell

things, but

also

to

have

a

good t im e.)

The

teacher p icked

up on the

s tuden t 's

analogy (l ine 25) and further developed the topic by involv ing s tudents in

exploring the locat ions of markets . Again draw ing on s tudents ' kn ow ledge

of the expression, "three

women m ake

a

m arket,"

th e

teach er solicited

from

the students that another cri t ical feature of the m arket was its funct ion for

social

interaction (l ine 49).

Here we can see that the rich l ing uistic resources of the m other tongu e en-

abled

th e

teacher

and the

students

to

collaboratively construe

a rich

picture

of

the

m arket w ith

a

n u m b e r

of

seman t ic features:

for

exam ple , noisy, busy, joy -

ous; w ith lots of activities going on; buying and sell ing; people from

different

villages and

clans meeting

up and

making

friends;

people performing

and

watching entertainment shows. Going

to the

m arket

(chan heui) was a

social

event that

took

place at regu lar intervals rather than every day because of the

lack o f transp ortation. W e can also see that the s tudents ' understanding of the

market

w as

m uch m ore sophist ica ted

due to the use of

their m other tongu e.

For example, the concept of

social interact ion

is m uch m ore sophistica ted

than jus t

"meeting

friends" and

"entertainment,"

and the concept of t ransac-

tion is mu ch m ore sophisticated than "buying and sell ing."

The

fo l lowing tab le sum m arizes

the

semant ic features

of the

m a rk et

in

the two lessons (see Table 6.2).

C O N C L U S I O N

In

this chapter, w e have looked at another very important aspect of the

learning space, that

is , the wa y in

w hich

the

object

of

learning

(in the sense

of the l ived object of learning) is construed by the learners when they are



6 . S E M A N T I C E N R I C H M E N T O F T H E S P A C E O F

L E A R N I N G

1 6 3

TABLE 6.2

Features

of the

M a r ket

in C M I a n d E M I

Lessons

EM I

Lesson

Funct ions o f marke t

•

S e l l i ng as

w e l l

a s

b u y i n g

• M e e t in g f r iends ( b e c a u s e o f poor

t r anspor t a t ion)

Opening

N o t open

da i ly

( n o r ea sons

g iven)

Funct ions o f marke t

•

Tran sac t ions ( f ood and o t h e r

t h i ngs )

• Soc ia l in teract ion be tween v i l lage s and c l ans .

Imagery

" T h re e w o m e n m a k e

a

m a r k e t"

( to

d ed uce

func t ions )—noisy ,

busy ,

a lot of

activit ies,

j o y o u s

socia l in teract ion .

Analogy

"Open a ir

n ig h t c l u b"— bu y in g

and

se l l i ng , f ood ,

en t e r t a i n m en t show s , hav ing a good tim e .

Locat ion

Access ib le to peop le from

d i f fe rent

clans and

vi l l ages .

Opening

N ot open

da i ly ;

poor t r anspor t a t ion , no t

e n o u g h

goods and p rod uce for sa le .

able to bring in their ow n experiences, their ow n culture, their fo rm er learn-

ing,

fo lk lore ,

and so

for th .

W e

referred

to

this aspect

o f the

learning sp ace

as

th e

sem antic

dim ension

of the

space

o f learning, a nd

proposed that this

s e-

mant i c

dimens ion

is

elas t ic, that

is ,

that

it can be

enriched

or

impoverished.

W e

i l lus t rated

how the

teacher enriched

th e

semant ic dimension

of the

space of learning by help ing learners to perceive the interre lat ionsh ip of as-

pec ts of the pheno m enon that were hi therto perceived as unrelated. B y in-

t roducing

n ew

semant ic dom ains

or

d ifferen t levels

of

knowledge

in

w h ich

the

phenomenon

can be

con st rued,

the

teacher enriched

the

learning space

semantical ly. W e have also illustrated how the learners themselves en-

r iched the learning space sem ant ical ly by br inging their ow n experiences to

bear o n the object of learning, and how they can thus col laborat ively con-

struct and ass ign new m eanings to the object of learning. Th e w ay in w hich

the

semant ic dimension of the learning space is enriched and thus helps

learners exp erience

the

object

of

learning

in a

certain

w ay in

each lesson

is

an instan tiat ion that wil l eventually lead to the en larging o f the sem antic po-

tential in w hich the object of learning is being construed. Finally, by com-

paring

the

di f ferences

in

semant ic

richness of

const rual

of the

object

of

l ea r n ing—in

c lasses w here learners have the necessary l ingu is t ic resources



164 T S U I

(mother tongue

medium), and

classes

in which they do not (second lan-

guage

medium)—we have illustrated the way in which language plays a

central

role

in the semantic enrichment of the space of learning.

E N D N O T E S

'The writ ten texts produced by the s tuden ts were in M odern S tandard Chinese .

The translations of the texts presented here are semantic translations but the syn-

tact ic s t ructures of the texts have been re ta in ed as far as poss ib le .

2

In

th is volume, characters and words spoken in C a n t o n e s e a re t ranscr ibed in

the Yale system, w h ich is

used

by some Can tonese-learning m ater ia ls produced by

the Ya le U nivers i ty , and by The U nivers i ty o f Hong K ong in it s C an ton ese-En g-

lish,

English-Cantonese

dic t iona r ies . (N ote that diacr i t ics that are used to indic ate

Cantonese

tones have been

left

out . These diacri t ics are very

di ff icul t ,

if at all pos-

s ible , to produce us ing Word, and some research repor ts us ing the Yale sy s t em

simply

do not

include

the

diacr i t ics .)

3

"Open

a ir nightclub" is the name given to a large , wel l-known, open-air n ight

m a rke t in Hong Kong . It does no t ex i s t anym ore in its o r i g ina l f o rm .



T h e S h a r e d S p a c e o f e a r n i n g

A m y B . M .

T s u i

M ar to n an d B o o th ( 1997) ex p o u n ded th e qu a l i t a t ive ly

d i f ferent

w a y s i n

w h i c h

lea rn ing c a n b e exper ienced : T h e learner m a y f o cu s l a rg e ly on the

situation in

w h i ch

the

p h e n o m e n o n

is

e m b e d de d ,

or on the

phenomenon

as

it

is revea led in the s i tuat io n ( see p . 83) . The y o bserved tha t the asp ec ts of

the

p h e n o m e n o n

and the

re l a t i o n sh ip s be tw een th em th a t

a re

d iscerned

a n d

he ld in aw ar en es s s imu l t an eo u s ly de t e r min e th e w ay th e p h en o men o n i s

ex p e r i en ced

by the

in d iv idua l . Therefo re

th e

s am e p h e n o m e n o n

m a y b e e x -

p e r i en ced in qu a l i t a t ive ly d i f ferent w ay s by in d iv idu a l s becau se th e a sp ec t s

and the r e la t ions h ips tha t they d iscern m ay be di f fe rent , and w hat i s he ld in

a w a r e n e s s s i m u l t a n e o u s l y

m a y

a lso

b e

di f fe rent . Wh en th i s h ap p en s ,

th e

l ived o b jec t o f lea rn ing w i l l be

d i f ferent

from the enac ted ob je c t o f

l e a r n i n g .

To b r in g abo u t s uc c e s s f u l lea rn ing , it i s necessary tha t the teac her and the

learner share

a

l a rg e co mm o n g r o u n d

in

r e la t ion

to the

o b j ec t

o f

l e a r n i n g .

T h e

task befo re

th e

teache r , therefo re ,

is

th reefo ld . F i r s t ,

th e

t each e r

s h o u l d

en su r e th a t

the

co n d i t i o n s

a re

there

for the

lea rner

to be

ab le

to

d iscern

an d

s i m u l t a n e o u s l y ho ld in awa reness the c r i t i ca l aspec ts o f the ob jec t o f lea rn -

i n g , and the r e la t ionsh ips be tween these aspec ts . Secondly , th e t e a c h e r

sh o u l d

b e

aware

of the

lea rner ' s exper ience

of the

o b j e c t

o f

l ea r n in g ( s ee

a lso Ale xan dersso n , 1994), and be v ig i lan t o f s igna ls from learner s

i nd i c a t -

ing a

lack

o f

co m m o n g r o u n d . Th i r dly ,

th e

t each e r sh o u ld

t ry to

w i de n

th e

s h a r e d c o m m o n g r o u n d .

These

th r ee ta sk s can n o t

b e

ach ieved in dep en d-

e n t l y

o f each o ther ; they a re in te r twined .

W hat does a l l th i s m ean to the p rac t i tioner , and how

r

i s th i s th reefo ld t a sk

r ea l ized

in

c lass room discourse? Befo re

w e

p roceed

to

address th i s que s-

t ion , w e

n eed

to

h ave so me u n de r s t an d in g

o f

w h a t

is

in vo lved w h en

t wo o r

m o r e p eo p le

a re

en g ag ed

in a

d iscourse

o f

some sor t .

1 6 5



166

T S U I

D I S C O U R S E A N D C O M M O N G R O U N D

When

two or

more people engage

in a

discourse

o f

some sort , they bring

w ith them a set of assum ptions that they bel ieve are shared between them .

There

are cer tain assumptions that per tain to communicat ion in general .

For exam ple, tha t these people speak the same langua ge, that they a re aware

of and observe s im i lar convent ions regarding discourse rules , tha t ne i ther

of them have speech and/or hearing im pairm ents, and so on. These assum p-

tions pertain to the channel o f com m unica t ion and not to a specific ut ter-

ance under discussion.

There a re

a l so assu m pt ions tha t

are

more specif ic

to

the com m unicat ive s i tuat ion. For exam ple, w hen w e talk to a co l league , we

assume that they have shared knowledge about people

and

events

in the

workplace that a re relevant to the day- to-day op erat ion, the l ines of respon-

s ib i li ty , and so on. However, e xac t ly how m uc h kno w ledge we share is not

known unt i l

w e

actu al ly enter in to

a

di scourse .

Le t us

take

the

fol lowing

piece

o f

conversa t ion—which

is

fabricated

bu t

w h i ch typ ica l ly occurs—

between two col leagues , A and B, for exam ple:

7.1

1

A: So the

meeting's been changed

to

Friday?

2 B : W hat m eet ing?

3 A: The departmental meet ing.

4 B : Oh, I

thought

i t w as

canceled.

5 A : A pparent ly not .

6 B: I don ' t know. A sk R ebecca. S he would know.

7 A: OK. Thanks.

When A asked B

w hether

the m eeting had

been

changed to Friday (line

1 ), A had cer tain assum ptions . A assumed that , f irs t, B knew w ha t m eet ing

A wa s

referring

to ;

second,

B

knew that

the

date

of the

m ee t ing

had

been

changed; third, i t was l ikely that B would be able to provide the answer.

However, A c ould not be abso lutely sure that these assum ptions were shared

unti l

B

responded.

B 's

response (l ine

2)

indica ted that

A 's

assump tion

w as

not shared, and

that

B did not

know w hich sp ecific m eeting

A w a s

referring

to. Bruner (1987) pointed out that reference typically "plays upon the

shared presupp osit ions and the shared con texts of speakers" (p. 87). A 's ref -

erence to the meet ing involved mapping A 's

subjective

sphere onto B's .

Upon hearing B's question, "What meeting?" ( l ine 2) , A real ized that th is

f irst assum ption wa s in

fact

not shared by B. A then im m ediately clarified

th e referent, that is, "the

meeting,"

by explici tly identifyin g it as "the depart-

menta l

meeting"

(line 3). B's response to A's clarif icat ion ( l ine 4 ) showed

that A's second assumption that the meet ing had been changed was not



7.

T H E S H A R E D S P A C E O F L E A R N I N G 1 67

shared, an d A 's subsequent response showed that B 's assumption that it had

been canceled

w as no t

shared

either

(line

5).

Finally,

B 's response

showed

that A's

first

assumption ( that B might know the answer) was not shared

( l ine

6) . B directed A to another col league, R ebecca. B 's assumption w as

that A

knew

w ho

Rebecca w as ,

and

that there

w as a reason for

directing

the

question

to

Rebecca .

This

assum ption

w as

indeed shared,

an d A

thanked

B

fo r the redirection ( l ine 7).

A t the end of the

exchange ,

the

comm on ground be tween

A and B had

widened .

There w as more shared knowledge between them now than be-

fore. An y kind of discourse is a process of w idening the comm on ground be-

tween part ic ipants ,

and

this

is one of the

m ajor m ot iva t ions

fo r

people

to

talk

to

each other. Discourse is therefore a

process

in which m eanings are nego-

t iated and disam biguated, as w el l as a process in w hich comm on grounds

are

e s tabl ished

and

w idened (see Tsui , 1994).

CLASSROOM

D ISCOURSE

AN D E S T A B L I S H I N G

C O M M O N G RO U N D

In classroom discourse, there are also cer tain shared assum ptions betw een

the

t eacher

and the

students.

For

exam ple, there

are

shared assum ptions that

students

should

fol low the

teacher ' s ins t ruct ion, that they should answer

que stions wh en c alled on to do so, and so on. These pertain to the general

classroom protocols that

differ from

cul ture

to

cu l ture; cul ture

in the

sense

of ethnic cul ture

as

w e l l

as

social class culture .

For

example,

in

m any A s ian

classroom s, the protocol requires that s tudents s tand up when they answ er

the

teache r ' s quest ions because

the

t eacher

is a

f igure

o f

authori ty.

In

class-

rooms where middle-class cul ture predominates , working-class chi ldren

are ser iously disadvantaged because they do not share the same assump-

t ions as

m iddle-class chi ldren. Classroom social izat ion

a nd

a ccu l tu ra t ion

are

im portant aspects

o f

classroom learning,

but in

th i s vo lum e,

we a re not

par t icular ly concerned wi th the shared common ground in this respect . W e

are

more concerned wi th

the

aspects

of

comm on ground tha t

are

pert inent

to

the

object

of

learning.

There are also assum ptions that the teacher an d the learners hold that are

specific to the

ob jec t

of

learning.

It is not

u n c o mmo n

for the

teacher

to be

w orkin g on certain assum ptions that are not shared by the students, or vice

versa .

W hen this happen s , the abi l ity of the teacher to negot iate and w iden

the

comm on ground be tween h imsel f

an d the

students

is

cri t ical

to

effective

learning.

Let us

take

as an

example some data

from a

pr im ary Grade

4

(P4) Eng l ish

lesson on "The W eekly Plan." (For the backgroun d of this lesson a nd other

asp ects of this lesson, see Lo & Ko, 2002.). Let us cal l this class, C lass A.

The intende d object of learning in this lesson is the use of the sim ple present

tense to indicate hab itual act ion. Th e teacher, Teacher A , presented a diary



168 T S U I

of Mickey Mouse tha t shows tha t he does

d i f ferent

act ivi t ies on different

days of the week . H e also does some of the act ivi t ies fo r m ore than one day.

After

get t ing the s tudents to focu s on "How

of ten

does he do (ac tivity)?," the

teacher wanted to

focus

on the tense used.

7.2 [English Lesson/P4A/Weekly Plan]

30 T: . . . he

goes

to the

l ib ra ry only one ,

one

t im e ,

O K ? O n e

t im e ,

31 OK? So we say once a week . Bu t why [do] w e add "-es" at

32

the end of the word "go?" [Teacher po int in g at the "-es"

33 ending on the bo ard.] Can you tell m e? [S s pu t up their

34

han ds.] Yes?

35

S 8: B e c a u s e he, she, it.

36 T:

Yes,

h e.

she,

it. but

w h a t

is

l inked

to the

tense?

T he

verb

...

37 the form of the verb? Sam uel?

38 S9: Present tense.

39 T: Present tense . W hat kin d of present tense? Sim ple—

40 Ss: Sim ple present tense .

41 T : W hy [do we use] "simple present tense?" W h y? W h y do

42 you think it is about simple present tense? B ecause it is

43 abou t _?

44 S1 0: [sit t ing in her seat] He do af ter school .

45 T: [po inting at S1 0] Yes?

46 S10: B ecause it is about ... he do

af ter

school .

47 T:

Yeah ,

it is

abou t

the

th ings ,

OK, he ,

M i ck e y M o u s e ,

he

48 M ickey M ouse, do [does] the thin gs af ter school . W e are

49 te l l ing people about h is hab i t . OK ?

From the studen t 's response in line 35 in the aforem ention ed excerpt, we

can see that w hat came to the fore of this studen t 's aw areness on hearing the

question, "Why [do]

we add

'-es'

at the end of the

word 'go'?"

i s

"subject-

verb agreement."

It is a

pe rfectly appropriate response

to the teacher's

ques-

tion. How ever, i t w as not w hat the teacher w as loo king for. This is evidenced

by the teacher accepting the answer bu t continu ing w ith the disjunct ive

"but,"

which is typical o f disagreement . T he answer

that

the teacher was looking fo r

w as "simple present tense" (see line 40). In fact it is both the third person sin-

gular

and the

simple present tense that necessitate

th e

inflection

of the

verb

"go." If the subject were the first or second person, there w ou ld have been n o

need

for the

inflection even

if the

verb w ere

in the

simple present tense.

A s the

discourse un folds, w e can see that the teacher was ena cting a script in w hi ch



THE SHARED

SPACE

OF LEARNING 69

th e

teache r 's focal aw areness

w as

very m uch

on the use o f the

sim ple present

tense in describing h abitual action (see line 49), and not subject-verb agree-

m ent . The

latter, however,

w as

very much

in the

student's focal awareness

when

they answered the question. The teacher, being unaw are of how the stu-

dents were experiencing the object of learning, dismissed valuable contribu-

t ions from the

students

as

irrelevant.

L et us consider another example taken from the physics lesson on the

reed relay repo rted in chapters 1 and 5, and se e the difference tha t w as m a de

by

a teacher who shared a large comm on ground w i th the s tudents . In the

lesson

on the

reed relay, after

the

s tudents conducted

the

second experime nt

( in w hich the teacher asked the s tudents to connect a m otor to both the s im-

p le

ci rcu i t [w i thout

a

reed relay ]

and the

com plicated ci rcui t [w i th

a

reed

r e -

lay]) ,

the

teacher explained

the

different outcomes observed

in the

s imple

circui ts in the two experiments .

1

First, she explained why the m o to r did not

rotate in the

s im ple c i rcu i t w i thout

a

reed relay. Then

she

w e n t

on to

expla in

wh y the LED l it up in th is c i rcu i t .

L et us examine the fol low ing extract:

7.3

[Phys ics Lesson/S2/CM I]

1

T :

. . . W h y

is it

that

it

[the LE D] works

in

this circuit? [po inting

at

2 the s im ple ci rcu i t w i th the LED] W hy was i t so w el l-behaved?

3

W hy did i t

[LED] l ight

up?

[nominate]

4 S :

Because

the

resistance that

th e

LD Rneeds,

no , the

current

that it

5

needs

is

smaller than [that needed]

by the

m otor.

6 T: Sav that once again , you are nght. I unders tand you .

7

S : LDR needs

8

T : Wh i c h is the L D R ?

This

one?

9 S :

Because

the

electric that

L E D

needs compared

...

10 T:

Elect r ic w hat?

11 S : Electric curren t is smal ler compared wi th the motor .

12

T : That's right. S o if I press i t [the push b utton sw itch] here, there

13 w i l l be enoug h current to make this LE D glow. OK? N o w , w e

14 found that

if w e

don 't

u se the

reed relay

[in the

circuit w i th

a

15

m otor], then there

are

problems because some circuits m ust

use a

1 6 reed relay

to

operate.

L e t me

give

you an

example

.. .

In

this excerpt , the teacher asked an open "w hy-quest ion" that required

the

s tudents

to

explain

why the

s imple ci rcui t connected wi th

an LED

w orked (see Fig. 2a in chap. 5). Th e stude nt w as trying to construe the ex pe-

r ience gained from the experiments and present it to the teacher . She was



170 TSUI

trying to relate the

reason

fo r the device lighting u p with th e size of the cur-

rent

that

was

needed

by the two devices

(the motor

and the

LED).

In

line

4,

we can see the

student struggling with this because although

she was

aware

of the

fact that

the

size

of the

electric

current needed

by the

motor

was

bigger

than that needed

by the

device that

l i t up

(LED),

she had

erroneously labeled

the LED as LDR, and had misrepresented electric current as resistance (see

lines

4 and 7). It is

clear that

the

student

had

some problems

in

construing

what she had experienced in the experiment through a m ean ingfu l l ingu is t ic

representation. The teacher, instead of

d i smiss ing

the student's contribution

as wrong, understood that the student w as formulating he r thoughts as she

went along. S he assured the student that she understood what she was trying

to say and

encouraged

he r to

represent

her

construal

of the

experience once

again.

As

soon

as the

teacher pointed

at the

diagrams

on the

board, where

the labels fo r the devices were given, the student realized tha t what she had

thought was an LDR was in fact an LED, and she corrected herself. The

teacher

further

helped the student to represent he r construal in more precise

terms by getting her to revise "electric" to "electric current. In contrast to

the previous classroom excerpt, (7.2), th e common ground shared by the

teacher

and the students was much larger. As a result, the student was able to

construe

h er

experience

in a mean in g f u l w ay and to

make

a va lu ab le

contri-

bution

to the

discussion.

STRUCTURE OF W RENESS

AND THE

SH RED SPACE

OF

LEARNING

T o

further elucidate

the

notion

of the

shared space

o f

learning,

let us

con-

sider

the notion o f structure o f awareness that w as discussed in chapter 1 .

W e

argued that

awareness

is the

totality

o f

experience,

and

th a t

characteris-

tically only

a

limited number

of

things come

to the fore of our

awareness

and the rest recedes to the ground. Marton and Booth (1997) referred to this

structure as figure-ground. However, what comes to the fore of

one's

awareness varies. When the teacher and the learners, fo r various reasons,

are working on d i f ferent assumptions, their structure of awareness m a y b e

dif ferent .

What is figura l to the teacher m a y b e ground to the learners, a nd

vice versa; equally, what

is f igura l to

some learners

m a y b e

ground

to

oth-

ers. When this mismatch occurs,

we say

that

the

space

o f

learning

is not

shared, or only partly shared.

L et us

compare data

from

Class

A

(the English lesson

on

The Weekly

Plan"

cited before) a nd another primary Grade 4 lesson on the same topic,

with exactly the same intended object of learning. Let us call the latter, Class

B. In

Class

A, the

teacher

put up o n the

board

the

diary

o f

Mickey Mouse

that

says

what he

does

from Sunday to Saturday. Above the schedule is the

question, What does

he do

after school? (see Table 7.1)



7. T H E

S H A R E D

SPACE O F L E A R N I N G 1 71

T A B L E

7 .1

English Lesson/Weekly Plan/Primary Grade 4/Class A

White Board Description

Mickey Mouse s Picture Wh at Does H e D o After School?

Su n d ay

M o n d a y

Tuesday

W e d n e s d a y

T h u r s d a y

F r i d ay

S a t u r da y

Library

P i an o Lesson

B a ske t b a l l

S w i m m i n g

Baske tba l l

S w i m m i n g

Baske tba l l

T he fo l lowing is an

excerpt

from

Class

A, f rom the

point

in the

lesson

wh en the teacher directed th e students' attention t o Mickey Mouse's diary

on the

board.

7.4

[English lesson/P4/Weekly Plan/Class A ]

12 T: ... So let us

look

at his

[Mickey Mouse's] diary,

O K?

What does

13

he do after

school?

OK.

[Teacher

points at the

diary

on the

14

board.] This

is the

thing that

he

does

af ter

school.

O K ,

what

15 does he do af ter school? [Teacher puts a strip o f paper with

16

question What does

he do

after

school?

on the

board.]

C an

1 7 you tell m e, What does he do after school? Anybody?

18

[Students raise their hands]. Yes.

19

S2: He

goes

to the

library

on

Sunday.

20

T : Yes, h e goes to the library on ?

21 S :

Sunday

22 T : Sunday. Yes, after school. OK? He says he goes to the library

23 after school.

"After school."

OK, how about... What

else?

How

24 about others?

25

[Students raise their hands.

The

teacher looks

at one of the

26

students signaling

to her to

answer

the

question.]

27

S3 : He has a piano lesson on Monday.

28 T:

Yes.

We

sav—we

don't say "on Monday" first. OK? The



172

T S U I

29 quest ion is "What does he do af ter school?" So he says that he

30

has a piano lesson af ter ? School .

31 Ss+T: S ch oo l

32 T: OK. Do you

unders tand?

33

Ss: Yes.

34 T: Yes, OK . How about th e other th ings? W hat does he do a f t e r

35 school? W hat else? [Stu dents raise their ha nds .]

36 S4: He

p lay basketba l l af ter school .

37 T:

Yeah ,

he

says

he

p l ay s baske tba l l

af ter ...

38 Ss+T: S ch oo l.

39 T : "Plays,"

[stressing

the "s"

sound ]

O K ?

Remember "p lays ,"

40 OK? W hat e lse? O n e mor e th ing . Sa m ue l?

41 S5 : He . . . he p lay s basketba l l on . . .

af ter

. . . ?

42 Ss+T: S ch oo l.

Here we see tha t when the s tudents were asked to descr ibe Mickey

M ou se 's d iary , they provided the act iv i ty and the day of the wee k (see l ines

1 9 and

27) . However , what

the

t eacher wan ted

to

e l ic i t

from the

s t u d e n t s

was wh a t M ickey M ouse does

af ter

school (see the teacher 's correct ion of

the

s tudents ' answers

in

l ines

22 to 23, and

l ines

28 to

30).

I t wa s

on ly

af ter

the

teacher m ade

it

c lear

to the

s tudents tha t they sho uld

not say the day of

the week ( l ine 28), tha t the s tude nts produced w ha t the teac her con sidered to

be the correct answ er ( l ine 36) .

W h a t

w as

h a p p e n i n g

in

th i s p iece

o f

d i scou r se?

H o w

m u c h c o m m o n

gr ound

w as

shared be tween

th e

t eacher

and the

s t u d e n t s? W h e n

th e

s tu -

d en t s p r od uced

th e "correct"

r esponse ,

in

w h a t

w a y w a s t h e

c o m m o n

gr ound w id ened ? Was th i s common g r ound pe r t inen t t o t he ob j ec t o f

l ea r n ing of the l e s son?

To unders tand the m ism atch be tween the s tudents ' answe rs and w hat the

teacher wanted to sol ici t

from

them , we need to see the i tem s on the w hi te

board as an integral par t of the s i tuat ion in w hic h the phen om ena of hab i tua l

act ion and

f req uenc y

are

em bed d ed.

On the w

r

hite

board were

the

fo l lowing

i tem s : M ickey Mouse ' s p i c tu r e ,

th e

d ia ry s t a t i ng w ha t M icke y M ouse

did

each

day of the

w e e k ,

an d the

ques t ion "W hat does

he do

af ter

school?"

T o-

gether they con s t i tu te a p iece of tex t tha t says tha t M icke y M ouse does some

act iv i t ies

tha t vary accord ing to the day of the w eek . The q ue s t ion "W hat

does

he do af ter

school?" provides

the

con tex t

f or

in t e r p r e t ing

the

ac t iv i ti e s

as ou ts ide school hours . T he aspects o f M icke y ' s d iary tha t were d iscerned

by the

s tudents ,

a nd

were

focal in

the i r aw areness , were

the

asp ects th at var-

ied:

ac t iv it ies

and

d ays

of the

w e e k

(as can be

seen

from

S2 's

and

S3 's

re-



174

T S U I

T A B L E 7 .2

Engl i sh Lesson/Weekly Plan/Primary G rade 4/Class B

Cind y T i m m y

Weekly

Days

of the

w e e k

S unda y

M o n d a y

Tuesday

Wednesday

T hur sda y

Friday

Satu rday

Plan

T h i n g s to do

Play t ab le t enn i s

Go to the l ibrary

Ha ve a

p i an o

lesson

Have

a d an c in g

lesson

Go to the library

Ha ve a

com pute r l e s son

Play

t ab le

t e nn i s

Have

a c ompu te r lesson

The i tem s on the w hi te board a l so co ns t i tu te a p iece of tex t . This tex t says

tha t

Cindy does some ac t iv i t ies each day of the week . The presence of

Tim m y m eans tha t there are two people involved in th i s p iece of tex t . The

variants

in

th i s p iece

o f

tex t

are the day o f the week and the activity-. T he

weekly p lan be longs to Cindy . T immy does no t have a weekly p lan . The

teacher had se t up a d ia logue be tween C ind y and T imm y wher eby T imm y

asks,

"What

do you do on (day of the week)'+ s'?" and C ind y answ er s , "I

(verb + ac t iv i ty ) on (day of the w e e k ) '+ s'." For e x a m p le :

T i m m y : W h a t do you do on Wednesdays?

C indy: I go to the l ibrary on W ednesdays.

B oth var ian ts, day of the w eek and ac t iv ity , w ere focu sed on s im ul ta-

neous ly by the s tudents and the teacher, and bo th w ere evalua ted by the

t eacher when she wen t t h r ough C ind y ' s week ly p l an w i th the s tud en t s .

W h a t

w as

invar iant

was the

quest ion

from

T im m y ,

and the

l in gu is t ic s truc-

ture of the

answers

from Cindy that provided the scaf fo ld ing for the stu-

dents . The teach er also drew the s tudents ' a t ten t ion to the plu ral form o f the



7. T HE S H A R E D S P A C E O F L E A R N I N G 1 75

days

of the

week

to

signify recurrence, which

is an

im portant feature

of ha-

bitual act ion.

After the teacher had gone through all the days o f the week and the cor-

responding act ivi ties ,

th e

teache r asked

th e

s tudents

to

sum m arize C indy ' s

schedule fo r T imm y and sol ici ted from the s tudents descr ipt ions o f f r e -

quency,

such as "you go to the library tw ice a week," "you play table tennis

three tim es a

week,"

and so on. A s these s t ructures

were

solici ted, the fre -

quency o f occurrence cam e to the fore o f the s tude nts ' awareness , an d the

day o f the

week receded into

the

ground. What

the

s tude nts held

in

thei r

awareness s im ul taneo us ly were the ac t iv ity and the f requency . Th is is evi-

denced by the fact that when the s tuden ts w ere asked to come u p w i th thei r

ow n

weekly

plans

and to

conduct

a

dialogue

asking

each

other

about their

week ly p l ans

and how

of ten they conducted

th e

act ivit ies, they

did not

have

prob lems .

In

Class

B, the

c ondi t ions o btained

for

discerning

the

c ri t ical aspects

of

habi tual action, w hich were nam ely

the

activity itself

and the

f requency

o f

occu rrence or recurrence. T he w ay that the teacher set up the s i tuat ion in

w h i c h the

ha bi tual act ion

w as

embedded enabled

th e

students

to

experience

the object

in the w ay

that

th e

teacher in tended.

The

structure

of

aw areness

of

the teacher and of the students converged, unlike in Class A, where the

teacher ' s

and the

s tudents '

foci o f

awareness

differed. W e

could

s ay

tha t

in

Class

B

there

was a

w ider shared space

o f

learning tha n

in

Class

A, and

that

the learning outcome—as evidenced by the s tudents ' oral performance of

the

t ask—showed tha t

the

teacher

in

Class

B w a s

more effective than

the

teache r in

Class

A in

designing

the

learning experience,

as far as the

t each-

ing of habi tua l act ion w as concerned.

N E G O T I A T I O N O F

M E A N I N G

A N D T H E SH ARED SPACE O F L EARNI NG

In the 7.1

conversat ion exam ple given

at the

very beginning

of

this chapter,

we saw

that par t ic ipants

A and B

w ere involved

in a

process

of

neg ot iating

the

referent for " the m eet ing" and widening the com m on ground that w as

shared between them .

In the

classroom excerpts (7.2)

and

(7.3),

we saw

that

w hen cer ta in assum pt ions were

n o t

shared betwe en

the

teacher

and the

stu-

dents , valuable con tr ibut ions

from

students could

b e

dismissed

or not

val-

ued. Beca use of the un equ al power relationship between the s tudents and

the teacher, s tuden ts w ere often unable to engage in the k ind o f nego t iation

of

m ean ing tha t

is

prevalent wh en

the

power relat ionship

is

sym m et rica l,

such as

w h a t

we saw in the

conversat ion between col leagues (7.1) .

It is

therefore impo r tan t

for the

teacher

to be

vigi lant

of

assum ptions that

are not

shared

w ith learners,

as

wel l

as to be

sensitive

to

signals

of the

lack

of

com-

m on ground, and to be a ble to respond to such s ignals by en gaging in a ne-

gotia t ion of m ean ing wi th the learners.



1 76 T S U I

Let us take, for exa m ple, an excerpt f rom the lesson o n the s loth , w hic h

was discusse d in chapter 6. In this lesson, the teacher was r ev is ing w hat the

class

had

covered

in the

prev ious lesson , tha t

is, the

descr ipt ion

o f a

p a n d a ,

and w hat de ta i l s need to be covered w hen the s tude nts w r i te a descr ip t ion of

an

a n i m a l .

7.5 [Chinese Lesson/P3/The Slo th]

1 T :

[Ho ld ing

up a

t ex tbook showing

the

chap te r

on the

2

panda] OK, today, we w i ll do some wr i t ing . Our

3

wr i t ing

w i l l

follow

th e

chap te r

on the

p a n d a . . ..

I

w a n t

4 you to

tell

m e , w h e n w e w r it e abou t an a n i m a l , w h a t

5 do we need to include in the co ntents? ... Put up y o u r

6 han d s . W ha t d o we need to w r it e abou t

first?

7 [A s tuden t r a i ses h i s han d . ]

8 SI:

Body.

9 T: "Body" is

w h a t?

1 0 S I : Hu h? [M ean ing he d oes no t und er s t and the q ue s t ion ]

11 T: Bo dy.

1 2

S s:

B ody [Students

say

th i s

in

E n g l is h , from their seats . ]

1 3

T : B ody. W hat e l se? [W r ites "body" on the boa rd .]

14

S2: The brain , [meaning

"head"]

15

T : Yes , the head . W hat e l se? [W r ites "head" on the

16 board]

17

S3:

Four l im bs.

1 8

T :

Yes ,

four

l im bs . . . .

any

m ore? Yes .

19

S4: The

sk in ,

th e

color

of the

fur .

20 T: Color.

Yes.

[Writes "color" on the board]

21

S 5: Appear ance .

22 T : A ppearance . In fact , the word "appearance." wher e

23 should we put it? [Referr ing to location on the board]*

24 Ss: In

front .

25 T: In front of four

l imbs?

26 S5: In front of

four l imbs.

27 T: In

front?

In

fact.

I th in k . .. [pauses]

28

Ss: The h e a d .

29 S6:

Af t e r

the

head.



178

TSUI

dents apparently understood

"appearance"

as m eaning jus t the facial appear-

ance

of the

animal.

This is

evidenced

by the fact

that they suggested that

th e

description

of

appearance should come before

the

description

of the

four

l imbs

in the

text,

and

after

the

description

of the

head.

Finally,

the

teacher

m ade explicit

th e

relationship between

"appearance" and the

specific fea tures

(see lines 30 to 32, and lines 30 to 40).

The

fact

that there are certain groun ds that are com m on, but that there are

also others that

are not

shared betwe en

th e

teacher

and the

students

is not u n-

usual in classroom discourse. There could be a num ber of reasons w hy this

happens, but frequently such divergent perceptions are caused by linguistic

means,

for

example,

by the

questions

the

teache r asks,

by the

pragm at ic

and

semantic presuppositions carried

by the

w ords used,

by the way the

teacher

responds

to the students' questions or responses, and so on. In this particular

excerpt, there w ere several cause s

for the

unshared ground. Firstly,

the initial

questions asked

by the

teacher, "W hat

do you

need

to

include

in the

content?

.. ." "What do you need to w rite about first?" (line 5 and line 6) were open to a

number

of

interpretation s.

It

wou ld have been approp riate

for

students

to

pro-

vide either

a

list

of

specific features

or the

superordinate

first. It is

clear

from

the data that the relat ionship between appearance, or "outw ard appearance"

to be

precise,

and the

other

features w as

very much

in the

teacher 's

focal

awareness, whereas it w as the specific features that were very m uch in the stu-

dents '

focal

awareness. S econdly, the unsha red ground wa s also caused by the

semantic ambiguity

of the

word "appearance"

in

Ch inese (yeuhng

m a a uh in

Cantonese) [ 4 f < . f f e ] can mean facial appearance or the entire outw ard appear-

ance.

T he

teacher

w as

using

th e

word

in the

sense

of

"outwa rd appearance,"

whereas

the

students were using

it in the

sense

of "facial

appearance."

W e can see, however, that the teacher w as able to respond very quickly to

signals

of

assump t ions

no t

being shared

by the

s tudents

by

abandoning

the

initial line

of

quest ioning

and

al lowing

the

students

to

list

the

specif ic

fea-

tures . The teacher w as also able to negot iate the m ean ing of the w ord "ap-

pearance," with

the

students

by

ask ing them where

the

word should

be

placed

on the

board,

and

guiding them

to see the

word

"appearance" as a

superordinate ( l ines 30 to 32). In th is way, th e t eacher w idened th e c o mmo n

ground shared between him self and the s tudents , so that even tual ly they

were

able to agree on a descriptive structure that form ed the scaffolding for

the

rest

of the

lesson.

In the

subsequent d i scuss ion am ong

the

s tudents

in

sm all groups, i t w as clear that the students had a good u nde rstan ding of "ap-

pearance"

as a

superordinate that subsum es specific phy s ica l fea tures .

COLLABORATIVE CO N STRUCTION O F M E A N I N G

A N D T H E SHARED SPACE O F

L E A R N I N G

In e lucidating the notion of the shared space of learning, we proposed that

there is another sense in w hich the space of learnin g is a shared space; that



7. TH E S H A R E D SPACE O F L E A R N I N G 1 79

is, w hen the space of learning is jo in t ly con st i tu ted by the teacher and the

learners throug h

the

co l laborat ive const ruct ion

o f

m ean ing .

The jo in t co ns t ruc t ion of m eaning be tween ch i ldren and adul t s i s w el l

documen ted . Ha l l iday ' s work on ch i ld l anguage deve lopmen t p rov ides

am ple exam ples o f how a ch i ld , th rough in terac t ion w i th an adu l t , is able

to

con s t rue exper ience in to m eaning . Typ ica lly , the ch i ld ' s response to the

envi ronmen t

is

interpreted

by the

adu l t

as

i nd i ca t i ng communica t ive

in -

tent ions ,

and

responded

to

according ly .

In the

course

o f

responding

to the

chi ld , the a dul t con t r ibu tes to the co-cons t ruc t ion of the m ean ing in the

discourse

(see, e .g . , H al l iday , 1973, 1975, 1 993). W el ls (1 986) provided

the

fo l lowing

exam ple o f co -cons truc t ion o f mean ing be tween a pa ren t

and a

2-year-old

child.

7.6 [Wells, 1986, p. 46]

M ark (2 ;3) is s tanding by a cen tral hea t ing radiator and can

feel

the

heat coming from it. He initiates the conversation by

sharing

this inter-

est ing

in form at ion wi th

h is

m other.

M a rk : 'O t , M u m m y ?

M other: Hot? [checking] Yes, that ' s the radiator .

M ark : Been- burn?

M other : B urn? [checking]

M a r k : Y eh

Mother: Yes, you know

it'll

burn don't you?

In this piece of data, as W ells (1 999) observed, the child respon ded to the

cen tral hea ting radiator

by

mak ing

a

comm en t.

H is

mother checked that

she

had

co rrectly interpreted the ch ild's u t terance , and told him that the radiator

w as

the

source

of the

heat .

The mother's

correct interpretat ion

o f the

chi ld ' s

ut terance enabled him to extend the exchange and bring in the word "burn,"

w hich was in turn extended by the m other as "Yes, you know i t w i l l bum ,

don ' t

you?"

S ubsequent ly

in the

discourse (not shown here),

the

child

w as

able

to

take over

the

m eanings that w ere ini tia l ly co-constructed

and

apply

them to a novel s i tuat ion where he saw a bonfire in the garden and w as able

to say tha t i t w as hot and that it w ould burn as w el l.

Let

us consider how this happens in classroom learning. In the history

lesson that w e discussed in chapter 6 , the concept o f

clan

w as taught in the

context of ear ly rural com m uni t ies in Ho ng K ong. In th is context , a c lan is a

c o m m u n i t y

o f

people w i th

the

same surnam e

w ho

live togethe r

in one

area,

and are also somew hat related by blood. The fol lowing is an excerpt from a

Chinese medium classroom (CMI), where Chinese was the students'

m other tongu e, in which the teacher explored w i th the s tudents why clans

were formed

and for

wh at purpose .



180

T SUI

7.7 [History Lesson/S2/CMI]

1

T: ... So,

people with

the

same surname stay together....

Why do

they

2 stay

together? Why do

they stay together? Why?

3 S: Convenient.

4 T: It's convenient. Would it be better

for

them to go their separate ways?

5

Would it be better for you to go your own way? Who says it's

6

convenient?

...

What

are the

advantages

of

living together?

7 S:

They

can

help each other.

8 T: Help each other. Yes, that's right.

Very

good.... What kind of things

9 do

they

need

to

help each other with?

I

want

to ask all of

you.

10 S: Farming.

11

T: Yes, farming, they need help from each other. You work on this part

12 [of the land] and I work on another part [of the land]. We help each

13 other. What else, apart from

farming?

14

S: Hunting.

15

T: Hunting, OK. But we know that it was an agricultural society already,

16 so there was not much hunting.

17 S: Raising animals.

18 T: Raising animals, that is, raising cattle and

sheep.

Yes. What

else?

19

What else?

20 S: Not to be bullied by others.

21 T: Not to be

bullied. Actually

this is

very important

To

protect each

other,

22 mutual protection, apart from farming together, living together.

2 3 Some students said looking for

food

together. There is also the function

24 of protecting each other. Why did they have to protect each

2 5 other? So that they would not be bullied, because they came to Hong

26 Kong from a

faraway

place and they did not know the place, right?

27 They did not know whether they would be disliked by other clans.

28 What if they were attacked by them? That's why they needed

mutual

29 protection. They had to be armed. In addition, there were blood ties as

3 0 well. Just now I told you that they had the same surname ... Another

31 function was to preserve the traditional l i f e style.

In this excerpt, the teacher posed a number of open questions. Each time

a student responded, the teacher took on the response and opened it up for

inquiry. For example, in line 2, the teacher asked why people with the same



THE SHARED SPACE OF LEARNING

1 8 1

surname stayed together and one student responded that i t was for conve-

nience ( l ine

3). The teacher

took

on the

response

a nd

asked

w hy i t was con-

venient . When no

response

w as for thcoming, the teacher rephrased the

word

"convenient"

as

"the

advantages

of

living

together"

(line

6 ), and

asked

the students

to

list

the

advantages .

As w e can see,

th is im m ediately elic i ted

th e

response "help

each

other"

(line 7) from an other s tudent. A t the end of a

sequence of in teract ion around the topic , a sem ant ic netwo rk relat ing to the

formation o f clans w as collaboratively constructed by the studen ts and the

teacher: that is, mu tua l help ( fa rming) ; mutual protection (so as not to be

bul l ied by others; line 20 and line 21); bloo d t ies (bec au se they a l l had the

same

surnam e and therefore had the sam e ancestor; l ine 29 and l ine

30);

and

preservation of the tradit ional

l ifestyle

(line

31).

The col laborative const ruction of the sem ant ic netw ork during the inter-

active process is i l lustrated in

Fig. 7.1.

Figure

7.1 show s the way in w hich the teacher and the s tudents co-con-

structed the space o f learning by engag ing in a nego t iat ion of me aning . For

exam ple , the word

"convenient"

suggested by the s tudent w as too vague ,

and so the teache r clarified and elaborated the m ean ing of "convenient" by

rephras ing it as "the advantages of staying together." The

teacher's

interpre-

ta t ion

o f the

s tudent ' s in tended m ean ing helped

to

move

the

discuss ion for-

FI G. 7.1. Co llaborative construction of a

semant ic

ne twork of formation of c lan.

Note: Words

underlined

are

contributions from

th e

teacher

and

other contributions

are

from

students.



182 T S U I

w ard, as can be seen from the imm ediately for thcom ing response from an-

other student. Had the teacher misinterpreted the s tudent ' s meaning, the

subsequent contributions from the s tudents w ou ld probably not have been

for thcoming

or they w ould have been

different

(see W ells , 1999). B y ask ing

the s tudents what the advantages o f s taying together were, the teacher

opened up a dimension of variat ion for exploring the benefi ts that people

gained

by

staying together. When

the

students

proffered "help

each other"

as an

ins tance

in the

dimension

of

advantages ,

th e

teacher took

on the re-

sponse and opened up a fur ther dim ension of variat ion f or ex plor ing th e di f -

ferent ways in which members of a clan needed to help each other . The

students suggested "farming," "hunting," "raising animals," a nd "not to be

bull ied by

others,"

as ins tances along this dimension. The teacher high-

l ighted the im portance of not be ing bu l l ied and rephrased it at a h ighe r

level

of abst ract ion by u s ing the phrase "m utual protect ion." Final ly , the teach er

contr ibuted tw o m ore reasons for the form at ion of clans : b lood t ies and pre-

serving tradit ional life s tyle . The interact ion between the teacher and the

s tudents was a process in w hich que st ions posed by the teacher opened up

dimens ions of variat ion that afforded opportuni t ies for s tudents to explore

the reasons for people to s tay together . These opp ortuni t ies w ere taken up

by the stude nts, and their con tributions w ere in turn us ed by the teac her to

open up further dimens ions fo r explorat ion. T he space of l earn ing opened

up was therefore a co l laborat ive effort be tween the t eacher and the l earners .

In

this sense, the space of learning was a shared space.

Embodied in the notion o f the jo in t con st i tu t ion of the space o f l earn ing is

also

the

col laborat ive c onst ruct ion

of

m ean ing am ong l ea rne rs . Th i s

is

par-

t icu lar ly evident w hen learners

are

engaged

in

g roup w ork .

For

example ,

in

chapter 6 , we saw how learners b rou ght the ir own know ledge of the w or ld ,

and

thei r previous experience,

to

bear

on the

ob jec t

o f

learn ing

as

they co l -

laboratively

constructed texts on the story of the sloth.

LIN G UISTIC

RESO URCES

A N D T H E

SHARED SPACE

O F

LEARNING

A s w e

have already pointed out , at tem pts m ade

by the

teacher

to

widen

the

shared space of learning may not always be successfu l . The cause of th i s

mismatch could

be

l inguist ic,

o r it

could

be due to the

fact that

the

structure

of the

learning experience brought about

different foci

o f

awareness .

In

classrooms

where the medium of instruction is not the students ' mother

tongue (i .e. , a l anguage in w h i c h the s tudents a re l ess com peten t ) , th e fail-

ure to widen the

shared space

of learning m a y be caused b y a lack of l ing uis-

tic

resources (p ar t icular ly

on the

par t

o f the

s tudents , a l thou gh som et im es

it

can also

be on the

part

of the

teacher).

Let us look at the fol lowing excerpt f rom an Engl ish medium lesson

(EMI; English

was not the

students' mother tongue)

on the

same history



7.

T H E S H A R E D S P A C E O F L E A R N I N G 1 83

topic

as the CM I

lesson just ci ted (and

in

chap.

6), on the

early rural com m u-

nity. In this lesson, the teache r asked the students to compare the diaries that

they had writ ten befo re the lesson, w ith those w ritten by a father, Tang Tai

M a n ,

and his

son, Tang

S iu

M a n,

in the

days

o f the

rural com m uni t ies ( these

w ere g iven as han douts). T he teach er 's intention w as to bring out the

differ-

ent

l ifestyles

of people today and

people

in the past .

7.8 [History Lesson/S2/EMI]

The

teacher asked

the

students

to

w rite

a

diary prior

to

this lesson

and

then asked them to compare their diaries with the two diaries on the

hando ut by Tang Tai M an and his son, Tang Siu Ma n.

1

T: . .. OK ,

look

at the on e of

Tang

Siu

Man , Tang

S iu

M a n .

Is it

2 different from yours?

3 Ss: Yes.

4 T: How different? Can you tell me how different? Stephanie ,

5 give

me one

difference.

6 S: [speaking very softly] I have not the chicken .

7

8

T: Yes , then w hat else? W hy [does] the boy have chickens ,

9 duck s , and pigs? W hat did he do?

10

S: [silent]

11

T :

Wh a t

did he do? How

come

he has the

chickens ,

ducks , and

12 p ig s? W ha t did he do in his dai ly life?

13 S: [silent]

14

T:

Unders tand

m y

quest ion?

15

S : [speak ing very softly, inaudible]

16

T :

W h a t

is his

work, Stephanie? Angela,

can you

help?

...

In line 4, the teacher took on Stephan ie's response that her diary w as differ-

ent from Tan g's, an d tried to open it up for inquiry by

asking

her how they

were different. Stephanie tried

to

explain that

she did not

rear chickens.

T he

teacher took on S tephanie's response and ag ain tried to open it up for further

inquiry

b y

asking

her why

Tang

S iu M an had

chickens, ducks,

and

pigs .

The

teacher was

ho ping that Stephanie would point

out the

differences between

life

in

ear ly rural comm uni t ies

a nd

life

in

mo dern u rban societies. How ever,

Stephanie w as tong ue-tied, even after prom pting f rom the teach er tw ice ( l ine

10

and

l ine 11 ). Finally,

the

teacher

had to ask

another student

to

help out .

Throu ghou t the w hole lesson, there w ere a num ber of ins tances in w hich

no response w as for thcoming, even af ter the t eacher had repeated or re-



184 T S U I

phrased the question. In other w ords, the teacher had considerable

difficul-

t ies trying to co-construct the space o f learn ing w ith the stu den ts due to the

students' lack

of

l ing uist ic resources.

A quant i ta t ive analysis was conducted on the two his tory lessons (one

EM I and one

C M I) that were discussed

in

this chapter

and in

chapte r

6 and

two other h i s tory lessons (aga in , one E M I and one C M I) teach ing the same

topic to see how

often

the teachers w ere able to m ake use of the s tu den ts ' an-

swers to open up the space for further inquiry, and facili tate the col labora -

tive

construct ion of m eanin g betw een teacher and s tudents . The f indings are

presented in Table 7.4.

W e can see from Table 7.1 tha t in the two EM I lessons, over half of the

students ' responses w ere s imp ly accepted or repeated by the teach ers w ith-

out

further

elaboration or c o m m e n t. T he s i tuat ion is a lmos t the m i rro r im -

age of the two CM I ( i .e . , m other ton gu e) lessons. It is not

difficult

to see tha t

in C M I c lassrooms, the teachers and the s tudents w ere engaged in

m a k i ng

sense of the object of learning col laborat ively. By contrast , in EMI

(nonm other tong ue) c lass room s, the interact ion w as ve ry much un id i rec-

tional an d the learners played a much more passive role.

C O N C L U S I O N

In

chapter 1 , we

proposed

the

notion

of the

space

o f

learning b eing charac-

terized by c lassroom interact ion in the

l ight

o f a

specif ic

ob jec t o f

lea rn ing .

A n d w e

pointed

out

that

th e

space

of

learning

is

cons ti tuted

by the

po ssibil i-

ties for lea rn ing brough t about b y w h a t i s takin g p lace in the c lassroom in

relation

to the

object

of

learning.

T he

po ssibilities

for

learning ( i .e . , w hat

w e have re fe r red to as the enac ted o bjec t of lea rn ing ) cannot be brou ght

about

by the

teacher alone,

or by the

learners themselves; they must

be

T A B L E 7 .4

Teachers

Responses

to Students Answers in E M I an d C M I Classrooms

Teachers 'Responses

to

Students '

Answers to Al l Teacher Quest ions

EMU EM

1 2

CMI 1 CM I 2

Rejection

Accept ing / repea t ing

s tudent ' s

answer

E xte nd ing s tudent ' s answer

No com ment /new q ues t ion

Tota l num ber

of

responses

0 1 ( 1 % ) 1 ( 1 % ) 1 (3%)

5 0( 6 9 .5 % ) 4 2 ( 5 9% ) 1 6 ( 1 7 % ) 1 2 ( 3 4 % )

1 6 ( 2 2 . 5% ) 1 4 ( 2 0 % ) 6 9 ( 7 3 % ) 2 2 ( 6 3 % )

6 ( 8 % ) 1 4 ( 2 0 % ) 9 ( 9 % ) 0

72 (10 0%) 71 (1 0 0 % )

95

( 1 0 0% ) 3 5 ( 1 0 0 % )



7.

T H E

S H A R E D S P A C E


joint ly consti tuted by both the teacher and the learners. In light of this, we

proposed, in this chapter, that the space of learning is a shared space.

The joint consti tut ion of the shared space of learning has very mu ch to do

with

the s t ructure of aw areness o f the par t ic ipants in a discou rse. If w hat co-

m es to the fore o f their awareness is

different,

participants talk a t cross pu r-

poses .

In a

classroom si tuat ion,

the

learners ' s tructure

of

aw areness

is

often

shaped

by the way in

wh ich

the

teacher organizes

the

learning experience,

and

the way in

w h ic h

he

presents

the

mater ials . Using data

f rom two

pri-

m ary Grade 4 lessons on "the w eekly

plan,"

we i l lustrated the way in w h i c h

the learners ' s t ructure of awareness was shaped by the mater ials that the

teache r put on the board, and the way in wh ich m ore

effective

learning w as

b rough t

abo ut w hen the teach er ' s s t ructure of aw areness accorded w i th that

of the s tudents .

T he

space

of

learning

is a

shared space

in the sense

that

the

interaction

between the teacher and the learners i s fel ici tous only when both part ies

share some common ground on which further interaction can be based. W e

have looked a t examples of c asua l conversat ion and classroom data to see

w h a t

happens w hen there is little or no com m on ground shared between par-

t ic ipants .

In the case of the con versation betw een tw o co l leagues (7 .1 ) , th e

interlocutors

had to

work very hard

to

w iden

the

comm on ground

in

order

to

advance the co nversat ion. In the ca se of the En gl ish lesson on the w ee kly

plan in prim ary G rade 4A, an appropriate con tribution by a student w as dis-

m issed by the t eacher because the lat ter failed to see the ra t ionale beh ind th e

s tudent ' s

answer , and hence an ex cel lent oppo rtuni ty fo r learning w as lost.

B y co nt ras t, th e c lass room data from the reed relay experim ent (7.3) and the

lesson

on the s loth (7.5) showed h ow po ss ib i l it ies fo r l earn ing were opened

up wh en the teacher was aware of the comm on ground shared be tween h im -

self o r herse l f and the learners . In these tw o exam ples, w e also saw how the

shared space

of

learning

w as

widened

by the

n egotiation

of

m eaning

be-

tween the t eacher and the learners in the lesson on the s lo th , and by the

teacher helping

the

learner

to

clarify

h is or her

thinking

and

lingu istic repre-

sentat ion

in the

lesson

on the

reed relay.

T he space o f learning is a shared space also in the sense tha t th e po ssibili-

t ies for l ea rn ing are jo in t ly const i tu ted by the t eacher and the learner. In the

Ch inese m edium h is to ry l esson ,

w e saw how the

teacher opened

up

possi-

bi l i t ies fo r learning by ask ing ques t ions on the basis of the s tudents ' re-

sponses (7.6) , and how, as a consequence of the teacher ' s quest ioning, a

semant ic ne twork

o f

"clan"

w as

co l laborat ively con st ructed

by the

t eache r

and the s tudents .

T he proposal that the space o f learning is a shared space join tly c ons ti tuted

by the teacher and the learners is an impo rtant on e from the perspec tive o f the

w ay

we describe teac hing and learning in relat ion to one another. Investiga-

t ions of teaching an d learning m ust take into considerat ion not only the possi-



186 T S U I

bilities for learning being opened up by the teacher, but also which

possibilities are actually made use of by the learners.

E N D N O T E

'The s imple c i rcui t wi thout the reed re lay carries a very smal l current and is

therefore able to l ight up the LE D, w hich on ly requ i res a very sm al l current to l ight

up. The

complicated c i rcui t w i th

the

reed relay

can

carry

a

very large current once

the reed switch is c losed and can therefore cause the m o to r to rota te .



I V

O n Improving Learning



190 LO ET AL.

O ur

point

o f

departure

is

that teaching

i s— or

sho uld be—a ra t ional ac t iv -

ity. In planning a lesson or a un i t , the teacher must take into account the

characterist ics of the students (e.g. , age, general a bil i ty ) as w e l l as the phys -

ical conditions

of the

classroom (e.g . , c lass s ize, equip m ent ava i lable ) .

However, a ll these

concerns mus t

be

translated into actions that

can

help

achieve specific goals, that

is, the

exp l ic i t capab i l it i es tha t s tuden ts

are ex-

pected

to

develop.

W e

call these cap abi l i t ies

th e

ob jects of l e ar n i ng . Even

in

the

m ost open classroom , students ' learnin g should

not be

acc id en ta l

bu t

should

b e the

resul t

o f

conscious at tempts

on the

part

of the

teacher

to

br ing

about the intended learning ou tcomes. In other words, at tent ion must be

paid

to the

w a y s

in

w h i c h

the

objects

o f

learn ing

are

deal t w i th

a nd

enacted

in

the

classroom.

Seen in this l ight, curre nt debates (e.g. , concerns abo ut the relat ive m er i ts

of

teacher-centered

and

s tudent-centered instruct ion ) that focus

o n

genera l

aspects, and not on

ways

of

dealing w ith

the

specific c ontent

of

learning,

are

of l im ited value both in term s o f providing learning op por tun i t ies for teach-

ers and in imp roving s tudent learning. T he t each ing a r rangem en t s ( such as

whole-class teaching

vs.

g roup teach ing ,

and the use of IT in the

c l a s s room )

should be of concern only i f d iscusse d in rela t ion to the sp ecif ic s of wh at is

taught

and

learned.

This

l ine o f a rgum ent para l le l s what K i lpa t rick , S w afford . and Findel l

(2001) referred to in the con tex t of ma them at i c s ed uca t ion :

M u c h deba te cen te r s

on

fo r ms

and

a pp r oa c he s

to

t e a c h in g : "d i re c t

ins t ruc t ion"

v e r s u s

" inqui ry ," " teache r -cen te red" ve r sus " s tudent-cen te red ," " t r ad i t iona l" ve r sus " re -

form." These labe ls m ake

rhe to r i ca l d i s t i nc t i ons

t ha t

of ten

m i s s

th e

po in t r e ga r d ing

th e qua l i t y o f i n s t ruc t i on . Ou r review of the

r e se a r c h m a ke s

p l a i n t ha t t he e f f ec t iveness

of

ma themat ic s teach ing

a nd

lea rn ing

does no t

rest

on

s im ple labe ls . Ra the r ,

the

q u a l -

it y

o f ins t ruc t ion is a

func t ion

o f

t e a c he r s ' know le dge

and use of m a t he m a t i c a l

c on -

t en t , teache rs ' a t ten t io n

to an d h an d l i n g o f s tudent s , and

s t u d e n t s ' e n g a g e m e n t

in and

use of

m a them at ica l ta sks,

(p .

318)

Several recent theories regarding the profess ional developm ent o f t each-

ers also appear to have focused on the different w a y s o f deal ing wi th the ob-

j ec t

o f

learning

in the

c lass room. Bas ing the i r a rgument

on a

s tudy

o f

California elementary school

teachers o f

m athema tics , Cohen

and

Hil l

(2000) pointed out that teachers ' opportunities to learn are a key factor af-

fect ing

classroom practice,

and

that such oppor tuni t ies exis t only when

teachers

are

asked

to

respond deeply

to

what they

are

supposed

to

teach .

They fou nd that profess ional developme nt act iv i t ies tha t al low ed teachers

to

leam about

the

cu rr iculum

had a

much

greater

effect

on

altering teaching

practices than those that appeared to be either gene ric o r per ipheral to sub-

jec t m at ter (Cohen

&

H ill , 2000). They even sug gested that classroom prac -

tice w as m os t e f fec t ive ly enhanced by those t raining a ct iv i t ie s that gave

teachers c oncrete , top ic-spe cif ic learning op po r tuni t ies . Their data also



8. T O W A R D

A

P E D A G O G Y

O F

L E A R N I N G

1 91

showed that

the

mathemat ics ach ievement

of

s tudents

in

schools where

teachers w ere provided with these learning o ppo rtunities

w as

considerably

high er than in those w ithou t such opportunit ies. They con cluded that inter-

vent ion s tudies must change what teachers do wi th the curr iculum in the

classroom

in

order

to

affect student learning. W hat matters, therefo re,

is the

enac ted objec t of learning, that is , how the obje ct of learning is ac tua lly

dealt

w i th

in the

classroom.

It is in this context that we introduce the idea of the "learning study." T he

learning study is based on the Japan ese style "lesson study," w hich w e feel

takes

the

object

o f

learning

as its

point

of

departure,

bu t

wh ich also incorpo-

rates

the

m ethodologica l concept

of the

des ign experiment

pu t

forward

by

A. L .

Brown (1992)

an d

Coll ins (1992).

W e

explain these ideas

in

turn

in the

fo l lowing sections.

LESSON

STUDY

Stigler and Hiebert (1999) introduced the idea of the lesson study (jugyou

kenkyuu) in

Japan

in

their book,

The Teaching Gap. T he

lesson study, they

argued ,

gives Japanese teachers a m odel of con t inuou s school-based pro-

fess ional developm ent , w hich the two researchers see as one of the main

reasons

fo r the

success

o f the

c lass room prac t ice re form s

in

post-w ar Japan

( and

the relat ively high achievem ent rates of Japanese s tudents in in terna-

t ional com parison studies). St igler and Hiebert (1999) explained the rat io-

nale of the

lesson study

as

fol low s:

T h e p r e m i s e

b e h i nd

l e s son

s t udy

i s s imple : I f you w a n t to improve teach ing , the

m o s t

e f fec t ive

p l a c e to do so is in the co ntex t of a c l a s s ro o m l e s s o n . If you s ta r t

w i t h

l e ssons ,

t h e p r o b l e m o f how to a pp ly r e sea r ch

f i nd ings

in the c l a s s ro o m d is a p p e a r s .

Th e im p ro v em e n t s a r e d ev i sed

w i t h i n

t h e c l a s s room in the f irst p l a c e . Th e ch a l l en g e

n o w

b e c o m e s

tha t o f

i de n t i f y i ng

the k inds o f

c h a n g e s

tha t

w i l l

i m p r o v e

s tuden t

l e a r n i n g

in the c l a s s r o o m a n d , o n c e th e c h a n g e s a re i de n t i f i e d , o f shar ing

t h i s k n o w l -

ed ge w i t h

o th e r t e ach e r s

w h o face s i m i l a r

p r o b l e m s ,

or

s h a r e

s i m i l a r

g o a l s ,

in the

c l a s s r o o m , ( p .

I l l )

In

a typ ical lesson study, a group o f teachers com e together and select a

topic to be dealt with during one or several "research

lessons"

(kenkyuu

jugyou}.

Members

of the

group draw

on

each other 's experiences,

and to-

ge ther

they d ecide on the intended objec ts of learning and work out a lesson

plan designed to achieve these goals . On e teacher w i l l then teach the lesson,

whi le everyone in the group o bserves. Th e lesson is then e valuated and the

plan

revised. Ano ther teache r w il l then teach the revised lesson w ith the oth-

ers observing, and a second round of evaluation and reflect ion wil l take

place. The research lesson is then docum ented so that the outcome can be

shared with other teachers. According

to

S t igler

a nd

Hiebert (1 999),

a

les-

son study

is

com posed

of

eight steps:



192 LO ET AL.

•

Def in ing

the

problem

• Planning the lesson

• Teaching the lesson

• Evaluating the lesson and reflec t ing on i ts

effect

• Revis ing the lesson

•

Teaching

the revised lesson

•

Evalua t ing

and

re f lec t ing again

•

Sharing

the

results

D E S I G N

EXPERIMENTS

A s such,

the

goal

of the

research lesson

is not

jus t

to

produce

an

effective

lesson, but , through careful p l ann ing and eva lua t i on , to ensure tha t the

teachers involved come to real ize why and how the lesson w orks . A lesson

s tudy is of

course

not a

control led experim ent

i n

w h i c h

one

factor

is

a l low ed

to

vary whi le others

a re

kept constant .

O n e

w ou ld ac tua l l y ques t ion

th e

value and the p ossibil i ty of a co nt ro ll ed exper im ent in such com plex a nd

con found ing

envi ronments

as

those

o f

educat ional set t ings . However ,

as

A .L. Brown (1992)

and

Coll ins (1992) suggested,

it is

s t il l w or th con duct -

ing

design expe rimen ts

in

edu cat ion , espe c ia l ly

in

c lass room resea rch .

A l-

though w e cannot control a ll aspects of the environment , argue Brow n and

Coll ins , we can

still

g ain considerable ins igh ts in to the operat ion of the m a-

jo r

variables through systematic intervention

and

unbiased observations.

Conclus ions

c an still be

drawn,

b y

com par ing

the

resu l t s ob ta ined

from

d i f -

ferent conditions, although w e have to interpret those re sults and guard our-

selves against making general c laims based

on

l im i ted observations .

T he

benef i ts

o f design experiments are that w e w i ll be able to contribute to the-

ory

development ,

and

improve pract ice

at the

s ame t im e .

T H E L E A R N I N G STUDY

It

w as in the spirit of

Brown's

and C oll ins ' design ex perim ents tha t w e tried

to r e fo rm ula te th e Japane se lesson s tudy in the research tha t w e report in the

latter part

o f

this chapter. Marton (2001) defined

the

learning study

in the

fo l lowing w a y :

A l e a rn ing s tud y is a s y s t e m a t i c a t t e m p t to a c h i e v e an

educa t iona l ob jec t ive

and learn

from

tha t a t t empt .

It is a

d e s ign

e x p e r i m e n t

t ha t

may or may not be a

lesson

s tudy.

Such a s tudy is a l e a rn ing s tudy in two senses . F i r s t , it a i m s a t

b r ing ing l ea rn ing

a b o u t ,

o r more cor rec t ly , a t

m a k i n g

l earn ing p o s s i b le . T he

s tudent s

w i l l

t h u s

learn , hopefu l ly .

Second , those teachers involved try to learn

f rom

the

l i terature, from

each o the r , from

th e s tudents , and n ot leas t , f rom the s tudy i tself , (p . 1 )

Specifically, in our own research fo r this book, w e w an ted to learn the po-

tent ia l

va lue

of the

theory

o f

variat ion from these s tudies .

T he

lesson study



8.

T O W A R D A P E D A G O G Y O F

L E A R N I N G

1 93

is an appropriate m odel as i t a l low s researchers and teachers to see how the

objects o f learning are de al t w i th in the classroom . T he learning s tudy dif-

fers

from

the Japanese lesson study model in that our research lessons are

based

on a

theoretical frame w ork

of

learning— nam ely,

phenomenography

( c f . Marton & B ooth, 1997), and variat ion theory— and w e w i sh to find ou t

how

w el l the theory has w orked. In th is w ay the learning s tudy is a learning

study not in tw o, but in three senses, as the researchers are supp osed to learn

from it as w e l l.

T he

cycle

of a

learning study comprises

the

fol lowing

steps:

1. Choos ing

and def in ing a specific se t of educat iona l

object ives . These

are the ca pab i l it ies or values to be developed during one or several

lessons .

2.

Finding

out the

extent

to

w hich

the

students have developed

the

capa-

bili t ies

o r

va lues targeted before

the

t each ing beg ins .

3.

De signing a lesson (or series of lessons) aim ed at develop ing these

capabi l i t ies

or

values .

The

p lanning work m us t t ake in to accou nt

the

exist ing

know ledge of the s tudents , the teache rs ' pr ior expe riences in

dealing with the objects of learning, and the research literature.

4.

Tea ching the lesson (or lessons) according to the plan .

5. Eva lua t i ng the lesson (or lessons) to see the extent to w h i c h the s tu-

dents have developed the targeted ca pa bi l i ties or va lues .

6 . D o c u me n t i n g

an d

d i s semina t i ng

th e

a im, p rocedures ,

an d

r e su l t s

obtained.

In

the nex t three sect ions , we desc r ibe three c yc les of a learning s tudy in

two separa te p ro jec t s . The f ir s t two cy cles w ere co ndu cted w i th in an ongo -

ing rese arch pro ject ent i t led "Cater ing fo r Ind iv idua l Di f f e rence s (B u i ld-

in g

on V ariation)," commissioned by the Educat ion Department of Hong

Kong S pecia l A dm inis tra t ive Region of the Peop le 's R epu bl ic o f C hina ,

w h i l e

the

thi rd cycle consis ted

of an

independent p ro jec t tha t employed

the

theory of var ia t ion in des ign ing c lass room lessons to he lp s tuden ts to

learn

e c o n o m i cs .

CATERING FO R I N D I V I D U A L D I F F E R E N C E S

B U I L D I N G O N

V A R IA TIO N )

The "Catering for Individual Differences (B ui lding on V ariation)" project

is a 3-year, ongoing research project undertaken by a team of researchers

from

the

F acul ty

of

Educat ion

at The

Universi ty

of

Hong Kong ,

and the

Hon g Kong Ins t i tu te

of

E ducat ion , w i th Pong

and Lo as

principa l investiga-

tors and M arton as consu l tant . As there are different w ays in w hich the t erm

ca ter ing for ind iv idua l

differences

can be interpreted, i t is there fore im por-

tant that

w e

explain

our

understanding

of the

term

and its

bearing

on the



1 94 L O E T A L .

aims of the project . T he project members bel ieve that because different

people

are bom

w i th different abil i t ies, charac teristics,

and

orientations ,

in -

dividual differences are a natura l phenomenon and are not a problem in

themselves. Individual

d ifferences

only become a problem in the classroom

sett ing, when

a

teacher

ha s to

teach

a

large group

of

s tudents

th e

same con-

tent. Th us, the project aim s at helpin g teach ers to find wa ys to enab le all stu-

dents—in a typical mixed-abi l i ty c lassroom set t ing—to leam what is

intended by tak ing into accoun t the s tuden ts ' diverse exis t ing know ledge

and unders tandings .

T o achieve this, the p roject team bel ieves that it is necessary to start wi th a

carefully defined object o f lea rn ing—tha t is, the cap abi l i t ies that s tude nts

are expected to acq uire . For exam ple , i f w e w ish the s tudents to u nderstan d a

certa in phenom enon, it fol lows that in order to accomm oda te individual d i f -

ferences, the teacher m ust f irs t have a deep and thoro ugh un dersta ndin g of

the different po ssible ways in wh i c h th e s tudents m ight unde rstand this phe-

nomenon. Research findings in phenomenography have shown

that

al-

though s tudents

are

un ique individuals , there

are

a lways

a

l im i ted num ber

of qual i ta t ively different wa y s in w hich they unders tand a par t icula r phe-

nomenon (Marton & Booth, 1997). These different w ays of unders tanding

arise m ainly because

a

different

set of

cri t ical aspects

of the

p h e n o m e n o n

are

discerned.

How do teachers gain access to such kno w ledge of s tudents '

exis t ing

u n-

derstandings? The team believes that teachers can first listen to, and leam

f rom, their studen ts. They can also share their findings wi th o ther teachers

in the

same school. Within

the

project , experience sharing w ith other teach-

ers takes place in col laborat ive groups co m pris ing teachers who teach the

same

subject a t the

same

level in one school. In this way, ind ividual differ-

ences becom e

a

resource

for the

teacher ra ther than

a

co ns t ra in t .

Bearing

in

mind

the

various

understandings students

m ay

bring

to the

classroom, and having identified the c ri t ical aspects of the objects o f learn-

ing,

the

group

o f teachers

move

on to

develop

a

research lesson that meets

those ends.

In

developing a research

lesson,

three aspects of variation are made use of

w ithin the project :

V a ri a t i o n

in

Terms

of Students


of

W h a t

I s

T a ug ht

Students understand that w hich they are supposed to leam in a l imite d num -

ber of

different ways .

O ur

research shows that teachers

w ho pay

close atten-

t ion to such differen ces (or varia t ions) , and w ho can bui ld on s tuden ts ' prior

understanding

and

experiences,

are

better able

to

bring abo ut

mean ing fu l

learning for their students. Students also learn more

effectively

w hen they

are made aw are of the different w ays in w hich their c lassmates deal w ith or

understand

the

same object

of

lea rn ing.



8.

T O W A R D

A P E D A G O G Y O F L E A R N I N G 1 95

Variation in

Teachers'

Ways of Dealing With Particular

Topics

As a

teac her gains expe r ience

over the

years ,

he or she

w i l l bu i ld

up a

good

work ing knowledge about the

dif ferent

ways in which s tudents dea l wi th

par t icu lar concepts

or

p h e n o m e n a ,

and

w i ll a lso develop wa ys

of

hand l ing

these

dif ferences .

Such knowledge i s ex t remely valuab le and should be

ident i f ied, sh arpened, sy stem atical ly ref lected upo n, and above al l , shared

wi th

o ther teachers .

Variation

as a

Teaching Method

In

previous chapters, we have shown that in any particular lesson there are al-

way s things that teachers vary w hile other things are kept unch ange d, and that

this

pattern of variation— w hat is varied and w hat rem ains un chang ed— is of

decisive

importance in determining how effective th e lesson will be. In the

"Catering for Individual Differences" project , teachers are encouraged and

provided w ith opportunities to

observe,

reflect, and

share ideas

about their own

lessons as w ell as the lessons of other teachers. T he aim of this is for the teach-

ers to find

optim al patterns

of

variation

for

dealing with

the

intended obje cts

of

learning in a

lesson,

a nd

thus develop m ore pow erful w ays

of

helping their stu-

dents to learn.

In the first yea r of the p ro jec t , tw o pr im ary schools and a team o f abou t 1 0

researchers were involved.

In

each school,

two

learning s tudy groups w ere

fo rmed, each com pr is ing

five

teachers .

T he

fo l lowing tab le sum m ar izes

the

backgr ound in fo r m at ion

of the

groups (see Table 8.1) .

W orkshops on the theore tica l f r am ew ork of the pro jec t were conduc ted

wi t h the teachers of each school before the learning s tudy. Fu ndin g was ob-

tained to allow an

extra teacher

to be

employed

in each school, so that each

of the 1 0

teac he rs involved

in the

s tudy gained

a

n u m b e r

o f

extra

free

pe r i-

ods , thu s enab l ing them to take part. The m ee t ings w ere

off icial ly

scheduled

at

suc h t im es that al l the teachers involved w ere free, and able to a t tend the

m e e t i n g .

T A B L E

8.1

Ba c k gro u n d In f o rma t io n o f t he Le a rn i n g S t u d y G ro u p s

D u r i n g t he F i rst Year of the Project

L e a r n i n g N u m b e r

o f

Teachers

School Study Gro up Leve l o f Study Subject Part icipat ing

A

A

B

B

1

2

3

4

Pr imary Grade 4

Pr imary

G r a d e 4

Pr ima r y

G r a d e 1

Pr imary Grade 4

Chinese L a n g u a g e

Mathema t i c s

Ma the ma t i c s

Mathema t i c s

5

5

5

5



1 96 L O E T A L .

Ea ch o f the learning study group s consisted of at least one researcher, a se-

nior research assistant,

and all

teachers teach ing

the

same subject

at the

same

level in that school. They m et once every we ek for 1 hour to plan the research

lessons. The group m eetings w ere audiorecorded, and summ ary notes were

kept

of

each m eet ing. Each cycle

of the

learning study consisted

o f

about

10

meetings,

and the

whole process

w as

structured according

to the six

stages

described previously. Each research lesson w as taught , in r u m , by all of the

teachers

in the

group.

A t

least

tw o

lessons were videotaped,

and

then ana-

lyzed

and

discussed

in the

group.

A n

im proved version

of the

lesson

was

then

developed and w ritten up. The s tudents ' perform ance w as a l so m easured be-

fore

and after th e lesson. O n average, each group com pleted tw o research les-

sons

in the first

year. School-based

and

joint school seminars were a lso

scheduled during the year to facilitate th e sharing of experiences am ong the

four

groups

of

teachers.

Tw o of the

learning studies

are

described here.

W e

believe that these studies no t on ly illustrate th e concept of the learning s tudy

and the use o f variation theo ry, bu t also th e l inguis t ic con st i tu t ion of

the

space

of

l earn ing

(wh ich

is

dealt with

in

chap.

3 of

th is volum e) .

A PRIMARY GRAD E 4 MATHEMATICS LESSON

O N UNITS AN D U N I T I Z I N G

T he

fol lowing

is a

learning study that

w as

carried

out by a

team

o f five

teachers

w ho

taught m athemat ics

at the

primary Grade

4

level.

T he

entire

cycle (from the incuba tion of ideas, to reflection and eva luatio n) took a total

of

nine meetings, which were distributed over

a

period

of 3

m o n t h s.

The Learning Study Cycle

Choosing th e Object

of

Learning . The first step was to choose a topic .

T he teachers chose fractions, as they felt tha t fractions presented some o f

the

m o s t diff icul t concepts

for

school ch i ldren

at

this level.

T he

seco nd step

was to f ind out why the s tudents had diff icul ty lea rn ing fractions; in other

words ,

w h a t

i t was

a b o u t

fractions

tha t m igh t

be di ff icul t fo r

s tudents .

Understanding

W h a t

Is

i f f i c u l t

and Critical.

The

teachers reflected

on

their ow n experiences of teaching fractions in the past, and shared these experi-

ences

in the

team m eetings.

The

follow ing questions w ere co ntinually raised:

• W h a t is actually learned, when learning about fractions?

• W hy i s

learning fractions

difficult?

•

W h a t

is it

that

makes

learning

fractions

difficult?

• How can we conceptualize these difficulties?

The un iversity consultant also introduced the

teachers

to the relevant re-

search literature, in

particular

Lamon's

(1999)

book

about teaching

and



8. T O W A R D A P E D A G O G Y O F

L E A R N I N G

197

learning fract ions . Lam on argued that learning fract ion s con st i tu tes

the ba-

sis for proportional reaso ning , and that the teaching of fract ions should have

a

pr imary

focus o n concep tual unders tanding

ra ther

than procedura l know l-

edge.

S he

also pointed

out

that

a

cr i tical aspect

of

fractions that s tudents f re-

quen t ly fail

to grasp w as units

an d uni t iz ing.

T he

team then reviewed

th e

students ' textbook

fo r

pedagogica l adv ic e .

To

their surprise, they fo un d that

the

textbook

not

only lacked

a

form al treat-

m e n t o f uni ts and uni t iz ing, bu t that its presentat ion o f f r ac t ions ac tua l ly

cou ld

have contr ibuted

to the

s tudents ' misunders tand ing .

T he

chap te r

o n

addit ion o f f ract ions , fo r

example , began w i th

the

fo l low ing d iag ram ( F ig .

8.1) ,

accom pan ied

by a

question that asked

for a

fract io nal notat ion

of the

shaded area:

F I G . 8 . 1 .

T he

d i a g r a m u se d

in the

c h a p t e r

on add i t i on o f

f rac t ions , from Mathemat-

ics (Primary 4 , Firs t Term)

(

1997),

p. 49.

C o p y r i g h t

©

1997

by

C a m b r id g e P u b l i s h e r s

Ltd. Re p r in t e d w i th pe r mis s ion .

Having iden t i f ied un i t s

and

un i t iz ing

a s a

problem area,

t he

teache rs then

not iced that s tudents could have made

tw o

per fec t ly leg i t im ate guesses

in

respon se to this que stion in the textb ook (i .e. , 14/8 or 1 4/16), dep en ding on

w hat they unders tood

as one

u nit . However,

the

textbook exp ected only

o ne

answer (i .e. , 14/8);

the

tac i t assump t ion

in the

textbook bein g that each ci r -

cle cons t i tu ted one un i t .

A t

this stage, the teachers

we re

convinced that they should

focus

on

t each ing

un i t s

and

uni t iz ing

and

make this

the

object

o f

learn ing

of the re-

search lesson. They were also eager to f ind out w hat p rio r know ledge the i r

s tudents would br ing

to

their study

o f

f r ac t ions .

Despite

the fact

that several aspects

o f

f r ac t ions

had

a l ready been taug ht

in

p r imary Grade 3, not all teachers were sure that the s tudents in t h e i r

c lasses unders tood

the

concepts wel l .

In

par t icular , they

fel t

tha t

the

s tu -

dents

needed to

understand

the

idea

o f equal

shares

in

fract ions ,

as

w e l l

as

being ab le to con duct a s imple compar ison of f r ac t ions , befo re they could

unders tand

the

idea

o f uni t .

Developing a Test. The

teachers then designed

a

test

for the

s tudents .

T he purpose was to co l lec t in format ion about th e s tude nts ' way s o f th ink ing



198 LO ET AL.

about f ract ions , especially w i th regard to those aspects that w ere expected

to be

difficult. Furtherm ore,

the

test

w as to be

used

a s a

pretest

to

provide

th e

team w ith a basel ine against wh ich the learning outcom es of the research

lesson

(as

measured

by the

same tes t ) could

be

com pared.

T he

test consisted

of three main themes (exemplar questions

are

shown below):

1 . The

concept o f

equal shares in

fraction,

for

example ,

Ques t ion : What fract ion of the diagram is

shown by the shaded area?

2 . Th e c o n c e p t o f fraction

size

( r e s t r i c t e d to t he c o m p a r i s o n o f

f r a c t i o n s

w i t h e i th e r th e s a m e d e n o m i n a t o r o r t h e s a m e n u m e r a t o r , f o r

e x a m p l e ,

Question: Is

1/2

of a cake (greater than/smaller than/equal to)

of a cake?

3.

T he concept of a uni t being referred to by a f ract ion , for example .

Quest ion: When 4 1 / 2 cakes are equa l l y d iv ided am ong 3 people,

how m any cakes does each person ge t? (You m ay draw diagram s

to

find

the answer.)

The resu l ts of the pretes t con fi rmed some of the teach ers ' spe cula t ions ,

and showed that there w ere few er s tudents

who had

m as tered

the

concept

of

uni t in

f ra ct ions than those

w ho

unders tood

the

concept

of

eq ua l shares ,

o r

were capable

of

com paring simple frac t ion s (see T able 8.2).

Planning

the Research Lesson .

Inform ed by the pretes t resul ts, the

teachers began to plan the lesson. They agreed tha t there sho uld be som e re-

vision of equ al shares bu t decided that th is should be t a u g h t in a separa te les-

son prior to the research lesson. The research lesson shou ld beg in w i th

compar ing fract ions bu t

focus

ma in ly on un i t s and un i t i z ing . There were

several rounds of lively discussion . T he result w as a fairly detai led plan that

w as

careful ly

del iberated

and

ful ly

di scussed.

A . T h e Lesson O p e n e r — C o n t e x tu a l iz a ti on

The plann ed lesson began by es tabl ishing a relevan ce s tructure ( i .e ., le t -

ting

the

s tudents view frac t ions

from a

po in t

of

view that they could im m edi-

ately

experience

as

mean ingfu l ) .

T he

s tudents w ere

to

di scuss

the

fo l lowing

problem

in

small groups (see

box on p.

200):



TABLE 8.2

The

Results

of the Pretest

Them e Question

Freq. o f Correct

Responses

Classes

A— E

(N

=

151)

E qua l

sh are s W h at

f ract ion

of the diagram is

s h o wn by the shaded area?

Shade

1/9 of a

square.

Shade

1/8 of a

c i r c l e .

Shade

1/3 of the eggs in the

basket .

69

87

16

87

C o m p a r i n g

1/2 of a

cake

is

(greater than

/

eq u a l

to /

smal le r

f ract ions

tha n) 1 /4 of the

same

cake

2/4 of a cake is (greater tha n / equa l to / smal le r

than)

1/2 of the

same cake.

2/5 of a kg is (g rea te r than / equa l to / smal le r

t h an ) 4/5 of a kg.

1 1 2 of an hou r is (greater than / equal to /

smaller than) 1/200

of an

hour.

U n i t s

and

Divide

2

cakes in to three equal parts .

How

U n i t i z i n g

ma ny cakes

are

there

in one

part?

W hen 4 '/2 cakes

are

divided among three

persons , how many cakes does each person

get?

W h a t

fract ion of

squares

is

shown

by

the

black squares?

W h a t

f ract ion

of the

to ta l number

of

objects

is

shown

by the

black

squares?

63

58

1 1 1

39

13

3

20

22

199



8. T O W A R D

A

P E D A G O G Y

O F

L E A R N I N G

201

were

in 1 /6 of

their pac k.

In

this instance,

the

size

of the

pack varied w hi le

the

fract ion

rem ained the same. The teacher then posed the quest ion: W hy

are the resul ts different w h e n the fract ion is the s ame? T he s tudents ob-

served

how the

number

o f

candies changed w i th

the

changing un i t .

D . Waff le Cakes

In

the next s tage, the teacher gave each group a paper disc that repre-

sented a round

waf f le

cake . In thei r groups , the s tudents had to cut out 1 /6

of the cake . When they

f in ished,

they w e re given 2 discs , and 1 i/2 di scs in

tu rn , wi th

th e

same task

o f

cu t t i ng

out 1 /6 of the

am oun ts g iven . They then

had to comp are the am ount o f cakes o b ta ined, and see how the s ize o f the

uni t

m a t te r e d .

T h e

d i f fe rence

be tween th i s ac t iv i ty

and the

p rev ious

o n e

was to

al low s tude nts

to see

tha t

th e

concep t o f

uni t

em braces bo th cou n t -

able

an d

uncoun tab l e amoun t s .

E .

Back to the First

Question

A t the en d of the

lesson,

the

teacher then returned

to the two

ques t ions

abou t the

fund-rais ing event that were discussed

at the

beg inn ing

of the

les-

son. The s tudents w ere to w rite out thei r own answers to the qu est ions m ak -

ing

use of

w hat they

had

learned

in the

lesson.

Quest ions:

• W ho has donated the m os t?

• W ho w as the most generous?

Teach ing t h e Les s on and

Reflect ing

on the Resu l ts .

A ll f ive

teachers

t au g h t their own classe s with the same plan. They also tried to observe the ir

col leagues teaching

the

same lesson,

and

shared their observations

after-

ward w i th

a

view

to

m odi fy ing

and

improving

the

p lan . Al though there were

some s l ight var iations w hen each teacher im plem ented the lesson plan , th e

teachers

a ll

fol lowed

the

structure

and

sequence

of

act ivi t ies

in a fai thful

manner .

T he sam e tes t that w as used for the pretes t w as adminis tered to the s t u -

dents

a few

days

after the

lesson

had

been taug ht .

T he

assessment i tems

re-

lating

to the

notion

o f

un i t

are

shown

in

Table 8.3.

T he

difference be tween

th e

pretes t

an d

post tes t re sul ts indicates considerable learning gains

by the

students .

After

all of the

teachers

had

t augh t

the

lesson, they

met on a

n u mb e r

of

occasions to evaluate th e entire process. A l though the teachers felt that they

had

been overam bitious

and had

packed

too

m uch in form at ion in to

th e

dou-

ble lesson (totaling 80 min.), they

were

in general q uite satisfied w i th w ha t

they had achieved, and were pleased to learn about the students ' learning

outcom es. S uggest ions were m ade o n how to f ine- tune the lesson plan w i th



TABLE 8.3

The

Dif ference B e twe e n

the P retest and

Posttest Results

Theme

Quest ion

Freq. of Correct

Responses

Classes

A-E

(N

=

151)

Pretest/Posttest

(% ga in

o r

loss)

Equal shares

Comparing

fractions

Un i ts and

Uni t iz ing

What fraction of the diagram is shown

by th e shaded area?

Shade

1/9 of a

square.

Shade 1/8 of a

ci rcle .

Shade

1/3 of the

eggs

in the

basket.

1 /2 of a cake is (greater tha n / equal to /

smaller than) 1/4 of the

same

cake.

2/4 of a cake is (greater tha n / equal to /

smaller than)

1/2 of the

same cake.

2/5 of a kg is

(greater tha n

/

equal

to /

smal le r

than) 4/5 of a kg.

1 /2

of an hou r is (greater than / equal to /

smaller than) 1/200 of an hour.

Divide 2 cakes into three equal parts. How

man y cakes are there in one par t?

W h e n

4 1 / 2

cakes

are

divided among three

persons, how

many cakes

does

each person

get?

W hat f raction of squares is shown by

the

black squares?

What fraction

of the

total number

o f

objects i s shown by the black squares?

45.7/68.9

*(+23.2%)

57.6/64.9

(+7.3%)

76 8/86 8

57.6/67.5

*(+9.9%)

41.7/50.3

*(+8.6%)

38.4/60.9

*(+22.5%)

73.5/81.5

(+8.0%)

25.8/45.0

8 7/4 7

(-4.0 )

2.0/44.7

*(+42.7%)

13.3/31 .3

14.7/32.0

*A significant change

in

percentage

is observed

w i t h / ?

<

0.05.

202



8. T O W A R D

A

P E D A G O G Y

OF

L E A R N I N G

203

more consolidation work at differen t points in the lesson. T he posttest re-

sults show ed that al l the classes obtained sub stantial gain when com pared

with the pretest res ults (see Table 8.4). T he effectiveness of the lesson w as

thus

evident.

A

PRIMARY G RADE

4

C H I N E S E L E S S O N

O N

TEXT CO MPREH EN S I ON

This w as another learning study carried out in the first phase of the "Ca-

tering

for

Individual

Differences

(Bui ld ing

in

Variation)" project . Seven

m eet ings, one hour each, were used for the com plete cycle .

Stage 1: Choosing a

S peci f ic Object

of

Learning

After m uch de l ibera tion , the teache rs decided to choose chapter 10 of their

course book,

A

Pen cil End , as the m ain teaching con tent . This chapter was

chosen

for two

main reasons: First, according

to

their teaching schedule,

this

lesson

w as to be

tau gh t around la te N ovember,

and so the

t im ing wo uld

be about right. Second, the text contained some special features that the

teachers con sidered to be w orthw hile for the s tudents to learn. The text was

in th e form of a story w ritten by a boy who

felt

that a 2-inch long pen cil end

w as

too

short

to be

use ful ,

and so

threw

it

away.

He

threw

th e

pencil

end

away three t im es, and yet each t im e i t reappeared on his desk. Fina lly he re-

alized tha t i t w as his m other who had picked up the penc i l and put i t back on

his

desk, hoping that

he

would

u se it

again

and not be

w as tefu l .

The boy was

then ashamed of his ow n action and used the pencil to do his homework.

In subsequent m ee t ings , the teachers identified five w or thwhi le ob jec ts

of learning :

TA BL E 8.4

The

Average

Scores of Different Classes in the Pretests and Posttests

Cl a ss

A

Class B

Class C

Class

D

Class E

Whol e class

Pretes t :

Average Score

6.38

6.89

3.77

3.94

3.63

5.13

Posttest:

Average

Score

8.78

9.14

4.83

5.31

4.78

6.85

Both

Tests:

Total

Score

12

12

12

12

12

12



204 LO ET AL .

1.

In the

text,

th e

same action (throwing away

the

penci l end) appeared

three t im es, yet the w ay in w hich the sen t ime nt of the boy w as conveye d in

each

case

w as

different.

T he

t eachers w ished

to

draw s tuden ts ' a t ten t ion

to

the way in

w h i ch

the

cho i ce

of the

ve rb s m a tched

the

ac t ions

and the

verbal

express ions ,

in

order

to

show esca la t ing

feel ings o f

d is l ike .

2. In the text , there were six words wi th the

"hand"

rad ica l [-f- ] or [ ^ ].

These

words can be considered to be in the s ame sem an t ic f ield as the word

n a h (Cantonese) [^ ] ( m e a n in g

"take"); al l the

w o r ds

a re

associa ted w i th

some act ion us ing the hand . Yet , each w ord has a s l ig ht ly

dif ferent

m e a n -

ing .

For e x a m p le , the w o r d taih ( Ca n t o n e s e ) [ -^ ] has the m e a n in g of

"carry , take ho ld of , or

l i f t i ng

s o m e t h i n g o u t " ; t h e w o r d

g im

( C a n t o n e s e)

[^ct]

has the

m e a n i n g

o f

"select

a nd

p ick up" ;

wing/\ihng

( C a n t o n e s e ) [ty]

has the m ean ing o f "throw"; laai (C an tonese ) [ 4& ] has the m ean ing o f

"puH";y/p (Cantonese) [4lc] has the m e a n in g o f "catch o r receive";

touh

(Cantonese) [}£) ] has the m e a n in g

offish

out ." In w r it ten l an gua ge , de-

pending on the con tex t, it wou ld be

more

ap propr ia te to use one of these

specif ic w ords ra ther than the w o r d

"take"

[ ̂ ] in order to convey m ore

p rec i s e mean ings a n d m a k e th e w r i tt en wo rk more e l eg an t . Y et in spoken

Ca n t o n e s e ,

it w o u l d b e p e r f ec t l y accep t ab l e , and in

fact

m o re n a t u r a l , to

use the

spoken form

of "take" [ ̂ ],

w h i c h

is l ing

(C an tonese ) [^] .

The

teachers w i shed to teach th e s tudents how to di s t ing uish th e me a n i n g a n d

usage

o f

each

o f

these w ords . Also, they w anted

the

s tudents

to

appreciate

tha t in w r i tt en l anguag e , the use of w ords h as to be mo re precise in order to

bring out the exact meaning to be conveyed.

3. T he text showed the different personal i t i es of the bo y and his m other.

The boy was

very imp at ien t

and

showed

h is

l ikes

and

dis l ikes ove rt ly .

The

mother w as more gen t le and sub t le . T h e t eachers sugges ted that the

mother's example could show

the

students

how to

relate

to

other

people,

such

as

their classmates.

4. In the

last paragraph ,

the

mother in troduced

the

idea

o f

conservation.

The

teachers w ished

to

cu lt ivate

in

their students

an

awareness

o f the

envi-

ronm ent and a posi tive at ti tude tow ard con servat ion.

5.

I t was the po l icy of the school that the Chinese panel head should

specify

the l earn ing ob jec t ives fo r each chapter at the b e g i n n i n g of the

school term. For th is chapter , a num ber of w ords and senten ce pat terns had

already been iden tif ied as teaching object ives , and these w ere to be assessed

in

th e exam ination .

On ly tw o periods h ad been ass igned for the t each ing o f th is chapter ,

and the t eachers fel t t ha t the re w ou ld no t be eno ug h tim e to cover eve ry -

th ing t ha t they w i shed

to

t eac h . They adm i t t ed t ha t they of ten

had to

rush

t h r o u g h t h i n g s super f ic ia l ly , an d tha t there w as l i t t le t i m e fo r i n -dep th

t r ea tme n t . As a r e su l t , m any s tuden t s w ere no t ab l e to l ea rn w e l l . Th i s

had a lways been the teachers' problem.

Af t e r

much di scuss ion , they



8.

T O W A R D A P E DA G O G Y O F L E A R N I N G 205

agreed tha t

fo r the

research lesson, they w ou ld

try to

f o c u s

o n

f e we r

o b-

j ec t s

o f

lea rn ing,

and

dea l wi th each

on e in

grea te r depth . They dec ide d

no t

to

f o c u s

on the

affect ive aspec ts (objects

o f

le a rn ing num bers

3 an d 4)

a t

th i s poin t , because they

fel t

that these ideas should be

in f i l t r a ted

in

the i r l e ssons th ro ugh ou t th e year . O f the three remaining aspec ts , they

fel t tha t

th e

choice

o f

w h i ch

to

f o c u s

o n

shou ld depend

o n the

s t u d e n t s '

pr ior exper ience and knowledge . There fore , to he lp them make an in-

fo rmed decis ion, they decided to wai t unt i l they could obta in informa-

t ion about the s tudents

from

the pre tes t .

Stage

2:

F i n d i n g

Out the

E x t e n t

to

W h i c h

the S t u d e n t s

H a v e

Developed

th e

I n t e n d e d C a p a b i l i t i e s

A pretest w as administered to all five classes of 148 students. O n average,

over 85% of students in each class (m ore than 70% in the w eakest c lass) dem -

onstrated an un derstanding of the words and sentence patterns

specified

by

th e

panel head (object

of

learning number

5), and

were able

to use

these

words

to fill in

app ropriately

the

blanks

o f a

text. Therefore,

the

teachers

de-

cided

that

it

would

not be

necessary

to

focus

o n

these aspects

in the

lesson.

To

test

the

s tudents ' understanding

of the

w ords w i th

the

hand radica l ,

two que stions were set. In the first question , three sentence s w ere given . For

each sentence, three characters

o f

very sim ilar m eaning w ere provided

and

the s tudents had to choose the m ost appropria te o ne for the par t icula r con-

text.

In the

second question, students were required

to f ill in

seven blank s

to

com ple te a

text. Seven w ords w ith

the

hand radical were pro vided

and

s tu-

dents

had to

choose

the

m ost appropria te w ord

for

each b lank.

The

resul ts

of

the

test showed that students

had difficulties

dist inguishing words with

the

hand

rad ica l .

The

word that

w as

found

to be

m o s t

difficult

for the

s tudents

w as "fish out" [$0]. In the first que stion, on ly 10% of the stu dents cou ld use

th e

word "fish out" [$0] appropriately.

In the

second qu est ion, only

tw o

s tu-

dents in one class, Class 4C, got all the answ ers correc t . A ga in, the character

"fish out" [ $0 ] w as found to be the most difficult, as only 10% of the stu-

dents used it correctly. Other difficult words were "take" [

^ ]

(20% co r-

rect),

"carry"

[H] (30% correct), and

"pick

up" [^] (30% correct). Th us, it

becam e clear that w ords with th e h and radical needed to be given special a t-

tention,

especia l ly

the

words

"fish

out"

[

- J £ )

],

"take"

[ ̂ ], and

"carry"

[^ ].

Another question required

the

students

to put two

groups

of

w ords

in or-

der of the strength of feel ing expressed. The first group consisted of the

words

"excited"

[ - *

-f^], "pleased" [Ht -§-], and "happy" [ ' j Jf£].The second

group co nsisted of the wo rds

"angry"

[£_

i j ( 3 ,

"discontented" ffi / * £ ] and " fu-

rious" ['1^ ^J]. On ly abo ut 30% of studen ts w ere ab le to put the first group o f

words in the

correct

order, and about 60% of students were able to put the

second gro up o f wo rds in the correct order.



2 06 L O E T A L .

To test w hether students w ere able

to

m atch

the

verbal expressions cor-

rectly with the feel ings o r sentiments expressed, they were asked to m a tch

three phrases with three verbal expressions.

For

example, students

had to

match the phrase, "M other said kind ly" with

"Don't

give up, you just have

to work harder next time." I t was found that about 60% of students could

ma tch

the

phrases with

the

verbal expressions correctly.

Th e resu lt of the pretest prom pted the teache rs to ma ke the decision to fo-

cus on the

first

tw o objects of learning:

• To be able to appreciate that the choice of verbs should m atch the actions,

and that the verbal expressions should effectively convey sentim ents.

• To be able to dis tingu ish the m ean ing and usage o f some w ords w i th

the hand radical , and to apprecia te that in writ ten lang uag e , the use of

words has to be precise.

Stage 3:

D e s i g n i n g

a

Lesson (Lessons)

A i m e d

to

D e v e l o p

th e

I n t e n d e d C a p a b i l i t i e s ( T h e I n t e n d e d

Objects of

L e a r n i n g )

Th e teachers shared their usua l m ethods of teach ing a text , w hic h typical ly

included going through

the

fo l lowing

five

stages:

1. B r ie f ly expla in ing

the

text

as a

w h o le

2. R eading the text a loud

3. E xp laining new characters and w ords

4.

Going through

the

questions

at the end of the

text

and

looking

at

each

paragraph in m ore deta i l

5. Teaching some of the sentence patterns and special l inguis t ic fea-

tures in the text .

T he

teachers

in

general

felt

that this routine, w hich they

had

been us ing

all

a long, w as som etim es boring, and that it failed to provide a structure that

helped

the

students

focus on the

objects

o f

learn ing. They hoped

that fo r the

research lesson , they could com e up w ith a better w ay of structuring the les-

son p lan in order to help the students focus on the objects o f lea rn ing by

means of suitable variations. I t was decided that tw o lessons w ould be used

fo r teaching—one for each object of lea rn ing. For the purpose of th i s chap-

t e r ,

only

the

lesson deal ing w ith

the

second objec t

o f

l e arn ing— w ords w i th

the hand radical— is described. Th e lessons of two c lasses (Class 4C and

Class 4H) were videotaped, and o nly data from these tw o c lasses are used

fo r

the analysis.

The Lesson Plan: Teaching

W o r d s W i t h

the Hand Radical . The l e s s o n

plan con tained the follow ing essential features, wh ich w ere aim ed at bring-

ing

ou t similari t ies a nd

differences,

contrasts, variation a nd invariance:



8.

T O W A R D A

P E D A G O G Y

O F

L E A R N I N G

207

1 . Students shou ld find all the w ords showing act ion that had a s im ilar

meaning

to

"take,"

and

that used

the

hand radical . Then they sho uld

com m ent on the text

after

all

these words

had

been replaced w ith

the

word

"take."

2.

W ords w i th

th e

hand radica l should

b e

d iscu ssed toge ther ,

to

show

the i r s imi la r i t i e s and cont ras t the i r d i f fe rences , for example ,

"drop"

[- •]

and

"throw" [#}]; "pickup" [ j f c ] ; "pickup"

[^] and

"take"[$r].

3. V ariations shou ld be used to help students discern the m eanin g of the

words ,

for

exam ple , using exam ples

and

nonexam ples.

F or

each pair

of words, a sentence was to be used and i ts structure kept invari-

ant—only the word with the hand radical would be changed.

This

w as

intended

to

enable students

to

discern

the

subtle

difference in

m eanings of the

different

words.

Stage

4: Teaching the Research Lesson

( the E na cted

Object of

L e a r n in g )

The

Lesson

of

Class

4 C . The teacher first asked th e students to find all

the words w ith

the

same m eaning

as "take" [ ̂ ]. She

then pointed

out that it

w as

c o m m o n

for the

students

to

take

all

these w ords

as

synonymous ,

and

that they tende d to use only the word "take," instead of m aking use of these

different

words .

She

told them th at

if

they a lw ays

did

this, however,

the text

w o u l d

becom e very boring. S he used the m etaphor of their m other cooking

th e same dish for every m eal; even thou gh i t was good to eat at the begin-

ning,

it

w ould become bor ing after

a

w hi le .

T he

teach er then

focused on the

five

wo rds:

"receive"

[ ̂ ], "fish out" [ ̂ ) ], "take" [ ̂ ],

"carry"

[ ̂ %] , and

"pick up" [ % fc ]. These w ere writ ten on the board.

She attended to the w ords one at a time, always

com paring

each o ne w i th

the w ord

"take"

[ ̂ ]. She used a sentence in which the use of e i ther w ord

was poss ib le . The difference in m eaning of the two w ords was m ade more

prominent by put t ing them in the same context . By keeping the sentence

structure invariant and varying the wo rds, the

teacher

focused the students'

attention on th at w hich varied, that is, the difference in the m eaning con-

veyed by the tw o sentences becau se o f the

difference

in m eaning of the tw o

words . Fo r example , sh e dealt with the tw o w ords "take" [

̂

] an d "receive"

[ ̂ - ] in the

fol lowing

way.

The

teac her asked

the

students

to

com pare

the two

sentences:

He took the penci l from her hand.

He rece ived the penci l f rom h er hand.

She expla ined that w hen the word

"received"

[ ̂ ] was u sed in the second

sentence, there was an im plication that the one holding the pencil (sh e) was



208 LO ET AL.

giving

it to the recipient

(him).

When the

word

"took" [ ̂ r ] was

used,

it had

a different imp l icat ion. The teacher added that the wo rd "took" in the first

sentence m ight

give

us the feeling that "he" was no t very p olite because he

took wi thout asking,

o r

w i thout be ing g iven

the

penci l

in the f irst

p l ace .

"Took" in the context o f the first sentence m eans that the ac tor is "he," and

"she" w as passive.

"Receive"

in the context of the second sentence means

that

the actor is

"she,"

and "he" is the pass ive recipien t .

T he teacher dea l t w i th the other words in a s imi l a r way .

The Lesson of Class

4H .

The

teacher

first

read

out

loud

a

piece

o f

text.

In

this

text , the word

"take"

was used m any t im es, som etim es inappropriately.

T he

teacher asked

the

students

i f

they noticed w hich w ord

w as

used most

of-

ten. Many students were able

to identify th e

word

"take."

Then

th e

teacher

asked, "What would y our teacher think if you wrote a composition with so

m a n y

"take's?"

M any students responded that the t eacher would n ot

like

it.

T he

teacher then asked

the

students

to find all the

words associated w i th

the

act ion

of the

hand. Nine words were found.

S he

then explained

the

meaning o f each w ord, role-played the act ion conveyed, and analyzed the

action of the han d. Fo r each pair of w ords, she also kept the sen tence struc-

ture invariant ,

b u t

changed

the

verb

and

asked

the

s tudents

to

c o m p a re

the

tw o

resu l t ing sen tences .

For

example , w i th

the

w o r ds

"drop" [ ̂ ] and

"throw"

[ /}],

she gave the fol lowing sentences :

•

Don ' t drop banana skins onto

the

floor.

•

Don ' t

throw

banana skins onto

the

floor.

She asked som e s tudents to com e out and act out how they "drop" some-

thing, and how

they "throw" som eth ing .

In the

subsequen t d i scuss ion ,

she

focused

on the

action

of the

hand

—

w hether

the

action

w as

large

or

sm al l,

the size of the swing , and the angle made by the arm. Then she said that o f

the tw o words that were used to fill in the blank in the same sentence struc-

ture, only

one of

them

w as

correc tly used

and

asked

the

students

to

ident i ty

the correct one.

S he

dea l t w i th

the

rest

of the

words

in

pai rs

and in a

s imi l a r way .

In

each

case, she focused on the physical movem ent of the ac t ion. For exam ple, she

stressed that with the wo rd

"carry"

[ H; ] , the arm should be held s t raight

down .

Final ly , the

teache r reread

the

text tha t

she had

read

ou t at the

b e g i n n i n g

of the lesson. This t ime, the s tudents suggested approp riate w ords to replace

the word "take" in each ins tanc e.

The En ac ted

Ob ject of

Learning .

W e see tha t bo th t eachers seemed to

have taug ht

in

very s im i lar w ay s. How ever, there

w as a

very im po r tan t d i f -

ference

in the i r ways o f dea l ing wi th th e ob jec t o f l ea rn ing . Wi th th e



8. T O W A R D A P E D A G O G Y O F L E A R N I N G 209

t eacher

of C lass 4C, the focus w as on the subt le d ifference in m ean ings o f

the

di f ferent w ords. By keeping the sentence s t ructure invariant and vary -

ing

the wo rd used, she

helped

the s tuden ts to focus on the d i f fe rent mean -

ings

of the words . These m eanings w ere made expl ic i t by the ir re la t ion to

the l in gu ist ic con text , that is , the rest of the sen tences. Fo r exam ple the ac-

tor versus rec ip ient meaning—impl ic i t

in the

words "took" versus "re-

c e i v e , " r e s p e c t i v e l y — wa s m a d e e x p l i c i t

b y t h e

i n v a r i a n t s e n t e n c e

structure.

On the

other hand, despite

the

fact that

the teacher o f

Class

4H

also presented

tw o

wo rds

in the

same l ingu is t ic context ,

she

focused

on the

m eanin g of each word o n i ts ow n and the ac t ion of the hand conveyed by

each w ord. Th e teach er did not re la te the wo rd to the l ing uis t ic con text to

help

s tuden ts d iscern

the

d ifferences

in

mean ing . Th is me thod

o f

dea l ing

wi th

the mean ings o f w ords in a

decontextual ized m anner

c an create prob-

l e m s fo r

learners

o f

Ch inese ,

as one

charac te r

m ay

change

its

m e a n i n g

w hen u sed toge ther w i th another charac te r (or charac te rs ) to form a w ord

or a phrase . For exam ple , when the teacher fo cused on the mean ing of the

wo rd

"carry"

[ _ ] , sh e em phas ized tha t i t had the mean ing tha t the arm

should

b e

held straight do w n. This

is a

correct interpretation

if the

word

is

used

in the co ntex t of

"carrying

a br ie fcase /shop ping bag," bu t not correc t

wh e n it is used in the con tex t of

"car ry ing

a lantern," for example , in w h i ch

case

the arm

w ould p robab ly

be

ben t

a t the

e lbow.

Stage 5:

F i n d i n g

the Students

L e a r n i n g

Outcomes

Because

the obje ct of learning w as to help the students to discern the sub tle

differences in the m ean ing of the different w ords associa ted w ith the act ion

of the

hand ,

and to be

able

to use

them approp riately,

the

pos ttest also tested

such

a capab ility in the students. Judging from the enacted o bject of learn -

ing

of the tw o c lasses (and i f the way in w hich the teacher deal t w i th the ob-

j ec t

of

learning

is inf luent ia l ) , it

would

be

expected that

the

s tudents

o f

Class 4C should perform bet ter than those of Class 4H. This was indeed

borne out by the resul ts of the post test. The quest ions w ere the same in both

the pretest and the posttest. Table 8.5 shows the results of the quest ion

where s tudents were given seven words with the hand radical , and were

asked to fi ll in seven b lank s in a text with the approp riate w ords.

Th e resu lts of the post-test show ed that the students of Class 4C dem on -

strated

significant

imp rovem ent . In the pre test, on ly two students were able

to

choose

all

seven words correctly,

but in the

posttest,

1 7

students

got all

seven

w ords co rrect . Of the five w ords that the teach er attended to, al l stu-

dents in the

c lass w ere able

to fill in

three w ords correct ly: "receive"

[ ̂ ],

"fish out," [^)], an d "carry" [ ^ % ] .

S ignif icant

im provement w as a lso found

in Class 4H, however the improvement was not as great as in Class 4C.

About

1 0

students

go t all seven w ords

correct.

For the

w ord "fish out"

[

$0],

the re la tive improvem ent w as about 47% in Class 4H, w hereas the im prove-



TABLE 8.5

Table to Compare the Results of the Pretest and the Posttest

Fil l ing

in the

Blanks

With th e

Appropriate

Wor ds

N u m b e r of S tuden t s C orrec t (Percentage)

St u den t

n u m b e r

Class 4C pretes t 33

Class 4C

posttest

33

Rela t ive improvement

4H

pretest

3 1

4H

pos t tes t

3 1

R el a t i ve

i m p r o v e m e n t

[1 ]

pick

u p

14

( 41%)

24

(73%)

54%*

7

(23%)

1 1

(35%)

51%*

[2 ]

#5

t h row

26

(74%)

27

(82%)

31 %

1 1

(35%)

18

(58%)

35%*

[3]

receive

24

(68%)

33

( 1 00%)

100%*

9

(29%)

22

( 71%)

59%*

[4]

pul l

27

(82%)

30

( 9 1 % )

50%

17

(55%)

24

(77%)

49%*

[5 ]

ft

fish ou t

9

(27%)

33

( 100%)

100%*

2

(6%)

16

(52%)

47%*

[6 ]

t ake

14

(42%)

32

(97%)

95%*

9

(29%)

18

(58%)

4 1 % *

[7]

carry

14

(42%)

33

(100%)

100%*

10

(32%)

18

(58%)

38%*

Key. Rela t ive i m p r o v e m e n t

=

i n e r e a s e

in % -

m a x i m u m p o s si b l e in c r e a se

in %.

* Words th at h ad been spec i f i ca l ly dea l t w i t h in the lesson by the t eacher .



8. T O W A R D A P ED A G O G Y O F

L E A R N I N G

2t t

m e n t was 100% in C lass 4C. For the word

"carry"

[ t̂. ], the relative im-

provement

in

C lass

4H w as 38% and in

C lass

4C, i t w as

100%.

In the question that required students to choose the m ost appropriate

word

to be

used

in a

sentence,

i t was

also

found

tha t

the

students

in

both

classes made significant improvement

in the

understanding

of the

word

"fish out"

[ ̂ ]. In 4H, the

improvement

was

from

10% to 61% of

s tudents

getting

it

correct,

whereas in

Class

4C, the

im provement

was

again greater,

from

21% to

94%.

A s w e m ent ioned

earlier,

these tw o studies w ere some of the first studies

(carried ou t

w i th in

a

research project with developmental ambit ions)

that

w ere based on the part icular theory of learning described brief ly in chapter

1.

Both s tudies proved

to be

successfu l

in

te rms

of

gains

in

s tudent ou t-

comes. Furthermore , they showed

a

phenomenon tha t

w as

also

found in

later

s tudies: Al though the teachers had agreed on the intended object of

learning, the enacted object o f learning varied betw een the groups, and that

the

res ults (the l ived object

o f

learning) varied acco rdingly.

Since these s tudies w ere carr ied ou t , m any others have fo l low ed

(22 by

th e end of the second year of the project), m ostly w ith results that are very

m u c h in

l ine with

the

resul ts

of the two

studies described

in

th is chapter.

(Reports

on other

learning studies conduc ted

in

this project

can be found on

the Internet at this address: http:/ /cidv.hku .hk)

The two

studies

w e

have jus t looked

at

cam e

f rom a

project w ith

a

strong

emphas is

on the

enhancement

o f

teachers ' professional development .

In

this way, the a im s of the project were close to those o f the Japanese lesson

study

m ode l.

The aim of the

study described

in the

fo l low ing sect ion

w as

primari ly to test theoretical con jecture s, and thus this s tudy w as c loser to the

idea o f the design experiment .

A

SECONDARY

GRADE

4

E C O N O M I C S

LESSON

O N T H E

I N C I D E N C E

O F A

SALES

TA X

The a im of

this learning s tudy

w as

threefold:

to find a pow er fu l way for

teachers to help secondary Grade 4 students h andle a rather diff icult bu t im-

por tant economic con cept ;

to

evaluate

th e effectiveness o f a

learning s tudy

in

the

improvement

of

teaching

and

learning

(in comparison to the

lesson

s tudy

approach) ; and to test the tenet o f a specific theory o f learning

(i.e.,

the theory

of

variation— that learning

to

experience

som ething

in a

certain

w ay is

cont ingent

on the

pattern

o f

variation

in the

c ri t ical aspects

of the ob-

j ec t

of

learning).

The

investigation also promised

to

demonstrate that

a

learning

s tudy cou ld

be a

design experiment (B rown, 1992; C ol l ins , 1992)

and

serve primarily

as a

research tool .

T he ob jec t of learning for this study was the capa bili ty o f taking into ac-

count the no tion of the relative elastici ty of dem and and sup ply in determ in-

ing the

distribution

of a tax

burden between buyers

and

sellers result ing



2 1 2 L O E T A L .

from the

introduction

of a

sales tax.

I t was

envisaged that

if

students could

develop

an

economic

perspective in understanding th e topic of the inci-

dence

of a

sales tax,

the different

w a y s

in

w hich they were able

to

under-

stand

the

econom ic phenom enon w ould increase.

Th e Economic

Topic

Used in the

S t u d y

The

economic topic used

in

this study

is

"the incidence

o f a

sales tax," taken

from the

Hong Kong economics curriculum

for

secondary Grades

4 and 5.

When

a

governm ent levies

a

sales

tax on

goods

and

services,

a

certain percent-

age

of the

cost

of our

purchase

as

consumers

is

paid

to the

government.

A t

pres-

ent, Hong Kong

does

not

have

a

general

sales

tax,

but a

limited number

of

commodities such

as

tobacco

and

liquor incur excise duty (i.e.,

a

particular

form

of

sales ta x).

The

Hong Kong government

is

cu rrently considering

a

gen-

eral sales tax,

and

this

has led to

heated discussions am ong

the

general pub lic.

M ost people believe that

if the

general sales

tax is

introduce d,

the

sellers

wil l

transfer

th e

entire

tax

burden

to the

buyers,

and

simply

raise the

price

of the

commodities

by the

amount

of

sales tax.

The

object

of

learning

for

this study

was the

capa bil i ty

o f

taking into

ac-

coun t the notion of the relat ive elast ici ty of dema nd a nd su pply in determin -

ing the distribution of a tax burden betw een buy ers an d sel lers tha t results

from the introduction of a sales tax . I t was envisaged that if students could

develop an economic perspective in thei r unde rs tanding of the topic of the

incidence

of a

sales tax ,

th e

different w a y s

in

which they were able

to

under-

stand

the

econom ic phenomenon w ould increase .

The view th at if a general sales tax is introduce d, the sellers wi l l transfer

the entire ta x burden to the buyers by raising th e price of the com m odities by

the

amoun t

of

sales tax,

is not fully

supported

by

econom ics . Econom ists

ar-

gue that instead of mak ing the buyers shoulder the

full

tax burden in every in-

stance,

th e

distribution

of the tax on a

part icular com m odity depends

on the

relative elasticity

of

demand

and

supply

of

that com m odity. A ccording

to the

law of demand and supply, whe n prices of a com m odity increase, th e quan tity

demanded falls, an d the qu antity supplied rises. Sellers are w il ling to supply

more

of a

com m odity w hen they

can

earn more

for

wh at they sell; buyers

are

less keen on purchasing a com m odity w hen they get less for their money. The

effect

on prices is therefore not a unifo rm price increase on all goods.

People need some

com m odities

more

than

others;

w ater

and

staple foods

are the classic exam ples. Even when the price o f these com m odities

nses,

the

quanti ty demanded wil l n ot drop sign ificantly. In other w ords, th e demand is

said

to be

inelastic,

or the

elasticity

of

demand

is low

( the quan ti ty dem anded

does

not

change

as

mu c h

as the

price).

For

other com m odities such

a s

luxury

cars an d jewelry, demand is highly

susceptible

to

price

change, and the quan-

t ity demanded changes m ore than

th e

change

in

price. Such dem and

is

said

to

be

elastic,

or the

elasticity

of

demand

is

said

to be

high.



8.

T O W A R D

A

P E D A G O G Y


Based

o n a

com m onsense understanding, sellers

of

com m odities with

in-

elastic

deman d w ill sim ply add the new ly introduce d sales tax to the current

prices,

and the

buyers w ill then

bear th e

entire

tax

burden. A ccording

to

eco-

nomic analysis, however, when determining the sharing of the tax burden,

th e

seller 's condition should also be taken into accou nt. For instance, for sta-

ple

foods (such

as

potatoes

o r rice),

people's demand tends

to be

inelastic,

but in the case of an especially good harvest , sellers have piles of unsold

stock

in

hand that they need

to

sell before

the

food spoils.

The

supply

is

more

or

less fixed over

th e

period

and so is not

very sensitive

to

price

changes .

In

such

a

case

of

oversupply,

the

supply

is

said

to be

very inelastic

and sellers m ay need to arrange to absorb part o f the sales tax in their p rice,

instead of passing i t on to the consum ers.

In general , the m ore elastic the dem and and the less elastic the supply, the

greater likelihood of the sales tax being absorbed in the price, and so the

sellers will share more of the tax burden than the buyers. Conversely, the

less elastic the dem and and the more elastic the supply, the greater the likeli-

hood of the w hole sales tax being added to the previous prices, in w hich case

the buyers w il l bear the w hole tax burden. How ever, in a s i tuat ion w hen both

the demand for and the supply of a commodity are elastic or inelastic, we

mu s t compare the elastici ty of demand and the elastici ty of supply. If the

elasticity

of

dem and

is greater

than

th e

elasticity

of

supply,

the buyers

have

the upper hand, and vice versa. In the case of staple foods, for exam ple, de-

m a n d

is

usually more inelastic than supply,

so the

buyers have

to

carry

a

greater part of the tax burden. O verall , the distribution of the tax burden b e-

tween buyers and sellers is a function of the relative elasticity of demand

and supply.

Des i g n

of the

S t u d y

Two groups, each with

five

economics teachers, part icipated in the main

study. On e of the groups fol low ed the Japanese lesson s tudy m odel . In this

group,

the teachers and a researcher

(who

did not

take

the lead)

discussed—

during three preparatory meetings, each of which lasted for around 2

hours—the ways in which the object of learning could best be handled.

Draw ing on their ow n experiences and the resul ts of a pi lot s tudy in w hich

students ' qu alitatively

different

understandings

of the

incidence

of a

sales

ta x

w ere assessed, the group developed a jo in t lesson plan for a series of

four lessons, w hich were then taugh t in five different classrooms.

The procedure was basical ly the same for the other group of teachers ,

with one ma jo r difference . In this group , the researcher actively participated

in the discussion, and introduced the theory of variation a s a tool for devel-

oping a lesson plan to the teachers. B oth the lesson p lan and the enacted ob-

jects

of

learning demonstrated teachers ' understanding

of the

theory

of

variat ion

as

applied

to the

part icular object

of

learning.

In the

fol lowing sec-



214 LO ET AL.

tion, this grou p is refe rred to as "the learning study group," whereas the

first

group

is

referred

to as

"the lesson study

group." T he

lesson study group

served

as a

reference

to

reveal

the effect of the

instru ction al design based

o n

the

theory

of

variation.

Using

th e

data obtained

on

teaching

and

learning, both inter-

a nd

intra-

group

comparisons were

conducted in

order

to

explore

the relationship be-

tween

th e

enacted objects

o f

learning

and

student understanding. This

investigation therefore com prises

a

learning study

and a

lesson study, with

th e

primary em phasis being on the comparison between these tw o studies. A sec-

ondary emphasis

is on

com parisons between classes w ithin each study.

T en

teachers participated

in the

main study,

five in the

learning s tudy

group

a nd

five

in the

lesson s tudy group.

T he

teachers

in the two

groups

had

8

years

and 7.2 average

years

of teaching

experience,

respectively. Fu rther-

more ,

in

Hong Kong, secondary school s tudents

are

divided into

five

"bands,"

where Band

1

represents

the

high est level

of

academic a t ta inmen t

and B a n d 5 the lowest . Four of the five classes in the lesson s tudy group

comprised Band

1 and 2

s tudents ,

and one

c lass

was of

Band

3

students.

The

learning s tudy group included one B a n d 1 , two B a n d 2 and two B a n d 3

classes. Students in the lesson s tudy group were thus classif ied as hav ing

somewhat higher expected attainment.

There

were altogether

356

students

in the age

range

16 to 1 8

years

and

they

all

s tudied econom ics

a s a

school

subject .

A ll the

lessons were videotaped

and

subsequ ent ly ana lyzed

in

term s

o f

the enacted objects of learning. A f te r the series of lessons, all 356 students

w ere required to com plete a wri t ten task, and f ive s tudents from each c lass

were chosen random ly

for

interview s.

The

w ri tten tasks

and the

interview s

were

to

evaluate student understanding

of the

topic concerned.

Prior to the main s tudy, a pi lot s tudy w as carried ou t w i th tw o groups,

each co nsisting of two teachers and their stude nts, in order to try ou t the re-

search design and test the ins t ruments set for eva lua t ing student lea rn ing.

M ore im portan tly, this pilot study attemp ted to identify the qual i ta t ively dif-

ferent

w a y s

in

w hich s tudents m ade sense

o f the

distribution

of tax

burden,

so as to provide inp ut for the m ain s tudy. A t the en d of the p i lot s tudy, th e

participating students ' understanding

of the

topic

was

probed

by

asking

them to answer the fo l lowing quest ion in w ri ting:

In

a

r ecen t

Legis lat ive C o u n c i l

m e e t i n g ,

the

proposal

to

b r i n g

in a

sales

tax to

H o n g

Kong was rejected. A new spaper then conduc t ed i n te rv i ews w i t h m e m b e rs of the p u b -

li c t o

canvas s op in ion s

on the

t ax . M os t people opposed

it.

The y sa id

tha t

pr ices

w o u ld

increase by the a m o u n t of the t ax . Do you agree

that

p r ices w ou ld increase by the

a m o u n t

of the

t ax?

W h y o r w h y

n o t ?

Answers from 158

students participating

in the

pilot study

were

analyzed

in

a

phenom enographic

way in

order

to

reveal their conc ept ions regarding



8. T O W A R D

A

P E D A G O G Y


the incidence

of a

sales tax .

In

addition

to

answering

th e

written qu estion,

a

subsample of 16 students w as interview ed about their understand ing o f the

phenomenon. The analyses of the data from this interview facil i tated the

analysis

of the

written data.

Th e pilot study revealed six qualitatively different w ays of conceptualizing

th e incidence

of a

sales

tax

(Co nceptions

A

through

F on

Table 8.6),

a nd

these

were used

as the

basis

for the

main study.

A ll six

conceptions w ere

identifi-

able in both the written tasks and student interviews, and

represent

the varia-

t ion in the w ays in w hich the students experienced the phen om enon .

The set of categories of description described revea l the different under-

s tandings am ong s tudents of the incidence of a sales tax, m aking up the di f-

ferent

conceptions or

"ways

o f

seeing."

Corresponding to the

different

referential aspe cts, w hich represent

different

m ean ings

o f the

incidence

of a

sales tax, there are different structural aspects, representing what the stu-

den ts discerned and focused on. B y com paring the concept ions , the cr i t ical

features of the concept ions w ere iden tified, nam ely the features that dis tin-

guished them from one another.

During the preparatory meetings for the main study, teachers in both

groups drew

on the findings of the

pilot study (i .e.,

the

students ' quali ta-

tively

different ways of understanding tax incidence), and agreed that the

cr i tical aspect of an econom ic w ay o f unders tanding w as the relat ive elas t ic-

ity

of

demand

and

supply. They then started

to

plan

a

series

of

lessons

around this

concept.

As

regards

the intended object of learning, two com-

monal i t ies

a nd

three critical difference s between

the two

groups were iden-

t if ied.

In

terms

of

similari t ies, both groups tried

to

establish

a

contex t

for

learning this topic

by

employing current news about

the

int roduct ion

o f a

general sales tax in Hong Kong, as wel l as an exam ple of an authen t ic gaso-

l ine bil l . This b uilding

up of

context

is in

accordance w i th

the

principle

of

building up a relevance structure for students, as espoused by Marton and

Booth (1997).

Furthermore,

i t was found

that

all

teachers

had

made systemat ic

use of

variat ion; in a sense the intuit ive use of variat ion w as a key feature of all the

teaching in the study. Both groups introduced variat ion sequen t ia lly in the

dimension

of

elasticity

of

demand

and

supply.

T he

teachers

first

varied

the

elasticity

of dem and against the invariant elast ici ty of supply, and then var-

ied the elast ici ty of supply a gainst the invariant elast ici ty of dem and , in or-

der to

di rect s tude nts '

focal

awareness toward

the

effect

o f

such e last ici ty

on

th e

distribution of the tax burden.

However , there were three major differences between the two groups:

First , al l the teachers in the theory-inspired group sought to f ind out the

w a y s in

w h i ch

the

students understood

the

phenomenon

of the

incidence

o f

a sales tax, and use these as the basis for developing their lessons. In con -

trast, only

one

teacher

in the

comparison group at tempted

to do the

s ame .

Second,

a ll the

teachers

in the

theory-inspired group wa nted

to

in t roduce s i-



TABLE

8.6

Categories

of

Description

for the Incidence of a Sales Tax

Leve l o f

Unders tanding Con ception Referen tial Aspect

Structural Aspect

O ne

O ne

O ne

Two

D

Tw o

Three

Tax is

ful ly

borne by

bu y e r s ,

and the tax

burden

is

related

to the

demand side

o f the

marke t .

Tax is fu l ly

borne

by

buyers,

and the tax

burden

is

related

to the

supply s ide of the

marke t .

Tax is

fu l ly

borne by

sellers, and the tax

burden

is

related

to

dimens ions o ther than

d em an d

and

supp ly .

Tax is

shared between

bu y e r s

and

sellers,

and

the tax burde n is re lated

Focused

on the demand

condi t ions of the market in

w h i c h

th e

goods

a re

s i tuated. Variat ion

is

brough t abou t

by one or

m o re of these factors , such

as the

n a tu re

of the goods.

Focused

on the

s u p p ly

conditions

of the

m arket

in

w h i c h

the

goods

a re

s i tua ted . V ar ia t ion

is

bro u g h t

abou t

by one or

more

of

these factors , such

as the m arke t power of the

sel lers .

Focused on the nonma rke t

mechan isms

of the

market

in

w h i c h

t he

goods

are

s i tuated.

Var ia t ion

is

b r ough t

abo u t

by aspects

o ther than marke t op era t ion ,

for ex am p le , g o v e rn m en t

i n t e rven t ion , and so on.

Focused

on the

e las t i c i ty

of

demand

of the

goods.

Varia t ion

i s b rou gh t abou t

to the dem and s ide of the by chan ges in dem and

marke t .

Tax is

shared

between

buyers

and

sel lers ,

and

the tax

bu rd en

is

related

to the

supply s ide

of the

m ark e t .

Tax is shared between

buyers

and

sellers,

and

the tax burde n is re lated

to

s imultaneous

interact ion

be tween the

demand and supply s ides

of the m ark e t .

condi t ions .

Focused

on the

elasticity

of

supp ly

of the goods.

Variat ion

is

brought about

by

changes

in

s u p p ly

condi t ions .

Focused

on the

re la t ive

elasticity

of

demand

and

supp l y

of the

goods.

Variat ion

is

brough t ab ou t

by

r e l a t i v e ch an g es

in

both

aspects.

2 1 6

AH

H



8.

T O W A R D

A

P E D A G O G Y

O F

L E A R N I N G

21 7

mul taneous

variation in elasticity of demand and supply, a l though none of

th e teachers in the comparison group planned to do so. T hird, all the teach-

ers in the theory-inspired group

endeavored

to introduce the variations in a

contextual ized

m anner, and by using the same produ ct ( red w ine) in every

case. In contrast, none of the teachers in the co m parison group tried to pro-

vide a context for students wh en dealing w ith variation in the elasticity of

demand and

supply,

nor did

they

use the

sam e goods

as a

context

for

learn-

ing th roughou t th e lessons.

Res ul t s of the S t u d y

The key

findings

of this study can be categorized into three areas: nam ely,

the

enac ted objects

o f

learning, student learning,

and the

relat ionship

be-

tween the enacted objects o f learning and student learning.

The En ac t e d Objects

of

Learning

A ll the teachers, in both the learning study group and lesson study group,

focused

on the

object

of

learning that

had

been agreed

on ,

that

is, to

help

students

to

develop

the

capability

of

taking into consideration

the

relative

elast ici ty

of demand and supply when looking at the incidence of a sales

tax .

Th e teachers did not begin by thinking abo ut c lassroom organizat ion;

or the teaching arrangements to be used; whether there would be group

work or

ind ividual study;

or

w hether they w ould

use

in format ion technol-

ogy

o r

no t. Instea d, they paid great attention

to the w ay in

w hich they should

deal wi th the objec t o f learning in the lessons.

The two

commonali t ies between

the two

groups that were identified

in

the intended object o f learning (i.e., the bu i lding up of a relevance structure

for

students and the introduction of variation in elasticity of demand and

supply

in a

sequ ential m anner) w ere also found

in the

a ctual enactment

of

the intended object o f learning (i.e., the enacted object o f learning) . How -

ever,

of the three critica l

difference s

be tween the tw o groups tha t w ere iden-

t ified in the intended object of learning, only the

second

and third critical

differences were

found

in the enacted object of learning. The teachers in the

theory-inspired group introduced simultaneous variation and contextu-

alized variation whereas those in the comparison group did not . The first

critical

difference,

w h ich is the solicitation of studen ts' existing understand-

ing of phenomenon, was not found because the students in the theory-in-

spired grou p were inhibited by a num ber of things, including the presence o f

a

cam era, an observer, and the use of Eng lish as the m ediu m of instruction.

In the intragroup comparison regarding the building up of a relevance

structure for

students

( as

shown

in

Table 8.7), three teac hers

in the

learning

study

group (Teachers 1 ,2,

and 3) did not

follow

the

agreed lesson plan,

an d

did not employ the example of an authentic gasoline bill to illustrate how



8.

T O W A R D

A P E D A G O G Y O F L E A R N I N G 21 9

sales tax appears in daily transactions. Although al l of the teachers at-

tem pted to reveal the studen ts '

different

w ays of unders tanding the dis t ribu-

tion of the tax burden between buyers and sellers (using th e exam ple of a

sales tax imposed on red wine), only three of them (Teachers 1, 3, and 4)

con duc ted a m inisurvey inviting students to express their view s. This part of

the lesson plan wa s not very

successful

in any of the classes bec au se o f the

reluctance of students to speak up generally in class.

However, al l teachers in the learning study group introduced simulta-

neo us variat ion

in

elasticity

o f

demand

and

supp ly (al thou gh Teacher

3 did

it m ore successfu l ly and wi th more s tudent con tr ibut ion than other teach-

ers). W ith regard

to the

contextualizat ion

and

consis tency

of

contexts ,

all

teachers in th is group organized their lessons us ing red w ine as the ex am ple

product . Three of the teach ers (T eachers 1 ,2, and 3) kep t this pro du ct invari-

ant throug hou t al l the lessons in order to m ake the s im ul taneou s variation in

elasticity

of dem and and supply eas ier to discern, w hereas Teacher 4 and

Teacher 5 did not u se it in the last lesson .

Table 8.8 show s that all teachers in the lesson s tudy group succe eded in

carrying out

w h a t

w as

stated

in the

lesson plan ,

and

tha t som e

o f

them in tro-

duced a ddit iona l tasks to enha nce the o riginal lesson plan . In order to bu ild

up a relevance s t ructure for the students to learn the top ic , Teacher 8 further

added

h i s own

personal experiences

of

sales

tax (from the

t im e when

he

lived in Can ada som e years before) , and brough t in a "giveaway" i tem from

a gasol ine s tat ion (a box of t i ssues) , which he showed together wi th the

w orkshee t on the gasoline bil l . Teacher 7 designed an ex tra w orkshe et in or-

der to he lp s tude nts to acqu ire the ski ll s to t ransform nu m erical data in to

graph format , and find out the tax burden be tween buyers and sel lers .

Final ly ,

w hen int roducing variat ion

in

elasticity

of

de ma n d

and

supply

s e-

quent ial ly , Teacher

9

further

included extrem e cases that were

no t

covered

in

the

lesson plan, such

a s

perfect ly elas tic dem and,

perfect ly

inelas t ic

de -

m a n d ,

perfect ly

elas t ic supply

and

pe rfect ly inelas t ic supply.

S t u d en t Learning

(The

Lived

Object

of Learning)

In

phenomenography ,

learn ing

is defined as a cha nge in the dynam ic s tate

of awareness

or the way of

experiencing (Pong

&

Marton, 2001) . Hen ce,

the present study describes student learning

in

accordance wi th s tudent

ways of experiencing the phenomenon or concept ions

identif ied,

rather

than merely count ing the percentage of s tudents who gave the correct

w ords or num bers as answers to quest ions set in a diagnost ic tes t . Studen ts

are said to have shown evidence of learning if they can successfu l ly display

advanced and pow erful concept ions of the phen om enon in quest ion.

A total of 356 students part icipated in the m ain study, in w hich Scho ol A

to School

E

belonged

to the

learning study group,

and

School

P to

School

T

belonge d to the lesson s tudy group. A l l s tudents were required to com plete a



[3 TABLE 8.8

®

Comparison With in

the Lesson

Study

Gro u p

—

The

Enacted Objects

o f

Learning

Teacher 6

B ui l t

u p

re levance st ructure

Y es

Revealed varia t ion in the s tudents ' No

ways o f u n de rs t an d i n g

Int roduced varia t ion in the Yes

d i men s i o n s

o f

e l a s t i c i t y

o f

deman d

and

su p p l y

in a

sequent ia l manner

In t roduced varia t ion

in the

c r i t ica l

N o

aspect of re la t ive e last ic i ty o f

demand and su p p l y in a

s i mu l t an eo u s man n e r

Co n t ex t u a l i / a t i o n a nd consistency N o

of contexts

Teacher

7

Y es

N o

Y es

(Add-on:

an

ex t ra

worksheet

o n

g rap h i ca l

representa t ion

of tax

i n c i den ce )

N o

N o

Teacher 8 Teacher 9

Yes Yes

(Add-on :

personal

stories about sa les t ax

an d g i veaw ay s f ro m

g aso l i n e s t a t i o n )

N o N o

Yes Yes

(Add-on: discussion

on

ex t reme cases)

N o N o

N o

N o

Teacher

10

Y es

Part ia l ly effected

(Di d

no t

co n du c t

a

class

su rvey)

Y es

(A dd- o n :

an

ext ra

workshee t on

g rap h i ca l

representa t ion of tax

i n c i den ce )

N o

N o



8. TOWARD A PEDAGOGY OF LEARNING 221

written task at the end of the series of lessons, and five students from each

class were chosen randomly

to

attend

an

interview

on the

same

day as the

last

lesson.

T he

data that were co llected

from

these

tw o

sources were an a-

lyzed, and the way s of experiencing that w ere iden tif ied w ere then catego-

rized

in

accordance wi th

the

outcome space (which

w as

described

in the

previous sect ion) .

T he

learning outcomes

( in

term s

of the

concept ions

de-

veloped by s tudents) are reported on a group basis , wi th a comparison m ade

between

the

learning study group

an d the

lesson study group,

as

we l l

as be-

tween classes w i thin each group.

T he

major qual i t a t ive difference

in the

unders tanding

of the tax

inci-

dence

lay in the

s tuden ts ' unders tanding

of the

s im ul taneous interaction

be-

tween the demand and supply s ide of the market ( i .e . , the s imul taneous

r e la t ionsh ip

betw een the elas t ic i ty of dem and and supply) . Abou t 73% of

th e learning study

group managed to show this

u nderstanding,

and

mani -

fested Concept ion

F ,

w hich took into accou nt

the

relat ive elast ici ty

of de-

m and and sup ply in determining the dis t ribution of the tax burden betw een

buyers and sel lers. In the lesson study g roup, ju st un der 30% of the studen ts

reac hed th is level of und erstan ding. The deta i ls are shown in Table 8.9.

A s

regards intragroup variat ion in the learning study group, there were

marked

d i f ferences in the

s tudents ' learning ou tcom e am ong

the

classes.

A s

w e

can see in

Table 8.10, School

C had the

bes t per formance w i th

the

w ri t-

ten

task, with 80.0%

of the

students expressing Conception

F in

thei r

an-

swers . S chool A ( 77.5%) fol low ed, and then School B (72.5%), School D

(66 .7%) , and

School

E

(60.7%).

T A B L E

8.9

Distribution of Conceptions for the Written Task

The Learning

Study Group

The Lesson

S tudy G roup

(181

students)

(175

students)

Group

Conception

A

B

C

D

E

F

Occurrence

9

4

8

25

4

131

Percentage

5.0%

2.2%

4.4%

13.8%

2.2%

72.4%

Occurrence

19

15

17

66

7

51

Percentage

10.9%

8.6%

9.7%

37.7%

4.0%

29.1%

Note. Chi - square

=

67.553

(df=

5;p< 0.001) .

N o

cel ls (0.0%)

have expected

coun ts

of

less than

5.

T he

m i n i m u m expected

count is

5 . 41 .



2 2 2 L O E T A L .

TABLE 8 . 1 0

Distribution of Conceptions W i t h in th e

Learning

S t u d y G r ou p —

Th e

Written Task

School

A

Conception (40)

A 1

(2 .5%)

B 1

(2.5%)

C 1

(2.5%)

D 5

(12.5%)

E 1

(2.5%)

F 31

(77.5%)

B

(40)

2

(5.0%)

1

(2.5%)

1

(2.5%)

6

(15.0%)

1

(2.5%)

29

(72.5%)

C

(40)

2

(5.0%)

0

(0.0%)

2

(5 .0%)

4

(10.0%)

0

(0.0%)

32

(80.0%)

D

(33)

2

( 6 . 1 % )

1

(3.0%)

1

(3.0%)

6

(18 .2%)

1

(3.0%)

22

(66.7%)

E

(28)

2

( 7 . 1 % )

1

(3 .6%)

3

( 10 .7% )

4

(14.3%)

1

(3.6%)

17

(60.7%)

Total

N u m be r o f

Conceptions

9

(5 .0%)

4

(2 .2%)

8

(4 .4%)

25

(13 .8% )

4

(2 .2%)

1 31

(72.4%)

In the

lesson study group,

as

shown

in

Table 8 .11 ,

the

percen tage

o f

Con-

cept ion

F was

s imi lar am ong

the

classes, w ith School

T

recording

the

h i g h -

est

score (38.5%), followed

by

School

S

(35.3%), School

R

(33.3%), School

Q

(20.8%),

and

School

P

(20.0%).

T h e Rel a t i o ns h i p Between th e E na cted

Objects

of L e a r n i n g an d S t u d e n t L e a r n i n g

T he d ifferences in the enacted object of learning (as show n by the different

patterns

of

variat ion made avai lable

in the

classrooms), were

ref lected in

student learning in term s of the ways of experiencing that were m anifes ted

by students

after

the lessons . The aspects of the phe nom eno n

that

s tudents

discerned m irrored the pattern of var ia t ions, m ore

specifical ly,

the obje ct of

learning experienced

by the

students

in the

class.

A s

seen

in the

data

o n

stu-

dent learning, the s tudents in the learning s tud y group (w ho were presen ted

with this par t icular pat tern of var iat ion) , learned more effectively than

those

in the

lesson study group.

Furtherm ore, w ithin the learn ing study group, the d ifferences in s tudents '

performance also seemed

to

coincide wi th

the differences in the

pa t tern

of



8. T O W A R D

A

P E D A G O G Y

O F

L E A R N I N G

223

T A B L E

8 . 1 1

Distr ibut ion

of Conceptions W ith in the

Lesson

S t u d y

G r o u p —

The

Written Task

School

P

Concept ion (25)

A

4

(16.0%)

B 3

(12 .0%)

C 1

(4.0%)

D 12

(48.0%)

E 0

(0.0%)

F 5

(20.0%)

Q

(53)

5

(9.4%)

3

(5 .7%)

3

(5.7%)

29

(54.7%)

2

(3.8%)

1 1

(20.8%)

R

(24)

4

(14 .3%)

3

( 12 .5% )

5

(20.8%)

3

(12.5%)

1

(4.2%)

8

(33.3%)

S

(34)

3

(8.8%)

2

(5.9%)

6

(17.6%)

8

(23.5%)

3

(8.8%)

12

(35.3%)

T

(39)

3

(7.7%)

4

(10.3%)

2

(5 .1%)

14

(35.9%)

1

(2.6%)

15

(38.5%)

Total

N u m b e r

o f

Concept ions

19

(10 .6%)

15

(8 .6%)

17

(9.7%)

66

(37.7%)

7

(4.0%)

51

(29 .1%)

variation m ade available in each classroom . For instance, Teacher 3 allow ed

more

flexibility

for students to introduce simultaneous variation in both

elasticity

of

demand

a nd

supply,

and at the

same time used

the

context

o f the

red

wine throughout

all the

lessons.

In

con trast,

Teacher

5 did not

allow

as

m u c h

flexibility

for students to introduce simultaneous variation, and did

not keep the product invariant for the last session. It w as co nseq uen tly found

that the students tau gh t by T eacher 3 achieved a better u nderstanding of the

topic than the s tudents taugh t by T eacher 5, a

finding

that m ight be attribut-

able

to the

pattern

of

variation made available

in the

lessons.

Reflec t ions

on the Study

From an analy sis of the teach ing in terms of the dim ensions of variation that

were opened up in the lessons—that is, those aspects that were varied si-

mul taneous ly and those aspects that remained invariant—the pattern of

variation critical

to the

developm ent

of an economic

un derstanding

of the

incidence o f a sales tax became apparent. T he teachers in the learning study

group handled the object of learning in a w ay that was pow erful in enhanc-

ing studen t learning. They did this by

focusing

o n the object of learning and



224 LO ET AL.

opening up s imultaneous var ia t ion in its critical aspects—that is, they

opened up the

relative

elasticity of demand and supply in a contextual ized

manner , and deliberately kept the product (red wine) invariant so that stu-

dents could

experience

a change in the way that they were aw are of the phe -

nomenon

in

quest ion. This approach wi l l

be he lp fu l to

teachers dealing

with

the

same object

of

learning.

In this study, the theory of variation w as examined in relation to its

effi-

cacy

when used

to

design

an effective

learning environm ent . From

the

data

on the

teaching methods

and the

students' learning,

the

learning study

(which bu i lt

on the

theory

of

variat ion)

w as

found

to be

very

effective in en-

hancing learning

in the

econom ics classroom ,

in

term s

o f the

possibil i ty

fo r

teachers

to

identify

critical aspects related

to

different

w a y s

o f

unders tand-

ing and to design the learning si tuation arou nd these cri t ical aspects. T his

m ethod w as foun d to considerably enhance the s tudents ' unde rs tandin g of

the phen om enon in que stion, that is , the inciden ce of a sales tax. Th e study

thus supports the tenet of the theory o f variat ion, tha t lea rnin g to see som e-

thing

in a

certain

w ay is a funct ion o f

experiencing s im ul tane ou s variation

in critical aspects

of the

object

of

l earn ing .

Finally, the f indings of the study seem to suggest that the col laborat ion

between teachers

in a

learning s tudy prem ised

on a specific

theory

o f

learn-

ing

( in this case, the learning study group prem ised on the theory of varia-

tion), is more effective than teachers w ork ing together w i thou t an expl ic i t

theoretical grounding

(as in the

lesson study group).

A s w e

m ent ioned ear-

lier,

more than twice

as

many s tudents

f rom the

learning s tudy group

reached a good u nders tanding of the topic of the incidence of a sales tax as

students in classes of the lesson study group. Th is

further

supports the no-

tion that

the

learning study

w as more

effective than

th e

lesson study

in al-

lowing teachers to im prove their teach ing , and thereby h elp students to leam

more

efficiently.

C O N C L U D I N G REMARKS:

L EARNI NG FROM L EARNI NG S T UDI ES

In

th is chapter, w e presented three ex am ples of s tudies aimed at im provin g

learning from the po in t o f view of the theore t i ca l background brief ly intro-

duced

in

chapter

1, and the

descript ive em pirical studies presen ted

in

chap-

ters

2

through chapter

7 . Our

basic idea

fo r

fac i l i ta t ing

more

effective

learning is thus as fol low s: Take as the po in t o f depar ture w hat it is tha t the

students

are

expected

to

learn ( the object

o f

learning);

f ind out

w h a t m a k e s

the difference betw een the stude nts w ho have a good grasp, and those w ho

do not; construct a space of l earn ing tha t makes i t po ssible for all s tudents to

have a good grasp of wh at is to be learne d; and finally, an aly ze the relat io n-

ship

between the

space

of

learning

a nd

wha t happened

in the

classroom (the

enacted object of l earn ing) , and the w ay in w hic h th i s re la t ionsh ip affected



8. T O W A R D A P E D A G O G Y O F L E A R N I N G 225

the learning outcom es ( i .e . , w hat th e s tudents have achieved). In our view, it

is th is procedure— w hich w as fol low ed by all the teachers in the three learn-

ing studies reported

in

th i s chap ter—that

led to the

success fu l learning out-

comes

as

evidenced

by the

study findings.

A ll

the

studies

in

this chapter

had

certain features

in

c o mmo n :

the

same

theoretical grounding and systematic evaluation, a focus on the object of

learning,

and

condit ions that enabled teachers

to

work collaboratively.

T he

first

study in this

chapter

was a clear dem onstration of how teachers

m ade u se of the theory of variat ion as a ped ago gical tool . However, we saw

that even

if the

teachers

had

previously agreed

on

wha t

to do in the

class-

room , when they carr ied

o ut the

actu al lesson, ea ch lesson

differed in a

n u m -

ber of important respects (as i s wel l demonstrated by the second s tudy

reported

in

this chapter).

T o the

extent that such

d i f ferences are

recogn ized,

they can be seen to accoun t for di f ferences in the learning outcomes ( the

l ived ob jec t

o f

learning) .

In the

second study,

the

better perform ance

o f the

studen ts in Clas s 4C over those in Class 4H in the po sttest can be at tributed

to the difference s in the enacted objects of learning in the respective lessons.

Learning to focus on the c ri t ical aspects o f the object o f learning through the

use

of an

appropriate pattern

of

variation

is not

easy,

and

does

n ot

come nat-

ural ly even

to

experienced teachers .

T he

th i rd s tudy quo ted

in

th is chapter

showed that teaching and learning w as m u c h more

effective

when the teach-

ers

were gu ided

by the

theory

of

variat ion.

B y creating the co nditions fo r teachers to work together a s a team using

an act ion research approach, we enable teachers to learn and develop to-

gether. In fact, the bene f i ts go

beyond this .

T he

three learning studies show

that the process of designing, co nduct ing, and evaluat ing research lessons

benef i t ted a ll three parties: the students, the teachers, and the researchers .

The students gained a better understanding of the object of learning, the

teachers learned

how to

handle

the

object

of

learning

in a

more

effective

way, and the researchers gamed further insight into the ways in wh ich the-

ory can be

translated into practice.



Epilogue

There is a widely held bel ief today that knowledge is becoming increas-

ingly impor tan t

in the

l ives

of

individuals

and in the

lives

o f

nat ions .

I f

this

is t rue, wh at kind of conclusion can be drawn

from

the studies reported in

this

book

w i th regard to faci l i tat ing the developm ent of know ledge on indi-

vidual and c ollec t ive levels?

The quest ion of prom oting the growth of know ledge can, of course, be

addressed

from

p ol i tical , econom ic,

a nd

social points

o f

view .

Our

perspec-

tive,

however, is pedagogical; w e are concerned w ith teaching and learning.

Teaching is a human act ivi ty involving someone teaching something to

someone else . There

is

someone teaching

(a

teacher) , someone t augh t

(a

learner or learners) and something taught ( the content) . In grammatical

terms, th e learner is the dative (indirect o bject), an d the content is the accu-

sative (direct object).

T he failure to

focus

o n

both

of these tw o

objects

at the

same t im e has hau nted educat ion for centuries . Foc us has , in the ma in, been

on on e or the other, but rarely on both at the sam e t im e. In one instan ce, the

emphas i s

has

been

on the

teacher

an d the

learner;

in

another ins tance,

the

emphasis

has

been

on the

teacher

and the

content

Learner-focused e ducat ion, w here the

focus

is on the learner, and on the

w a y s

in

wh ich teach ing

is adjusted to the

learner 's nee ds,

h as

very m uc h co l -

ored the 20th century movement cal led "progressivism." T he m ajor ity of

university educationalists in the W est probably subscribe to this orientation.

Where the

focus

is on the content , that i s , on the knowledge to be

learned, we ca l l th i s the " t radi tional i st " approach to educa t ion . A cco rding

to this approach, the mos t im por tan t th ing is that the t eacher has a good

mastery of the

content;

he or she has to be

good

at

w h a t

her

students

are

supposed

to

become good

at . For the

t radi t ional is t approach,

it is of

pri-

mary impor tance tha t the s tudents a re exposed to cer tain k inds o f con t en t ;

227



228 E P I L O G U E

w hat i s covered in t each ing i s v i t a l . Th e "back to bas ics" m ove m en ts be-

long to this school of thought .

In the politics of education, these tw o orientat ions—progressivist and

t radit ionalist— have replaced each other

in an

ever-recum ng cycle

o f

peda-

gogical fashio n. This w e bel ieve is a m a jo r obs tac l e to improv ing pedagog i -

cal pract ices . In fact, pedagog ica l p rac t i ces w i ll o n l y i mp r o ve w h e n equa l

considerat ion

is

given

to

both

the

learner

a nd the

c o n t e n t .

T he

reason

w hy

both or ientations m ust be considered together i s very s im ple: There can be

no learning without a learner, nor can there be any l earn ing w i thout some-

thing learned. W e therefore ha ve to foc us both on the learner and o n the co n-

tent

o f

learning

at the

s ame tim e .

Let us

look

a t the

qu e s t io n "W h a t

is to be

l earned?"

In the

p a s t ,

sy l l a -

buses w ere fo rm ula t ed

in

te rm s

o f

ca t ego r i e s

of

c o n t e n t .

T he

qu e s t i o n

o f

W h a t is to be learned? w as answered in t e rm s o f d i f ferent par ts o f ma t h e -

matics, history, English, philosophy, and so on (e .g . . f ract ions , second-

grade equat ions ,

th e

French Revolu t ion , Wor ld

W ar I I,

i r regular verbs .

Ch uang Tzu , e t c . ).

B u t

w h a t

is to be

l earned

i s

never s im p ly

a

case

o f

f rac-

t ions

o r

C h u a n g T zu ,

o r

a n y t h i n g

of the

l ik e . W h a t

is to be

l ea rned

is

c a p a -

b i li ti es , tha t i s , w ha t the s tude nts a re expec ted to becom e cap ab le o f do in g

( in the widest sense). F or example , be ing ab le to express quant i t i es in

terms o f rat ional num bers , an d carry o u t ar i thme t ic o pera t ions w i th ra t io-

na l

numbers;

o r

having

an

unde rs tanding

o f

Chuan g Tzu 's v i ew

of

h u m a n

exis tence ,

an d

be ing ab le

to see

c o n t em p o r ar y p h e n o m e n a

in l i g h t of his

concep t ion o f Tao i sm.

Such ca pab i l i t ies are w h a t w e re fer red to in th i s book as the o bjec ts o f

learning. The concept of an

objec t o f learn ing

inc lud es bo th the learner

and the con tent; it is def ined in terms of the con tent i t sel f ( referred to as the

direct object o f learn ing in chap . 1) and in term s of the learn er ' s way of

handl ing

the

c on ten t ( re fer red

to as the

ind irec t objec t

of

learn ing

in

c h a p .

1 ).

Thus , w e canno t ta l k abou t th e ob j ec t o f l e a r n in g w i t h o u t r e f e r ri n g to

th e learner an d the con t en t a t the s ame t i me . O u r p o i n t i s

tha t

th e p r i ma r y

focus o f educat ion should be on bo th the l earner and the co nten t , and no t

on one o f them alone. Fai lure to focus o n bo th w i l l resu l t in lopsided per-

spect ives .

N o t

p a y i n g a t t e n t i o n

to the

l earners ,

to how

t h e y ma k e

sense—or should make sense—

of the

c o n t e n t , r e s u l t s

in an

e m p h a s is

on

j u s t w ha t i s covered— or shou ld be covered— by t each e r s "who know the i r

sub jec t ," and no t how the con ten t is handled, o r shou ld be ha nd led.

Currently, however, content tends

to be

u nderp layed

in

W estern educa-

t ional thinking, result ing in the resurgence of tw o i l lus ion s, albeit in

differ-

ent forms . O ne i l lus ion is the old dream of f inding "the art of t each ing all

th ings to all men." This phrase first appeared in the

subti t le

of C o m e n iu s '

book The

G reat Didact ics in

1657, w hich

i s

seen

as the

first sys t em at ic

at-

tempt to develop a science of teach ing. B ut the dream that w e can teac h any -

thing to anyone, i f only w e can find the r ight m ethod, i s probably older tha n



E P I L O G U E 229

that .

It is

s t i l l very m uch al ive today, a l tho ugh

the

m ethods people com e

up

wi th

differ, of course , f rom t im e to time. Cu rrent ly m any people a re ta lk in g

abou t cooperative learning, IT-supported forms of learning, project work,

problem-based learning, and so on as the

pa ths

to the perfec t art of

t each ing .

However , after reading this

book;

it should be quite c lear that there are

specif ic

con dit ions necessary fo r learning spe cif ic objects o f lea rn ing . T he

condit ions differ from one ob jec t o f learning to another , and we have to find

out in each par t icular case w ha t these con dit ions are .

Peer

learning , IT sup-

por t , project work,

and

problem-based learning

may be

a r r angements

fo r

learning

that have great po tent ia l , but no general approach to instruct ion can

ever ensure that th e spe cif ic con dit ions necessary fo r the lea rn ing of

spec i f ic

objects

o f learning are brou ght about . In order to do this , w e m ust take the

specif ic ob jec ts

o f

learning

as our

poin ts

o f

depar ture .

The o ther i l lus ion i s about "gener ic capabi l i t ie s . " The cur rent l ine of

r ea son ing

goes

som e th ing like the f o l l o w i n g : W e a re f ac ing an e x p o n e n -

t ia l growth of knowledge . Widespread use of IT and the In te rne t a round

the g lobe , m eans th a t bas ica l ly a l l of th is know ledge i s ava i lab le to every -

one . As we do no t know w ha t k ind o f know ledge our s tuden t s w i l l need

wh en they grow up , the bes t th in g w e can do i s to equip them w i th ca pa bi l i -

t ies

fo r

ob ta in ing know ledge ins tead

o f

e q u i p p i n g t h e m w i t h k n o w l e dg e .

Thus

the e m p h a s i s is on gener ic capabi l i t ie s , such a s learning to l e a rn ,

r ead ing to lea rn , lea rn ing s t ra tegies , th inking s t ra tegies , coopera t ive

sk i l l s , com m un ica t ive sk i l l s , flex ib i l i ty , c rea t iv ity , and so on . W h a t is of-

ten

f o rgo t t en is tha t knowledge is

fu n dam en ta l ly

w a y s of seeing the w o r ld .

Gener i c cap ab i l i t ie s

do

exist ,

but not as

ind iv id ua l t ra i ts ,

or as a

type

of in-

t e l l ec tua l

musc le tha t deve lops independent ly f rom knowledge

a nd

c o n -

t en t . Gene r ic capab i l i t i e s a re w a y s o f dea l ing wi th dif ferent top ic s ,

con ten t ,

knowledge ; they do not re fe r to what peop le have o r w ha t they

are ; they re fe r to w ays in w hich

peop le

ac t . Gener ic cap abi l i t ie s a re do-

m a i n

spec i f i c . T he

fact

tha t a

person p ossesses

the capab i l i ty o f, say, ha n-

d l ing words c rea t ive ly , does

n o t

necessa r i ly imply tha t

th e

pe r son

possesses the capabi l i ty of dea l ing wi th num bers , m usica l or l ing uis t ic

tones , or econom ic t ransac t ions in the same w ay. Gen er ic capa bi l i t ie s de-

velop th roug h hand l ing som e th ing spec i f ic :

th e

m othe r tongue , c a lcu lus ,

q ues t ions

abou t the ecolo gical survival of our planet , and so on.

There seems to be another widely held bel ief , par t icular ly am ong educ a-

t ional

pol icymak ers , tha t language

is the

object

o f

inquiry

o f

l inguis ts ,

and

p ay in g a t tent ion to lang uag e pedag ogica l ly is the responsibi l ity of l an g u ag e

teachers

only . Discuss ions about lang uage in the context o f educa t ion have

la rge ly

f ocused on i s sues o f ef fect iveness a nd

efficiency

in a t ta in ing lan-

guage prof ic ien cy. W e hear concerns expressed by the com m unity about the

dec l in ing langu age standards of

both

learners and teachers , and that som e-

th ing

m ust be done about the language prof ic iency of language teachers and

learners .

W e

seldom hear com pla in ts about

the

lack

o f

a t tent ion paid

to

I an-



230

E P I L O G U E

guage by subject teachers, such as teachers of mathemat ics , science, and

history.

N or do we

hear discussions abo ut

the effects of the use of

l anguage

on the

learning

of m athemat ical concepts, scientific concepts, and h istorical

concepts, fo r exam ple. T he relationship between lang ua ge and learning has

been narrowly confi rmed

to

language learning.

The exposit ion of the importance of the role of langua ge in bringing abou t

learning

is not

som ething new. Several decades ago, especially

in the

1970s,

a

number

of

scholars

had

already drawn attention

to the

importance

of

lan-

guage in education, and had made a strong case for p aying at tent ion to lan-

guage across

the

curriculum (see, e.g., Barnes, 1976; Barnes, Britton,

&

R osen, 1969; B ritton, 1970). P articu larly inf luential

w as the

work

of

M ich ae l

Halliday, wh o

showed that w hen

a

c hi ld leams

a

l anguage ,

he or she is not

j u s t

engaged

in one

kind

o f

learning,

bu t is

learning

the

foundations

of

learning

it -

self: Learning

is a

process

of

making meaning ,

an d

l earn ing language

is

learn-

ing how to m ean (see, e.g., Ha lliday , 1973, 1975, 1978, 1 993). T here fore , it

w as

argued, every teacher

is a

language teacher .

At the

t im e, wh en

the

lan-

guage awareness movem ent

w as

l aunched

in the

U ni ted Kingdom , l anguage

in

education w as made a compulsory m odule in teacher education programs

(see Hawkins, 1984).

T he

"language across

the

cur r icu lum "

initiative,

w h i ch

is one o f the

most important moves

in

educat ion ,

w as

unfortunately

not

sus-

tained (see Hawkins, 1999).

Wha t

w e

have tried

to do in

this book

is to

re vital ize

the

discuss ion about

th e

role

of language in learning by showing th e critical role that language

plays in bringing abou t the necessary co ndit ions fo r l earn ing . O ne necessary

condit ion

for

bringing abou t learning

is

that students

are

able

to focus on the

object

of

learning

and

discern

i ts

c ri t ical features.

W e

have dem onstrated that

language

is

crucial

in

structuring studen ts ' aw areness

so

tha t they become

fo-

cally aware

o f the

critical fea tures

of the

object

of

learning,

in

bringing about

simu ltaneo us awareness, both sync hron ically

and diachromcal ly , and in

ma k -

ing important conceptual dist inctions. W e have dem onstrated tha t because

language m akes meaning,

the

ability

of the

students

and the

t eacher

to

neg ot i-

ate

meaning

and to

const ruct meaning col laborat ively through language

makes qualitative d ifferences in the sem antic dime nsion of the space of learn-

ing

that

is

being c onsti tuted. A nother necessary co ndit ion

for

b r ing ing about

learning

i s

that

th e

space

of

learning

is

shared

by the

s tudents

and the

teacher.

W e

have dem onstrated that language plays

a

cri t ical role

in

es tabl ishing

as

wel l

as in

widening

a

shared comm on ground. W hen

the

ground

on

w h i c h

a

specific

object

o f

learning

is

enacted,

is not

shared,

th e

qu al i ty

of

learning wil l

be

adversely affected.

W e

have shown

the difference

l anguage makes

by

com-

paring

the

classroom discourse

of

students learning through their mother

tongue w ith that

o f

students learning through

a

second

and

w eaker language.

When students

a re

learning through

a

languag e that they

can

barely

use to ex-

press

themselves, they are inevitably handicapped because they do not have

the necessary resources for mak ing mean ing . There is a com m only he ld b e-



E P I L O G U E 231

lief, especially am ong edu cational policym akers, that learning throu gh a sec-

ond

language is no more than learning the technical vocabulary in that

language. This simplistic view shows

a

lack

of

u nderstanding

of the

role

of

language

in

learning.

W hat we have demonstrated in th is book is that there are spec if ic condi-

t ions that

are

necessary

for the

learning

of specific

objects

of

learning.

T he

w ay

in which these o bjects of learning are handled and the extent to w hich

the necessary condi t ions are brough t about through languag e in the class-

room are of decisive importance for what the students can possibly learn

(and w hat they actua l ly learn).

There are, no doubt, general condit ions necessary for learning, such as

l ight , space, exposure, feedbac k, and a min im um level o f activity am ong the

learners.

There

m ight also be necessary condi t ions of learning that are spe-

cific to different groups. Some learners m ay not be able to learn som ething

wi thou t

sensu ous ex perience , for instance, w hile others are able to learn the

same thing

by

sym bol ic m eans ;

fo r

some there

m ay be a

great difference

be-

tween actual ly seeing som ething and ju s t hear ing som ething descr ibed,

w hereas for others there m ay not be an y difference at all . B ut we are not talk-

ing

ab out necessary condi t ions

for all

kinds

o f

learning,

or

about necessary

condit ions for specif ic groups of learners, but about necessary condi t ions

for the

learning

o f

specific objects

of

learning . These con dit ion s have

to be

discovered for every specific object of learning. Teachers should be en-

gaged in f inding out w h a t the spec if ic condit ions a re in every specif ic case,

and

h ow they can be brought about.

When these

con ditions are discovered,

teaching w i ll become

a

much m ore pow er fu l

and

m uch m ore profess ional

enterprise .

In the

last chapter

of

this book,

w e

described some teachers engaging

in

such

an

en terprise. They cam e together w i th spec if ic objects

o f

learning

as

their

po in t o f departure. They did not start w ith questions about general ar-

rangements

and

general teaching methods,

bu t

asked questions about

the

specif ic objec ts of learning to be dea lt w ith during a lesson or during a se-

quence

of

lessons. They also asked questions about

the

nature

o f the

capa-

bilit ies

they wanted

to

develop

in

their stude nts,

the


for

developing these capa bi l it ies , how those condi t ions cou ld be m et , and the

kind o f

ar rangements

and

metho ds that could

b e

used

to

create these co ndi-

t ions. These

teachers

did not

start w ith questions abo ut generic at tributes;

they

asked quest ions about

how

domain

spec if ic

g eneric at tributes co uld

be

embedded in the

specific

objects of learning.

W e

hope that

the

ex am ples described

in

th is book have succee ded

in il-

lus t rat ing

w ha t w e believe to be the three core elem ents necessary for dra-

mat ica l ly improving learning in schools. T he first e l emen t is a pr imary

focus

on the

objects

of

learning.

T he

second element

is a

collaborative

effort

am ong teachers in planning and enac t ing the o bjects of learning in the class-

r o o m, as we l l a s ref lect ions on the enactment that a re f i rmly focused on the



232

E P I L O G U E

objects of learning. The third element is powerfu l theoretical tools that

guide this planning , enactm ent

and

ref lect ion:

a

theory

o f

learning

and a

the-

ory of the role o f languag e in learning. W e hope tha t th is book has dem on-

strated ho w

these

three elem ents together can m ake a

difference

in learning .



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Alexandersson ,

M. , 165

B

B arnes, D. , 230

B e hr ,

M. , 72

Bere i t e r ,

C, 8

Ber l ine r , D. C., 8

Berry, M . , 1 13

Biggs , J. B., 62

Booth ,

S ., 8, 11 , 22, 89,

153, 165, 170, 193,

1 9 4 , 2 1 5

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Y. D., 8

Br i t t on , J., 26, 35, 230

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Brown, G. A. , 128

Bruner , J . , 166

Chros towsk i ,

S. J., 66

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J., 60

C o ck in g ,

R. R., 8

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Col l i ns , A . ,

191,

1 9 2 , 2 1 1

Cor tazz i ,

M . , 62

Gu s h i n g , K. S., 8

DeGroot , A. D., 7

Edmondson ,

R. , 128

Egan, D. E., 8

Ehr l i ch , K., 8

Findel l ,

B., 190

Car l s son ,

B., 23

Carpenter, . P., 14

C e s t a n , M . L., 32, 33, 34

Chan , S., 141

Chase , W . G., 8

Cheng, K. M., 61

C h i , M. T. H., 8

Chik , P . ,

1 3 , 43 , 91 ,

1 21

Garden , R. A., 66

Gardner, H. , 60

G laser, R ., 8

Gonzales, E. J . , 66

Gregory ,

K. D., 66

Gu, L., 56, 57, 58, 59, 60

G u r w i c h , A. , 19

239

H

E

F

G



240

A U T H O R I N D E X

H

Hall iday,

M. A. K., 24, 25, 26, 27, 28,

139,

1 7 9 , 2 3 0

Harel ,

G., 72

H a w k i n s , E., 230

Hiebert,

J., 45, 66, 191

H i l l ,

H . C . ,

1 90

Ho, D. Y. F., 62

Hoare ,

P., 143

Hua ng ,

R., 62

J

J in ,

L. , 62

K

Kan, F., 157

Kilpat r ick, J . , 190

Ko, P. Y., 1 0 ,4 6 , 91 , 167

Kress,

G. , 117

K w a n , T . , 4 3 , 9 1

N g , P . P . , 43, 91 , 11 4

o

O ' C o n n o r ,

K. M ., 66

O gb or n , J . , 117

Paine , L . , 6 1 , 6 2

Pa ng , M. F., 91

P o n g , W . Y . , 2 1 9

Po st, T., 72

Pow, S., 121

Qian ,

M ., 46

R

Rosen, H. , 230

Ru nesson, U. , 67, 91, 1 21, 157

Lamon, S . J . , 196

Lee, S., 61

Lee, W. O., 62

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Lesh, R . , 72

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Y. M . J. , 60

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1 0 , 9 1 ,

1 67

L undgr e n , U. P., 128

Lybeck, L. , 153

M

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M a r t i n , M. O., 66

Mar t ins , I . , 117

Mar t insson , M. , 153

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165, 170, 192 , 193 , 1 94 ,2 1 5 , 21 9

M atthiessen, C., 24, 139

McGi l l i cuddy, K. , 117

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G. A , , 9

M o k ,

I . A.

C . , 7 5 , 9 1 ,

1 21

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Mo x ley ,

S. E., 15, 16

M ul l i s ,

I. V. S., 66

N

N e u m a n ,

D., 7

Sabers ,

D. S., 8

Sal jo ,

R., 90

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Schwar tz , B. I. , 8

Seybol t ,

P. J., 60

S i m o n ,

H. A., 8

Sm ith, T. A. , 66

Soloway,

E., 8

Stevenson,

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Stevenson ,

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Stigler, J. W ., 45, 66, 67, 1 91

Svensson , L., 11, 58, 74

SwafFord,

J., 190

T su i ,

A. B. M. ,

11 4 , 1 21 , 128, 157,

1 67

Viogt , J., 36, 37

V u o l a b , K., 28

W

Wel l s , G., 179, 1 82

Wistedt, 1., 153

Wong, S . Y, 121

R

Q

S

TT

V

L

P



242

S U B J E C T

I N D E X

M

M a t h e m a t i c s

lessons, 32-34, 36-37, 62-63,

66-73,75-84,86,91-94,

140-141, 196-203

div i s ion , 74

div i s ion-quot i en t , 92-93

Phy sics lessons , 1 17-1 21, 128-136,

169-170

reed relay , 114-121

Presuppos i t ions , 1 1 7 , 166,

1 78

Classroom Discourse and the Space of Learning

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