Piaget’s)Studies)in)Generalizaonmyweb.clemson.edu/~campber/campbellpiagetgeneralization.pdfPiaget’s)Studies)in)Generalizaon...

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Piaget’s Studies in Generaliza2on Robert L. Campbell Department of Psychology Clemson University June 2, 2012

Transcript of Piaget’s)Studies)in)Generalizaonmyweb.clemson.edu/~campber/campbellpiagetgeneralization.pdfPiaget’s)Studies)in)Generalizaon...

Page 1: Piaget’s)Studies)in)Generalizaonmyweb.clemson.edu/~campber/campbellpiagetgeneralization.pdfPiaget’s)Studies)in)Generalizaon RobertL.)Campbell) Departmentof)Psychology) Clemson)University)

Piaget’s  Studies  in  Generaliza2on Robert  L.  Campbell  

Department  of  Psychology  Clemson  University  

June  2,  2012  

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The  triptych

Recherches  sur  l’abstrac.on  réfléchissante  (1971-­‐1972;  published  1977)    • Studies  in  Reflec.ng  Abstrac.on  (2001)  

Recherches  sur  la  généralisa.on  (1972-­‐1973;  published  1978)  

Recherches  sur  les  correspondances  (1973-­‐1974;  published  1980)  

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Two  ques0ons

Abstrac2ng  and  generalizing  are  supposed  to  be  2ghtly  linked:  any  property  that  has  been  abstracted  supports  generalizing.  1.  Can  reflec2ng  abstrac2on  and  

construc2ve  generaliza2on  lead  to  errors?  

2.  Are  there  levels  of  abstrac2ng  and  generalizing  (or  are  levels  to  be  defined  in  structural  terms  only)?  

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Chapter  2:  Combining  lengths

Jean  Piaget  and  Alex  Blanchet  Children  line  up  rectangles  on  the  table  to  

meet  length  targets  • 24  rectangles,  length  and  width  numbered  along  the  sides  • Single  length  and  double  length  targets  

Trick  ques2on  (using  only  rectangles  whose  length  and  width  differ  by  3,  go  from  target  length  n  to  target  length  n+2)  

How  many  combina2ons  of  lengths  for  1,  2,  3,  4…    rectangles?  

 

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Chapter  2:  Combining  lengths

1)  “Induc2ve  [generaliza2on]  is  limited  to  applying  to  new  objects  a  scheme  already  known  by  empirical  abstrac2on  (or  by  reflec2ng  abstrac2on,  but  only  when  the  scheme  was  constructed  prior  to  the  generaliza2on,  without  this  construc2on  intervening  in  the  mechanism  of  the  same  generaliza2on)”  (p.  44)  

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Chapter  2:  Combining  lengths

2)  “Construc2ve  generaliza2on  […]  gives  rise  to  new  forms  by  comple2ng  or  differen2a2ng.    This  second  form  of  generalizing  thus  marks  progress  in  intension,  but  naturally  also  in  extension  (insofar  as  it  is  subordinated  to  intension);  hence  it  creates  new  contents,  or  enriches  empirical  contents  by  providing  them  with  new  forms.”  (p.  44)  

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Chapter  2:  Combining  lengths

“In  general  terms,  induc2ve  generaliza2on  is  based  on  observa2ons  [constata.ons]  or  on  just  the  results  of  ac2ons,  whereas  the  construc2ve  kind  generalizes  the  ac2ons  or  opera2ons  themselves,  broadening  and  comple2ng  the  forms  that  they  already  had.”    (p.  44)  

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Chapter  2:  Combining  lengths

“In  sum,  at  every  level  we  find  both  induc2ve  generaliza2ons  and  construc2ve  generaliza2ons  (whether  pre-­‐exis2ng  generaliza2ons  that  serve  as  frameworks  or  current  generaliza2ons  that  serve,  so  to  speak,  as  drivers).    But  it  is  apparent  that  the  construc2ve  generaliza2ons  come  to  predominate  more  and  more  over  the  induc2ve,  and  subordinate  them  via  a  con2nuous  process.”  (p.  46)  

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Chapter  2:  Combining  lengths

IA  (5-­‐year-­‐olds)  – Meet  single  length  targets  without  much  trouble  – Not  adept  at  mee2ng  double  length  targets  with  the  same  rectangles  (which  then  have  to  be  rotated)  – Center  on  the  length  or  the  width  of  the  rectangles  – Fail  to  differen2ate  among  possible  combina2ons  

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Chapter  2:  Combining  lengths

IB  (6-­‐year-­‐olds)  – Begin  to  coordinate  aligning  and  rota2ng  – Otherwise  rely  on  “groping”  (tâtonnements)  to  meet  length  targets  

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Chapter  2:  Combining  lengths

“A  construc2ve  generaliza2on  is  involved,  of  course  in  part,  to  the  extent  that  the  subject  begins  to  understand  that  a  non-­‐square  rectangle  has  two  dis2nct  dimensions,  and  that  in  turning  it  one  necessarily  finds  a  new  length  L  or  W:  hence  the  possible  use  of  rota2on.    But  all  there  is  to  this  is  a  preliminary  step  whose  purpose  is  to  establish  the  meanings.    Consequently  it  is  a  simple  general  framework,  not  a  mechanism  that  takes  into  account  the  passage  from  one  ac2on  to  the  next.    […]  the  child  is  in  no  way  yet  able  to  infer  the  consequences  of  a  par2cular  rota2on;  it  is  thus  only  in  regard  to  the  results  of  his  ac2on  that  he  refuses,  accepts,  or  generalizes  such  akempts,  and  to  the  extent  that  it  remains  like  this,  the  generaliza2on  is  obviously  s2ll  induc2ve.”  (p.  37)  

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Chapter  2:  Combining  lengths

IIA  (7  and  8-­‐year-­‐olds)  – Children  begin  to  make  inferences  rela2ng  the  length  and  width  of  the  same  rectangle  and  of  different  rectangles  – They  rely  on  explicitly  on  the  numbers  inscribed  on  the  rectangles  

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Chapter  2:  Combining  lengths

“The  reac2ons  of  the  present  substage  IIA  mark  a  notable  advance:  the  child  notes  both  dimensions  of  a  given  rectangle  right  away  and,  by  groping,  puts  them  into  rela2on  with  the  dimensions  of  the  others.    Hence    construc2ve  generaliza2on  begins  to  take  off.    From  a  simple  framework,  it  becomes  an  instrument  of  quan2fica2on  that  subordinates  the  values  L  and  W  that  are  being  added  to  the  predicted  length  of  the  alignment  needed  to  reach  the  target.”  (p.  39)  

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Chapter  2:  Combining  lengths

“The  first  indicator  of  this  transforma2on  in  the  func2on  of  generalizing  is  that  the  subject  really  understands  the  two-­‐target  problems.    He  grasps  right  away  (or  nearly  so  […])  this  it  isn’t  a  maker  of  hilng  one  target  amer  another,  but  two  at  once,  with  the  same  elements,  some  of  which  merely  need  turning  to  L  or  to  W.”  (p.  39)  

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Chapter  2:  Combining  lengths

“[…]  concrete  opera2ons  are  just  beginning  at  Level  IIA,  which  means  that  deduc2on  is  s2ll  akached  to  material  ac2ons  and  to  what  has  been  noted  about  objects;  hence,  it  proceeds  by  abstrac2ons  that  are  pseudo-­‐empirical  and  not  yet  reflected,  as  they  will  be  in  the  formal  stage  around  11-­‐12  years  of  age.    The  stage  difference  is  par2cularly  marked  for  the  impossible  solu2ons:  none  of  these  subjects  understands  the  general  reason  why  with  differences  of  3  between  L  and  W  the  total  length  of  the  alignment  cannot  be  increased  by  2  units.”  (p.  40)  

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Chapter  2:  Combining  lengths

IIB  (9  and  10-­‐year-­‐olds)  •   “Long  stretches  of  trial  and  error  for  the  two-­‐target  problems  because  ‘I’m  trying  to  calculate  it’”  (p.  41)  • Realize  why  the  trick  problems  are  insoluble  • Arrive  at  an  incorrect  addi2ve  rule  for  the  number  of  possible  combina2ons  

     

   

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Chapter  2:  Combining  lengths

“In  many  studies,  notably  on  causality,  Level  IIB  appears  to  mark  a  regression  from  IIA  on  certain  points,  yet  on  further  analysis  we  note  that  the  subject  is  actually  discovering  new  problems  that  complicate  the  task  for  him,  yielding  the  impression  that  he  is  on  a  wild  goose  chase  (qu’il  cherche  midi  à  quatorze  heures).    In  the  present  study,  the  phenomenon  is  par2cularly  striking:  while  the  subjects  are  doing  more  and  more  reasoning,  there  is  no  observable  progress  in  the  results  at  Level  IIB;  instead,  there  is  some  apparent  backsliding  whose  cause  remains  to  be  found[…]”  (p.  40)  

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Chapter  2:  Combining  lengths

“[…]  the  subjects  do  more  deducing  than  at  Level  IIA  and  omen  carry  out  calcula2ons  before  no2ng  [the  results  of  placing  the  rectangles],  an  indica2on  of  progress  in  construc2ve  generaliza2on.    In  par2cular,  they  react  beker  to  the  impossible  solu2ons  […]  But  precisely  because  they  seek  to  reason  before  ac2ng,  the  risk  of  error  increases  and  they  engage  more  omen  in  groping,  which  is  one  reason  for  the  apparent  steps  backward”  (p.  41).  

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Chapter  2:  Combining  lengths

III  (11-­‐12  years  of  age)  – Deliberate  use  of  deduc2on  – Immediate  calcula2on  of  the  dimensions  of  each  rectangle  needed  to  meet  two  targets  (though  this  is  not  error-­‐free)  – Correct  explana2ons  of  the  impossibility  – Computa2on  of  the  number  of  possible  alignments  of  n  rectangles  (the  set  of  2n  “base  associa2ons”)  

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Chapter  2:  Combining  lengths

“By  contrast,  at  Stage  III  construc2ve  generalizing  prevails  decisively,  on  at  least  two  points.    On  the  one  hand,  the  double  target  problems  at  last  yield  the  elabora2on  of  a  deduc2ve  method  allowing  the  appropriate  coordina2ons  for  heterogeneous  par22ons  to  be  controlled  through  calcula2on.    Hence,  as  a  corollary,  the  understanding  that  the  trick  problems  (differences  of  3  for  an  elonga2on  of  2)  are  insoluble,  which  presupposes  the  ability  to  sum  the  differences.”  (pp.  45-­‐46)  

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Chapter  2:  Combining  lengths

“On  the  other  hand,  the  problem  about  the  number  of  possible  alignments  for  a  given  set  of  rectangles,  which  at  Level  IIB  s2ll  elicited  only  incorrect  addi2ve  solu2ons,  is  finally  solved.    This  is  a  remarkable,  nearly  pure,  instance  of  construc2ve  generalizing  (once  the  4  possible  combina2ons  of  2  rectangles  have  been  noted  through  pseudo-­‐empirical  abstrac2on).”  (p.  46)  

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Chapter  2:  Combining  lengths

“Let  us  keep  in  mind  first  that  while  it  is  easy  to  construct  a  table  of  the  stages  in  the  development  of  a  no2on  or  of  a  structure  (be  it  preopera2onal  or  opera2onal)  that  are  due  to  the  func2oning  of  abstrac2on  and  generaliza2on,  abstrac2ng  and  generalizing  are,  by  contrast,  merely  func.ons  (in  the  biological  sense,  whereas  no2ons  and  structures  are  organs).    A  func2on  (such  as  nutri2on  in  its  innumerable  forms)  is  permanent  and  uses  diverse  organs,  so  it  has  no  stages  as  a  func.on.”  (pp.  43-­‐44,  my  italics).      

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Chapter  2:  Combining  lengths

“Conversely,  it  presents  mul2ple  forms  of  func2oning  2ed  to  organs,  and  the  biological  problem  is  thus  to  know  whether  the  func2on  “creates”  the  organ  or  vice  versa.    From  the  cogni2ve  standpoint,  we  think  that  the  func2on  of  generalizing  gives  rise  to  structures  that  advance  its  func2oning,  leading  to  novel  structures,  and  so  on.    The  stages  that  we  observe  are  stages  of  structures,  but  analyzing  them  permits  further  analysis  of  func2oning,  which  gets  more  advanced  level  by  level  (albeit  without  allowing  func2oning  to  be  their  sole  determinant).”    (p.  44,  my  italics)  

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Levels  again

•  In Chapter 2, Piaget maintained that levels should be defined in structural terms only

•  But Studies in Reflecting Abstraction presents levels of reflecting abstraction (and notes cases of reflected abstraction at Level IIB)

•  By the time he drew up his “General conclusions” (Chapter 14), Piaget was having second thoughts about levels of constructive generalizing

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Abstrac0ng    (Piaget,  1977/2001)

•  …  Metareflec2on  Reflected  abstrac2on  Reflec2ng  abstrac2on  Empirical  abstrac2on  

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Generalizing  (Piaget’s  “General  conclusions”,  1978)

Construc2ve  generaliza2on  (advanced)  

Construc2ve  generaliza2on  (basic)  Induc2ve  generaliza2on  

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Integra0ng    (Piaget’s  “General  conclusions”,  1978)

?  Synthesizing  integra2ons  Comple2ve  integra2ons  Coordina2ve  integra2ons    

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Generalizing  (Henriques,  1978)

Formal  generaliza2on  Operatory  generaliza2on  Induc2ve  generaliza2on  

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The  lineup

Metareflection (Formal generalization)

Reflected abstraction

Constructive generalization II

Synthesizing integrations

Reflecting abstraction

Constructive generalization I

Completive integrations

Empirical abstraction

Inductive generalization

Coordinative integrations


Piaget’s Stage Model of Development - Stony Brook · Piaget’s Stage Model of Development • Qualitative differences across age • Child is an active participant in their own

Piaget’s Stage Model of Development - Stony Brook · Piaget’s Stage Model of Development • Qualitative differences across age • Child is an active participant in their own

Piaget’s Theory of Cognitive Development

Piaget’s Theory of Cognitive Development

Piaget’s Theory of Cognitive Development

Piaget’s Theory of Cognitive Development

PIAGET’S STRUCTURALISM AND LINGUISTICSsajms.com/.../uploads/2017/02/Piaget_Structuralism_and_Linguistics.… · PIAGET’S STRUCTURALISM AND LINGUISTICS Sandhya Shankar1 Abstract

PIAGET’S STRUCTURALISM AND LINGUISTICSsajms.com/.../uploads/2017/02/Piaget_Structuralism_and_Linguistics.… · PIAGET’S STRUCTURALISM AND LINGUISTICS Sandhya Shankar1 Abstract

Jean Piaget’s Stage Theory of Cognitive Development

Jean Piaget’s Stage Theory of Cognitive Development

UDI Advanced Topics DMA and Interrupts Robert Lipe UDI Development Team Lead E-mail: robertl@sco.com.

UDI Advanced Topics DMA and Interrupts Robert Lipe UDI Development Team Lead E-mail: [email protected].

Interpretable Reinforcement Learning Inspired by Piaget’s ...

Interpretable Reinforcement Learning Inspired by Piaget’s ...

Piaget’s Cognitive Development · Piaget’s tasks are culturally biased Schooling and literacy affect rates of development. Summary of Piaget: Criticisms Demand characteristics:-the

Piaget’s Cognitive Development · Piaget’s tasks are culturally biased Schooling and literacy affect rates of development. Summary of Piaget: Criticisms Demand characteristics:-the

Piaget Realized: Testing Piaget’s Preoperational Period

Piaget Realized: Testing Piaget’s Preoperational Period

Acquiring Piaget’s Conservation Concept of Numbers ... · Piaget’s influential research on the conservation concept has a wide-reaching impact even in modern-day settings. This

Acquiring Piaget’s Conservation Concept of Numbers ... · Piaget’s influential research on the conservation concept has a wide-reaching impact even in modern-day settings. This

Piaget’S Cognitive Development Theory

Piaget’S Cognitive Development Theory

Cognitive Development: Piaget’s Theory and Vygotsky’s Sociocultural Viewpoint.

Cognitive Development: Piaget’s Theory and Vygotsky’s Sociocultural Viewpoint.

Jean piaget’s cognitive stages

Jean piaget’s cognitive stages

Piaget’s Theory - PENDIDIKAN TEKNIK INFORMATIKA DAN … · Piaget’s Theory •The first “cognitive” theory, developed by Jean Piaget beginning about 1920. •Piaget observed

Piaget’s Theory - PENDIDIKAN TEKNIK INFORMATIKA DAN … · Piaget’s Theory •The first “cognitive” theory, developed by Jean Piaget beginning about 1920. •Piaget observed

Piaget’s Theory of Conservation

Piaget’s Theory of Conservation

Piaget’s Theory of Intellectual Development - spc4erp.com · Piaget’s Theory of Intellectual Development is therefore very welcome. Thanks to the joint efforts of a Piagetian-trained

Piaget’s Theory of Intellectual Development - spc4erp.com · Piaget’s Theory of Intellectual Development is therefore very welcome. Thanks to the joint efforts of a Piagetian-trained

Identify Piaget’s 4 stages of cognitive development

Identify Piaget’s 4 stages of cognitive development

Piaget’s Perspective

Piaget’s Perspective

Jean Piaget’s Theory

Jean Piaget’s Theory

Piaget’s Stages of Cognitive Development

Piaget’s Stages of Cognitive Development