Technology in Education: Looking Tormrd 2020

RAYMOND S. N m BNN Laboratories Inc

UWRENCE ERLBAVM ASSOC-, PUBLISHERS 1988 Hillsdale. N w Jersey Ham and h d o n

'liechrology in 2020: Edua&ing a Ohme Population 213 mmm Y. mALcoa

Tkadwds Assistants: What Could 'I;echndogy Make Feasible? 265 JYYWIZTIYLL

The Use d T&hrology to Impma b )(g, Classroom Relationships 275 r r m u y n . ~

lbchndogy in EduSim: Ft&ble lrdtuences on Con6ep4 Purposes and Maods 285 wuma-rrurawul

9 Putting Knowledge to Use

WHAT ARE THE DIUEWSK)NS OF THE PROBLEW

k m - r d . h b * ~ c P r r i c P l r u i t h t h i n a i m t u b r r h r t ~ ~ dncbpcddo~hdcpcadclulldcarnrnnmrt.Tbirrppovhhrrkd aocmrmcerhitJr#nioru,chuVirythucQrrsm~thae~dqnded wbtrnrdmaLParrwkntbqpduate(Hinth, l987).Ranrrrwuehpa- rpcEcire.it~koamcqrriacdcuthtplndadkmn@rithrrwh~ a , e i t h a r r h w d r b o d ~ m e w r a a m ~ t b C q p . l i q d m u y w = p o M e m d r i s l = d ~ ~ r u a ) . ~ - ~ C b i p n m . 4 & & C b c c l985;Runkk, lWYI;Sq.l,Oipam, &Gk+z l985).Butuue w e . i n t h ~ t h t f d l u u , ~ c g n i t i r c t b c a i r a r r c o m m r n d i m m u c t i o a incgnitiverLilLritborumkhndrloaromthmkdgeemphuis,

Ath iTdcaptn-ood-probk!mnumar~cogrr i t iurc ien- t i r o u m c f r o n r c o m ~ t i v e c r o a s u l ~ a U d i u i n t h 1 9 6 0 1 d l W ~ & - s i g n e d t o t a t ~ c g n i t i r c c o ( r t ~ u c 1 \ p c . d d D n r u l ~ d d l i t e ! n 9 . Bruner 0966) had t h t tk d m - " cd nature d rknl thiak- ing, such as markmrtiul mamhg with -bob md quachns, d multi- plerlrrifiutoqrcbemahrtbeirormrrLe. f a t e m ~ ~ = d S D I - mal opcmtiarul But contrary a, a t a m k mearch ~mukdmag+armscriolvmdrktrranrhurukuncdinvknl andotba~t iS tp fob lQ Idv iog( rehbykbar rogdCan-

Human Cqniah. 1985). A 6 D l l n h i n f l u a r e a m c f n r m r t r r d i a ~ c o g r i t i * r ~ d Y t n r r

~ d o P r # u c b a r ~ t h 8 t e r r m r m i r r r d q ~ r t u d m a a m d t o ~ f i w n N ~ t h g ~ m i r u L m p h p i a l ~ t i a Q a b . w d 0 n ~ a p a i m c a w i t h m ~ o b ~ S h . l U I I f n r m t h e f r m r e d t h i r m t b o a ~ r b e g I w t m a o a S o n n r l ~ ~ ~ with kmbtaxk (disarp. 1983). Sh*rcQ OSn) prr#rtr .imrlr+ hdbgs f o r ~ ~ ~ ~ b i y ~ . .

~ 0 a R r t i a l c O p i - tionnmc, i t a p p c u r v e q ~ b y i r w r r r t i o g i n ~ ~ a r m.thrmrtia.SamccolridatkaarrnJrrlidit).dmuchKbod~ q u r r t i a r u b k i f i t d o a n o t i m p . a a r ~ ~ ~

A f i f t h . ~ b n a l ~ i r t b c b e l i d m n a d y ~ t h t U n i t e d S o o a b u t i n ~ ~ r r t i m J a ~ ~ ~ ~ G f C 8 t B l i n i n . J 8 p m . t b t ~ . n d S n d m . ~ o t b e n , t h t ~ c m r - . . p ~ m p $ ~ ~ d c o a d m o n t k m i r d t o t b i ~ ~ .aprrbwly, P l . n f 9 q . e - d wntrrtiop.q.in~kpadprogrmminl.Ibccpnmt i n r t r P c c i o a a f a r a r c s a r l ~ A m a i a n h Y J m k i n ~ a c h y e a r ~ i n p u t a m c l n r n d t b c d q t h d ~ a r m m i t m a r o a o r b i r a - p a m i a n . ( k ~ ~ ~ , ~ t h i r d . r d . t b k ~ m r h c erridmt,tbe~papLfd~ ' Jperrakhnlaom t r r n d r m r r u d * a m f i r ~ a o d r d . c t n i t k r b e a m c . m l L e d . m d k a l n i n g t o t h i n L p r # x d ~ - ~ ~ ~ d p 8-2, Shil. 1981-karma -ad rirbin di.arc -)

Altbapsh i p a m p k , tbir lint d Umtrii* f a c t a oo tk pr#nt kvd d a m m t i m i n t k d d ~ '" r ~ p r o b k d ~

~inthecmtur~,Tbotndikeurricdout~kuningrmYCtrrtPdiam tat Willi.m Juaer' 0890) hypotbair on tbc rpedficitf d ltlnwd h b i i It waathCLlcanmmhr~mKbOOltoItML.tin,mcmmarhforiu ~ t i l i t y u f o r i u m t i c a p t c d ~ ~ d ' h m u l d i d p l i P e ' S o r l e u n - ingothercurriculumtopicr.Tlu~qlotiwfindinlFfromtherc~tionr (lhdik, l a 4 ; Thordke & Wboduorth, 1901) dcmrt.ocd tbt diriplirrc hypothrirandhlpedaparupmpaiodof ~ m A m a i a n r c b o o l - ing(Crrmin. 1961). S i u g u w n ~ u r p m u c d ~ f o r t b t d j d l o g i c . marhrmrtia, and rciaaa. but puticPkrly for canplm p r o ~ ~ j . Aa m the case of Latin, w k aponabca~r t rader outcotma have ken c a d d y ucredforprogrPmmins,findinlph.Rnotbenpmnhbg(&Pkod.b, (=kmau, & Mawby, 1986; MilojtosiC. 1983; Obon & Sohay, l987; b & Kurknd, 1 9 8 4 ) . ~ r m r r ~ a n d m u a ~ r r ~ J i d d m a r e l i m i f i - c r n t ~ d a , t b a e ~ c o ~ m e f ~ ~ ~ ~ ~ t n i n i n g f o r gcna;rliubility ofepe& n%ambg rltillr bepoad pmpmmhg amma (tg.. debugging; Clrscr. 1986).

As an alernrtivc to the belief that kaming r+ma topics gcncdy diaciplina the wortingr d a pung mind. T h m d h and W d w o n h 0901) o&rrdarpecificaurrfntheorybPrdantbcidadidlPtiC.lekWPO.On thiatharg,trrnrdrrofLrrorrledgeorkamingwiUoccmknreenmalLm- * a a t h e e r r b J h c n a W r l m m t . ~ ~ k . a m r ~ - r i ~ ~ ~ o f t h i a c o m m o n d r m m t t h o a y h r H p a r b t t d e r c r r i P c c ~ a amociadonintbcoycumto~cemeduatian(Bmrm.BrrrrsDad.~- nra. & Campione. 1985; we E l k 1965; Gylrc. 1968; Olyood. l949).

w c m M n v ~ , S r h u ' a t b c r u g e ) - ~ J I I M l r b ~ i a M n v c O m m a n . I t i a a n d e r ~ ( I l t b o p e h d t m ~ , k q P r e m r m n r ; l mrborthbighlc l s )mm-(AI) tbeaiadp. lu6adl tun- * , - ~ . m c ~ * c o m p " - , m d ~ i n b n c t i a n . ~ " a o d . y u r ~ d r C i r v l l i n t h c ~ r r p a m - t a t i o n ~ ~ ~ ~ i n r h i c h r u c h ~ ~ ~ ~ u r b u i l t (CubaDell& Minton, 1983; W-. 1918. l979). A crmmra ehmm a p p d to tnnrfa also appnrr m Pbbon. Mpacba, and Eqdbc&", 0986) aocaunt of kuning di&rrnt rrord-pnmdng ~ptenrr.

- Th unita id the trader meaic in such tbcaria differ fmn the phgricrl or symbolic elanenta d TharndiVa thcoxy, but the bgk d th appnmch ia identical. Instead d common phpicll danmEl m rinutioar, tbcarirtr now count

t b r ~ b d p d u i f y t h e ~ m d d 8 & ~ c g a i d r c r t n r r h . r b m u g h t t o b e a r o p p m r 6 a V k b r k f I y a m m . r i r r h i a ~ d i n - trod~~rd.btdfinAirwu8ppFopri . t t .b anmidastrrpr6aamorrfPn- d . m m t l l a r r c c p t h a n c i t b a ~ a o ~ ( d . ~ l956).He u g u a t h a t t r m r S t r m U a t b e r k r r r d i n m d d f J l l t 0 t h ~ ' r p r i o r 1-that irdklmtktmmkrdorutim. kinkgrrm'a(1956)a- dan.rrcmrvidrranyi.lmtifi'bkaRuirdankhen~trroormorrhrmr dpabmanuuatrrnrdnfrrpction. Thc study of trpnrSrr in prychology and education therefore rrquLa re-

tbrCPd@hp#.pcd.tgialrrcammcld.doaLarrSnmdrq.Wted leunial*

R t d r o ~ ) u g u a t h . t i o 8 p p r o p r k t c ~ ~ u L c f k a l l r k n l .ritbmetic. Such c f k a are maled in S c r i k lad h h r m ~ i d 8 (1982) ntudy ~ ~ ~ d ~ r a f a r ~ h i g h r b o d r u r l r n k i n a r r i a d&iPIO1*hy-bOf-p.drinl.Tbcd.irlrrortnrcrr h i l h t f f h d b k i n c h e a r i t b m r c i c ~ ~ P w d . ' I b t h i g h r b o d ~ r m ~ i n t G a i W b m n c r r ~ . r i t h m e d c p o b l c m r d a M n d a l m i - o f ' - rcrnbcgierbOfopimiudan,rudmoaratirmedtoa~tbcir rknl-l#nwd p r o d d rub.

ReraicL and Ormrvan 0987) haw danoarnratd thou@ hpping inrtr9c- tion" that oat a n provi& inuructional support for young chikirrn's intrgra- tiondtbcirpctialerpcrimainmathnuticrrithYbodLnorledgr Qildrrn may dirpl.). &ill in wing baae-ten d p l k b k s @icoa blocks) to rrpmmtrrricccnnumknand~outmatchingapmtiarrinthnro r r p s a n t r t i a u l m e d i . . \ r h i l e ~ m a k i n g a r o r r i n ~ vllucmwrittcnrabtrocaon

. pLcc and addition p m b h The inmnivc mapping

inrtnrctionuudhuthtachryidethcchildtolinktheummt;rrdthc b u e l p o a n \ r i t h ~ ~ ~ r d ~ ~ ~ T b c r r i t r m 6 i # m i r d c p i c a c d u ~ a r c c o r d a f b l o c k r m n i p r k t i a r v u t h c h i l d r r n ~ b m r r a r s u ~ t h w r i t t c n ~ t h n u n i p l L b k m c d i . . ~ u i t h formaproadrmlbugminwzittmuithwcicdidnotrmttaronerrnSto 6 we& after such immmkn. Mapping irvnuctioa app#rcd to have taught children rbat to look for the link8 benrrca their paid Lnorraedge d bue- ten rda- and the written uithmcdc alpdun (Ptctito. 1985).

T h r r i r a x e l a t c d k c k d ~ f m m ~ d ~ ~ t h r m . r i r r C h a t r o l k t o ~ d K h o d r m t h r m t i s r r b a r ~ f 8 l ~ T h i r * ~ a n c a r l y f i v l i r r P d G r y d C d t ( l 9 6 7 ) . ~ ~ t h t L i k r i i n f u m t n n u x a r M y d - a n d - ~ i n u r u t h t M their dl-being in life situatiom but had littlt a d c m a d q d matkm.ttr u a ~ P l e f u l a ~ c t L n o \ r l t d s c r p r a n . A n d ~ ~ d %" ( l 9 8 ! 5 ) r r c e n t l y d b a r r t r c d t h u ~ B ~ ~ t l r i n 6 w - m a I l y d e r r l a p e d a m n t i n 6 ~ t o r d r t ~ u i t b m a i r p o M e n r i n t h ~ t h u * c r n n n r a l r r i n K b o o l .

R # Q t e r h p o g . p b i c r t P d i a d ~ p g b p t t o t b t ~ ~ r e R l h r s x ~ ~ w h o u ~ y m a t h r m . t t r m p m c t k d . a i . i t i a ~ a a ~ , m.nuinp~,ddittipgFrr.Iss?;krc.M~.&&k~. l 9 8 4 ) , a ~ a u J I w i t h d a i r y a r d a r i n t b t ~ ( S a i b z u r & F ~ 1 9 8 2 ) r o l k b u t i r r m a r n r S a r r d t o ~ P r b r u c h . r w ~ i t t m ~ a. Inaxelatedvein. RrmicL(l987)norathatmurychiIdrenf.ilto& chatthSonaJrulataughtinKboolandthcirarmmrlepmrln mathematical inNitiolr arc rrktcd.

*- ThdtrrnrturrobhawththinLrrdap~oblrmdhrrdontraoc

appmpriatcornacfora2nr6cl.dmathanuiul~pevnciakrcvcakdin

Anaammts of Lnowledge-acquisition trmsfer pmvidc the paradigm cue af educational Plnrftr studies. such u Thorndits studies on tmn& d learn- ingfmn Lotin. orpblronu J . ' s ( l 9 8 6 ) s t u d i a d h a r r ~ ~ l u e i f i n t uoxdprocaor.&cotbeeuedltuningto~trraccodmc(formim d ~ r a c u c h d t h i r p d i p d p r i n e t b c ~ d h m k r d k u n - i D g S l l A d k ~ ~ ~ h C m r r l e g * 1 9 ( 8 ; ~ 1 9 6 5 ) . b O o b r a r r a thatthirduictmxmferpupdi lpn~mperimpdqtkPi lrBCr~- tionrl tmaapmt (such as ktin. or a pnlg-2 Imepy; Ph & Ihrkpd, 1984)anthsubject lsaist ingLporkdeebue.Th~onc1~ubt0~borr p r C i p r t r p r t C a L n o r r ~ i n t h r a r a r u b r e q P m t ~ . ~ ~ t h . t ~ ~ d ~ ( d , r t ~ d d , a P d i a d ~ ' ~ 8 a l & i v C

efs#a: Kurland, b, Ckm~at, & Mnrby, 1986) ~q yield ', '- d- 6KO)kQ~~thImleuningironimporantrrl . t ireaotbc~dprior L p g l l k d g e i n t m x m f e r ~ p ~ ~ o c

T h k c o n s t r v c t i c i s t ~ - t h ~ t h t ~ b d d m l l & m d b g i n t c n a r d p r i o r ~ o r a m c e p r u l ~ - h r ~ p l b e c a n t m a t a p p l u m t i n t h e c u e a f ~ k 8 1 n i n g @ r i r r r , G m u ~ e . & Tibaghk. 1985; Hawkim & b. 1981.. Limn, l986; & Ftqbag. 1985; WMt&PiPa.l985).Tbcridrrpmdfinrlinoirthatp ' ' -dLnmkdge p m i d a a a a c c p h u l S a m d n d o n t l u t ~ p r o c a a m p p t m e c t ~ dipenaticactivitiaandthcnbuildon.ThekcyPocionirthutheIcuoa's priorLnow,ledgeisgbnaotiw, d in~ratt tmptto lrndartradtbt~min-

~ h ~ a f i n ~ h n b n g b e e n d e 6 n e d u a r h i h f m m c m b n t - d e p e n d m x k w u k d g C w . r b a e L r r a r l e d g e d * ~ u r ~ - to their initial contat of acquisition, to more amtea-& gemdhatioa of

Mamxeady,CdeandIpdattherh~dCrm~Human C o g n i b 0979, 1983, 1984) have critically rekud amtributi- of dcvcl- opmend and cognitive pycholosl, u~thmpology, and sociology to the under- ~ d ~ i n d n i d ~ i n a d h u c c o m e t o r c q u i r r ~ r p v m r ~ t ~ b o r r e r p a i m c c d ~ n a u c c a u r c c t c d . T h y y r p e ~ r ~ c u l m n l p . c - tiara thcor7(l985), ~~whichtheLindrdroc ir lrmtr?mchi ldrrn p o r t i d p o t c i n c o a t r i b u o t t o t b e ~ o l ~ d ~ m d ~ h i C h ~ d e r n b p m m r a n d ~ ~ c r r r r r 6 a u i r a . T b a c ~ ~ ~ mtdcdncdinmmrdphpialbamsdrctirr(p butintamrdthemcm- ingdthaertt inlpca#racadbythepeapltpxwent,Slrhm~ amctptbd~incrrlnmpmvidcsmimpomntSoord. t iocrbrin- ~ t b c d i m c n d a r r d t h c h m u ~ ~ p o M a n i n ~ . In the are of cprrau cognitive thoria d i&~ thia qPation d inter-

p m c d m b e r t h 8 n o b j a t h l y ~ ~ m e r ' ~ 1 3 t h e b r d r b o r ~ b begged. The pmducdonr in pruiuaion rpcarrr modding human thought arthepodain)urorbdecrrpramt . t iorr lwrrortr in~s im~uc part d the thorib3 coaa~ction d the p b l r m situatiom. The quation b begged because th problem-robing context ir i n a x p d . not m apaimen-

Mdit irmiiat lumcaaa~Prrrr6amqkinaoduced.Eutiertbe . . . d w m c a o n m & b e ~ 1 1 # ~ 1 0 0 ~ ' s a ~ 0 ~ 1 t o d t h ~ b i l i q d ~ .rdrLilbd~aproblandnudan.Critiulmthuwap~obkmut~- tk a d motivational facton chat arc ill underrtood. How ~tudcnta 6td about thirupabilitiaofpnforrmnceinkaming&candmstkdyI&cttbeir inmatnaadyin~~but inkuning ioc l f .Harr ircbedhpob- t ionto~ inprrr irrmtmangrtuchfor~-rr )cruuLrro \rbdgc in a p b k m omtion influenced by rlf-dkacy. fear d f.ihtrr, anxiety, in- cdaurcc d mirula. or other anotiod block (cg.. Mrirhmbaum. 1977))

RatuchanacAi.rrrmmt motkthindicatathuifchiMrrncaoaived ~ r r a u a b k % n t i y " r h a t d t q u c r c y i F e R i l a l ~ ~ mthrth.nanTnaaDcnul"rtdrliibtokioerrutdthroryh&,thn cbeyare~tomanmnpnaulhihmsandappnwchproMrm3ohrh3g e ~ n o ~ t o k u n f r a n . b u t . r ~ t o b o L a r u t o r t o f i i l @ r r c t & Ellior. 1985). Diener md I)crccL 0978) have d k b p i h d kaeryorimttd- a d "bclpka" rnoagia for p m x i q hilure feedback in problem rohring. Brunrtein and Ohrich (1985) nuk an analopu rlhrinrttrn between the dam- oxkntcdrrrucgytogoantonerreraro. 8 n d t h r ~ t c o r k n a c d ~ o c e y d ~ - i l l g a n e ~ ~

M k ~ * L a o * r l i t t l c a b a a t b o r r r u c h d i f 6 a a u ~ p . b uiw.Yutbtentityrierr, thbdprCramegy, a n d t h c a a ~ r c n o c g y cm8nh.rccrippliaecavtquawakkuPa~rbartbtf.btram t b n t u r i P c r i t a b l y ~ t o ~ d L P o r b d g e t r m r 6 t r u r . i c r r d a8 hilun!a (.Lo re p.pat, 1980).

Sccdag098S)mrltrr the important o h a v a h that, d i k e inrdnrr- daQ.tbtdtopraideparitirrt~donrlarndibbortlurrSndcLill a a i n i n g h a s k m r c n r c c o g n i t c d a n d ~ h r n A L r l ~ h v i 0 r r l ~ d e r r l i n g w i t h a # t m c n t p r o g r m r . i m e d a t ~ o k d q , ~ ~ , a n d h g U l A t . t t r r -

E ~ c n r r w h l i m i C e d f i n A i r w . r t b e w r p g l a t ~ ~ ~ ~ ' I b c c o e i o c r J t m r l ~ t o ~ ~ o r n r L a ~ b a t i m - p i i a t h u r p C h ~ ~ ~ ~ o a L m r r r l e d g e ~ ~ knrtrdicdinthcpltrrrrl~th.t~rbemtbemnhrth.nnp.ib d~Thirnmcountcrtothrrmmantrr?bpmtinthe l ianuurr d c h i l d r r P ~ T m P i P r i a n y P L O t m b C d " ~ f ~ ~ ( . o r t h ~ m l c e t o u t ~ chuoctr' ' d a ~ g a m c t h a t c a ~ t i n t r i n d c m O t m h ( l r p p a , 1 9 8 5 : bWme, 1981).

i r a ~ ~ ~ t b r l r r n n k r d m n m m c l l e r k r r r r c n t h e k u n - ingd&dnutiau.'IhrYbcrkuidt~k~if&~r*.il.bk in the situation in which t m h r i a appropriate are h u e d at th time of ~ , b 7 ~ & W i t h a h a a r o c c p a . 0 r a 0 8 m o r ~ ~ C O Q - m t o p C b u a a l m n 8 . ~ s a a m u n t m d m i l l t m T b o r P d i L r , ~ ~ d r m m a " ~ E r m t h u g h m o m S n ~ i n h ~ r t r \ d d n u - tionelanam, s c h . n t ' s t h o r i a d d ~ ~ ( 1 9 8 2 ) d ~ t i o a panaru in rruogiaq 0986) rbo take a multiple-cue approach.

T b m ~ m a d d e d c a n p l a i g t o t h ~ d a n d ~ m u l - tipkcmn~inLporrbdemcquidtioaforrubrqucntLpa*rbdee~IUot just any combinadan of multipk aampla will suf6ce. and which mnge of aumplancbwcn, andthwqwncrinwhichtbe~~~mplaarcofSmd, will pmbablyinflucncethbmdthdrthctntalillrSrrorwwillokaR~ making. Yet very little r d has , - - 5 d t y aammd . . dairabk c h ; m c r m r a c r d e u m p k ~ f o r ~ a . r i m 9 1 l y a p p m p h t e ~

S c a n e m c u e h ~ t h u r r p r a c n t a t i R l o f t b c l u ~ o o ~ o f category imanca sbould k captured m exampla d for inrtru- (Eli0 hAndawm. 19WFfied&HdprL, 1984).dncea~i@cruleunbutrutty erprrr th arnpkx Ymdy mrmblanca" (RPrch. 1978) among m t t u h Catcsorymambarfim~trmrSn~apPmprktt.

h r m u r o t h r ~ ~ c u e ~ t h i m p o r c v r e ~ t h sockdtunlrrlcrrrpadth~pAa~.(IhilArm'snativccultwala- pcxienca - used u bridging activities in the r u c u d d rchool-bad KEEP prognm of tat comprehension instruction with Polynai?n Hawaiians (Jor- dan, 1985).

inam~.d,&Bom's(l985)Co~progrunm~tb. i~bgrLriUroE6cn mdtipleeumplaButthyut111d-liScd~tiolrrruchuplurnine501. ~ o r c b a m i n g a c u c e z d o m c a r n d d a r ~ t h 1 p ~ 1 ~ n # ) r ~ ~ d d ~ r t i l k b o r c b o d m p i a a z h u m a ~ a ~ arts. G l u a ' s 0984: also m EfcdaiLcn. 1984) rreanmmd.tions thu higher- order thiaking rtilk be taught - rithin rubjm-matm dormirv ap- pun+lanictiRintbtrrrr?+drrcctran. . .

Untilmmiamocciap.np-rrkmtraepzchk&bkarthiRlc,itrrmr l eaamabkcoaygcr t thr tarrpamt . t i rdgM~darntmrLar~ d c a n e d c 9 h m n q . - a ~ i s d p d i s g i n - r c h o d d o r u d - l c h o d ~ k m ~tuatiaar.~pwidttbtaunplad~inmpaion.conuaucuerd pmr6acaaridatd~ppmprkterhorrldrbo.idin.hlrLnr'scragorlformn- tionandLmorrbdgcRprrwnt.tion.IthpaerrdyillllgdClrtood\IfYtbQa- plicidystacingpaiodplaor~ordcfini~inldditiantooraeh~or ~ ~ p l a k ~ , a r u f i i e i c n t ~ ~ ~ ~ m p A a ' n r t r n r h r p l g c C f o f r u c h ~ h r r b e a r ~ b o ~ w i t h t u b j e c t ~ t m m d r u b j c c t r ' p r ; o r h r o r r k d e c ( - ~ ~ i n p m ) .

Feuasoin.Ralld.~.dMilkr(l980)trpinforPnnrSrrofconccpg or skills in their prrcollcgc thinbg-skilb p ~ o ~ r u n with %ridging." Bridging

m PEA

~ ~ a l m a J p r i r r e i p k d t h e n b d ~ r n d a r o r c b a r i t m r f r inmuldpltdturtiow el.. in-richKiarr~rrod.lararntm

Bruuford. Sacin, Arbitmur-Smith, and Vye 0985) dircPr bow kucnrdn'a p r o g r u n . ~ d ~ c h i l d r e n w i t h k u n i r y d i f f i c u l t i a . h r r t u d a r o #,matetbdrormcum*andePrhLluthc~dtbccrrmplaabar ~Tbacbrid#jngaccirit iahudorrrndm.L.:( l )~prmrprrPdcno todrawmtbe irarmerpr iara : (2 ) thyrrraGrtbcp~hrf in iocq of application d Pripcipla d the uudcnta* Hie apricDea: (3) ctudcno' ~ ~ e 3 ~ m p k r ~ m d i y a a e t h i r ~ : d ( 4 ) i n r u n - t iac ingtbcpr ioc ip le inavarktyd~~~~ta t senanmpp.nr f&Bmd Cunpioae 0981) daar'k thir approach u aplicit instruction in the mmge of LMIlkdge applicability. The uumption ir that thia inrPuctid mategy will enanlngc.ccaofarzrrdtrrbkL;Mnrledgcd~intbefaturr.

Bridginsbodyawdparcofthetramfcrproblan. bmme~ k h p a more difficult u an educational b.rricr to promoting tnns€er hi the problem of radial arnrlrtion between two di8bmnt aturith-paaprioll w: tbc child"r-t3l3idfrom~erpaiara-dtboreplom#cdbytherp#kl- i t e d r i t U a t i a m d t b t S m n r l c d u e r d a r d ~ . b ~ t b c a p p r o p i u c mapping between the hml7i.r and unfimili.+ damh in metaphor comprc- hcnrianbach.lknginsproca.

A l ~ ~ b d g b g ~ a p p e ~ r p ~ ~ ~ ~ r i n n N c 6 o p . l t a h - nique for pmmoting Lparrledsc trader, little b Lnrm aboyt what may be t h c b a t w a y s ~ ~ p u x p a a ) t o ~ ~ ~ ~ ~ ] r t b C w b r i d g i n g ~ d o n r . foraample.thmugh~nch*ortdiypvnaor~(asmFeuarain. 1980). or in mma of mulhcdh materials such as interactive *ideodbc bra^- ford, Shnrood. & Huelbrbg. 1985).

B u t c o n f l i c o a h t ~ ~ a p p r o u h m d i d u e n t i 8 l p r o p a r b d w h y rchoolinghuparmfulawequaroaforcognitirea~umtuurrdby apaimadaltrBnmr(l966)~thatitbthe~raPolnld~y l i 6 t ~ ~ 1 f r o m t b e ~ l a l n i n g r i t u a ~ d r b o d t h a t r m l r r r p o r i b l t d t e p e r ~ f o ~ h ~ r r k r u b t r t h u r ~ a ~ b g d d p r r c d c l l ~ . La~~986)nrggarrtbutbtrccprrd~irtburcbodmrptpopidtpep arat ionborl i fkinnnrtr?a-frcctuma;uitd.ul . tben~ . . Prm6n wil lSdlor* .Tbtrpcci f ikdag.niut iond~ut ikat iaarhaJdnot , b y t h i r d u k . c c a r n t , ~ b ~ . . I h t e , o r r r r . T h t m h . n r r m r n t o f a ~ ~ b o I i c ~ t . d a n r t . L n ~ ~ ~ ~ d ~ mrrninp thraagh acboobg pirnmubly depmdr cnr thir dcacbmmt fnm tbc k d o o r r .

P t r t i t o ( l 9 8 5 ) n y l s a c l ~ t h i r c o n f l i c t b y ~ t h u ~ o&nI#mingaf&andpaiPdpla6orpobntiol~ifappmprirte~ cmbemndttopactiaihDa*bdgcInckPigmingafoamahcatiaatoplmroa ~ l w c w i l l P e e d t o ~ t b c o b a m c t a r t m a u d ~ ~ r s t h ~ p p o r r 5 D a t r p n r Q a d k a T n i n g , m d ~ ~ e m b ~ d c m a c p karning m pbkm-solving activities taken from m y lifc Othari+.

cognitive scnvgia inrtruction, Imnc taught accutirt, rlf-m.ruarnrnt aratgia and none a c h i d trader d rlilb taught. Sirwx that time, many inwsigatiollr have dkctly caught df-mmagummt cogniti.t rLillr and bund dramatic and maintainable trader of kPrPiPg C&CD (rcvkm by Behnont, Butterfield. & Ferrtni. 1982; Bmwn a d., 1985). For example, Brown, Cam- pione. and Barclay 0979) taught aelf-monitoxing techniqplcl for c_.rimndng mc m a d i r r a r m d f o u n d k u w n ~ t h w n o * & h m d b I w n - ing to prore d.

Ourult imatelpl l irfor~tokcancoe.chr-iadepndmtthiplrn, kunar, mdprobkmdvcn. Tothbend. rturlcaanecdtolcunacc\rck thinking 3;ilb. such u goal aethg, strategic plpnnins, cbc- for accurate pllnmcution, goal-prograxlldmbg, pknernhutioa. and *revson. Y e t r r c k n o w ~ c k r r w m m d i a d ~ ( B e c k & C l r p Q o c S 1986). w d b g (Bmior & Sadamab. 1985). mathanab (Schoen6cld. 1985). and rimrr inrtrPcdon (Hamn. 197l). that th fundPmmul c u d $me- for con- trolhgthjnkingandkUpineprocenaareundertho#cba'rarntrd.not t h e a 9 d m o . T h c c a n a r t c u e i r t h ~ o f t h ~ a ~ d ~ procerainthidimdcdua&mrdkcctdmapprmtiarbiprrktiolol.u in or uilaing ( G d & krt, 1982).

S c b o d r ~ a n b u f m t h ~ f i d i n s p r # a i n w h i c h r m d a r o uLtoscrthae~~1tirerolaforthircmnrelf-ngul.tion.~lwncrrini- tially Rquirr and benefit from explicit support m manqhg d gPidins th

- ~ p k r i t i c 8 d ~ e w c o g n i t i v c ~ t i a . A n ~ ~ t h u . i m r t o d D l m c a n - pla&i&ing~rhaPMtbneforekdePtlopmmtlnfrrrpondRintbc following sense; that the prompa or other rtrucn~a it provider for fatming

~ d i n c t i a v f o r p n m o c i n l ~ p u v d r r i n e d u c u i m m f u c o n . a d e r c d h . v c m d n l t w i t h ~ l o p i c d i n t c n i b d ~ ~ ~ Yet many acbool dormen d.oc~te linking the kadng of difhcnt subject Qmrinr for greater knowhdge a-ada in conmt, of application or acquisi- tion. For example, Ohm'r law u taught in inpodu~tor~ ir rady in- aududasrsimpkpropaniarrl~hnmubarurier(B-LGrsaro. 1984). Brrarlord, Sbarrood, and Huelbring 0985) dl ruch cPrricuhrm ini- ti8tiRl to arrrcame such Unproductirr ir0l.h qnmgidc dui(n, in which thc*rbokirgrumthurtbtarmdthpuaThgorliru,&intatinLed learning offer greater yield d Pndmurding t l ~ ~ the d y d -red 8ubjccn

k a r u p ' * d r h o o h d u r i n g t h 1 8 1 0 1 i n ~ F h m % W . P u L r ~ t d t h e p m n k n t m c e t c u h i n g w r b o d r i n ~ d a n e m p h r b o n h v - ingchiMrrno&rsc,dacrik, l r r d u p d m u n d d c u h u n ~ t y b u i l d i n g on tbdr ermpdpy aperienca. Beuw d thre rmphua. John Dtuq con- sidered Parker Wx fither d progrerivt education" (C-. 1961. p U9). PuLr'8progrunru8nutounding~1~~~1unding,writing.rpelling,md uithmaic pafarrmare rolrrd. PuLr 0901-1902) abo dedopd imnnmtior appnrwbatoinmrd.tingcrrrricuhnnrPbpCaoomrbctbeir~morr obvhntothechild. M a n y d h i s t c c h n i q 9 a u t h m r l i . r ~ , i n c h d h g c h W 8 aeation of their arm nor# for reading and writing, the c a n h - t i a r d a u d i a d b ~ , p c " p , ~ , d f p d I i a g i n t b c ~ c o n t t x t a a f c m v u n t i o n m d w r i t i n g , d t h ~ d d m a r t p d i a withart. nmrkmrtia. r a d n i t i n g i n ~ r r r i a d r m b ~ ~ ~ l r ~ W u O r k . n d l 8 h ~ ~ D c r r e j 8 E u n c d k ~ S c b o d t o o k a ~ a p p n m c h , ~ u i t h t h e h m r l i . r ~ ~ t o ~ i t s ~ w i t h t h e b a m d a d u e b c i c , ~ ~ t , ~ . d ~

T b a t h i r c o r i c r l ~ u t r i p n i f t . m b e a u m e t b a c r p c b . l ~ ~ b y d r c a r u n a ~ r u a r r 5 i ~ u ~ c h i l d r m ' r i a m a o d & - d ~ a c r o u ~ b a a a d u i a r a d k p l d r c b o d ~ R a n t h probkmrdunTelatcdkuningintbtdif6amr~rubpeadirc\rrcd i n n c e o t ~ o n m d m c l r r h ~ p a r q a ~ d m c r h o d r $ ~ r l i & - i n g t b c h m k d g e l t a i n e d i n t h ~ d ~ r u b j K a r i t h i n + b o d r r a J d k rorthrhilc Although it n uagic hat the problem of cmmsarricahrm aegrcgation has not changed much m ll0 pars, we ham much man ropht-

B r i d g @ i P r a u c t i o n . ~ c h i n g t h . t c c m ~ p ~ d ~ m ~ contaa, th provision of multiple aampla of know- Pmrfrr. qncqht ic curriculum design-d tbae aaivith could cootribute to thc creation d an educrthd culture that a m n u a p tmdcrmh.nrinp ltlrning d think- ing p- Un6Dmuuttly. th C U ~ W & U chui.c. It t perhrp more c o m p r & a m i i k w h c n u d ~ a d a c r i p i . C m m b y r n t h r o ~ o r e t h - n o g m p h m t h u r . r a p r r r c r i p t k a r m b y a l u c ~ o n . ~ m d t e c h - nologha. Yet it#mreund.ltotrytoandaruPdhowto buildrachcan- mu- or cultmu, particukrly beawe we have ren how, daaiptivcly, ~ ~ 1 t u r r l ~ r r r t i c c l r e a n t o b e t h ~ S a r r a m a r t u d m t ' r ~ d a probkm dtuation as orrt for which aurr6a d pmiau knrmkage U pouiik. or important, or mnth th

Itiallighlydgnificlntthat\rbmthhmerian~ . . fotthklmhce- ment of Sckncc 0984: abo ace Cok. 1987) look3 at d hundred pmolkgc prosrunrfbrtachingmathrmtiaandat5emxinwhichmirroritiadrrnncn pafannedasruuxddyurrhiocm.t.r tkyfoundtbtpro(punrrhutda n u m b c r d 6 m t u x u T b t ~ p i c m r r r r r a b t h u r r r r r r h . l ~ ~ thacmrhichtbarwaspaticlldb ' Ibtqnthdtbtrbodcduu- tidutthgrrithcammunitykarniag.~,tbae~mntinnityumr t h e g n d c ~ u p t h m u g h c o l l e g c i n t l u q u a l i y a n d ~ d d i e r - i n g s m d e d ~ ~ ~ t h w ~ H o r i u r n t . n y , t h r r ~ p u m a l , i n d a r t r ~ d ~ d c a n m t m i t y ~ t h u w w i n - d i n h a v i n g t h r u d m a ' ~ 8 n d r d c r r c k u n i n g r r o n t . I n etrnce.thacrrrcarfulprogrnnrhadkenabktodehcaculturcchatsaid t o ~ t h u ~ d l u r n i n g h r r r d ~

R a c u e h k P c e d c d o n b t o ~ R I c h ~ c P h r u q r b i c h I t . L c t o k ~ r d r t e d t o t h g d d ~ ~ 6 0 4 w l c c d r t ~ d RaaicL (1987) hu h c d o c i t s a ~ n q h m f i x ~ . *

dsuchcmirraunmo604I#mingtothink~(a)ulf -dirracd d r s Q w m r ( a n r h r t t o r o r t o n : ~ ~ ) ; @ ) d j l C p l q O l l . . " rubathrn - d u r a ; ( c ) d - g o ~ p t m r p a s _ u k

!k&l~mwhichthinLinppn#aerurcmuhapl ic i t .ormod- eled, wan to proridc imporcant dDItaing amdumnn

. . hkplrninstotllinkd ~ d p v r r f e r h t o n e L m m m ~ ~ ~ p r ~ b k P l ~ r i t h i n a b m d l l r m l i n such as reading, writing, or mathunatia (CoIlim & Brown, m pmm-b; h b c -

tu & B n m , 1984: Sard.nulk, badm, & Sainb.ch, 1984; scbaddd, 1 9 S ) . ~ r p p e u t o r n h m o t h L ~ m t h i n k ~ l 9 8 7 ) . ~ o r d n c h ~ i n c d p E I d o n i r r r i d m c r r u t o p p o a m n t d e r S w Cbpdiw APPlrrJicuhpI (Cdlirr & Bmm. in ptem-b). It ir d Imrt.t what t h t b a r a d r p c h ~ u l c , h u t H ~ . r ( ~ ~ p a i d c r a J a m C o r t h i n L i r r p inrhichrPehurti . it iaoomctokwcnm~amtnitioor(ScbomBtld. 1987).

O ~ d m o d c l i n ( J m t i r i n r p f i i c i a u . s m & n a n c e d m t . a u r p c h ~ t h m r r d r a 8 n d r ~ b j t c t t h e i r o m ~ ~ m n m m l l n i q rclccioDmdmppartkcritiqueInpuddp.~inthb#irlbolrcdpmrt- irml (vypsky, 1978). 8 chiM m y ktm emirion the new upbi1idahorrbcdh.rtifanlythtLrrorrledgethothaperronh.d a r o n i b P a e d r r r r r ~ T b a c r h i n k - J a d ~ ~ 8 b o ~ k childrrn'a dfsarrcpcl, tbcir belie6 in w i m k tbcir btdip~~ can k d e r d a p e d 0 r ~ ~ ~ e n t i c ) , ~ t h i r b a l i P ( p 8 b a a t ~ , ~ ~ r r . d o r b a ~ d i m b l i n g ~ b l o c L t o e i t h e r t h ~ 1 ~ ~ a b i - ti- or appliation rida a# trrnrdcr of m. S i methods have ken pmmacd b hpat (1980). Tershnwill.LoDs#ltol#nra,rmdnftladbrnrtopmrroacacultlrrr

fortrrruSrrm~d.m#QIIby~hnorrbdgcinrrrc,caaccpaaamob forandartradiry,8ndu8n8fcrd~8kilhuanacdPitfanPlltoth r o d J a r n t r u * d & ~ .

S u c h c h n a l p t ~ d . m w m ~ l l U y k ~ t o . m b a i t y r t n r - t u m ~ For in an education that taka conveying funaionrl Lporrbdec in mul- apleconcaa~,dwhichaiam~onpriorapaiawxrthcchild b r i n g a m t h e d . m a r m f r o m t h e ~ m d . c d o r u d ~ & t h b a P o f a u t b m i q i n ~ c k r r # m w i l l h ~ . T h p r i m y d i r a u w d t h e d a m # n ~ ~ t o r h i h f m m t h e ~ - D o p p L P o r r X ? ' f r u n e (Mehan, 1979). a cauinnrl rceprgatnc

. . m l c f m ~ r i t h t h m r ) u ? r i n a ~ r d t . t o a p c i n w h i c h b t a r r h ~ a f i m a i o d m l t , i s r o # d Itrrring-DoppLnorXtodoWor-w4tcanpp&rithXmurircu W a r e r m ' W h t c m p p n u L P d X Y ~ d . l i r , r b k h . ~

qqlropkte (cg.. - ~.\rtiar & h. 1987). c ~ t b c a b d i t i o P r l ~ . t p r r d t h t l ? . r t u r ' a ~ u . i l - L B o r i q ( l ~ ' m a r t dcdhbodumltrmr. ---

~ ~ c d k ~ k n r r a r t h e r r r t r r h o ~ ~ ~ ~ ~ ~ ~ . i q d ~ 8 n d i n p m t O d Y m e a r h . g m d . a a ~ t r P r L a ~ ~ d k r u n t i . l . i d r m t h i r t r r r v d o r m r t i r r ~ I n p u t i c p k r , r c r r i n d k m r m c r b o b f o r ~ a c r r b a r k u n b c l r r t o ~ L r r o \ r l e d e c t h 8 t r c P d c n ~ - h . . c h ~ ~ ~ h ~ h e r p e r t & ~ & t h i r d l d b o r r t h q ~ r t r h a p ~ . n d t o ~ d b p i E d m I l K h ~ ~ f m t h c p r n p a a d t h i n k i q ~ w h i c h e d u a t i m w i l l k d k c t e d .

J p p h i c r r p ~ d t h i r ~ ( e . g . . aaaaraptnchrortmp: N o d &Gowen. 1984)-butaoandccaonicwhiteboudch.trarldkdto& uansfcrpki i i l t i er toa~probImrri tP . t ionopenBmdkuniunor

byo#cburmdahrBtudmaSIlchrrpamtatiarrrrorrld b c a ~ i l ~ b k b r t h ~ t ' s ~ m f a t u r r p r o b k m r o h r i n g . i n a # w u a r o f h n r c p l . a b o l d a d o n c ' s c o m p h u l ~ b o k b u i l t a p , m d within which new knowledge would need to be'integratcd. I predict that the

&Y apaiart. sPch~erpaiarcindudaDot~rponturcarrinoaaaiarrwith

O b ~ e m ~ e r a d ~ b u t ~ ~ ~ w i t h i n - 6 n m a l t u c h i n g , m a P o r i a d ~ ~ w h n p P a d o l r u t n i e d . r o d a b a r t h i d i n g ~ u t b c y ~ i n p o b l a n m h h g . T b a t u t t b c r u o u n x a B o r t b e h m n m ~ m Y h i r v d ~ f . ..

I t k ~ c l c a r t h u S o r r m l r d a r a ~ t i m h . r p r i d i m R c f f i c i m t ~ t o ~ p r i o r k l i c 6 r F u f r a n b e h y a b P k ~ a r d t n t r c a n c t o r k n l w i t h i P t r i Q O C k l j d ~ b a m ~ ~ t b c i P r t r r a c o o r d d i f f t . n k m . r e r t . i P ( ~ & ~ , ~ ) . B ~ t t b c i t a r t t r n m m r r L m a r d i € k u l c k a r r w ~ d r c i m c c c d r u u i a P ~ ~ t b i r ~ p O b k J b o g c r b a t ? d t h u ~ d a d d ~ f m n 8 ' ' tivc,pqingcbr.ttmt;mcoQIPCCPCP.IprrZCQE6dt9d10CDltharmL 6 o a m ~ r t n n ~ . ~ n o r r L p o r o t h a r b t . I - - dac-

- t i v i d a r b o p k l m r L r r r r A m a ' k l j e b ~ ~ ~ A P d ~ n - - 1rrrbrtmbt.achkliebmmt6mk%md.~Hav- ing ken Samd. kuning and teaching activitkr a n then acme-u does

Baeiba and Surdunllia (1986). P a h a u d Brawn (l984);. d Scbom- 6tld 0985) dl utilize methodr for m a b # trader procaa expihit (tSlh & Brown. in pmm-b). For a given con- or cognitive W, live moddiag d iuappIk.tionmmultipku~1cauldbtmprdcd.i.opcialdirL~6Dlr artlececdr8ngcofproblanrarQrmiar.d\rbmoae~tbertudma to&approp&tc~tiavfmtn tbecuawleeped. Tbtrpmrroold khighlyiStCI.Ctnr, a u b l i n g l c r t L d b d p i t a r c u d m t h d ~ m c a r - q i n g a n u i t h n e w k n o w l e a g e ~ a c t i v i t i u a f t e r o b r m i n g m ~ d multipk bridging involving that knuukdge.

R@&m d y s i s of the det.ilr dope'1 own arnrder pdmmmm u well am th- of others rhould be pmbk. by rephying pFobkmlohring epLoda (Conina & Brown. --a). The modding rctiritia rlcatd d d i t id ly b e b u e d o n w l : ~ o f k n u u ~ a ~ h t o t b e p o b k m . ; h l l r i a r u d-lik(Stanbcrg. 1986,aE6arrmwAlggatiau)lad~tbacrith the problem duKI of finmd education in matkmticr. a h c c and litemcy. Thephrue"cvcrdayliZc"isapkaholdaforthecultudydc6ncdnormrd a c t i w that d t u t c cultld practiar

~ p h i c ~ u t n c c d e d t o c ~ n t n i t o a ~ d ~ * S c r i b 1 ~ ~ a n d C d c ~ 9 8 l ) d c J h r m l p m c t i c y ttuthdpIh.perhupewpk inaculturr~ad"utheurL;rarproblanrf.dnetbanmaatp.tion.Harr d o t h a c i n b c r p m c d " ~ e l e m c n u " d ~ ~ ~ c a n c t o b e u P d a r t o o d orpuuivcd?Arethatai~dif6rrmtmdinPindch.nuerdrcboold nonschool environments that will be important to take into account in design- ing such bridging activities? If we have - to thr qudom, our &- t i o n d d a n a i m f o r m u l d p k a a m p l a d ~ a ~ m d d m a b o d r forintlpdpcinstbananaldhavcmactb#miul~.Bea~tbteray- c l a y l i k + a i n s l d b u n d W i n b e ~ t o ~ . c r o r ~ g o r t p c r o r ~ c o g n i t i v e s t u d i c s w i l l k c c n m l m t h e d c s i g n d ~ . c c i v i t i a r u p poncdbY~-loghr

T h 6 c r r m i l a b l c t u m r i a l # t t r r P r r ~ ~ ~ t o ~ probkm-r)bhg strategies fall rbort when judged q a b t tbac a mn- dudr.bampluindudc Wumpur, a f m t a q g . m t ~ m m c h r t i l L i n logic, probability, dccimion ady& l~maeay, and Rocky3 Boots, in which audcnacururccompoddollrdBodeur~gaoadiPeTclriryamphity tobuiMrmchinathatcomealivcar,thrmn. InnirkrareareanylinL madctom-rcbod~or~~td-rbodrruoningdtp.tiarrAso~tbrrtart m u u r r , r p C h ~ l i n k " ~ d k ~ ~ k l a l r b o d ~ i n i t i a ~ a n d e n r i c h t h ~ o f a i s t i n g p a P b k m r o h i n g r d t - ware. as Pogrrnr and Buchanan'a 0985) work has dananrp.ttd with cornpen- m t o r y ~ f o r e k m ~ r b o d ~ p o a l ~

S c m r r c m t ~ h a l k g r r n t o a d d m t b a t b r i d g i n g ~ d aa Sunbulff's S u d Math. It quires mathematical m a a h g to a o k d- world problems. such as bat-buy shopping, trip phming, and bdding con- r ~ u c t i o n . E f f o r ~ t o m e e t t h c w & t c r i ? r r c r r r L o ~ m ~ ~ ~ ~ ~ B u r L ;

d ~ ~ S D c ~ r h u i a y i n ~ ) t o J D Q I t h e ~ d a h n ' m n d a a p a i a u u a a n , t b t ~ p # r d H a r m * m a d a a f k u n h y u r r i t d o u t m ~ ~ o r h n h r i m p o r u n t c u a k d t o .d* l l l~ inaneduat iau l~Harbar ldrucherpa imoaknorrd dd?UlhUdhklikmh.tlC~tekctnmk*mrmaia- th.th.colgrniacdba.pproprkttrrPierrldapplicdmthtpriaa- paiawradindi*idurbrithinhmth.tbrP.d~inmnrdntomprob- k n u ~ k m s d c 3

Saneputdthrnrramtberdifticultquationrmwkinclrriflr- tionofprobkmtlpr. kauKratialorg.nl .t iondprobLm~bwbat uana to provide much of the parer behind the erpert Prpbkm-mMr ease in .car tmmfer-appmpri.te knddgc.

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