OF
HANDBOOK
CHILD
PSYCHOLOGY
'S
FormerlyCARMICHAET MANUAL
OF CHILD PSYCHOLOGY
PAULH. MUSSENBntron
FOURTHEDITION
VolumeIII
DEVELOPMENT
COGNITIVE
John H. Flavell/Ellen M. Markman
VOLUME EDITORS
JOHNWILEY & SONS
NEW YORK CHICHESTERBRISBANE TORONTO SINGAPORE
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M a i n e n t r Yu n d e r t i t l e :
Cognitive develoPment.
( H a n d b o o k o f c h i l d p s y c h o l o g yv; ' 3 )
l n c l u d e si n d e x '
H'
l . C o g n i t i o ni n c h i l d r e n l ' F l a v e l l ' J o h n
l' Child
s
e
r
i
e
s
l
l
l
M
.
I
D
N
L
M
:
E
l
l
e
n
ll. Markiran,
psychologY'WS 105 H23541
vol.3 1554s [15s4'13] 83-3468
sitzt.ii+z 1983
lBF723.C5l
rsBN0471-09064-6
Printed in the United Statesof America
1098765432r
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS-
3
R O C H E L G E L M A N , U t t i v a r s i ho' f P e t r n s t l r a r t i a
RENEE BAILLARGEON. Urrivcrsin' of Pennstlt'ania
CHAPTER CONTENTS
OVERVIEW 167
A S S E S S M E NO
T F T H E C H A R A C T E R I Z A T I OONF
C O N C R E T E O P E R A T I O N SI 6 8
A r e T h e r eS t r u c t u r e sd ' E n s e m b l e ?
168
D o M u l t i p l eC o r r e l a t i o nO
s btain'l
168
Are Sequences
as Predicted? I 69
Test of the Logicomathematical
Model
170
A r e W i t h i n - D o m a i nR e l a r i o n as s
Predicted? 170
l s P r e o p e r a t i o n aTlh o u g h tR e a l l y
PreoDerational? 172
I n d u c i n gS u c c e s so n C o n c r e t e - O p e r a t i o n a l
Tasks
115
A C L O S E RL O O KA T T H E D E V E L O P M E NO
TF
S O M EC O N C R E T E - O P E R A T I O N A L
CONCEPTS T79
ConservationD
s u r i n gM i d d l eC h i l d h o o d
179
N u m b e rC o n c e p t s
l8l
AbstractioV
n e r s u sR e a s o n i n g l 8 l
Countingin Preschoolers? l8l
An InteractionBetweenNumber Abstractorsand
ReasoningPrinciples
182
S o n r eI n r p l i c i tK n o w l c d- e
l cD o c s N o t I m p l r F u l l o r
E x o l i c i tK n o w i e d s e
84
C o n t i n u o u sQ u a n t i t yC o n c e p t s
189
Conservation 189
O t h e rC o n c e p t so f C o n t i n u o u sQ u a n r i t \ , l 9 l
C l a s s iifc a t i o n
I93
Background 193
C l a s s i f i c a t i oann d B a s i cC a t c g o r i e s 1 9 6
Primacyof BasicCategorization 197
C l a s s i f i c a t i oann d H i e r a r c h i eos f C l a s s e s 1 9 9
C l a s sl n c l u s i o nR e v i s i t e d 2 0 8
M o r eo n t h e S a m eT h e m e s
210
OVERVIEW
theoryas well asour own views on the cunentstatus
of the theory.The resultis a review that is critical.
yet in agreementwith someof the fundarnentaltenets of the theory.Thus, we acceptthe positionthat
thereis much tclbe leamedabout cognitivedevelopas
mentby studyingthe acquisitionof suchconcepts
number,space,time, andcausality.We alsohaveno
quanel with the idea that cognitioninvolresstructures that assimilateand accommodateto the environment;indeed,we do not see how it could be
otherwise However, we do questionthe notionof
chartherebeingbroadstagesofdevelopment.eac-h
acterizedby qualitativelydistinctstructuresAs we
will see,the experimentalevidenceavailabletodai
no longersupportsthe hypothesisof a majoi qualitative shift from preoperationalto concrete-operationalthought.Instead,we arguefor domain-specific descriptionsof the nature as weli as the
developmentof cognitiveabilities.
Our reviewof Piagetianconceptsstarts\\ ith mattercof structureand endswith mattersof funt'tion, or
developmentproper. That is, we take up frrst the
Our task was to examinePiagetianconceptsin
light of recentresearchand theory on cognitive development.This breathtakingassignmentwas made
somewhat easier by the fact that elseuhere in the
Handbook there are discussionsof the first (sensorimotor intelligence)and last (formal operations)
of Piaget'sproposedstagesof development.This
allowed us to focus on Piaget'stwo intermediary
sta-ees
of development,those of preoperationaland
concrete-operational
thought. But we still had to
makechoices.In the end, we tried to put togethera
review that would reflect the impact of Piaeetian
*Supported in pan by NSF grants to Rochel Gelman and fellosships to RendeBaillargeon from the NSERC of Canadaand The
Quebec Depanment of Education We thank our edi(ors and K
C h e n g .C R C a l l i s t e l .R C o l i n k o f f . J M a n d l e r .m d F . t r ' l u n a v
for their careful readingsof an earlier draft o[ this chapterand E
M e c k f o r k e e p i n gu s o n t a s k A l l n e w t r a n s l a t i o n s ot fh eF r e n c ha r e
d u e t o R e n d eB a i l l a r g e o n
S U M M I N GU P
ZI3
Structuresof Thought?
213
S t a g e so f C o g n i t i v eD e v e l o p m e n t ? I l l
H o w D o e s D e v e l o p m e nH
t appen?
2l-5
Whence Come Structures?
211
A C o n c l u d i n gR e m a r k
720
NOTES
220
REFERENCES 221
168
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
)f'ftrrland then the how ol cognitivedevelopment
We beginby exanriningsomeof Piaget'sideasabout
the nature of preoperationaland concrete-operational thought,We then review in some detail the
research
thathasbeenconductedin severalcognitire
domains includingnumericaland quantitativereas o n i n ga n d c l a s s i f i c a t i o nI n t h e f i n a l s e c t i o n $, e
examinePiaget'sideasaboutthe sourcesof cognitive structures
and the processes-assimilation.
accommodation,equilibration.and so on-that accountfor their development.
spectivetakrng)is indeedrelated Anotherhasbeen
to explorethe preschoolchild's alle,eed
intellectual
incompetence
relativeto the older child. Still anotherline ofevaluation,closelyrelatedto the third,
hasbeento devisetrainingstudiesthatmightbrin_e
to
the fore unsuspected
competenciesIn the next sections. we rerierv some of the rvork that has been
donealons eachof theselines
Are There Structuresd'Ensemble?
Do Multiple Correlations Obtain?
Many studieshave been conductedto compare
children'sabilityto classify,seriate,conserve,measure.give predictionsand explanations.
assumeanWhen testedon the standardPiagetiantasksin
other'svisualor socialperspective,
andso on. Most
thestandardway, preschoolchildrentypicallyen in
such studieshave failed to show high interconelatheir responses.
Thus, when askedwhethera boutions betrveenthe various abilities tested (e.g.,
quet composedof six rosesand four tulipscontains
B e r z o n s k yl.9 7 l ; D i m i t r o v s k y& A l m y . 1 9 7 5J; a m more rosesor more flowers, they quite invariably
ison, 1977: Tomlinson-Keasey,Eisert. Kahle,
answermore roses Similarly, when presented
with
Hardy-Brorvn, & Keasey, 1979; Tuddenham,
rvith
two evenrowsof chipsandasked,afterwatchingthe
l97l). Suchfindingsarenot reallyinconsistent
experimenter
spreadone row. whetherthe two ros's
Piagetiantheory.Piagetneverreallyclaimed( I ) that
still containthe samenumberof chips,preschoolers all ioncrete-operationalabilitiesarebasedon, or are
typicallvrespondthat the longerrow hasmore.
derivedfrom. a sin-eleunderlyingstructure;or (2)
No oneseriouslyquestionsthereliabilityof these
abilitiesemergein a
that all concrete-operational
(and other similar) observations,which have all
strictly parallel, perfectly synchronousfashion
(Vyuk, 198l). To thecontrary,Piaget'srvritingsare
beenwidely replicatedWhat is very muchat issue,
however.is how preschoolers'
theorderof
failure on the stanclaimsconcerning
filled with theoretical
dard Piaeetiantasksshouldbe interpretedThe fact
emergencervithineachdevelopmental
stageof disthat childrenlessthan 6 yearsof age typicallyfail
tinct co-enitiveabilities, with the earlier abilities
thesetasksand thatchildren6 yearsof ageandolder
viewed as precursorsof, or as prerequisitesfor, the
typicallvsucceedon thesetaskssuggeststhatthere
Iaterabilities.For example,Piaget(1952a)argued
are imponantdifferencesin their cognitivecapacithat numericalreasoningis the productof the joint
ties.The questionis, How shouldthesedifferences developmentof the child's classification
and seriabe characrerized?
tion abilities.In addition.Piagetoften notedin his
Piaget's account of the differencesinvolved
empiricals,ritingsthat cognitiveabilities,once acgrantinethe olcierchild reversiblestructures,
quired,are not alwaysapplieduniformli'in all conor operations.while limiting the youneer child to inetexts.Instead,cosnitiveabilitiesare frequentlyaPversiblestructures:
hencethe useof thetermsoperaplied in one context at a time, rvith considerable
tional and preoperational
to describethe co_enitire ddcalagesbetrveensuccessiveapplications.Thus,
capacities
of the olderand rheyoungerchild respecPiaget( I 962) reportedthatchildrendo not conserve
tively Piagetbelievedthat children's(at first connumberbeforetheageof6 or 7: mass,beforethease
creteandlaterfomral)operationsareorganizedinto
of 8: rvei-sht.
beforethe age of l0; anciso on.
r,vell-integrated
sets,or structuredwholes. and he
All.of thesetheoreticaland empiricalclaimsoband his colleaguesdevelopedlogicomathematical viously mitigateagainstthe possibilitl'of anyone
modelsto characterizetheservholes.(The reader
finding high correlations
betweenchildren'sperfor*,ho is not familiar wirh thesemodelsis refenedto
manceon man-vor all of the concrete-operational
F l a v e l l . 1 9 6 3 ;C r u b e r a n d V o n t c h e . I 9 l 7 : a n d
tasks.Contraryto what is sometimesheld to be the
P i a g e t .1 9 4 2 ,l 9 - s 7 )
case.investigators'
repeatedfailureto find high corEvalLirtionof rhc theory of concreteoperarions rclationsacrosstasksdoesrrotconstitute
definiteevh a sp r o c e e d eadl o n gs c v e r al i n e s .O n e h a sb e e nt o
idcnceagainstthe notion of a concrete-operational
a s s c s rsr h e r h esr u c c e s os n d i f f e r e n P
t i a e e t i atna s k s
nrentalityin the (relativelydiffuse)senseintended
( e q . , c o n s c r v a t i o nc.l a s s i f i c a t i o ns.e r i a t i o n p. e r b y t h e t h e o n ' S t i l l . s u c hc o n s i s t e n t lnyc g a t i v er e A S S E S S M E NO
TFTHECHARACTERIZATIO
ONF
CONCRETE
OPERATIONS
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS
sults do raisedifficultieswhen it comesto the interpretation
ofcertainstudies.Psycholoeists
andeducatorsoften attempt to relate children's performance on a given task to their Ievel of cognitive
(e g., preoperational.
developnrent
concrete-operatronal)as assessed
by any of the standardPiagetian
tasks.\\rereit the casethat perfornrance
on all standardPiagetian
taskswas highlyconelated,then,obviousll'.any taskwould be asgood asany otheras a
test of rhildren's masteryof concrete-operational
thought But aswe just saw, thatis far from thecase.
For this reason,studiesthat reportrelationships
between, say, children'sability to use metamemorial
strategies
andchildren'sabilityto conserve(takento
demonstrate
theirentryinto theconcrete-operational
stage)are difficult, if not impossible,to interpret
vis-d-visPiagetiantheory
Are Sequencesas Predicted?
The studieswe discussedin the previoussection
testedfor the synchronousremergence
of different
abilities during the concrete-operational
period.
Other studieshavetestedwhetherthe order in which
abilitiesdevelopwithin thatperiodis aspredictedby
Piagetiantheory.Severalinvestigators
havefocused
on the developmentof numerical reasoningin the
child. As mentionedearlier, Piager(1952a)maintained that the conceptof number developsfrom the
coordination of classification and seriation structures. According to Piaget(1952a),rheconstruction
of number
consistsin the equatingof differences,i.e., in
writing in a single operation the class and the
symmetricalrelationship.The elementsin question arethen both equivalentto one another,thus
participatingof the class,and differentfrom one
anotherby theirpositionin theenumeration,
thus
participatingof the asymmetricalrelationship.
(p 95)
Piagetiantheory generally assumesthat success
on standardnumber-conservation
tasksindexesa
true understanding
of number and that successon
standardclass-inclusion
tasksindexesa true understandingof classification.If Piagets (1952a) account of the developmentof the conceptof number
was correct,one shouldnot find childrenwho pass
standard nunrber-conservationtasks well before
they passstandardclass-inclusion
tasks.As Brainerd (1978a)recentlypointedout, hori,ever,exactly
the oppostiesequence
obtains.The vastmajorityof
childrenconservenumberby age6 or 7; but it is not
until age9 or I 0 thatthey truly undersland
theprinci-
169
p l e o f c l a s s i n c l u s i o n( s e e a l s o N , 1 a r k . r a nl g. l S :
W i n e r , 1 9 8 0 ) .S u c h f a c t sc l e a r l yc a l l i n i . rq u e s r r o n
the claim thatnumericalreasoningis th: oroducrtrf
thejoint development
of classification::.ldseriaricrn
abilities. Additional evidence againsrihis claini
c o m e sf r o m a s t u d yb y H a m e l ( 1 9 7 4 )
H a m e l( 1 9 7 4 )a n a l v z e d
P i a g e r ' s( t 9 - i i a )a c c o u n r
of numberand concludedthat it predi.-isa strong
r e l a t i o n s h ibpe t w e e n(:l ) n u n t b e rc o n s e n a t i o nt :l )
provokedcorrespondence;
(3) sponranerrus,
tharis.
unprovokedcorrespondence;
(4) seriatiern:
(5) cardination-ordinationl
and (6) class inclusion The
conelationsbetweenthe variousnumberiests\\ere
si_snificant
and quite high ( 50 to 80r Likewise.
correlations benveen the multiple-classification
tasksand the various number subtasks*,ere also
significant, ranging from .45 to 66 Howerer.
therewere no significantrelationshipsberrveen
rhe
class-inclusion
taskandany of the other rasksDodwell (1962)reportedsimilar results.
There are other studiesthat fail to observesome
of thebetween-taskpredictionsderivedfiom the theo r y ( e . g . , B r a i n e r d ,1 9 7 8 a ;K o f s k y . 1 9 6 6 ;L i t r l e .
1912).Thereareeven studiesthat fail to observerhe
same sequenceof developmentacrosschildrenwhetheror not the sequence
is predictedbr the theory. Forexample,in a longitudinalstudy.TomlinsonKeasey,et al. (1979) found that i3 of 18 subjects
passeda class-inclusion
task beforethe\ conser\ed
amount, 12 passedit after, and l3 passedit at the
sametlme.
What shouldwe makeof investieatorsfailurero
confirm the between-taskssequencespredictedbi'
the theory?Should we take it to su_egesr
rhatPiaget
was wrong in claiming that the concrete-operational
stageis characterizedby the coordinatedemergence
of superficially disparate but structuraliv related
cognitiveabilities?Not necessarily.It ceruldbe argued that to do so would be to confuserheissueoi
whetheror not specific abilities develop in the order
predictedby Piagetiantheorywith the moieqeneral
issueofwhetheror not abilitiesfrom diffeientcognitive domainsdevelopin a well-inte-erated.
coordinatedfashion.Pia_eetian
theorycouldbe nghtin sup
portingthe generalissueand still be rvronsin an1,oi
its specificpredictions.Piaget's(l952at 3;countoi
the developmentof the child's unders::ndingof
numbercouldbe wrong-and as we will see.Piaset
(1915a. 1977)himself later abandonedhis earlier
account-but the generalhypothesisth:i developnlentin otherdomainscontributesto theenergenc'e
of thechild's conceptof numbercould st!::be right
Thereobviouslyis no rebuttalto this :igumenr
A s t h e s a y i n , e g o et sh .e p r o o fi s i n t h e p u d d : n gW h a t
170
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
[ ) i u ' ' c . c ( itahnc o r yn ] u s tp r o v i c l ei s a s a t i s f a c t o r - r ' a c c o L r l to f n L r n r c r i c(aol r c a u s a l o
. r s p a t i a lo. r l o e i c i l l .
c t c ) d c v c l r r p n r c rni r a p
t o s i t sr e a l n o n t r i v i ai ln t e r a c t i o n sb e t r i ' e e d
n o n r a i n sT o t h e e x t e n t h a t s u c ha n
ilcc(lunt cirnbe proVi dcd, thento thesanreextentrvill
t h c n o t i o no f a s t a g eo f c o n c r e t co p e r a t i o nbse r e i n f o r c e d ( A s r v er v i l i s c cb e l o r v ,h o r r e v e rr.h et r e n di n
recent)/earshasbeento move arvarfronrstage-like.
accounts of developactoss-the-cognitive-board
appearto focus
nrcnt N'lorcand nrore,investiqators
o n t h e p o s s i b i l i t lo, f p a r a l l e l ,d o m a i n - s p e c i fliicn e s
o f d e v e l o p n i e n) t
lest of the LogicomathematicalN{odel
Ir is sonretinres
arguedthat thc reasonrvhy investisatorshavefailedto find high correlations
benveen
variousconcrete-operational
abilitiesor have failed
to confimr the order in rvhichtheirabilitiesdevelop
has to do u,jth the rvay in rvhichabilitiesare meas u r e d( s e eF l a v e l l ,1 9 7 2 ;J a m i s o n& D a n s k y ,1 9 7 9 ;
Tuddenhanr,l97l). Different investigators
usedifferenltasks,Further,it is not als,aysclearwhether
the tasks used provide a good test of the abilities
i:nderstudy ln addition, therearestatisticalnightrnares Ho\v doesone estimatemeasurement
effor?
Is it constantacrosstasks?And rvhatif one finds
only one child whose performancecontradictsthe
expectedpattem-should the theory be rejected?
One rvayto get aroundsomeof thesedifficulties
is to u'ork directly from the logicomathematical
rnodelof concreteoperarionsPiagetand his collaborators proposed Osherson(1974), for instance,
usedGrize's (1963) axiomatizationof theseoperations.The choiceof this axiomatization
*,asbasedin
Iargepart on Piaget's(i967) endorsement
of it Further.Crize's axiomsareeasilyinrerpreted
into sratenrentsaboutclassesand relations.
To start,Osherson(1974) deriveda set of theorenrsthatfollowedfrom Grize's( 1963)axioms.He
thentranslateda subsetof the theoremsinto a setof
l e n g t h - i n c l u s i oann d c l a s s - i n c l u s i ot an s k sd e s i g n e d
to embodl'thederivedtheoremsand,thus,providea
t e s t o f c h i l d r e n ' sa b i l i t y t o u s e t h e m F i n a l l y .h e
madepredictionsaboutthe patternsof successes
and
failures that should obtain Thar is, he specified
rvhichtaskschildrenshould passor fail, given thar
thcy,had passedor failed certainother tasks.The
predictionswere basedon the anall,sis
of which and
horv rnanvaxiomsa particulartheoremrvasderived
'lo
froru.
illustrate.assunreTheoremsI and 2 rvere
d c r i v c df r o n rA x i o n r sI a n d2 , r e s p e c t i v e al yn dT h e orcrn7 q'asderivedfrom Axionrs I and 2. The child
u,ho passcdthe task dcsigncdto testfor Theorenr7
l i k c r v i s eh a v e p a s s e dt h e t a s k sd e s i g n e d
shoLrld
to
t e s t ' l - h e o r c n Ir sa n d 2 b y l l i e n r s e l v e s
O s l r c r s o n( 1 9 7 + )t o u n d t h a t d e s p i t ea n o v e r a l l
c o n r p a r a b sl eu c c c srsa t co n t h e I c n e l h - i n c l u s i oann d
c l a s s - i n c l u s i ot ans k s t, h c p a t t e r n o
s f e n o r s m a d ei n
the t\\,o setsof tasks\\'cfc nor comparable.These
f i n d i n g ss u s s e srt h a tt h e l o g i c o m a t h e m a r i csar lr u c turesproposedbv Piagerand his collaboratorsare
not appropriatefor modelineperformancein these
t r v ot a s kd o n r a i n si n d e e d .o n e m i g h rt a k et h e s er e s u l t st o c a l li n t oq u e s t i o tnh ei d e at h a tt h es a n r es t r u c t u r e su n d e r l i ec h i l d r e n ' sa b i l i t y t o s o l v e I e n g t h - i n c l u s i o na n d c l a s s - i n c l u s i op nr o b l e n r s .
A t t h i s p o i n t .h o w e v e r o. n e m i g h rp o i n to u t r h a t
Osherson'sfindings need no longer be taken into
accoulttas there have been chan-ges
in the formal
theory of concrete-operarional
thought, as well as
furtherdevelopments
in theeffortsto axiomatizethe
t h e o r y( P i a g e t ,1 9 7 7 ;W e r m u s ,1 9 7l ) . I n a d d i t i o n ,
one could argue(as before)that even if Piagerian
theory, in spiteof its recentrevisions,still fails to
providean adequateformal descriptionfor the logicomathematical
structuresunderlyingconcreteoperations,one neednot concludethat no suchstructures exist: perhapsone has not )e( succeededin
finding their propercharacterization
Whether or not the revised Piagetian model
servesas a bettermodel has yet to be determined.
But as Sheppard(1978)pointedout, it is not clear
thatthe more recentaxiomatizations
are all thatdifferentfrom the originalones
Are Within-Domain Relations as Predicted?
Investigators'repeatedfailure to verify the developmentalsequences
describedby Piagetiantheohas
led
manv
authors
to doubt (he claim that
ry
cognitiveabilitiesemergein a coordinated,orderly
fashion acrossdomains Perhapsfor this reason,
someauthorshavesoughtto test the developmental
predictedby the theory rvitftindomains
sequences
ratherthanacrossdomains.lf one interpretsPiagetian theory to mean that performancewithin each
thatareorganizedinto
domainis basedon opera(ions
a rvell-integrated,reversible strllcture, then one
might expectto find relativelyhigh conelationsbetween taskstestingabilitiesassumedto be derived
frorn thatsamestructureHowever,attemptsto verify this particularhypothesishave not faired rvell
C o n s i d e rf,o r i n s t a n c et .h e w o r k o f H o o p e r ,S i p p l e , G o l d m a n .a n d S u i n t o n ( 1 9 7 9 ) a n d K o f s k y
( 1 9 6 6 ) .r v h ot e s t e dI n h e l d e a
r n d P i a g e t ' s( 1 9 6 4 )d e s c r i p t i o no f t h c d e v e l o p m e notf c l a s s i f i c a t i oanb r l i t i e s K o f s k y ( 1 9 6 6 )f o u n d t h a t a l t h o u g hs h ec o u l d
discerna rarrkorder of difficultt' for her differenr
c l a s s i f i c a t r ot an s k s o, n l r 2 7 c / co f h e r s u b j e c t fsi t t h i s
p a t t c r n H o o p c ra n d h i s c o l l e a g u e(sI 9 7 9 ) l a t c rr e p l i c a t c dK o i s k r 's o v c r a l ld c v c l o p n r e n t asle q u e n c e
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS
Sonreof their findingsalso led thenrto doubt that
of only
the development
this sequencerepresented
strLlctureFor instance,
one comnronclassificatory
Hooperet al foundthatthe abilityto multiplyclassrnatrixtaskdoesnol
in a cross-class
es as assessed
problems.
predictthc abilityto solveclass-inclusion
l n d e e d , t h e r ' . l i k e m a n y o t h e r s( e . g , B r a i n e r d ,
1 9 7 8 aD
; i m i t r o v s k y& A l m y . I 9 7 5 :D o d w e l l ,1 9 6 2 ;
H a m e l , 1 9 7 4 ;K o f s k y , 1 9 6 6 1T u d d e n h a m ,l 9 7 l ;
tasks are
Winer, 1980) found that class-inclusion
much more difficult-and are accordingly solved
much later-than are other concrete-operational
tasks.They concludedthat somefour separatefacoI classificatory
tors contributeto the development
abilities.
of orderStudiesthatexaminedthedevelopment
ing abilitieshave yielded comparableresults(Di; u d d e n h a m1,9 7l ) . T u d m i t r o v s k y& A l m y , 1 9 7 5 T
correlation
denhamreporteda .28 (nonsignificant)
betweenthe ability to seriateand solvea transitive
inferencetask. Dimitrovsky and AImy compared
children'sabilityto seriateandreorder.thatis, place
backin orderstimulithataremixedup beforethem.
Of the 408 childrentested,134passedthe seriation
task;in contrast,only 4l passedthereorderingtask
Attempts to confirm Piaget's(1952a, l9'15a,
pre1977)predictionthat the ability to compensate
cedesor co-occurswith the ability to conservehave
According to Piaget, the
also been unsuccessful.
thattheamountof liquid
child who truly understands
in a glassis conservedwhen it is pouredinto a container of different dimensionsalso understandsthe
principle of compensation:"conservation. . . involves quantitiesthat are not perceptive,but haveto
be constructedby compensationbetweentwo different dimensions"(Piaget,1967a,p.533).In his first
presentationof this position Piaget (1952a) preliquid would
dictedthat all childrenwho conserved
reveal an understandingof compensation. This
task
meantthat a child could passa compensation
and fail a conservationtask but not the reverse.In a
subsequentpresentationof the argument, Piaget
consideredthe kinds of predictionschildren at different stages in the developmentof conservation
shouldmake beforethe transformdtionphaseof both
tasks(e.g., Inthe conservationand compensation
&
1966;Piaget&
Smock,
helder, Bovet, Sinclair,
Inhelder, 1974). At an initial stage.the nonconservershouldpredictthattherewill be conservation
after the transformationand that the rvaterlevel in
thenerv beakerwill not change. At thesecondstage.
shouldpredictthattherewill not be
thenonconserver
and the waterlevelwi1lchange.Finalconservation
ly, the true conservershouldpredictthat the water
l e v e lw i l l c h a n g ea r r dt h a tc o n s e r v a t i owni l l o b t a i ni n
171
the faceof this perceptualchan_qcIn eitherversion
of the conservation
account,oneshouldnot observc
a child who passesthe conservation
task and. nevertheless,fails the compensationtask Piagetand
Inhelder( I 963) reportedthat all but 57oof children
rvho conservedwere able to anticipatethe level of
water that would be reachedif the contentsof a
standardbeakerrverepouredinto a beakerof different dimensions.Althoughdetailsof the dataarenot
presented,
Piaget(1952a)notedthatalmostall children who conservedpasseda compensation
testthat
requiredchildrento pour asmuchwaterinto anempty beakeras there was in a standardbeakerof differe n t d i m e n s i o n sP i a g e ta n dI n h e l d e(r1 9 7 1 )a l s or e porteda studyof the abilityto passconservation
and
compensationtasks in supportof their accountof
conservation However, thereare now many studies
that do not supporttheir account.
but
Acker (1968)found children*'ho conserved
failedthe anticipationtaskusedby PiagetandInheld e r ( i 9 6 3 ) . L e e ( 1 9 7 1 )f o u n d t h a t w h e n c h i l d r e n
were requiredto passboth testsof conservationand
in orderto bejudgedtrueconservers.
compensation
the proportionofconserversfell from I I of i5 to 6 of
15.Gelmanand Weinberg( 1972)reportedthat llVo
of their subjectswho conservedfailed to compensate,that is, failed to match the waterlevel of the
standardwhen pouring the "same amount" lnto a
beakerof different dimensions.
More recently, Acredelo and Acredelo(1979)
testedthe extendedversionof Piaget'saccountof the
relationshipbetweenthe abilitiesto conserve,compensate,and anticipateconservationor compensation. They reported that3'7 57o of their samplerevealedsuccessand failure patternsnot predictedby
Piagetiantheory. Thesedisconfirmingpatternswere
expected with their alternative identity theory of
conservationhowever. This altemative theory allows children to conserveeven if they fail to comp€nsate.Such children are viewed as being in an
early stage of conservation;they focus on the absenceof an addition/subtractionoperationor the irrelevanceof displacementtransformationsand pay
little attentionto the perceptualconflictthatobtains
afterthe transformation.Children thengo on to learn
.
of conservation
is a consequence
thatcompensation
This fits with GelmanandWeinberg's(1972)obserof the comPensation
vation that the understanding
conprinciple,as manifestedin verbalstatements,
tinues to develop well after the age at which the
child's ability to conservcliquid may be takenfor
granted.Further, it removesthe puzzleof ho* a
*'ithout prechild could understandcompensation
relation-as Piagetwould
supposingan equivalence
havethem do
172
R O C I . I EG
L E L M , AA
N N D F E N E EB A I L L A R G E O N
I r r s t l t t . L ' \c n \ \ ' l t c n\ \ c i l s s c s lsl t c P n t g iei l i n l r c a i l r r s cl r cl c c l sn od c s i r cl o i r r l l u c n cI tci :l i s l c n ctt) o ;
( c g c l t r s s i l - r u : r t i o r rt o t c l l h i n r i r r l rt l r i r r r :n: ( ) i u n l i k c u c c r ( : r i nt r , I t co. i
e o u n tr v i t h r ni l s i n c l cr l o n t a i n
s c r r : r t i ocr o
r ,l t s c r \ / i l t i o tnh)c. r c s u l tcsl on o tl c n t sl t r p ( l l l l \ \ l n gt ( ) ( ) nc] o n V c r s i r i i o\ \nh L - r c \ c r v o n ct l r l k s
'l'hc
p o rt t L rt l r ct l t c o r r
i d c ut h i r ct o n c r c t c - o p r . r a t i o n i l l l l - x ) r lrltl n t s c l l - a nndo c r n cI i s t c r r s("P i l e c t .1 9 5 9 .
1r
t h o u ! h t i s n o t d c p e r t c l c notn o n c o r c v c n : a \ a t i r l
l))
s t r u c t r . nd
c s' c n s c n r b l ci s p r o b l b l vr c i a r . - tdo r h ct u n t
D o r o u n r ct i r i l d r errct a . l lbr c l i c v ct h a tl n o b s c r v c r
r i \ \ i l \ t r o n t l ) i u g c t ' ss t i l s ct l t c o n ( c g B r l r i t r c r r i . s t l l r r ( i i nign l d i l ' t c r c n lto c u t i o nt h u r rt h e i r ss c c st h .
I 9 7 S i r 1. 9 7 8 b F
: c l d r n a nl.9 S 0 :F i s c h c r l.9 E 0 :F l r s l r n c t h i n g t l r e t 's c cI R e c c n t\ \ o r k b , r '\ l a s a n _ q k a r
v c l l I 9 8 2 : S i c g l c r ,1 9 8l : b u r s e c r L l s oD i i r i s o r r . \ . l c C I u s k c r i' \. l c l n r _l er . S i r r r s - K r r i g l \r'tl.u g h n . a n c i
K i n c . K i t c h c n e r&
. P a r k c r .1 9 8 0 ) E v i d c n c ct h i r r
F l i r v e l(l 1 9 7 - l a
) n db r L c n r p c r sF. l r r v c i la. n d F l a v c l l
p r e o p c r a t i o n at hl o u S h tn t a Yn o r b e o r c o p e r a t i o n a l ( 1 9 7 7 )i n d i c a t c st h x t t h c : r r s \ \ ' c r o t h i s q u e s r i o ni s
r n a k e si t c v c n h a r d e rt o n t a i n t a i n
t h e s t a q ca c c o u r t t
n c g a t i \ ; el n t h c s t u d \ b r \ l a s a n e k a yc r a l . a c a r , l
r r i t h d i f f e r e n tp i c t u r e so n c a c l rs i d c r v a sh c l d v e r t i c i r l l ri n f r o r r to f c h i l d r c nr v h or r , e r ca s k e d :" \ V h a r
l s P r e o p e r a t i o n aTl h o u g h tR e a l l y
d t tr o r r s c c l " n n d ' \ \ / h a rc l o/ s e e l ' A i l o f r h e 3 Preoperation?
al
v e a r - o l d sa n d h a l f o f r h e 2 - v e a r - o l d st e s t c d r e T o s a yo f a i h i l d t h a th er sp r c o p c r a r i o ni as rl o s a y
sponcled
correcrl), In rhe studv bv Lenrperset ai .
r n o r ct h a n t h a t h e h a s n o c o n c r e t e
o p e r a t i o n sP, r e c h i l d r e nI t o 3 r , e a r o
s f a g er rc r es i v e nh o l l o r rc u b e s
o p e r a t i o n atlh o u g h ri s n o t d e f i n e d( o r e x p l a i n c d ) r l i t h a p h o t o g r a p o
hf a f a n r i l i a o
r b j e c re l u e dr o r h e
s o l c l v i n t e r n t so f * , h a t i r l a c k s li t i s a l s o s l i d t o
bottorn
o f t h ei n s i d e C h i l d r e n ' st a s kr v a sr o s h o r vt h e
p o s s c ssse v e r adl o n r i n a nct h a r a c t c r i s t i cAsc. c o r d i n g
p h o t o g r a p hi n s i d et h e c u b e t o a n o b s c r v e rs i t t i n s
to Piagetiantheory,.the preoperarional
iltild is egoacrossfront thenr Lentperset al foundthatvirtuallt'
c e n t r i co r ( t o u s et h em o r er e c c n lta b e i c) e n t e r e dH i s
a l l c h i l d r e n2 r , e a r sa n do l d e rr u r n e dt h ec u b eo p e n r e a s o n l npgr o c e s s easr ep e r c e p t i obno u n d h
: e i se a s i ing arrnr Ji'ont tltcmsehrs to face the obsen,er
I y d i s t r a c t ebdy t h ep e r c e p t u ao lr s p a t i apl f o p e n i cosf
T h e s er e s u l t si n d i c a t et h a rr h e1 ' o u n g
c h i l di s n o t s o
objectsand. for thisreason.oftenfailsro detectmore
ego!'entric
as to believeothersseervhatet'er
/rc sees
a b s t r a c ti n
. v a r i a n rt e l a t i o n a
s m o n go b j e c t sl n a d d i W h a tt l r e nc o u l d b e r h es o u r c eo f r h ey o u n gc h i l d ' s
t i o n . t h e p r e o p e r a t i o n ac lh i l d i s u s u a l l yu n a b l et o
d i t f i c u l t lo, r r P i a s c ta n d l n h e l d c r ' s( I 9 5 6 ) n r o u n t a i n
c o o r d i n a t ei n f o r n r a t i o na b o u t s t a t e s a n d t r a n s t a s kl
fomrations
F l a v e l l( 1 9 7 4 )d i s t i n g u i s h ebde t r v e etnh e c h i l d ' s
Are preschooiers
rruly preoperational'?
A hostof
identificationof v,lnt object anotherseesand the
r e c e nitn v e s t i s a t i o nhsa v er a i s e dq u e s r i o nasb o u t h e
morecornplexconceptof /rorl rheobjectis seen.The
v a l i d i t yo f t h i s c h a r a c t e r i z a t i oInn. _ q e n e r at lh, e s e
findinesof Masan*tkay
et al ( I 974), Lemperset al
studiesshorv that under certainconditions.even
( 1 9 7 7 ) .a n d o t h e r s( e g , C o i c , C o n s t a n z o&. F a r younepreschoolers
behavein a nonegocentric
mann i l l . 1 9 7 3 )i n d i c a t et h a t t h e r u d i m e n t a na, b i l i t y t o
ner. isnoremisleadingperceptual
cues.integrare
indetermineu,hatanotherpersonseesis presentby aee
formationabourstatesand transformations,
and so
2 The ability to recognizehorvan objector a scene
on.
appearsto another person developsmuch more
Consider the claim that preschoolers
are egos l o u , l r 'B
. o r k e( 1 9 7 5 )s h o r v e dt h a tt h ea s e a t w h i c h
centric ln the perspective-taking
raskdesignedby
children denronstratenonegocentricperspectiveP i a g e ta n d I n h e l d e r( 1 9 5 6 ) .c h i l d r e na r e s h o \ \ , na
takineability is heavily,influencedby suchtaskvarimodelof threemountains.A doll is placedar various
ablesasthe natureof the testdisplaysandthe typeof
positionsaroundthe modelandchildrenareaskedto
r e s p o n s ree q u i r e d B o r k e ' s ( 1 9 7 5 )p r o c e d u r ew a s
indrcatehoq, the mountainslook to rhe doll from
t h es a m ea s t h a ro f P i a _ e a
en
t d I n h e l d e(r I 9 5 6 ) , r v i t h
e a c ho f t h e p o s i t i o n s C
. h i l d r e nl e s st h a n6 1 , e a rosf
t\\o importantexceptions First. trvo of the three
age tend to choosea pictureor snrall replicathat
displals Borke used\\'erescenescontainingfanriliar
d e p i c t st h e i r o * , n v i e w r a r h e rt h a nr h ed o l l ' s r i e u .
to1'objects Displal,I consisced
of a snraillake with
A c c o r d i n gt o P i a g e a
t n d l n h e l d e (r 1 9 5 6 ) ,r h ev o u n _ q a t o 1 s, a i l b o a ta, r n o d e o
l f a hodsea
, n da n r i n i a t u r e
c h i l d i s " r o o t e d t o h i s o r v n v i e r v p o i nirn t h e n a r h o r s ea n dc o r v D i s p l a 12. c o h t a i n ed i f f e r e ngt r o u p r o r r e sat n dm o s tr e s t r i c t efda s h i o ns. o t h a rh ec a n l l o t
i n _ eosf n r i n i a l u r ep e o p l ea n d a n i n r a l isn n a r u r a sl e t i n r a e i naen ) ,p e r s p e c t i vbeu th i so u , n ' '( p 2 4 2 ) S i n r t i n s s( e g . a d o g a n d d o g h o u s c )D i s p l a r ' 3* ' a s a
i l a r l r . r v h e n a s k e dl o d e s c r i b er h e * o r k i n e s o [ a
r c p l i c ao f P r a _ q ae nl d I n h e l d e r ' s( 1 9 5 6 )t h r e em o u n \ \ , a t erra po r t o r e p e a t o a n o r h ecr h i l da s t o n , h eh a s
t a i n s S e c o n d .l l o r k e a s k e dh e r s u b j e c t iso i n d i c a t e
-lhis
b e c nt o l d . t h c 1 , o u n ec h i l d d o e sr c r r i b l r ' .
r sb c t h c d o l l ' s p c r s l ) c c t i vbc 1 'r o t a r i n gd u p l i c a t e os f t h c
CONCEPTS
A R E V I E WO F S O M EP I A G E T I A N
l a ti d i s p l a v sO n D i s p l a y sI r r n t 2j . I J o r k cI ' o u n ct h
a n d4 - 1 , c a- or l dc l r i l d r c rcro l l c c t l \r t s s c s s ct ldt cd o l l ' s
I ) e r s p c c r j vico r a l l t h r c e p o s i t i o n st c s t c db e t r v c c n
on Pilget ancl
19% irnd9i9l oithe tinre In contl'ust.
s rve 42% rncl -1l n h e l d e rs d i s p l a l ' .3 - y c a r - o l d g
) , c a r - o l d6s7 % c o r r e c rt e s p o n s cl sb r t h e t h r e ep o s i t h a th e r r c s u l t s" t a i s c c o n t i o n s B o r k ec o n c l u d e d
s i d e r a b ldeo u b ta b o u t h ev a l i d i t to' f P i a g e t ' cs o r t c l u and
childrenareprintarilvegocentric
sionthat1,oung
i n c a p a b loef t a k i n gt h ev i e up o i n to f a n o t h epr e r s o n ,
with tasksthatareare appropriate.
When presented
perceptual
cven vetJ, roung subjectsdenronstratc
p e r s p e c t i v e - t a k i nagb i l i t y ' ' ( p 2 4 3 ) , A d d i t i o n a l
supponfor Borke'sconclusioncontesfl'onra recelit
study by Flavell. Flavell. Green, and Wilcox
( ' 1 9 8l ) F i a r e l l a n d h i s c o l l e a - g u feosu n d t h a t p r e schoolersunderstandthat objects with dift'erent
sides (e -e,. a house)look differentfrom different
perspectives.whereasobjectsrvilh identicalsides
( e . g . , a b a l l ) l o o k t h c s a n l ef r o m a l l p e r s p e c t i v e s
the resultsof Borke ( 1975)and
Taken to-eether,
Flavellet al . ( I 98 I ) clearlyindicatethatchildrenas
young as 3 yearsof age (l) are awarethat an individual looking at a display (e.9., a house)frorn a
positionother than their orvn will have a different
view of the display;and (2) areableto computehow
the displaylooksto this individualundercertainoptimal cohditions.With time. childrenbecomemore
and more proficientat identifyinghow a displayappearsto anotherindividual It shouldbe notedthat
this abilitycontinuesto developwell into the school
years.Huttenlocherand Presson(1973, 1978),for
childrendo better
example,found that school-aged
tasks if they are allowed to
on perspective-taking
walk aroundthe covereddisplaybeforegiving their
response.
resultshavebeenobtained
Similarnonegocentric
in other t1,pes of perspective tasks. Markman
(19'73a)found that preschoolerscolrectly predicted
that 2-year-oldswould fail on a memory task but
on a motoric
would achievesomedegreeof success
task.ShatzandGelman( I 973) reponedthat4-yearolds used shorterand simpler utteranceswhen talking to a 2-i'ear-old than when talking to peers or
typicallyinvolved
adults.Speechto the 2-year-olds
remarks aimed at obtaining and maintainingthe
child's auentionas well as show-and-telltalk. ln
speechusually inmarked contrast,adult-directed
volved commentsabout the child's own thoughts
or supand requestsfor information.classification,
port. Speechto the adults also includedhed-qes,
which arecommonlyassumedto markthe speaker's
recognition that the listener is better infornred.
older, and so on (Gelman& Shatz.1978) Maratsos
173
( 1 9 7 - l )r c p o r t c ct lh a t - l - a n c l- 1 - r ' c a r - o lpdos i n t c dr o
i n c i i c a t ct h c p o s i t i o n so i t o r s t o a s i - s h t c ud d u l r
W l r e n t h c s a r n ca d u l tc r t r c r c dh c r - c r c s .h t l r v c r c r .
c h i l d r c nt r i c c l - a s b c s t a s t h . ' r c o u l t l - t o d c s c r i b c
rn.
the tovs lcspcctivcposition,<Likerrrsc \,1ar-r
Clecnbcrga
. n c l v l o s s l e(r 1 9 7 ( r r) ep o r t c dt h a tc h i l g sJ r c c o s n i z e rdh a ta p c r s o nu ' h cdr i d
d r e na sr o u r . r a
n o ts e ea ne v c n td i d n o tk n o \ \ t, h i se v e n t K
: nou'ledgc
o f t h e e r e n tc o u l db e s h a r e do n l v b v t h o s er i ' h oh a d
r v i t n e s s ei ld T h e s ea r eh a r d l vt h es o n so i t h i r r g os n e
r v o u l de x p c c tf u n d a m e n t a l lcv' g o c e ni tcf t h r n k e r tso
b c a b l er o d o ( f o r f u r t h e re v i d e n c es e eD o n a l d s o n .
1 9 7 8 :S h a t z .l 9 7 8 l S / r n t - -t .o l I I I , t ' h a p ) ) )
l n a l l f a i n r e stso P i a g e r r. r c s h o u l dp o i n ro u t t h a t
oi thc 1-oung
our criticisnrof the characterization
moreto interpreters
child asegocentricis addresscd
andfollorr'ers
of Piagetrhanto Piagerhinrselfln our
sun ey'of theCenevanliteraturesinceI965.we ne\'h et e r n re g o c e n t r i cA s V ) , u k( l 9 8 l )
e r e n c o u n t e r et d
noted. Piagetswitchedto the term terttetedin iis
later writin-ssto avoid the surplusnteaningof the
ternr egocentnc.
What evidenceis there that the preoperational
intended?
One
child is centered,in the sensePia-eet
versionof the centrationhypothesisholdsthat the
preoperational
child's failureto consenenumberor
q u a n t i t yi s d u e , i n p a r t , t o a p r o c l i v i t l ' t oc e n t e ro n
o n e d i m e n s i o n( e . g . , l e n g t hi n t h e c a s eo f n u m b e r
heightin the caseof liquid consen'aconservation,
tion) andignoretheotherdimension(e g , densityin
width in thecaseof
thecaseof numberconsen,ation,
liquid conservation).However, Anderson and
Cuneo(1978)providecompellingevidenceagainst
this version of the centrationhyporhesis.In one
study,children5 yearsof ageandolderwereshorvn
rectangularcookies that varied systematicallyin
width and in height.Their taskwas(o ratehow happy a child would be to be giventhedifferentcookies
to eat. During pretesting,childrenweretaughthorv
ofa long
to usetheratingscale.This scaleconsisted
rod rvith a happy face at one end and a sadfaceat the
other The children'staskduringthetest\\'asto point
to the placeon the rod that reflectedtheirjudgment
of ho',vhappy or sad a child ivould be if he ate a
cookie of a given size. Analysesof the ratings
yielded significant effects of both *'idth and
height----evenfor preschool subjects. ln a subsequent study, Cuneo(1980) obtainedsimilarresults
with 3- and 4-year-oldchildren. Anall'sesof the
children'sratingsindicatedthat they \\'ereusrnga
height + width rule to evaluatethe areaof the test
cookies As before,therewas no evidenceofcenteri n g o n o n ed i m e n s i o n .
of the preoperaWhat of the characterization
174
R O C H E LG E L M A NA N D R E N E EE A I L L A R G E O N
t i o n a cl l r i l da sp c r c c p t i obno u n dl . \ n c a r l r c o n s c ra\ t r o nt n r i r r i n g
s t u d VL r yB r u n c rc t a l ( 1 9 6 6 )a p p c a r c d
t o I e r r j s u p p o r lt o t l l i s c h a r a c t . ' r i z a t i oCr rh i l d r c n
\ \ / c l cs h o \ \ , nt r r o i d e n t i c ' rbl e a k c r si i l l e d * , i t h u u r e r
a n d r r c r e a s k e dw h c t h e ro r n o r r h e yc o n t a i n e rdh c
s a n l c3 n r o u n t N
, e x t . c h i l d r e nr r e r cs h o r r na t h i r d .
c n r p t r b e a k e ro f d i f f c r e n td i n r e n s i o n sT h i s n e r v
b e a k e r v a sp l a c e db e h i n da s c r e e na. n dt h ec o n t e n t s
o f o n c o f t h e o r i e i n a lb e a k e r sr r a s p o u r e di n t o i t
Children\\,erethen askedrvherherthe screened
and
t h e u n s c r e e n ebde a k e r sc o n t a i n e tdh e s a n t ea n t o u n (
of u,arer Ir tr,asfound thatcliildrenrverelesslikelv
t o g r re u p t h e i ri n i t i a lj u d g n r e not f e q u i V a l e n c$e, i t h
lhe scr.-en nrP
sPnl
r ' - _- " '
:
A c o n s e r v a r i osnt u d vb y M a r k n r a n( 1 9 7 9 r) l a k e s
i t d i f f i c u l t t o a c c e p r h e B r u n e re t a l , p o s i t i o nr h a r
children'sfailureto conservereflectsthe perceprion
boundqualitl,of their rhoughtprocesses.
ir,larknian
asked-{- and 5-vear-oldsto parlicipatein oneof nvo
versronsof the numberconservation
task The only
differencebetrveenthe lrvo versions\\/asthe terms
usedto Iabelthedisplal,s.In one version-rhe srandardPiagetianversion- c/assterms(e.g. . trees,soldiers.birds)*,ereused In the otherversion,collection terms (e 9.. forest, arm1,.flock) rvereuscd.
C h i l d r e ni n t h e c l a s sc o n d i t i o nd i d p o o r l y I n c o n trast.children in the collectionconditionaverased
3.2 conect judgmentsout of 4 arrd rvereable to
provideexplanationsfor their judgments Because
b o t h r e r s i o n so f t h e t a s ki n v o l r e dt h e e x a c ts a m e
displal's. one cannot explain rhe class subjecrs'
failureto conserveon the groundthat preschoolers
areperceptionbound.Subjectsin both experimenral
condirionsobviously had equal opportunityto becomedistractedby the perceptual
appearance
of the
posttransformation
displays.The factthatrhecollection childrendid not raisesdoubraboutthe validity
of thecharacterization
of the preoperational
child as
fundamentallvperceptionbound.
Additionalevidencethatpreschoolers
arenot ai\\,aysperceptionboundcomesfrom studiesthatexamined their ability to distineuish berrveenappearanceand reality. Fein (1979), for insrance,
found rhat by age 3 childrenhai'eno difficultydist i n g u i s h i n gt h e p r e r e n da c t i v i r i e si n v o l v e di n p l a y
f r o m o t h e ra c t i v i t i e sF. l a v e l l ,F l a v e l l a
, n dG r e e n( i n
press)reportedthateven3-year-olds
havesomeability to distinguishbetu,eenreal and apparentobjecr
propenies In oneexperinrent.childrenrvereshorvn
a r v h i t ep a p e rt h a tI o o k e dp i n k r rh e np l a c e db e h i n da
p i c c eo f p i n k p l a s t i c .l r , l o r et h a nh a l f o f r h e3 - r e a r o l d s t . ' s t e dc o n e c t l yd i f f e r e n t i a r ebde t r v e e rnh ea p p c a r a n c(cp i n k )a n d t h er e a l i r l , ( * h i t e o
) fthepapcr
l n a s i m i l a rv c i n .G e l r n a nS, p c l k e& M e c k ( i n p r e s s )
f o u r r dr i t i r t3 - 1 , c a r - o i dr csc o q n i z ct l m t n c l o l lu n c la
p c r s o ni l r e n r o r ea l i k e p e f c c p t r . l r l tl vi r r n a r c a d o l l
a r r da r o c k B u t t h e l i l s o u r r c l c r s t a r r d -euis, i c l c n c e c l
llv spoirianeou
s n l l t e n t st o t h i se l - f e c t - t h aat d o l l
co
c a no n l r " p c r t e n d * a l k . s i t .c a t .a n ds o o r r
\ \ / o i k b y C e l n r i L r rB u l l o c k a n c i\ . l c c k ( 1 9 8 0 )
s b o u i) , e ta n o t h e rc h a r a c t c r i z a t i o n
r a i s e sq u e s t i o n a
o f p r e s c h o otl h o u g h r .u , h i c h i s t h a r p r e s c l r o o l c r s
h a v e s e r i o u sd i f f i c u l r vr e i a t i n ss r a r e s( i n P i a s e t ' s
t e r n r s ,i i g u r a t i v ek n o * , l e d c e a
) nd transformations
(operatir,e
knorvledcet The expcrintentrvasbased
o n P l e r l a c k ' s( 1 9 7 6 if i n c l i n gt h a rc h i n r p a n z c easr e
a b l et o s e l e crth ea p p r o p r i a ti n
e s r r u m e n( er . - e. a s c i s sors)to relatetwo diiferentstatesof an object(e g .
a r v h o l ea p p l ea n da c u t a p p l e ) I n r h eG e l m a nc t a l
study,3- and4-year-olds
\\,ereaskcdro selectoneof
t h r e ec h o i c e - c a r drso l i l l i n t h e m i s s i n ge l e m e n ti n
three-itelnpicture sequencesTest sequences
had
e i t h e rt h ef i r s t ,s e c o n do. r r h i r dp o s i r i o e
n m p t y .E a c h
c o n r p l e t esde q u e n cceo n s i s r eodf a n o b j e c t( e . g . ,a
cup), an instruntent(e g . a hamnter).and rlie same
objecttransformedbv the applicationof the instrument (e g , a brokencup) Half rhe sequences
dep i c t e df a m i l i a r e v e n r( se _ e. c u r r i n ga p i e c e o ff r u i t ) .
h a l f d e p i c t e du n u s u ael v e n t s( e e . s e * , i n gt h e t w o
halvesoi a bananatosetheror drarvinson a pieceof
fruit) Perfornrance
in both age groupswas nearly
perfect, indicatingthat the children could reason
about the relationshipbetweenobjectstatesbefore
and after the applicarionof various instruments
I n a s e c o n de x p e r i m e n tG
, e l m a ne t a l ( 1 9 8 0 )
showed 3- and 4-r,ear-oldspicrure sequencesin
which the deleteditem rvasalwaysthe instnrment.
The children'stask\\ asto relatethetwo objectstates
first from one direction(e.g., rvholeapple,cut apple) and then from the oppositedirection(e g., cut
apple,n hole apple) As in the firsr experiment,performancein both agegroupswas veryeood,indicating thatchildrencouldrepresent
reciprocaltransformations.Gelmanandher colleagues
concludedthat
althoughpreschoolers
may not a/rr'alsbe able to
representthe sanreobject statesrvith referenceto
(e g., pretransformation
reciprocaltransformations
and posttransformation
displaysin a clay-conservatio.ntask).thereareclearlycasesrvherethey can do
I n t h i s s e c t i o n ,u e h a v er e v i e i v e da n u m b e ro f
studiesthat indicatepreschoolchildrenare not fund a m c n t a l l ye g o c e n t r i c ,c e n t e r e d .o r p e r c c p t i o n
b o u n d T h e g e n e r a il m p l i c a t i o no f t h e s es t u d i e si s
t h a t t h e n r e n t a l i t r o f t h e p r c s c h o o lc h i l d i s
q u a l i t a t i r e l yn r o r es i n r i l a rt o t h a to f t h eo l d e rc h i l d
t h a n P i a s c t i a nt h e o n 'I e a d so n e t o s u s p e c tT h i s i s
n o t t o d e r r y ,o b v i o u s l y t, h e c o g n i r i v el i n r i t a t i o nosf
CONCEPTS
A R E V I E WO F S O M E P I A G E T I A N
l / J
nrentalchrldrenreceived32 problenrsetsrvith6 tria l s i n e a c hs e t ;h a l f t h e p r o b l e n r isn r o l v e dl c n g t h ,
half number On eachtrial the childrenrvereasked
rvhichnvo of threerows of chips(or sticks)had the
same(different)number (or length):teedback*as
thenprovided.On Trial I of eachset.theanaysu'ere
arrangedto elicit a correctanswer.eren if the child
ofthe displal'.
s,asattendingto inelevantproperties
This was done by arrangingthe displaysso thatthe
Thus,
relevantand inelevantcueswere redundant.
I n d u c i n gS u c c e s so n C o n c r e t e - O p e r a t i o n a l
for example,two rows containingthe samenumber
Tasks
of equallyspacedchips were alignedone abovethe
other.A third row containinga differentnumberof
Accordingto Piagetiantheory,leaminginvolves
chips ',vasplacedso that its ends *ere not ali-sned
theassimilationof novelinformationto a previously
ri,iththe endsof the other rows. On Trials2 to 5 of
changes
in
the
existingstructure,u,ith concomitant
theproblemset, the childrenwatchedasthe experiincoming
inforto
the
as
it
accommodates
structure
mentertransformedone or two displaysso that the
relemation.Hence,if thereis nocognitivestructure
(length-relevant)
cueswerenou' in
number-relevant
vant to an input, therecan be no assimilationand
(length-inelenumber-inelevant
with
the
conflict
likewise no accommodation-in other tvords, no
on the basis
responded
vant)
ifchildren
cues.
Then,
learning.One implicationof this vie* is that chilerror. On
an
they
made
cues,
(e.g.,
number-irrelevant
of
part
capacity
possess
of
a
structural
dren who
at all, allorvTrial 6, inelevantcueswerenot present
transitionalconservers)are more likely to benefit
ing Gelman to determinewhetherthechildrencould
from training than are children who possessnone
accuratelyrespondto length and number.
(lnhelder.Sinclair,& Bovet,
(e.g., nonconservers)
BecauseGelman createda conflict betweenpert974).
and quantitativecues within eachproblem
ceptual
We would like to turn the Piagetianargumenton
thought she was providing children rvith
set,
she
argue
the
followwe
would
like
to
is,
its head.That
attention training (Harlow, 1959; Trabasso &
ing: to the extent that preschoolerscan be shown to
benefit from training on some concrete-operational Bower, 1968). As we will see, thereare other interpretations.But whatever the interPretation,the
task, then to the sameextent they can be assumedto
training worked. During learning-settraining, non(at
relpossess leastpan ofthe) structuralcapacities
conservingchildren quickly reachedplateau;when
the
mental
strucIf
it
is
true
that
this
task.
evant to
askedto choosetwo arays that containedthe same
tures of preschoolersare more like those of older
(different) number (length), they respondedon the
children than was traditionally assumed(as we conbasisofquantity. Further,they transfenedwhat they
cluded at the end of the previous section),it should
learnedon posttestconservationtasks Performance
be possibleto designsimple trainingconditionsthat
taskswere near
on length- and number-conservation
tasks-and
induce successon concrete-operational
justify their
to
were
abie
children
and
we
ceiling
As
competencies.
hitherto
concealed
thus reveal
choices.The majority of liquid- and clay-conservawill see later, that is indeed possible.
tion trials also yieided correct choicesand explanaIt usedto be commonplaceto claim that training
tions. Finally, the effects of training were marnabilities (see
had no effect on concrete-op€rational
rainedover a period of 2 to 3 weeks.
Flavell, I 963, for a review of the earll' uaining literjust
The Gelman (1969) training experimentis typhouever.
the
ature).In recentreview sources,
classifiedas one in the leaming theory tradi(e.g..
ically
Beilin,
l97l,
reached
conclusion
is
opposite
t i o n ( e . g . , B e i l i n , 1 9 7 1 , 1 9 7 7 ;M o d g i l & M o d g i l '
1977;Brainerd& Allen, 1971;Modgil & Modgil,
1976).It is no longer obvious to Gelman(Gelman&
1976;Munay, 1978).Sincethesereviewsourcesare
holds. ReGallistel, 1978)that this characterization
available, we focus on a selectnumber of studies.
createda
Gelman
problem
set,
each
within
that
call
Gelman (i969) worked rvith 5-;'ear-oldswho
cues'
quantitative
and
perceptual
between
conflict
liquid
number.
length,
failed on preteststo conserve
Feedbackprobably guaranteedthat thechild noticed
amount, and clay amount. Childrenin the experithe conflict. Perhapsthe study accomplishedwhat
mental group received a learning-settraining on
Piagetiantheory requires for training to be effeclength and number tasks that was designedto focus
tive-that the child encounter a conflict between
relationsand away
attentionon quantity-relevant
schemes.Beilin (1977)makesa similarsuggestton
relations.In all, the experifrom quantity-irrelevant
t h ey o u n gc h i l d A f t e ra l l . p r e s c h o oclh i l d r e nd o f a i l
c o n s e r v a t i o nc ,l a s s i t r c a t i oann. d s e r i a t i o n
standard
tasks.As rvewill seein the nert section.hoq'ever,it
because
is no longerclearwhat suchfailuressi-snif1'
discoverthatstartlingly
nroreandnroreinvestigators
modestamountsof training are sufficientto ntake
conserversout of nonconseners,senatorsout of
and so on
nonseriators.
I / O
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
i l b o u rt h e l c u r n i n g ' s eptl o c c d u r cB u t n o t e t h l t f o l
t h i s i n t e r P r e t a t i ot onh o l o .l t i s n c c e s s a rtyo a s s u l l l c
t h a tt h c s u b . i c chtl d b c c u nt o d c v c l o ps o r l l cq u a n t l t ) '
s c h e n r e sO t h e r i v i s et .h e r ec o u l dh a r e b e e nn o c o n flict ior thesubtect
P i a - e e t i ar rna i n i n gs i u J i e sf o c u so n h i g h l i g h t i n g
s n d t h ee v i d c n c ei s g o o d
o sr c o n f - l i c t A
conrradiction
. s p e c i a l l y\ \ ' i t h
t h a t r h i s t r a i n i n , cea n b e e f f e c t i v e e
e
v
i
d
e n c eo f h a v i n c
c h i l d r e nw h o s h o r vs o n r ei n i t i a l
t
o
o
p
e
r
a
t i o n at lh o u g h t
p
r
e
o
p
e
r
a
t
i
o
n
a
l
r n o r e df r o m
( l n h e l c l e rS, i n c l a i r f. t $ s v e t . 1 9 7 4 ) H o r v e v e ri.t i s
tr
n o t c l e a r t h a t s u c h t r a t n i n -ies c i t h e r s u f f i c i e n o
neccssaryln a thoroughrcviewof the vastarravof
pg
r o c e d u r e sB.e i l i n ( 1 9 7 7 )p o i n t e d
cont'lict-trainin
out that sonte conflict-trainingprocedures\vork
: m e d s l u n dl .9 6 l a .
( e g . L a f d b v r e& P i n a r d .1 9 7 4 S
l 9 6 l b : W i n e r .1 9 6 8 a) n do t h e r s d no o t( e . g . ,B e i l i n .
. o h l w i l l& L o w e . 1 9 6 2 )
1 9 6 , i : 1D, . S m i t h ,1 9 6 8W
thatdo not
Funher. a varietyof trainingprocedures
\
\
o
r
k
R
e
v
e
r
s
i
b
ility-training
i n d u c ec o n f l i c t sa l s o
i
n
c
a
s
e
s t u d i e sa r e a c l e a r
Point.
The Wallachand Sprott( 1964)studywas probastudy.It
reversibility-training
blv thefirst successful
involveda seriesof problems,each using two disp l a l s . o n eo f A r d o l l sa n do n eo f N b e d s .T h e n u m b e r
of itemsper alray varredfrom problemto problem.
Within eachproblem.childrenwerefirst shownthat
eachdoll fit in a bed: thenthe dolls were removed
from thebed andeithertherow of bedsor the row of
-dolls was spacedfurther apart or closer together.
Children who said therewere no longer as many
bedsas dolls rvereshorvnthat eachdoll did havea
bed The idea rvasthat rhe children rvould learn reversibilityand.thus,be ableto predictthatthe dolls
would alwaysfit back in beds.Roll (1970)followed
up on the Wallach and Sprott(1964) study and included transfertasksto seeif the learningwas re( 196I b) extinctionmethod
sistantto the Smedslund
transfer
Therestill was considerable
havestudiedthe effect
A varietyof investigators
watchmodelswho do conof havinga nonconserver
serr,e(e.s., \'lurray. 1972. l98l: Silverman &
& S t o n e .1 9 7 2 ) l n g e n ; ilverman
G e i r i n g e r1
. 9 7 3S
eral. the opportunityto interactrvith, or simply
was found to
watch.conserrersand nonconservers
helpinduceconservationBotvinandMunay ( 1975)
who failed to conserve
assignedblack first-graders
mass. weight. amoun(.and numberto one of trvo
k i n d so f m o d e l i n gc o n d i t i o n sI .n o n ec o n d i t i o nt.w o
in a
participated
and threeconservers
nonconservers
n e g a nr v i t h t h e e x p e r i d i s c u s s i o nT. h e d i s c u s s i o b
mcnter's requestthat eachchild participatein the
tasks
and rvcight-conservation
mass-c()nservrtion
Thc childrenrrerc then left on their owll to discuss
thcir dift'ercntilns\\'crslnd reachln a!.:rccttlcntA
s e c o n dg l o u p o I n o r r c o t r s c n ' cstast c h e dr v h i l ct h c
e r p e r i m e n t c rt c s t c d l n o t h e r g i t l u p o f c h i l d r c n
'fhcse
c h i l c l r c nd i d n o t p a r t i c i p r t er n a s t r b s c q u . ' r t t
a d r l r r l r a ta
i cn l o l l l l t
d i s c u s s i t r nB o t hg r o t r p s h o r i ' c d
a) su c l l
t
a
s
k
s
(
t
o
n
t
a
s
s
r
i
a
r
r
d
e
i
g
h
t
o i s p e c i f i ct r a n s l e r
tasks)
(
t
o
a
n
d
l
e
n
g
t
h
t
l
u
m
b
c
r
g
e
n
e
r
a
l
t
r
a
n
s
f
e
r
as
o f t h e e x p l a n a t i o rrrisr t ' n b v t l t eo r t g i Cornprrison
rttlcdottt
nal conserversand the trainedconscrvers
weresllllthe possibilitl,that the trainedconservers
plv mirnickingrvhat thev had hc'ard The ori-cinal
c o n s e r \ e rw
s c r en t o r ei n c l i n e dt o s i v ec o n l p c n s a t t o n
t h e i rl u d g a n d r e v e l s i b i l i t ya c c o u n t si n . l u s i i f v i n g
n r c n t st:h e t r a i n e dc o n s e r v e rwse r en r o r ei n c l i n e dt o
point out that nothinghad beenaddedor subtracted
$'ereinclevanr The lator that the transforniations
rsv e r ea l s o p r e v a l e n ti n
e
x
p
l
a
n
a
t
i
o
n
ter kinds of
\ l a r k m a n ' s ( 1 9 7 9 ) c o l l e c t i o nc o n d i t i o n .a n d h e r
sublectswere even Younger
A r e r e s u l t sl i k e B o t v i na n dl r ' l u n a y ' (s1 9 7 5 )c o n hypothesisthat conflict
srstenr',viththe Pi'agetian
l hose children
c o n d i t i o n sc a u s e dd e r e l o p n l e n t T
conditionprobarrho participatedin the discussion
bly did enter a stateof conflict and becausethey
eVentuallyreachedagreement$ith the conservers,
theycould be saidto havealsoresolvedtheconflict
Hower,er,we find it more difficult to maintainthis
position for the childrenrvho simply watchedrhe
Evenif rve
andnonconservers
testingof conservers
allow that somg "inner" conflictoccurrednld u'as
resolved,a problemremains Horr could theopportunitl' simply to watch a consenerbe effectiveso
quickly unlessthe child alreadt had some understandingof quantitativeinvariance.)
L i k e u s , G o l d ( 1 9 7 8 )m a i n t a i ntsh a t i t i s a p p r o priateto concludethat a child hasan understanding
of quantityif very Iittle preteste\perienceleadsher
ro focuson quantity:"lf this occurs.it seenrslikely
'training' was due simply to the
that the successful
subjectof theexperimenter's
by
the
reinterpretation
ofa conservation
question,andnot to theacquisirion
concepa
t s s u c h " ( p . 4 0 7 ) . A s i m i l a ra r g u m e nrt s
m a d e b y D o n a l d s o n( 1 9 7 8 ) a n d M c G a n i g l ea n d
Donaldson(1974) who show that-l- to 6-,vear-olds
aremuch more likely to consen'eii rhetransfornrations are made accidentallyby a naughtl"' teddy
bear.
A s i m p l et r a i n i n gs t u d l 'b y G o l d ( 1 9 7 8 )y i e l d e d
(around
with his position Subjects
resultsconsistent
The
trials
pretest
eight
5',/:1'sttt of age)2weresiven
disposttransformarion
resembled
pretestdisplays
p l a y s i n t h e s t a n d a r de q u i r a l e n c ea n d n o n tasks.rhat s. thc t\\'oro\\'s
conservation
equivalence
rveredifferentor the sanielengthrespectivelyDur-
CONCEPTS
A R E V I E WO F S O M EP I A G E T I A N
ins the pretests,the child rvastold to countthe itenls
'
in cach row and tlten u'as lskcd u'hetherthe t\\'o
rorvshad the sarnecardinll valuesor not (whcrcthe
numbers in each row were differcnt) A control
group of children was shou'nthe santepretesrdisplaysandrvassinrplyasked*'hethertherowshadthe
sanrenumberor not. That is. theyrverenot askedto
deternrinethe specificvaluesin eachdisplaybefore
conserstandardposttransfonnation
beingasked.the
yielded
renrarktests
The
transfer
questions.
vation
able results Of the 29 childrenin the experirnental
consened on thetrvo
group,22 and20 respectively.
tasks.What is nrore,
standardnumber-conservation
when retested6 weekslater,22,20, and l9 children
conservedon the number, beads,and liquid tasks
reWectively And l4 rveeks later. conservation
scoreswereslightly betteron all threetasks!In contrast,noneof the controlgroup(N = l9) consen'ed
on any taskat any time.
Gelman (1982) gave 3- and 4-year-oldsa brief
pretestexperiencemuch like the one Gold (1978)
177
r e l a t i r eh e i g h t st h a t c o l r e s p o n d etdo t i : : d i f f e r c n t
c o l o r s F o l l o w i n g t r a i n i n g . c h i l d r e n\ i : r e t e s t c d
rvithoutfeedbackon all l0 possiblepair. .ri sticks
As before.only the topsof the sticksu'c'i:r isrblcso
t h a tc h i l d r e nh a dt o r e l y o n t h ec o l o ro f i h e s t i c k st o
decide*,hich q'aslongeror shorter The '':ucialtest
involvedthe BD pair and the adjaccntBC and DC
pairs. Recall that children were not trariedon the
B D c o n r p a r i s o nF. u r t h e r n r o r ed,u l i r r gt i : : n i n g .t h c '
B, C, and D sticks were as often thc lL-iJeras the
on
shorterstick in an array. The correctrelDonses
1p!l/6 (u'ell
the BD comparisonrangedfrom'78c/a
abovechance).As predicted,successon ihecritical
testpair was highly correlatedwith a ch:.,js abilitl'
in
to rememberthe relative valuesof the el-:ments
the BD and CD pairs
en
s dO ' R e g a n( 1 9 . 1 tt r i e dt o
De Boysson-Bardia
Trabasso( I 9?I t results
and
Br1'ant
accountfor the
without granting the children transitire inference
abilities We think their alternativeinierpretation
presumesthatyoung childrengo out of theirway to
make their task difficult for themselvesConsider
used.Childrenwere askedto countone of two disthe threeassumptionsniadeby de Boysson-Bardies
plays: indicateits cardinal value; count the other
and O'Regan. First. they assumethe childrenonly
display;indicateits cardinalvalue;and thendecide
the
learn the pairs of stimuli AB, BC, CD and DE
whetherthenumberin eachrow wasthesame.ln
alsoassociatelorrgwith A' short s ith B; /on3
of
3
They
with
sizes
worked
set
phases,
children
pretest
with B, s/rort with C; and so on Seconcichildren
and 4 The standardconservationtasksinvolved set
treat sticks that are labeled both long and short as
of differencetrials)
sizesof 5 (and4 on conservation
and l0 (or 8). To Gelman's surprise,the pretest nonentities.The effect of this step is t'r eliminate
labelsfor all sticksbut A, which remainslong, and
experiencetransfenedto both the smalland the large
gave
sort
of
E, which remainsshort. Finally, childienlearnto
the
same
children
addition,
settrials.ln
associatelong wirh the stick that is pairedrrith A and
explanationsobservedby Markman (19'79).
sftortwith the stick that is pairedwith E Thus,they
The, vast majority of training studies have
assignB (of the AB pair) a long label and D (of the
But therehave also
focusedon the conservations.
DE pair) aslnrtlabel. Havingdoneall this.rheycan
beensuccessfultrainin-sstudiesof children'sability
'oasis
of a
pass the critical transfer trials on the
(or
inferences.
related)
to drarv transitive
to a
opoosed
as
strategy
leaming
paired-associate
(197
that
l)
suggested
Trabasso
and
Bryant
one. Harris and Bassett(1975)
youngchildren'sdifficulty with transitiveinferences transitive-inference
found no evidence to support this rlternattve
was rnore a problem of memory than logical inaccount.
ference.Accordingly, they gavetheir subjectsmemandO'Regant 1973)acThe de Boysson-Bardies
ory training. They showed their subjectspairs of
thal theBn'antand
the
claim
by
was
motivated
(A,
count
D,
E)
that
B.
C,
sticksfrom a set of five sticks
of
theoFEration
not
use
(
did
I
subjects
I
9?
Trabasso
a
discrimination
)
and
color
Using
length
in
differed
transitivity.Without acceptingtheir pa:red-associlearningprocedure,they taughtchildrenwhich of a
ate hypothesis,it is possibleto make rhis point in
pair of sticks was the longer (or shoner)stick. To
anotherway, asTrabasso( 1975)showe; Trabasso
start,childrenweretaughttheAB pair.thentheBC,
ordered
ri'ere
testedthe hypothesisthatchildrenconst:..r;l
shorvn
a
thev
CD, and DE pairs. Subsequently,
"read' their anthen
and
stimuli
of
(other
images
linear
than
the
pairs
of
sticks
of
selection
random
swersoff theseimages.This, indeed.s;emsto be
BD pair) and were againrequiredto learnwhich of
what childrendo; but then adultsdo likerrise Both
the two was the longer (or shorter)stick. Children
children and adults have been found i.t r'oostruct
were never shown the actual lengthsof the sticks
u'itlt
whenconiittnted
orderedlinearrepresentations
during training;the bottomsof eachpair of sticks
iiilerences
represen:
that
materials
variety
of
wide
a
protruded
to
the
were hiddenin a box and theirtops
i n h e i g h t , w e i g h t . h a p p i n e s sa, n d c r : : t n i c e n e s s
sanreheight. Thus, they had to leam to code the
178
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
i ntto cLarrn
( R i l e 1 , 1. 9 7 6 ) E v e n i f o n e d o e sn o t \ \ a
(
1
9
7
I
)
s
u
b
j
e c tus s e dt h e
t h a tB r y a n ta n dT r a b a s s o ' s
g
e
t t i n ga r o u r l ( l
n
o
i
s
t
l
t
e
r
e
t
r
a
n
s
i
t
i
v
i
t
y
.
o p e r r r i o no f
the filct rhat they were ablc to constructan ordered
sct oI ntcntalobjccts On the Piagetianassulnpliorl
that performancereflects availablestructures'It
nrustbe thatchildrenhad availableat leastan ordering relation (see Gelman, 1978. for further
evidence)
Sonremay object that the Bryant and Trabasso
(1971)study providedextensivetrainingand feedback With so many feedbacktrials, perhapsthe
conceptof transitivityrvastrainedin and not simply
uncoveredFindingsfrorn a studyby Timmonsand
S m o t h e r g i (l l1 9 7 5 )a r g u ea g a i n sst u c ha p o s s i b i l i t y
These authorsworked ivith kindergartenchildren
u ho did poorly on tasksrequiringthemto seriatesix
valuesof brightnessor length.The childrenwere
given same/differentjudgment trials on either or
both dimensionswithout feedback.This training
was sufficient to facilitate seriation performance'
BecauseTimmons and Smothergilldid not run a
task during posttestlng.one
transitive-inference
the seriationperformancewas
that
might still object
not basedon an operatoryscheme.We submitthisis
unlikely given Brainerd's(1978a)and Bryant and
of the early
Kopytynska's(1976) demonstrations
(see
Brainerd,1978afor a
useof transitiveinference
Sipple (1978)also
and
review). Hooper, Toniolo,
scoresof
receiving
children
kindergarten
reported
3.65 and 4 46 out of 5 on length and weight transitivity tasks.
As for conservation and transitivity, it is now
clear that preschoolersbenefit from training designedto alter their typical classificationsolutions'
Nash and Gelman (cited in Gelman & Gallistel'
l9?8) gave 3- to 5-year-oldchildrenexperienceat
sorting a set of eight wooden blocks that varied in
size. shape,and color. To start, the childrenwere
told to "put the blocks togetherthat go together'" If
necessarythe experimentershowedthe child a rt'ay
of doingthe taskor evenaskedthe child to copyher
son Sorting experiencecontinued until the child
hadsuccessfullysortedthe blocks in trvo ways On a
day, the child wasaskedto place25 toys
subsequent
into one of five clear plasticboxes.The toysrepresentedfive categories(fruits, vehicles,kitchen furniture, flowers, and animals)and were withdrarvn
one at a time from a bag. The block-sortingexperiby taxonomic
encehelpedchildrenson consistently
category,as did the opportunityfor childrento sort
the toys until they achieveda stablesort on two
who
trials.Ofthe 3-' 4-, and5-year-olds
successive
ag
n d t o y - s o r t i n eg x p e r i : n c e6,6 9 2 .
h a db l o c k - s o r - t i n
837c. and 89c/o respectively. used taxonomic
catcgorres.
As in the case of conservationand transitivity
training,classificationtraining neednot be extens i v ec o n s i s t e n t l yS m i l e ya n dB r o w n( 1 9 7 9 s) h o w e d
prefer to sort nlaterialsaccording
that preschoolers
to thematicasopposedto taxonomicrelationsNer'enheless,they can and do use both kinds of relations.Further,they can be trainedto usetaxononllc
relationsconsistentlySrnileyand Brotrn's training
involved showing children triads that represented
both a taxonomicand a thematicrelation In each
anciexplained
triad. an experimenterdemonstrated
in the
(or
response
thenratic
response
the taxonomic
controlgroup) The opportunityto observethe experimenteruse taxonomic criteria influencedthe
children'schoices-thesewere thenpredominantly
t a x o n o m i cM
. a r k m a n ,C o x , a n dM a c h i d a ( 1 9 8 1r e) taxfrom graphicsortsto consrstent
a
shift
ported
onomic sorts in 3- and 4-year-oldswhen askedto
sort objectsin plastic bags ratherthan on a table
the use
Apparently,the latterconditionencourases
of spatialand configurationalrelations
4- to
Odom,Astor,andCunningham( 197i)-eave
classia
matrix
on
trials
repeated
children
6-year-old
fication task and found a significantdecreasetn errors over trials: "This strongly suggeststhat repeated presentationsmay be required to obtain a valid
of a young child's cogniti"eability to
assessment
classifymultiplicatively"(p.'762).It likewiseraises
the possibility that the ability to classify taxonomicallyis underestimatedin standardprocedures
where children are assessedon the basisof one or
two sorting trials. As Worden (1976) points out'
most classificationstudieswith adultshave them
classify repeatedlyuntil a stable son is achieved
The failure to do the samewith childrenmay elicit
immature preferencesbut these need not preclude
ofa given
theabilityto assigncorrectlytheextension
class.
The trainingliteratureon classinclusionyields
resultsthat are in line with what by this point is a
theme;it is possibleto "train" a child on
consistent
manyconceptswith limited trainingexperienceSiegel, McCabe, Brand, and Matthervs(1977) prouiO.a l- and 4-year-oldswith but six trials, with
feedbackto their answersto suchquestionsas " How
many red buttonsare there?" "Hou many white
"Are the red
buttons?" "How many buttons?"
from
groups
benefited
ones buttons?" Both age
great\\'ere
gains
4-year-olds'
training.althoughthe
er on a posttest.Judd and Mervis (1979)drerv 5-
CONCEPTS
A F E V I E WO F S O M EP I A G E T I A N
year-olds'attentionto the fact rhat thc resultsof
and subcouutingthe nlentbersof thc superordinate
ordinateclassescortflictedrvith their erroneousanquestionTheexpertnretrswertotheclass-inclusion
tal group reccived such training oll but three
problems Yet 23 of the 30 childrenin this group
rvereperfect on Posttests
the view
Overall,the trainingliteraturesupPorts
their
than
competent
nlore
that preschoolcrsare
imtasks
operational
concrete
failure on standard
plies.Sonteauthorsgo furrherandtakethcseresults
in thecognltlvestructo suggestthatthe differences
and older childrenare minituresof preschoolcrs
mal-'if thereareany at all We believethat sucha
do fail the
conclusionis premature.Preschoolers
casesneed
in
many
do
they
tasks:
Piagetian
standard
or trainingto revealsome
tailoredpretestexperience
and,eventhen,theyoftenshowlimited
conlpetency
transfer. Before we accept an hypothesisof no
to takea close
it is necessary
qualitativedifferences.
preinabilities
as
the
well
as
abilities
the
look at
grant
schoolersshow.Althoughwe admittedl)'must
his or her capacimore capacityto the preschooler,
ties could still be limited comparedto thoseof the
older child. In the following sections.rve focus on
conthe developmentof quantityand classification
cepts. We chose these Piagetianconceptsbecause
enough researchhas been done to permit a careful
analysisof how cognitive developmentin thesedomainsmight proceed.In addition, the researchis far
enough along for us to start to addresssome of the
generalissuesraised by Piaget about the nature of
cognitivedeveloPment.
A CLOSERLOOK AT THE DEVELOPMENT-:OJ-
coNcEPTS
borucnETE-oPERATIoNAL
b'olrrE
ConservationsDuring Middle Childhood
Of all the Piagetiantasks, the conservatlonones
arethosethat havereceivedthe mostattention'Hundreds and hundreds of studies have considered
whether a nonconservercan be trainedto conserve
and, if so, underwhat conditions. A countlessnumber of studies have investigatedthe effects of socioeconomicstatus(e.g., Gaudia, 1972',Hanley&
Hooper, 1973); schooling (e.g., Price-Williams,
Gordon, & Ramirez, t969); IQ (e g., Field, 1977;
Inhelder, 1968; linguistic prowess(e.g., Siegel'
1977); and variations in the conservationtasks
(Bryant, 1974; Mehler & Bever, 1967) on the
emergenceof conservation.Despitethe abundance
of researchactivity, there is one issuethat has receivedvery littleattentionoutsideofGeneva:thatis'
179
thc conservatronof discrete
betrvcen
thr'relatit-rnship
q
u
a
n
t
i
t
i
e sT h i s i s a c e n t r aql t r e s t i o n
c
o
n
t
i
n
u
o
u
s
ancl
in muchof therecentGencvanwork ou conservatlon
( e g . l n h e l d e re r a l . l 9 ' 1 4 ' , l n h e l d eBr l,a n c h e rS. i n c l a i r .& P i a g e t .1 9 7 5 ) :
Somesubjectshad greatdifficulty in applyinga
reasoning*'hich had provedadequatefor probl e n r sd e a l i n gw i t h d i s c r e t ce l e m e n t tso o t h e rs j t rvere
ttraterials
uationsrvherequasi-continuous
usecl.This would suggestthatthe developmental
link betrvecnthe conservationof discreteand
quantitiesis neithersimplenordirect'
continuous
( l n h e l d eer t a l , 1 9 7 4 ,P . 8 0 )
We agree,although,as will becomeclearat theend
of this section.for somewhatdifferentreasons.
of disWe questionwhetherthe understandings
ln
similar'
that
are
all
quantities
creteandcontinuous
way
to
obis
a
quantities,
there
discrete
case
of
the
of the quantitiesrepretain a specificrepresentation
sented-that is, to count. It is alsopossibleto usea
rule of one-to-one correspondenceto deterrnine
ri'hetheran equivalentnumberof itemsis presentin
are
t*'o displays.No such quantificationprocesses
(1981)
quantities.
Siegler
continuous
for
available
at leastmatprovidesevidencethatthesedifferences
rer to adults.He showedadultsthe posttransformation displaysof the number-,liquid-' andmass-conservationproblemshe planned to use with children
and askedthem to judge whether the displayswere
equalor not (half were and half were not). The adults
were always correct on the number problems,and
they often counted.In contrast,they werecolrecton
only 60Vo and 6l%o of the mass and liquid problems-presumably becausethey had no veriltcation
procedures.
Further,as notedby Schwartz(i976)' theconditions of applicationof arithmetic oPerationsdiffer'
dependingon whether discreteor contlnuousquantities are involved. Consider: "Two peachesand
two peachesmake four peaches" versus"A cup of
waterat I 0" C addedto a cup of water at 10"C make
a glassof waterat 20' C. " The formeris conect;the
latter is not. Or consider: "Two peachesand three
pearsmake five piecesof fruit" versus " 100 cc ot
''
alcohol and 90 cc of water make I 90 cc of liquid'
At a more basic level' the natural numberscan be
usedby themselvesas adjectiveswith count nouns
(e.g.,one boy. six apples),but not with massnouns
(e.g., one rvatcr).The useof countwordswith continuousquanlitiesdependson the selectionot some
attributeover which to quantify (e g ' volume or
180
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
d e n s i t l )a n d t h e c o r r e c tc h o i c co f u n i t . T h u s , i t r s
of water.
to talk of one,qallonor one-elass
acceptable
the
issues
a
fes'
of
are
but
but not one water.These
raised by Schwartz rvhen contparingknowled-ee
aboutdiscreteand continuousquantities AII such
Ieadto theview thatthedevelopment
considerations
of the understandingof discreteand continuous
q u a n t i t i ecso u l dd i f f e r .S i e g l e r ' s( l 9 8 l ) r e e x a m i n a of liquid, mass,and numtion of the conservations
ber poinrsin this direction.
Siegler (1981) testedchildren raneing in age
from 3 to 9 yearson 24 number,liquid, and massproblems.Within eachsetof 24 probconservation
lems. the trialswere designedto obtainmeaningful
patlemsof yes/noanswersto thequestionof whether
displayswere equivalentor
the posttransformation
not. They were not always equivalentbecause
Sieglerusedadditionand subtractiontransformations
ones.On the
as well as the standarddisplacement
basisof his own previouswork as well as that of
Piaget's (1952a)-Siegler preothers---€specially
dictedthat the children'sjudgmentswould be consistentwith oneof four different rules, with development involving a move from Rdle I -+ Rule II +
of a rule to a
Rule ill --+ Rule lV. The assignment
givenchild wasto be doneon thebasisof thepattern
of his responsesto the posttest transformations.
judgedon thebasisof one
Childrenwho consistently
dominantdimension(e.g., lengthon numberproblemsand heighton liquid problems)rvereto be classified as Rule I users.Children who also considered
the subordinatedimension(e.g . densityon number
problemsand width on liquid problems) when the
valuesof the dominantdimensionwere equalwere
to be classifiedas Rule Il users.Rule III children
would be thosewho always consideredboth dimensionsbut could not resolveconflicts and, therefore.
performed at chance on such trials. Children who
respondedto all trials on the basisof transformation
type were to be assignedRule IV.
As it turnedout, judgmentson the conservation
of liquid and masstaskscould be characterizedwith
but trvo rules, I and IV That is. therewas no e\fldenceof transitionrules; the tendencyto use Rule I
declinedwith age and the tendencyto use Rule lV
increasedwith age. In both cases,the trend to use
Rule lV was not completeby 9 yearsof age.
on the number-consequence
Thedevelopmental
sen ation taskswas decidedlydifferentfrom that obtasks.lf chilsen'edfor the two continuous-quantity
dren u,ere observedusing Rule I. they were the
younser children. But even the 4- to 6-year-olds
werenrorelikely to usc one of trvo advancedrules,
of
cither the expectcdRuie iV or a cotr-rbination
R u l e sI a n dl V . r v h i c hS i e g l e ird e n t i f i eassR u l cl l l a
to
Accordingto Siegler,Rulellla reflectsa tendenc-'Rule IV If
sonietinresuse Rulc I and sontetirnes
rvasaddedto a roqi, it rvasjudgedto Itave
anythin-e
of rvhetherthe rows becanreequal
more regardless
because
of theadditionor whetherthc rows differed
in length A similarstratesywas invokedwhensubtractionoccurred When there rr'asneitheraddition
nor subtraction,childrenusedRule I
Alnrostall 7-, 8-, and 9-year-oldsusedRule IV
thefailureto idenon numbertrials Parenthetically.
tify any Rule II childrensuggeststhat the relative
densityof items in the displayshad little salience
( B a r o n ,L a w s o n ,& S i e g e l ,1 9 7 4 ;G e l m a n ,I 9 7 2 b ;
Smither,Smiley, & Rees, 1974).Returningto the
Siegler(1981)resultsfor numberconservation'the
children,that is, thosewho useda comtransitional
binationof Rule I and Rule IV, were betterable to
deal correctly with addition and subtractionthan
other transformations. No differential effect of
type occunedwith the two continutransformation
ous-quantityconservations
abilAs one might expect,number-conservation
comparedto theotherconservation
ity wasadvanced
in thetwo continuabilities.Children'sperformance
ous taskswere remarkablyalike, which gives more
evidencefor the hypothesisof a common structure
for the liquid and masstasks(Tuddenham,197l).
Siegler(1981) providesa plausibleaccountfor
the differencesin strategiesusedacrossconservatlon
tasks,a child can
tasks.On number-conservation
that is, one based
correctly,
useup to threestrategies
on counting, anotherbased on one-to-onecolreand anotherbasedon the analysisof the
spondence,
transformationsperformed In the liquid and mass
tasks,only the latteris available.Thus' Sieglerconcludesthat liquid and masstasksmay be harderthan
numberconservationOur objectionto this account
is simplythatit doesnot go far enough.Presumably,
the useof a given strategyreflectssomeunderlying
as
concept Otherwise,why that particularstrate-sy
opposed to some other strategv?What does the
young child know about numberthat leadshim or
her to shift from one strategyto anotheras the need
arises?Moreover,thereis moreto theunderstanding
of the
of continuousquantitythan an appreciation
roles of relevant and irrelevant transformations
(Schwartz,1976).In an effort to achievesome Insighton the matter,we will go over what is known
aboutthe developmentof notionsof discretequantity. We will then returnto consideringconceptsof
c o n t i n u o u qs u a n t t t Y .
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS
Number Concepts
Abstraction Versus Reasoning
Celman (19'12a) distinguishedberrveenru o
kindsof numericalabilities:(l) the abilitieswe use
to abstractthe specificor relativenumerosityof one
or moredisplays-Celman and Gallistel(19?8)call
theseour ttuntber-abstractionabilities: and (2) the
abilitieswe use to reasonabout number--Celman
andGallistelcall theseour number-reasoning
abilities These abilities,which derive from arithmeric
reasoningprinciples, allow us to reach inferences
about the effectsof transformations,the relations
thathold betweensets,and theeffectsof a combination of operations.Thus, we know not only that
additionincreases
anddecreases
setsizebut alsothat
theeffect of.additioncan be canceledby subtraction.
Onereasonfor makingthis distinctionis to highli-eht
the possibilitytharnumber-abstrabtion
andnumberreasoning abilities could interact--cspeciallyin
youngchildren.In particular,GelmanandGallisrel
thoughtthat a preschoolermight be able to reason
only aboutthosesetsizesfor which he canachievea
specificnumericalrepresentation.When the taskrequiresreasoningaboutnonspecified
values,asis the
case,lnmany conservation
tasks,rhechild might fail
to revealreasoningabilities.Suchconsiderations
led
Gelman and her collaboratorsto investigatethe processesby which preschoolersrepresentthe number
of items in a display and the effects set size has on
tireirnumericalreasoningabilities
Counting in Preschoolers?
There are two primary candidateprocessesby
which a preschoolercould representnumber,These
are counting and perceptual apprehension.In the
Iatter case, the argument is that young children
might be able to recognize-twoness
and threeness
by
virtue of a pattern-detection
process.If so, onecould
argue,as Piaget(1952a)has, that the young child
haslittle, if any, understanding
of number.First,the
recognitionof patternscould be directly associated
with labels,just as is the recognitionof a threedimensionalobjecr. The child need not know rhara
displayof 3 itemscontainsmore rhana displayof 2
itemsand lessthana displayof 4 irems.Second,on
the assumptionthat the range of set sizesthat could
be apprehendedis related to the span of apprehension. the ability to represent"number" shouldbe
limited to small set sizes.Since this is, indeed,the
case(seeGelman &,Gallistel, 1978,for a review).
the arsumentcould be madethattheyoun-echildhas
l i t t l e .i f a n y , n u m e r i c aal b i l i t y .
The idea thar the preschoolerperceivesdif-
181
ferencesin numerositt,without some concontitant
understanding
of nunrberis discrediredby a convergingset of researchfindingshorvever Finr. although rt is true thar rhe young child's ability to
judge accuratelyhow many itemsthereare in a display dropsoff rapidlyaroundsersizesof 4 or _5.she
still knows that a set size of 7 items containsmore
itemsthandoesa setsizeof 5 items:likewise.rhata
setsizeof I I itemsis greaterin numerositythanone
with 7 items.As GelmanandGallistel(1978)report.
3-year-olds
in theCelmanandTucker( I 975)erperiment tendedto representlargerand largersersizes
with numberwords that come later in the counting
sequence,
even thoughthey encountered
the rariationsin setsizein a randomorder.Thus,the 3-rearolds tendedto use the number words two. rhree,
four, five, six, ten, and elevento represent
sersizes
o f 2 , 3 , 4 , 5 , 7 , I l , a n d l 9 r e s p e c t i v e l yO.l d e r c h i l dren were more accurate,althoughthey too made
errorsin assigningnumericalvalues Such results
hardlyfit with thecharacterizarion
of numericalability that follows from an apprehension-only
hrpothesis To the contrary,rhey suggestthat youngchildrenknow somethingaboutcounting How elsecan
one accountfor the tendencyto usenumberwordsof
higherordinalvaluesfor the largersersizes?Bur to
grant preschoolerssome understandinsof counting
is to go againsta commonnotion-that earlycounting is but rotecounting,but the simplereelingoff of
words in a list without any appreciationof the facr
that these words have numerical meaning. \\-hen
researchers
began to consider the possibilitl.that
very youngchildren'scountinginvolvessomerhing
morethanreelingoff numberwords (e.g., Fuson&
Richards, 19'79; Gelman & Gallistel, 1978;
Schaeffer,Eggelston, & Scott, 1974; Shorrrell,
1979),theysoonfoundthatthis wasthecase.Young
childrendo havean implicit understanding
of counting and its use in quanrification.
What is involvedin the understanding
and useof
counting? According to Gelman and Gallistel
(1978),successful
counringreflectsthe coordinated
applicationoffive principles:( I ) theone-ro-one
correspondence
principle-all items in an arraymusrbe
taggedwith uniqueta_es;
(2) the stable-order
principle-the ta_ss
usedto correspondto items in an array
must be arrangedand chosenin a stableorder;(3 r rhe
cardinalprinciple-the final tag usedin taggingthe
items in an array representsthe cardinalvalue of rhe
anay; (4) the abstractionprinciple-the first rhree
principles(i.e., the how-to-countprinciples)can be
appliedto any collectionof discreteitems;it marrers
not what the items are. ,,vhether
thev are homose-
182
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
real or imagined, actual
neous or heterogeneous.
objectsor only spacesbetrveenobjects,and so on:
principle-the orderin
and (5) theorder-irrelevance
is irrelevant;it matters
which itemsareenumerated
not whethera -eivenobjectis taggedas one (1), tti'o
(2). three(3), andso on, aslong asthe how-to-count
principlesarehonored.
Therearethreereasonsfor maintainingthat preof the counttng
schoolershavesomeunderstanding
principles.The first is that counting behaviorsin
young children are systenlatic.Perhapsthe most
is
compellingevidencefor theclaim of systematicity
(
noncall
1979)
and
Richards
the useof rvhatFuson
standardlistsand what Gelmanand Gallistel(1978)
call idiosyncraticlists.TheseappearIn very young
when they counteven
children(i.e ,2t/z-year-olds),
smallsetsizes,andin somewhatolderchildrenwhen
they count larger set sizes.Although the lists are
nonstandard,they are neverthelessused systematically. Thus, for example, a 2%-year-old child
might say "2, 6" whencountinga 2-item arrayand
"2. 6, 10" when countinga 3-item array (the one'
one principle).The samechild will use her own list
principle)and.
over andoveragain(thestable-order
will repeat
present,
are
items
many
how
asked
when
the last tag in her list (the cardinalprinciple).The
fact that young childrensettleon their own lists suggests that the counting principles are guiding the
searchfor appropriatetags' Such elrors in counting
are like the enors madeby young languagelearners
(e.g., I runned).In the latter case, sucherrorsare
takenas evidencethat the child's use of languageis
rule governedand that these rules come from the
child herself. We rarely hear adult speakersof Enclasses)say runglish (outsideof psycholinguistic
ned, footses,mouses,unthirsty,and so on. Gelman
andGallistel( 1978)usea similar logic to accountfor
groups of objects into one collection, and then
countingthe numberof objectsin thatgrouP.Across
beganto
half of thechildrenspontaneously
sessions,
employ a more efficient algorithm than they had
beentaught.This was to counton from the cardinal
value of the greaterof the to-be-addednumbers.
Gelman(1977) also reportsthat 3- and 4-year-olds
when confrontedwith unexcount spontaneously
pectedchangesin the set sizeof a given anay. It is
hardto maintainthatthecountingbehaviorof young
children reflects nothing but rote leaming. How,
use to solvesimple
then to explain its spontaneous
arithmeticproblems?In this regard, it is of interest
that Ginsburgand his colleagues(e g., Ginsburg,
1982)reporta similaruseof countingalgorithmsin
unschooledcultures.
An Interaction Between Number
Abstractors and Reasoning Principles
The strong version of the interactionhypothesis
is that young children will not be able to reason
arithmeticallyunlessthey reasonaboutnumerosities
they can representaccurately, Working from this
assumption,Gelman (19'72b)focused on whether
preschoolchildren could apply a number-invariance
schemewhen askedto considersmall setsizes(2 to 5
at most) but not larger sets. The paradigmused in
thesestudieswas developedto control for many of
the possible confounding variablesin the standard
conservation paradigm, for example, the child's
failure to understand the use of "more," and
"less," the child's tendencyto be distractedby
changesin irrelevantvariables,and so on (seeCelman, 1972a).The paradigminvolvedchildrenin a
two-phase procedure. During Phase I, children
learnedto identify one of two rows of items as the
winner. and the other as the loser. Identification
could be basedon either a differencein the number
the presenceof idiosyncraticlists.
of itemsor a redundantperceptualcue, thatis, length
basic
A secondreason for believing that some
young
guide
the
or density. The identificationphaseinvolvedcoverto
serve
principlesof understanding
young
ing and shuffling the two displaysand then asking
is
that
counting
at
skill
of
child's acquisition
the child to guesswhich of the two covereddisplays
children spontaneouslyself-conect their count er(rvhich were side by side) was the winner' Chilrors and often are inclined to count without any redren's answersto probequestionsrevealedthat they
questto do so. lndeed, they will apply the countins
to)
s.
establishedan expectancyfor two displaysof specifthey
be
types,
procedureto a variety of item
you.
ic numericalvaluesduring this phase.PhaseII began
Presumwhat
have
or
candy,
steps,piecesof
unbeknownstto the children. Dependingon the expracticetrials make it posabll', theseself-generated
perimentand condition children were in, the experisible for the child to develop skill at applying the
in eitherone or
principles.A third reasonfor creditingpreschoolers mentermade a surreptitiouschange
numberinelld
be
cou
Changes
displays.
the
of
invent
both
with counting knowledgeis that they can
the display'
shortenine
or
(e.g.,
lengthening
evant
countingalgorithms
a new
substituting
item,
an
of
color
the
changing
47:-year-olds
(1977)
taught
Groenand Resnick
numbe
also
could
objectfor a familiarone)' They
to usea countingalgorithmto solvesimpleaddition
more
or
one
or
subtracting
(e.g.,
adding
berrelevant
problenrsThc algorithmconsistedof first counting
items).
groupsof objects,then combiningthe
two separate
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS
Gelnran(1977) found that when set sizeswere
small and when addition/subtraction
involved but
one item, even2t/z-and 3-year-olds
respondedcorrectly when they encounteredthe unexpected
changesin thearray.Changesthatu,ereproducedby
number-irrelevanttransformationsrvererecognized
as such. Chan_ges
that were producedby numberrelevant transformationswere likewise recognized
as such The childrenoften intimated,in their own
way, that therehad to havebeensurreptitious
addition or subtractionto producethe observednumber
change.Onechild claimed"one flew out. " Another
said "Jesus rook it." When asked,they also said
that the effects of addition (or subtraction)could be
undoneby subtraction(or addition).In the conditions where children encountered unexDected
changesin the lengthof a display,color of items,or
type of items, the children would say thesewere
irrelevant becausethe numbers were the same as
expected.
On the basis of these findings with the magic
paradigm, Gelman and Gallistel (1978) maintain
that preschool children do know that addition and
subtractionare number relevantand that displacemenl and substitutionare numberinelevant. This
knowledgeis, in turn, relaredto theability to decide
whether two arrays representequivalent or nonequivalentnumericalvaluesand,if not, which is the
greater(seeGelman& Gallistel,1978,chap. 10,for
details).Note that this statementappliesfor the magic paradigm where displays are placed side by side
and where children achievespecificrepresentations
of number.Children'sreactionsduringphaseII tell
us that they know the conditionsunderwhich a specific numerosityis preservedand the conditionsunderwhichit is nor.Suchresultsdo r?o,tell us whether
children know when an equivalence or nonequivalencerelation betweentwo setsis conserved.
It was the latter considerationthat led Gelman
andGallistel(1978)to acceprPiaget's(1952a)view
that the number-conservation
taskrequiresthe useof
a principle ofone-to-one correspondence.
They further maintainedthat preschoolerscould not use this
principle becausethey could not reasonabout nonspecified numerical values: hence, their failure on
the traditional conservationtask. Our review of the
training literature (see Is Preoperarional Thought
Really Preoperational?) makes clear that this hypothesisregardingnumber-abstraction
abilitiesand
the use of arithmetic-reasoningprinciples make too
stronga claim.
The Gelman (1982) conservation-rraining
experiment was designedas a test of the Gelman and
Gallistel( 1978)hypothesis.The ideawasto encourage young children to recognize rhar the specific
loJ
cardinalvalueof rhe rrvodisplaysplacedone above
the olher was either the sanreor different It was
hypothesizedthat children would then be able to
conser\,e
on small set sizes(4, 5) but not largerset
sizes(8. l0) As ir turnedour, 3- and 4-year-olds
consened on all set sizesand gaveexplanationsfor
theirjudgments.Becausemostchildrenthisagecannot countaccuratelyset sizesgreaterthan4 or 5, the
only u av they could have conservedequivalence
judgntentsfor largerafiays was on the basisof oneto-oneconespondenceAnd suchexplanationswere
offered. particularly by the 3-year-olds.
Gelmanand Gallistel'saccountof conservation
resemblessomewharPiaget's(1975a, 1977)more
recent rrearmentof number. Piaget's (1952a) early
treatmentfocusedon the role of transformations.In
his laterwritings,Piagetturnedhis attentionto the
conditionsthat a child must recognizebefore he or
she can deal with transformations.
He maintained
the child first discovers the correspondencesbetween two statesto make comparisons.At this early
stage, rhe child can determinecorrespondences
but
is unableto apply the rules of transformations.Next
in developmenthe can use transformationsbut only
after he establishescorrespondences.Finally, the
child understands
the systemoftransformationsas it
generallyappliesto quanrity. We suggestthat Gelman andGallistel'sdistinctionbetweennumberabstractionand reasoningprinciplesparallelsPiaget's
distinction between correspondence and transformation.
By Piaget's(19'75a)account,it shouldbe possible to observe"precocious conservation" if a child
can be brought to recognizethat one-to-onecorrespondenceindicates a conesponding number of
items. Indeed,Inhelderet al. (1975) succeeded
in
producing precociousnumber conservation.Their
experimentsinvolved showing 4- and 5-year-olds
displays in one-to-onecorrespondenceand then a
seriesof item-removaland replacementtransformations. For example, one item in an array was removed and the child was asked if the number of
items in both rows was the same;then that item was
put back into the array but at a different positionand
againthe child was askedabout equivalence.The
ideain theseexperimenrswas to highlighr rhe "commutabilirr"'of itemsin a discreteset,thatis, thatthe
act of addingan item at one poinr (in space)is undone bi rakingout an item from anotherpoint in
space.Norethat taskslike theseinvolve permuting
the posirionsof itemswirhin the set. In contrast,the
standard conservation task involves displacing
items. Accordingto Inhelderet al. (1975), "when
one simply displacesthe objects,the child only artends to rheir point of arrival and does not concern
184
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
himself with the fact that the\ llave beenrctrtoved
f r o m a n i n i t i a lp o s i t i o nt o b e a d d e de l s e s h e r e "( p
26)
rvith
Piaget( I 977) takesthe fact that experience
thc "contmutabilit\"' of itr'ms transfcnedto the
for the view that it is the
task as eYidence
stanclard
of comnrutabilitvthat underliestrue
understanding
S/e arenot sure First.Gelnran(1982)
conservation.
c
h
i
l
d r e nl e n e t hc h a n s e sS. e c o n dn. o s u c h
did show
t r a i n i n gw a s l e q u i r e di n M a r k n i a n ' s( 1 9 7 9 )s t u d y '
indeed,no trainingat all rvasrequired In addition'a
c l o s e rc o n s i d e r a t i oonf t h e l n h e l d e re t a l . ( 1 9 7 5 )
experimentsmakesclear that their children were
cardinalvalues Gelalsocountingandrepresenting
man (1982) arguesthat thesethree setsof results
togethershow thattherearesomespecialconditions
cortheprincipteof one-to-one
thatmakeaccessible
likel,v
the
rnore
child.
the
respondenceThe younger
the tendencyto restrictarithmeticreasonlngto conditions where the child can achievespecificrepresentationsof number.Nevenheless.thereis sonre
values-an ability
abilityto work with nonspecified
that will eventuallydominatethe initial tendencyto
to conditionswherethe
restrictarithmeticreasoning
of numrepresentations
specific
child can achieve
ber. We suspectthis is related to the fact that the
youngchild's skill at countingandknowledgeabout
counting go through a considerableamount of
development.
Some Implicit KnowledgeDoes Not Imply
Full or Explicit Knowledge
Counting. Although Gelman and Callistel
(1978) claim that even 2%-year-oldscan obey the
how-to-countprinciples,the)'do not meanthat childrenthis age haveexplicitknowledgeof the principles. Nor do they meanthat liftle or no development
occurs past this age-indeed, quite the contrary
Gelman and Gallistel point out that first there are
limits on how many items a child can count' how
long a tag list shecan remember,how well shecoorinvolvedin
dinatesthe many comPonentprocesses
the countingprocedure,and evenhow'r'ell shetags
unorderly arrays(Potter& Levy, 1968;Schaefferet
a l . . 1 9 7 4 S h a n n o n 1. 9 7 8 ) .B u t w i t h p r a c t i c ec o m e
skill and speedand ereaterefficiency (cf. Case &
Serlin, 1979).The periodover which this skill accrues is protractedat leastinto kindergarten(Fuson
, 979).
& Richards1
GelmanandCallistel( 1978)found thatthe number of items in a set interactswith the tendencyto
apply the cardinalprinciple As set size increases'
the tendencyto usethc lasttag to indexthe cardinal
value of the setdropsoff Somehave suggestedthat
t h i s n i c a n st h e c h i l d d Q c sn o t l e t h a v ct h e c a r d i n a l
principle as part of her countingschenlc Cclnran
a n d C a l l i s t e lt r r a i n t a itnh e y d o . b u t o n c e a g a i ni t s
a p p l i c a t i o ni s a t f i r s t v a r i a b l e W h a t e v i d e n c ei s
t h e r et h a tt h cc a r d i n apl r i n c i p l ei sa v a i l a b l ee.v e ni f i t
i s a p p l i e ds p o r a d i c a l l rI 'f?C e l m a na n dG a l l i s t eal r e
correcttlratthe variableuseof thecardinalprinciple
dein a youne child derivesfroni the perfornrance
there
principles'
mands of applying the counting
should be conditionsthat elicit its consistentuse
And when attentionis drawn to the role of counting
in quantification.the likelihood of its use should
lncrease.
If 3- and 4-year-oldsdid not have the cardinal
principle available.Markntan (1979) should not
in its useundera
havebeenableto shorvan increase
changein questionconditions.Yet. shedid To exthatcardinalnumbertasks
pand.Markmanreasoned
requirechildrento thinkof a displayasan aggregate
to which a particularnumberapplies.As we mentioned earlier,Markmancontendsthat classterms,
the
for example,children.trees,soldiers.emphasize
individuality of the members in an aggregate'
whereascollectionterms,for example,class'forest.
army, leadone to think of a displayas an aggregate
to which a particularcardinalnumberapplies'Accordingly,Markman(1979)predictedthat children
would find it easierto apply the cardinalnumber
principlewhencollectionterms.asopposedto class
terms, were usedto describethe display
condiChildren in Markman'scollection-terms
nursery
"Here
is
a
follows:
as
were
instructed
tion
schoolclass(forest,etc.) Countthem. How many
children(trees,etc.) in the class?"Childrenin the
class-termscondition were told: "Here are some
children(trees.etc ). Count them'
nursery-school
How many children(trees,etc.) in the class?" Set
childrengave
sizeswere4, 5, or 6 Collection-terms
the last number in their count list on 867oof the
childrenwereaslikely
trials.ln contrast.class-terms
to recountthe arrayasto repeatthe last number The
tendencyof young children to recount a display
when askedhow-manyquestionshas beencited as
evidencethat they do not yet havethe cardinalprinciple (Fuson & Richards, 1979;Schaefferet al''
lg'74). If so, Markman's (1979) results are
inexplicable.
Recently,Gelmanand Meik (1982)conducteda
direct test of the ideathat performancedemandslim-
puppet whether it was right or wrong' They were
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS
185
alsoencouragcd
to correctrltepuppets errors Notc
5 ) . A l n r o sa
t l i c h i l d r e nd o t h i sb y s r a r r i n ag t o n ee n d
t h a tr h cc h i l d r c nd i d n o t h a v ct o g e n e r a ttch e c o u n t or anorherof the array,therebysettinsthe stagefor
ing pcrfornrance
thentsclves:
rheyonll'had to lnonithemodifiedcounttrials.Thesestartwith theexperi_
tor it for confornranceto the countingprinciples.
menterpointingto some itenr in the ntiddleof the
Childrendid very well For example.the4-vear-olds
arral,andsaying, "count all thesebur makethis be
'
attenrptecl
to correct90Voof the puppet,serrorsand
the I
On subsequent
trials. the child is askedto
did so correctl\,93Voof the time The comparable
m a k er h ed e s i g n a t ei dt e m t h e 2 , 3 , 4 , . . a n d . r *
figures for the 3-year-oldsrvere707c and 94o/orel, tharis. I more than the cardinalvalueof the set.
spectivelyThe failurefor GelmanandMeck to find
The 5-year-oldsare nearlyperfecton rhe modified
an effect of set size meansthat the childrendid as
countrrials Further,theytry to saysoniething
abour
well on set size 7 as they did on set size 20. Ob_
ho\\,movementof the itemsper sedoesnot affectthe
viously,the childrenhad implicit knowledgeof the
taggin_e
processPerhapsmosrimportantin thisconcardinalprinciple
text. they say they cannordesisnateany item x f I
When ali factsare considered.it seemsreason(6 in rhecaseof a 5-item array)because,.thereare
ableto saythat),oun-s
childrendo honorthe cardinal
only 5. I needanorher1." Clearly, rhesechildren
principletjut thartheir tendencyto do so is restricted
have achievedan explicit understandingof carandfirstrevealedin only certainconditions.Furrher.
dinaliryvis-d-visthecountingprocedure.put differtheyneedto practicethe applicationof the countin-s
ently.theyknow a countis conservedno matterhow
procedure,presumablyso as to automatizeit and
the items are ananged.Perhapsthis is a stepping
therebylimit the amountof attentionrequiredin its
stoneto theuseof one-to-onecorrespondence
in the
use(cf. Case& Serlin, 1979;Schaefferetal, l9l4).
typicalnumber-conservation
rask.
The effect of this is to make it easierto focus on the
Justas thereis developmentfrom an implicit to
cardinalvalue-and. we suspect.acquireexplicit
an explicitunderstanding
of thecardinal-count
prinkr\owledgeof the cardinalprinciple.
ciple so thereis, of course,for the othercountine
In consideringthe foregoing,it is essentialto
principles. Apparently, 3-year-oldscan indicate
recognizethe distinctionbetweenimplicit and exwhich count sequenceshave double count, omit,
plicit understanding
ofprinciples.This distinctionis
errors.and so on, but only older childrencan say
youn-g children
rvell knorvn in psycholinguistics.
why (Fuson& Richards, 1979). Mierkiewicz and
are grantedimplicit knowledgeof linguisticstruc_
Siegler(1981)find that 3-year-oldsare able ro rectures well before they are grantedexplicit knowl_
ognrzesomecountingerrors,especiallytheskipping
edge of any of these(cf. deVilliers& deVilliers,
of an item. They also find 4- and 5-year-oldscan
1972;Gleitman,Gleitman,& Shipley, 1912) The
recognizea diverseset of counting enors (omitting
explicit knowledgeis often characterized
as meta_
or addingan extratag, skippingan item, or doubly
linguisticknowledge,a knowledgetharconrinuesro
countin_q
an item).What is more,theyalsorecognize
developinto adulthoodand is a functionof general
that it is all right to count alternateitems and then
educationlevel, training in linguistics,and so on
back up to count the remainingin-betweenitems or
(Gleitman& Gleitman,19'19).A similardistinction
to startcountingin the middleof a row. But it is not
regarding knowledge of the counting principles
until children are school aged that they are able to
helpssort out someseeminglycontradictoryconclusay why an error-freecount sequencethat involves
sionsaboutcountingprinciples(Greeno,Riley,.&
the alphabetas tagsis a bettercount trial than one
Gelman, I98 l). When childrenas youngas 3 years
that usesthe conventionalcountwords but includes
of age are asked to count repeatedlya set of given
errors(Saxe.Sicilian, & Schonfield,l98l). Thus,
value, they areindifferent to theorderof the items as
we seethe developmentof an understanding
of the
it changesacrosstrials. Such behavioris what one
one-oneand stable-ordercounting principlesbewouldexpectif thechild had an implicitunderstandcoming more explicit. Saxe and Sicilian(in press)
ing of the order-irrelevance
principle.It does not
alsofoundthat, despitea youngchild's rendencyto
index explicit understanding
of this principle. Inself-correct,the ability to say whether they were
deedexplicitunderstanding
is at bestweak in the 3accuratedevelopsafter 5 yearsof age.
year-oldchild. However, the developmentof exIt is not only the explict understanding
of the
plicit understandingof this principle is well adcountineprocedurethatdevelopsbut alsotheapprevancedby 5 yearsofage. This is illustraredin the 5ciationof thefact that countins is an iterativeprocess
year-olds'performance
on a modifiedcountingtask
thatis unbounded.
Evans(1982)reportsthatkinder( s e eG e l m a n& G a l l i s t e l ,1 9 7 8 ,c h a p .9 ) .
gartenchildren typically resist the idea that each
The modifiedeounrtaskrequiresrhara child first
additionof one (l) item will increasenumber.Incounta Iineararrayofx heterogeneous
items (e.g.,
terestin-qly.
theirresistance
is highly conelatedwith
186
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
their ideasof what constitutes
a bi_gnumber..fhese
areusuailyunder100or rnadc_up
combinations
lil<c
"forty-thirry-a hundred." Apparently.
children
needsomeexperience*,ith Iargishnuntbers
before
theycan move on to thc reco-snirion
thatcountinsis
irerarive.At thc next ler,elof development.
childien
talk abouta million and other largenunrbers
when
askedwhat is a very large nunrber.But even
this
advancement
doesnot _guarantee
that they will ac_
cept the consequence
ofcontinuediteration,that is,
thatthereis no upperboundon thenaturalnumbers.
progressiveboot-strapping
of one level of under_
standing to rhe next with intermediateplateaus
where children assimilateenough examples
to
achieve(in Piagetianterms)a reflectiveabst)action
of theirearlierlevelsof knowled_se
to a new levelof
understanding
Just as the understanding
of countingdevelops
th-roughsteps,so apparentlydoesthe understanding
of arithmetic principles, equivalence proceduresl
and conservation.
Arithmetic pinciples.
Fundamentally. the
principles of addition and subtractionrequlre
that
one understandsthat addition increasesani subtrac_
tion decreasesthe numericalvaluesof sets.Several'
studiessupportthe view thatpreschoolchildren
have
some understandingof theseprinciples.Smedslund
(1966)had 5- and 6-year-olds
indicarewherhertwo
arays of equal value (N = I 6) were equal;
rhen the
arrays were screened.When one of the anays
was
transformedby addingone objecrro it or subtractine
one object from it, the childrenwere able to indicat!
which array containedmore objecrs The
samefind_
the occurrenceof a screenedadditionor subtraction
by comparing the. pretransformation and
oost_
transformationvaluesof arrays.Thus, prescho;lers
understandthe directionaleffectson numerosity
of
additionand subtraction
andcan,undersomeconditions, infer their unobservedoccurrence.
The value of the augendand minuend affect
the
preschoolchild's ability to solve simple
tasks in
mentalarithmetic.StarkeyandGelman(19g2)have
tested3-, 4-, and5-year-olds
on a varietyofaddition
andsubrraction
tasks Eachtaskbeganbv havingthe
child establishthe nunrberof penniesheld
in the
expenntentcr'sopen hand The chiid rvas
asked,
" H o w m a n y p e n n i e sd o e st h i s
b u n c hh a v e ? , , T h e
expenrnenterthen closed her hand and
thereby
screenedthe augend(or minuend)arra1,of pennies
and placedthe addedarrayin rhe handholding
the
a u g e n dw h i l e s a y i n g (: l ) , , N o w I , m p u r t i n - e
x pen_
niesin my hand;ho* manypenniesdoesthis
bunch
have?" or (2) ,,Now I'm rakins x pennies
out.
. " The two valuesto be addedor subtracted
were never simultaneouslyvisible problems
in_
volving zero were nor used.The majority
of the 5_
year-oldscould solveproblemsthat involved
stan_
ing with I to 6 itemsandthenaddingor subtractins
I
to 4 items. The 4-year_olds
did well on probleirs
involvingthe additionor subtractionof I or 2 items
to (from) sersizesof I ro 4 items. At least50Zo
of 3_
y e a r - o l d s c o u l d m a n aI g+e l , I + 2 , 2 +
1,3_ l,
3 - 2, and4 - 2. Thus, therervasan interaction
betweenset size and age. As expected,many
chil_
dren used a counringalgorithm,even rhou;h
rhe
Items were screened.
Preschoolershave at least some implicit under_
standingofthe inverserelationship
betweenaddition
and subtraction.Starkeyand Gelman (19g2)
in.
c l u d e d s o m e xI+- I , x - | * l , x * 2 _ 2 , x _ 2
* 2 tasksin their experiment.The vastmaioritv
of 4_
and 5-year-oldssolved theseproblems*herel. :
t
through 4. And even rhe majority of 3_year_olds
could arrive at the correctanswerfor valuesof-r =
l, 2, and 3 and for problemsinvolving a + l _
I
,
sequence.The studiesby Brush (1972) andCoooer
et al. (1978) make it clear that inversionrasksare
more difficult for preschoolersif thechjldrenhaveto
representtwo arrays(generatedby an iterative,tem_
poral one-to-oneconespondenceprocedure)to
start
and then make judgments of relative numerositv
after transformationsare performed on one of the
anays, for example,.r and x + I - 1. And when
arrays of equivalent Ns are placed one above the
other, therebyintroducinga conflicting sparialcue,
the tasksbecomeeven harder-although not impos_
sible, A similar trend holds for compensarionra;ks,
that is, wherethe two zuraysareequalto stafl(r =
),)
and then the act of adding (or subtracting)of I (or
more) irems to array x is compensatedby the act of
addingor subtractingsomenumberof itemsto array
y. Indeed,Starkey(1978)reportsthatcompensation
tasks wherein spatial cues conflict are harder than
the standardconservationtask.
So once again we see more arithmeticcomDe_
tence in preschoolersthan expected;ho*euer, the
developmentof understandingoccurs over a pro_
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS
tractedspanof years-in somecasespasrthe tinte
the child conservesnumber(seeSiegler& Robin_
son, 1982, for a similar point for older children).
Regardingthis latter observation,it is notervo(hy
thatmanyofEvans's(1982)subjectscouldconserve
number and still not acceptthe idea of conrinued
iteration We expectthatresearch
designedto follow
theshiftfrom an implicit to explicitunderstanding
of
inversionandcompensation
will reveala simjlarpattcrn to that observedregardingthe countingprinciples and iteration.That is, we expectthat children
needto havesomeexperiencewith local rulesbefore
theycan move on to recognizethe generalityof that
rule. As in the caseof the countingprinciples,they
have the benefitof some implicit understanding
of
the principles of addition and subtractionas well as
their own counting algorithms with which to steer
the courseof acquisition.
Equivalence. The developmentalstoryregard_
ing the understanding
of equivalence
involvesa by
now familiar account. At early ages,thereis at least
an implicit understandingof the equivalencerelation; to start, this understandinghas an on-again,
off-again characteristic, and its development is
protracted.
In their account of the preschooler'sarithmetic_
reasoningprinciples,Gelman and Gallistel(1979)
maintain that the young child recognizesan equiv_
alencerelation. For evidencethey point to the way
young children behavedin thosemagic experiments
when the surreptitiouschangeinvolved transforma_
tions that were irrelevant to number, for example,
Iengthening, item-type substitution. In nearly all
cases,the children regardedthe alteredarray as still
equivalentto the original array. When the children
who noticedthe changeswere probedaboutthe reason for their equivalencejudgment, they charac_
teristically indicated that the number of items was
the same, even though other featuresof the display
were not. Irr Gelman and Tucker's (1975) experi_
ment, there was an opportunity for children to con_
struct two equivalent displays to give themselves
two winners. Half the children did just this. It is
difficult to explain such findings without allowins
that the young child's arithmetic-reasoningprincil
ples include an equality relation.
A similar line of evidenceand argumentled Gel_
man and Gallistel (1978) to maintain that preschool
children recognizethat a differencebetweennumerositiesdoesnot satisfy an equivalencerelation.Further, in the casewhere x * y, the child believesthat
either r is more than y or that y is more than x. In
short, the child recognizesthat an ordering relation
holds betweenx and y. Siegel (1974) showedthat
187
preschoolers
couldconsistcntlyrcspondto a nunreri_
cal-orderingrelarionbetweentwo sers Bullockand
G e l n r a n( 1 9 7 7 )s h o w e dt h a te v e n2 % - y e a r - o l dcsa n
c o n r p a r et h e s e t s i z e p a i r o f 1 , 2 u , i t h 3 . 4 a n d ,
therefore,select3 (or 4) as the winner af(er first
learningthat I (or 2) wasrhewinner Interestinglv,
it
rvill bea good while beforethevery youngchild will
use correctlythe terms "more" and '.less" (e g .
Clark & Clark. 1977)
We have alreadydiscusscdthe trvo_candidates
procedureby which preschoolers
achievea representationof numericalequivalence---<ounting
and
one-to-onecorrespondence.In Gelman's (e g ,
1972a,1972b)magic experiments,rherewas no obvlous way to use a rule of one-to_oneconesDon_
dence:the arrayswere placedside by sidc. Under
theseconditions,countingservedas the algorithm
by whichchildrenmadejudgmentsof equivalence
or
nonequivalence.
Becausethe preschooler'sabiliry
to countaccurately
is limited,it is no surprisethathis
ability to use a counting algorithrnto determine
equivalenceis too. Thus, Saxe (1979) finds that
youne preschoolchildren can use the countingprocedureto establishequivalencebetweena standard
smallsetand anotherset.It is not until 5 or 6 yearsof
agethatchildrendo the samewith muchlareersets.
Studiesby Brush(1972),Bryant(197a),Cooper
et al. ( I 978), and Starkey( I 978) showrhatrhereare
conditionsunder which preschoolchildrencanreach
a decision about numerical equivalence or nonequivalenceon the basis of one-to-onecorrespon_
dence.Such conditionsinvolve controllingfor the
potentialconflict with spatialextent. piager(1952a)
describesthe various stageschildren pass though
beforethey can use a principle of one-to-onecorrespondencein the face of conflicting cues.
Work by Russac(1978) and Saxe (1979) provides evidencethat the ability to use a countingalgorithmto determineequivalencedevelopsaheadof
the ability to use one-to-onecorrespondence.Russac'sresearchis especiallyinformative on this matter becausehe used a test of one-to-onecorresDondence that did not require the child to ignore
competrngspatial extent'cues. The counting task
involvedshowing5-, 6-, and 7-year-olds
cardi with
7 , 8 , 9, or l0 dots. The children were theninstrucred
to countthe numberof dots and put the samenumber
in a box. In the correspondencetask, the child was
asked,without counting,to put as many itemson a
card as were already there; the instruction was to
place the blue items beside the red items, thereby
alleviatingthe possibility of confusion with spatial
extent. The proportion of correct trials was .96,
1.00,and .95 respectively
for rhe 5-,6-, and7-year
188
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
figurestbr thc
old groups.ln contrast.therespective
task r.i'ere. 125, 3 13. and 688
correspondence
An earlierstudyby StockandFlora( I975) nrakes
clear
that thele is developmentin the ability to
it
appl1,thc one-to-oneconespondenceprocedurc
W h e r e r sR u s s a (c1 9 7 8 )h a dc h i l d r c np r o d u c e q u i v alence.Stockand Flora did not They showedchildren displayscontainingalternatingred and blue
dots rvlierethere were 3. 5, 6, or 8 pairs of dots.
Control taskshad one extrared (or blue) dot. The
subjectsrvere in preschool(i age, 55.8 months),
(i age,70.2 months)andfirst grade(i
kindergarten
a-ee,81.5 months);their taskwas to indicate,without counting,whetherthe numberof red and blue
dotswasthe sameor not. The proportionscorrectof
equiyalencejudgments on this single-row corretaskwere .33, .66, and 1.00 for the prespondence
school, kinderganen,and first-gradegroupsresPecrively. In contrast,the proponionscorrectfor the
double-row task used by Brainerd (1973)
we should
rvere 00, .07, and .18. Parenthetically,
task was
note that this Stock-Floracorrespondence
task.
easierfor the childrenthana length-ordination
This reversesBrainerd's(1973) findingsregarding
the acquisitionof ordinalandcardinalconceptsand
highlightsthe critical role of taskcomplexityin asof developmentalsequences(Brainerd,
sessments
l e n d s u p p o r t o P i a g c t ' s( 1 9 7 - 5 a1. 9 7 7 )h y p o t l r c s i s
of nuntberconservatiott
rhata child's understanding
fronl theabove
goesthroughlevels The suggestion
s t u d i e si s t h a te x p l a n a t i o ni sn v o l v i n gr e r e r s i b i l i t y ,
of reverand thereforean explicit understanding
sibility, developlater-an accounttltatis consistent
rvith Piaget's.A similarconclusionwas reachedby
Botvin and Murray (1975)regardingthe conservation ofcontinuousquantity.Their trainedconservers
as
ofadditionandsubtraction
referredto theabsence
oPeration;
rvell as the inelevanceof a displacement
they did
unlike their controls, naturalconservers.
argunot refer to reversibilityand compensation
explaments.Whetherit is thecasethatreversibility
nationsbecomeprevalentat a laterageis notknown.
Thus, as reasonableas the hypothesismay be, it
needsfurther support.
The kinds of explanationsofferedb1'Gelman's
(1982) preschoolersgo againstGelmanand Gallistel's (1978) account of what might distinguish
precociousconservationsfrom thoseobtainedIater'
Recall that they hypothesized that preschoolers
rvouldnot be able to use a principleof one-to-one
when applying their reasoningprincorrespondence
ciple regardingequivalence.Gelman(1982) finds
that they did; indeed,if anything,the voungerthe
child the greaterthe tendency.Of the 3-year-olds'
explanations,2l%o wereof this type as opposedto
t97'7).
(
only9Voofthe 4-year-olds'explanationsThus, the
Floraand Stock I 975) notethattheir single-row
and Gallistelhypothesishasto be modified
for
example,
Gelman
explanations,
explicit
task elicited
''there's 2, and 2, and 2. . . . " for a judgmentof
to acknowledgethat therearesomeconditionswhere
children as young as 3 can accessone-to-onecorree q u i v a l e n c e" t; h e r e ' s2 a n d 2 . . . a n d i l e f t o v e r "
judgments.Clearly, the children
It may be that Gelmanand Gallistelare
spondence.
for nonequivalence
the tendencyof preschoolersto yoke
about
correct
were using a principle of one-to-one colresPonof operationalknowledgeof nurntask,
application
poorly
double-row
their
on
the
dence.Still, theydid
ber to quantificationproceduresthat can determine
indicating that their ability to apply the corresponrelationholds.That
whether,in fact, an equivalence
denceprinciple was not yet completelygeneral.We
is, they may be more dependenton havinganempirisuspectit is a very, very long time beforethey will be
cal confirmation of a judgment of conservationthan
able to follow Cantor's proofs regardingtransfinite
at
an
older children. ln Piagetianterms, this would innumbers.Again, there is some competence
pronot
volve a dependenceon using correspondence
it
is
is
restricted;
this
competence
age
but
early
cedureswhen applying operatoryknowledge.Older
applied generally and is probably not explicitly
Perchildrencanthink solelyin termsof operations.
understood.
hapsthis happensat the time whenchildrenlikewise
Consemation. Markman (1979) suggeststhat
articulateoneor more versionsof a reversibilityhythe kinds of explanationsoffered by young conserpothesisas regardsnumberconservation
vers differ from those of older natural conservers'
judgnrents
Sunmary. We havereviewedevidenceon the
justified
their
equivalence
Her subjects
of countins,addition
young child's understanding
either rvith referenceto the irrelevanceof the transand subtraction,equivalenceand nonequivalence,
formation(e.g., "you just spreadthem"), or the
ln all cases,it canbe seenthat the
andconservation.
or a spefact that nothingwas addedor subtracted,
moreaboutnumberthanwas aspreschooler
knows
cific referenccto number. She fails to rePort any
as
5
or
6 yearsago. Howerer, despite
little
(1982)
as
that
sumed
found
to reversibility.Gelman
reference
develthere is considerable
competence.
this
early
explanakinds
of
the
same
used
her 1'oungsubjects
asif
t i o n sa s d i d M a r k m a n ' s( 1 9 7 9 ) .T h e s et w o s t u d i e s opmentthatwill occur.lndeed,it beginsto look
A R E V I E WO F S O M EP I A G E T I A NC O N C E P T S
thc developntent'"villbe l)loreptotractedthln one
misht havcexpected.Thus.theresecntsto be a parad o x i c a lr e s u l t .t l r a ti s . n r o r ec o n t p e t c n ci e
n t h ep r e operationalperiod but lcss in the concrete-operationalperiod We rvill returnro whatwe nrakeof this
paradoxjn the final secrionof the chapter
C o n t i n u o u s - Q u a n t i tCy o n c e p t s
Conservation
We have seen that preschoolers
know that the
operationsof additionand subtraction
chansenumber. whereas those involvin_edisplacementor
chanqein item type or color do not. Further.preschoolerscan in somecasesuse this knowledgein
explanationsof their nurnber-conservation
judgm e n t . B e c a u s ei n a d u l t . s c i e n t i f i ct h o u g h t ,q u i t e
similar reasoningprinciplesare appliedto a wide
raneeof continuousquantitjes,for example.Iength,
mass,heat,electriccharge,onenrightthinkrhegeneralizationto continuousquantitywould be a small
stepfor the child. One might expecrit to bc easyto
apply the sameexplanations
with continuousquantities. In somecases,this seemsto havehappened.
'Gelman(1969)
reportedtransferfrom trainingon
len_sth
and numberitemsto lengthand numberconservationas well as liquid and mass.The explanations regardingmassand liquid involvedappealto
the inelevanceof the transformations
of displacement, pouring, and the like. Bur if the only thing
involvedin thedevelopment
of the understanding
of
conservation
of continuousquantitywerethe recognition of rhecommonstatusof suchoperations
vis-irvis length, liquid, and malleableclay, then surely
the natural development of these would follow
quickly after the stable understandingof number
conservation.Training studiesdesignedto build the
development of an understandingof continuous
quantity on that available for number conservation
shouldbe successful.Yet, judging from a seriesof
Genevantrainingstudies(lnhelderet al., 1974;Inhelderet al., 1975),this doesnor seemro be true.
Before we look at thesestudieson the relationship
betweennumberand continuousquantities,a brief
digression is in order.
The conceptof length, which is probablythe
easiestof the continuousquantitiesto understand,
can be understoodat two levels(at least) A great
dealofreasoningaboutlengthcango on withoutthe
notion of a unit-as Euclid long aeo demonstrated.
Lengthsmay be ordered,equivalentlengthsrecognized,and so on, withouteverconsidering
thequestion of how many unitslong a lengthis. To question
how long a length is, is to considerlengthat the
189
sccondlevel The questionof hou, lons a lenerhis
requiresthe arithn'retization
of theconcep(of nracni t u d ea n dt h ea r b i t r a r y c l r o i coef a u n i r E u c l i da n dt h c
otherGreek mathentaticians,
havin-ediscoreredtlte
problem of inconrnrensurables-whichrcars rrs
head when one tries to let nunrbersreprcsenr
lcngths-kept their geometryand arirhmeticsrricrlr
s e p a r a t(es e eK l i n e , l 9 7 2 , f o r a ne x c c l l e nttr e a r n t e n t
of this topic).
At the secondlevel we identify. the understrndi n g o f l e n _ s tehn t a i l sa n u n d e r s t a n d i nosi s c a l i n gr h c
processes
by which numbersmay be nradero repies e n tv a r i o u sc o n t i n u o uqs u a n t i r i e sH. i s t o r i c a l l ir, h. c
developmentof processesfor scaling continuous
quantitieshas gone hand in hand wirh the der;elopment of a scientific understanding
of thosequantities.Although it is perhapsobviousro adulrsshar
len_sth
is and, therefore,how it musrbe definedtbr
purposesof scalingand how in principlero scaleir
once defined, the samecannotbe said for hearor
electriccharge.Even liquid quantiry.on extended
consideration,behavesin a way thar presentsrhe
would-beapplierof numbersrvith perplexineproblenrs.Recall that the abstraction
principleof counring assertsthat the identityof the unit is inelevanr,
However,this is not true for liquid quanrirv Three
cupsof water plusthreecupsof alcoholdo not1,ield
six cups of liquid. This is becauseliquid mass.bur
not liquid volume, is conserved
whenmutuallysoluble (i.e., missible) liquids are combined Scalin_e
(i.e., measuring)heat, electriccharse.liquid rolume, and so on, cannotbe donesatisfactorilv
in rhe
absenceof some scientificunderstanding
of these
quantltles.
The point of theseremarksis thatthe applicarion
of arithmeticreasoningto conrinuousquanrirvis nor
asstraightforwardas it may seemat firsr Evenin rhe
caseof length,thechild musthavetheideaof magnitudesthat can be counted,that is, measured.
As \ve
will see,the problemof the unit is not trivial.evenin
the caseof length or sweetness(Strauss& Starr'.
l98l). Now back to the Genevanstudiesthat hare
focusedon trying to leadthe child from his abilitvto
makeordinal comparisonsto onesinvolvin_q
an understanding
quanof the fact thata givenconrinuous
tity can be consideredin termsof units.
The findings of Inhelderet al. (1974)hi-ehlight
the difficulty a child who conservesnunrbercan
havewith lengthtasks.They alsoshou rharir is nor
enoughto be able to count and consenenumberto
be able to conservelength.In one experimenr.
children were shown two roads made up of the same
numberof matchsticks,laid end to end to yieldtrro
continuousroads.A small woodenhousewasglued
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
F i g u r e 1 . I l l u s t r a t i o no f t h e e l i e c t o f t r a n s f o m ] i n go n e r o s o [
r n a t c h eas n d h o u s e s(. A f t e r l n h e l d e r S i n c l a i r .a n d B o v e t , 1 9 7 4 'p '
r 3 8)
the child to realizethat items *ithin a displayare
commutable.The issuewas whetherthe argument
of
could be developedto explainthe understanding
rvere
dethat
experiments
The
quantity.
continuous
signedto inform the issue involved different small
coloredpiecesof clay. Thesepiecescouldbe left as
suchfor testsof number conservationor put together
"in going
for the continuoustests.lt turnedout that
subjects
continuous.
the
to
from the discontinuous
'operatoryenvelop' (a
the
for
substitute
regressand
collection whose quantity equals the sums of the
parts, and which is conservedduring form or shape
'preoperatoryenvelop'rvherethe
iransformations)a
totalquantityis, in general,more" (Inhelderet al',
1974.p.46). To get beyond this, the child has to
understandthat the small pieces which were rolled
into a clay ball are "commutable" underdisplacement. To do this requiresknou'ing that it does not
matter to where the pieces are moved nor does tt
matterwhat shapethe piecesor the whole object are
as they are moved.
We confessthat we have a lessthan full understandingof the recentPiagetiantheoryof rvhattakes
ol
the child from nonconservationto conserY-atlon
to
relates
in
tum'
this.
how
continuousquantityand
us,
For
quantity'
ofdiscontinuous
theunderstanding
rhe recentexperimentshighlight the difficulty chilthe childrenseemednot to know.
dren havewith the notion of a unit of a quantrty'a
al.
Findingssuch as the above led Inhelderet
fact that is not dealt with in this new accountof
(1974) to conclude that lhe relationshipbetween
conservation.The child who says that 7 short
of number and lengthrvasquitecomconservation
matchsticks cover more ground than 5 long
setofexperiments,lnhelderet
plex. In a subsequent
matchsticksis making a fundamentalenor by comal. studiedthe relationshipbetweennumberandthe
paring units of differentextents.This, u'e submit'
iontinuous quantity in a malleableclay ball. This
t..urc b...rt. he doesnot yet thinkof length.inour
(1975a)
more recent
work takesoff from Piaget's
secondsense,where relative lengthsare consldereo
accountof numberconsen'ation,thatis, theneedfor
to the middle of each matchstick.Thus' the same
numberof housesappearedon two roadsof equal
length. The exPerimenterthen rearrangedthe sticks
in onerow into the Patternshownin Figure1. There
u,ere children who maintainedthat after the rearrangement,the numberof housesin thetwo displays
remainedthe samebut that the lengthof the roadsdid
not; the resultingroad in Figure I was said to be
shorter.Some children said that both were the same
becausetherewere the samenumberof matches-as
if to takethe length task and treatit asa numbertask.
This may seema perfectly goodanswerif we assume
that the child realizedthat therewere an equal number of equal units in each. However, a further task
showed that the children rvho respondedthis way
wereindifferentto the issueofequalityofthe units.
Consider a condition where the length of the individual sticks(i.e., of the units)in eachrow varied
themselves in length. Thus, a row with 5
matchsticksstretchedend to end was as long asone
with 7 shorterpieces of u'ood also laid end to end
Believeit or not, some childrensaid that the latter
would be a longer road to traversebecauseit had 7
pieces.Thesechildren failed to realizethat the units
in both rows were of different sizes themselves
Therefore,the comparisonwas not valid, a fact that
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS
rvithrefcrenceto a countablcunit of a fixed nragnit u d e .I f t h e c h i l d l a c k st h i s i d e ao f l c n g t h ,t h c n h e
c a n n o tb e c i nt o u n d e r s t a ntdh a th e i s m i x i n ga p p l e s
and oranqeslet alonc comprehendthe conditions
tunderrvhichhe might be ableto conrparenunrbcrs
t h a tc o u n tc o m p a r a b luen i t s( S c h w a n z1, 9 7 6 ) S i r n i larly, whenaskedto comparetwo clal' ballsthatare
eachnradeup of threesmallerpieces.rvedoubtthat
thechild recognizes
thattheabiliti,to decornpose
the
c o n t i n u o uqsu a n t i t i e isn t o p i e c e si n t h i ss i t u a t i o ni s
an exampleof a generalprinciple,thatis, that continuousquantitiescan be represented
in unitswhich
therebyrendersthem rneasurable.
Indeedrve doubt
that the child who quantifiesdiscretesetsrealizes
that he has both encountereda unir problem and
solvedit.
Given that the countingprinciplesare applied
indifferentlyto differenttypes,shapes,colors,and
so on, of objects;a child neednot know that counts
involve the iterativeproductionof 1et another'one
(l). The problemofthe unit in counting(and,therefore, discretequantification)is solvedfor the child
principle.Yet, thiscould
by virtueof theabstraction
be, and probablyis, an implicit understanding
of the
principle at first. Recall that it is a while before
children come to realize that the successivenatural
numbers are generatedby an iterative process. It
would seem hard to understand (hat continuous
quantitiescan be representedin terms of concatenatedunits rvithoutthe latterbeing implicitly understood;but eventhis is not enough.The child hasto
know what dimensionto quantifyand, as shownby
the examplesof heat, electrical charge, and even
liquid volume,this is far from obvious.
We seem to be in disagreementwith the Genevanson two matters.First, althoughthey do point
out the quitedifferent statusof the notion of unit visir-vis discreteas opposedto continuousquantities,
they maintain"the fact that the unit is given in discretequantities,and mustbe construcred
in continuous quantitiesis important, mostly \f irh respectto
measurementwhich comes in long after conservation" (lnhelderet al., 1974,p 54). As indicated,we
seea closerrelationship
betweenthedevelopment
of
an understanding
of continuousquantitiesand the
developmentof measurementconcepts.Strauss&
Stavy,( l98l) providea lovell,exampleof this relationship in their work on the child's conceptof
sweetness.As children develop the ability to use
more powerful scales,for example,ordinal versus
intervalscales,so they come to understand
the variables that do and do not affect the srveetness
of a
liquid. Second,the Genevansseemto suggestthat
the understanding
of a given continuousconceptis
191
a n a l l - o r - n o nm
e a t t e r .W o r k b y S h u l t z ,D o r e r , a n d
A r n s e l( 1 9 7 9 )h i g h l i g h t st h e d a n s e ro f s u c ha n a s sunrption.They point out that chansesin shapecan
and do alter quantityundercertaincondirions,and
Iikeivise,that some propertiesof a containercan
profoundly affect whetherthe liquid in rt is conserrredover time.
If the sameamountof wateris pouredfroma tall,
narrowcontainerinto a very wide but shallorvdish,
as opposedto a yet taller and nano\\'erglass.there
will be a differencein the amountsin eachcontainer
when both are measured24 hr. later. For the sreater
the exposedsurfaceof the water, the greaterthe rate
o f e v a p o r a t i o nS. h u l t ze t a l . ( 1 9 7 9 rr e p o nt h a t l 0 year-oldchildren who passedthe standardliquid
conservation
did poorly in predictingthe 21-hr.differencethat would obtain asa functionof diff'erences
in degreeof exposed surfaces Lest one think that
suchtricks can be performedonly underconditions
of thepassage
of time, it shouldbe soberingto know
thatsomesbapetransformations
tharinvolvecontinuousquantityalterthe amountimmediatell. Shultz
et al. go over the fact that the shapechanges
oftwodimensionalclosedfigures can alter the areaor perimeter of that figure Becausemost of us eitherdid
not learn or have forgotten the relevantgeometric
proofs, we are likely to do as the lvlcGill University
undergraduates
did-maintain a judgmentof conservationwhen we shouldnot. Shultzet al. (1979)
were able to teachtheir subjectsaboutthe effectsof
shapetransfbrmationson closed tuo-dimensional
figures, and they did so "on the premisethat the
effects of shape transformations could best be
graspedif the quantities were readill''identified in
standardunit measures"(p. t tl).s
We have come a long way from the Siegler
(1981)paperon conservation.We uere dissatisfied
with his accountof the differencebetrreenconseryaof
tion of numberand the two continuousquantities
liquid and clay amount. It was not becausewe
thoughtwhat he saidwas wrong. Rather.it *as becausewe thoughtit wasjust the beginningof a longer accountof how childrenthink abouttheprocesses
of quantification-anaccountthatu ill haveto allow
for the continueddevelopmentof someconsen'ation
beliefs as a function of knowledge about a given
domainand how to define units in that domain.
Other Conceptsof ContirtuousQuantitl
Given the possibility that children rrill go
of
throughtwo levelsat leastin their understanding
continuousquantity, is there any eridencelor the
understandingof the first level at an earlyage.rWork
by Brainerd(1973)and Trabasso(1975)sho*'pre-
192
R O C H E LG E L M A NA N D R E N E EB A I L L A F G E O N
schoolersable to orcletthc relativclengthsoi sticks
rvhcnthcv cannotknorvtheirexactlerrgthsindeed.
the evidenceof an early ability to nlake transittve
infercncesabout Iengthand weight fit u'ell in this
context And the rvorkon functionso{'Piaeetet al
( 1 9 7 7 )i s n r o t i v a t e d
b 1 't l r en e c dt o e x p l a i nt h e p r i (i e , relativeextents)over
rnacyoIorderjudgrnents
judgmentsbasedon quantificationdurine the pteschoolvears.Piagetwantsto arsuethatconceptsof
ln a
nunrberand extent are not yet differentiated.
sense\\e agree.
quanlf rvearerieht thatconceptsof continuous
in
terms
quantifiable
as
recognized
not
tity areat first
of sonreunit. we shouldbeginto seeresultsreporting findingsof suchearlyconceptsof othercontinuous quantities.Levin's researchon the development
of time conceptscan be interpretedin this context
( L e v i n . 1 9 1 1. l 9 ' l 9 t L e v i n , l s r a e l i , & D a r o m .
1 9 7 8 ) L e v i n ( 1 9 7 7 )p r e s e n t e5d- t o 6 % - y e a r - o l d s
ancl8%-rear-oldsrvitlrthreediffelent tasks These
and linear-tinie
rverethe still-time,rotational-time.
taskwasdesignedto be more
tasks.Eachsuccessive
compler than the previousone. We focus on the
still-tinre task. which asked children to decide
whethertu,o dolls sleptas long as eachotherand if
not which slept longer.The childrenwereaskedto
answerthesequestionsafterwitnessingfour conditions:( I ) the dolls went to sleepand woke up at the
sametime. (2) the dolls went to sleepbut one woke
up filst. ( 3 ) one doll wentto sleepfirstbut bothwoke
up together,and (4) one doll went to sleepfirst and
woke up before the other, however both slept as
did well on thefirstthree
long. Eventhe 5-year-olds
problems, Moreover, their explanationsmade it
into accountand
clear thel' were taking succession
theirdurationjudgmentsin termsof the
rationalizing
relativestartingandendingtimes As taskcomplexity increased-in item 4 of the still-timetaskaswell
as in othertasksthatput time and otherfactors,like
speedand extent, into conflict-the youngerchildren's performancescoresdecreased.Levin and her
is due to
arguethat much of the decrease
colleagues
by ineletheyoungchild's tendencyto be distracted
vantvariables.We alsosuspectthatthedeveloplnent
skills is involvedfor muchthe
of time-measurement
outlinedaboveregardingothercontinsamereasons
uous quantrtles
Funherevidencefor an early ability to perform
comes
of continuousquantities
relativecomparisons
fronr erperirnentsthat requirechildrento match a
standardrr'ithanotherdisplay.Gelman( 1969)found
that her 5-year-oldsubjectscould selectthe two of
threesticksof the santclengthif noneof the sticks
(e -e..Anoverlapped.Andcrsonand his colleagues
d e r s o n& C u n c o , 1 9 7 8 :C u n e o . 1 9 8 0 1\ \ ' i l k e n i n g .
198I ) repeatedlyreportchildrenrrf this ageable to
indicatehorvmucharea,time. distance,andsoon. is
in a given displayor event;childrenas
represented
young as 3 are able to point reliably to different
r e l a t i v ep o s i t i o n so n a s c a l e T h u s . f o r e x a m p l e .
Cuneo( I 977) had youngchildrenindicatehow happ1'(or sad)they would be eatinga particularcookie
u,here over trials the area of the cookie varied
srstematicall)'.
W i l k e n i n g ' s( 1 9 8 1 ) r v o r k r a i s e st h e p o s s i b i l i t y
that 5-year-oldchildren make intplicituse of arbitrary units. As such. it could be thatlaterdevelopmentof this ability is betterthoughtof as thedevelof the role of
opmentof an explicit understanding
measurement vis-ir-vis decisions of relative
amounts.Wilkening points out thatall researchon
the child's understandingof the relationshipbetween time. speed.and distanceinvolvesa choice
paradigmwhereinthe child is requiredto choosethat
animal,that train, or what have 1ou, that rventfurtheror fasteror took longer.and soon He suggests
that theseparadigmsmay have iailed to revealan
earlyability to integrateinformationfrom trvoof the
dimensionsin order to reachan inferenceaboutthe
third becausethey are not appropriatetestsof this
ability. Instead,he arguesthat they are testsof the
child'sability to ignoreone or moredimensions(cf
Levin, 1979). The proof of the argumentlies in
Wilkening's( 198I ) results.Subjectsin eachof three
agegroups(5, 10, and adults)rveretestedon three
velocity,distasksthat requiredsubjectsto intesrate
tanceand time. We considerthe tlrst.
The velocity-timeintegrationusk involveda display of a dog sittingcloseto the e\it of its den. The
dog and its den wereon the left sideofa 3-m by l-m
screen.A bridgeled out of the denacrossa lake. A
metal strip, fixed to the bridge, servedas a scaleto
*,hich subjectswere to attach an animal-a turtle,
guineapig, or cat. Subjectsrveretold thattheseanimalswere afraidof the dog rvhenererit barked,and
that, wheneverthe dog barked,the animalsstarted
runnin-eacrossthe bridge and sroppedshen the
barking stopped.Note that the threeanimalshave
differentialnaturalspeeds.ln a pretest'eventhe 5the correct
i'ear-oldscould arrangethe animalsin
rePresent
can
they
mean
this
order. Not only does
do his
could
Wilkenin-e
it
means
velocities,
relative
experiment.Children (and aduks. of course)listenedto the dog bark for either l. 5, or 8 sec and
thenplaccda given animalat the sPoton the bridge
he could have reachedduring thesebarking interto rhe
rals. Becausea centimeterscale\\as attached
centimeters
in
distance
the
strip,
metal
the
back of
CONCEPTS
A R E V I E WO F S O M EP I A G E T I A N
variable All agegloups
servedasthetruedependent
time andvelocityvalueswith a
irnplicitlyintegrated
nrultiplicativerule This is revealedby si-enificant
interaction
effectsin an analysisof variancebetwcen
time and vclocity. How did suchyoungchildrendo
datashow thatthe
this?Wilkening'seye-movenlent
children(aswell as the older subjects)followed the
imaginarynlovementof an animalalongthe bridge
When the dog stoppedbarking,they pointedto the
position their eyes had reached Becausethey adjustedthe rateof their eye movementsas a function
of animal, the fact that the time x velocitf interactionswere significantis explained.
Wilkeningpointsout that the ability to integrate
distanceand velocityto judge time requiresthe use
of a division rule. likewise the ability to judge velocity as a function of distanceand time. Furthermore, the definitionof the unit is morecontplex,as
demandsof tasksthat
arethe informationprocessing
requiretheseintegrations.The youngestgroup did
not succeedon distance,that is, the velocity task,
rvhere successis defined in terms of the use of a
division rule. Whetherthesevelocitytasksrequire
an explicit understandingof the relevantunits of
measurementremains a question for further research.What is clear now is that even young childrencan, undersomeconditions,makeconectjudgmentsof relativeamountsof continuousquantities.
Still, thereis much room for development.
Classification
In an earlier section (Assessment
of the Characterizatiotrof ConcreteOperations),we discussedthe
role classificationstructuresplay in Piaget's(1952a)
theory of the developmentof numericalreasoning
In this section,we focus on Inhelderand Piaget's
(1964) theory of the developmentof classification
skills, and on the implicationsthis theory has for
conceptacquisition.a
Conceptshavetraditionallybeencharacterizedin
terms of classesand class-inclusionhierarchies.
Like classes,conceptsaresaidto havebothan intencomponent.The intension,
sionalandanextensional
or definition,ofa conceptspecifiesthecriterionelementsmust satisfyto be regardedas membersof the
concept. The e-rtensionof a conceptconsistsof all
the elements that are appropriately described as
membersof that concept. (The readeris referredto
Schwartz, 19'77,for a review of a philosophical
that proposesan alternativeapproachto con"r'ork
c e p t s ,a n dt o S n r i t h& M e d i n , 1 9 8l , f o r a r e v i e wo f
psychological research conducted within this
approacn.
)
193
( 1t 9 6 4,)
T o V y g o t s k y( 1 9 6 2 ) . l n h e l d earn dP i a - e e
andOlverand Hornsby( t966)-all of rvhontshared
thc traditionalview of conceptsas classes-the
\\,asof spccialrnstud\ of children'sclassifications
tcrestfor two reasonsFirst.it wasthoushttltatanalyses of the structureof children's classifications
would shedlight on the structureof their concepts
and.nroregenerally.u,ouldshow hos'this structure
thelogicalclassstructure
approximates
successively
of adults'concepts Second,it was hoped that an
of the basisof children'sclassifications
exanrination
would reveal somethingof the content-ri'hether
concreteor abstract---oftheirconcepts Becausethe
young child was viewed as locked in a concrete,
t l..
i n i m e d i a tree a l i t y( e . g . ,P i a g e t ,1 9 7 0 :B r u n e r e a
1966).it was predicted(e.g., Olver and Hcrnsby,
1966)that young children would establishequivalenceson the basis of perceptualsimilarities,
whereasolderchildrenwould rnakeuseof ntoreabstractcntena.
Background
Structural Properties of Children's Groupirtgs. According to Inhelder and Piaget(1964).
beginswhen the child groupstosether
classification
two objectsthat look alike in somewa\ . The child's
abilityto discoversimilaritiesbenveenobjectsis rrot
regardedas sufficient, however to warrant the conclusionthat the child can classify.True classificaof clastion is saidto involvetheactiveconstruction
sificatory systems
Inhelderand Piaget( I 964) begantheirinvestigaskills with a detailedexamination of classification
tion of children'sproductionsin free-sortingtasks
Thel found threemain phasesin the developmentof
ln the first phase(2 to 5/: years),
freeclassification.
graphiccollections,three types of groupingwere
obtained:alignments,collectiveobjects.and cornplexes.All threetypesarebasedon contigurational
variablesratherthan similarity.The child becomes
of theobjects,
distracted
by the spatialarrangement
or b1' the descriptivepropertiesof the rvhole.and
buildswithout regardfor similarity.The seometric
situational
designobjectsform or therepresentative.
c o n t e n t h e y e v o k e ( e . g . , a t r a i n .a c a k e .a c a s t l e )
swav the child's attentionaway from the perceived
likenessand differencesof the objectsthemselves.
ln the secondphase(5t/t to 7 years). nongraphic
c o l l e c t i o n st h, ec h i l d i s n o l o n g e rn r i s l e db y c o n s i d erationsof patterns:objectsare assignedto groups
on lhe basisof similarityalone.lnhelderand Piaget
list ibur typesof nongraphiccollectionsAt thelcast
adranced level, a nulnber of snrall groups are
tbrnred.eachbascdon a differentcritcrion Further.
194
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
only someoi the objectsthatconstitutethe arrayare
assignedto groups.The secondtyPe of nongraphic
collectionsagain involves various small groups
basedon a multiplicityof criteria At thislevel,howremainder:all of the
ever, there is no unclassified
At the next level,
classified
are
the
array
in
objects
fluctuationsof criterion are eliminated.Objectsare
now assignedto groupson the basis of a single,
stablecriterion without any remainderand without
overlap. At the founh and most advancedlevel,
groupsfomred on the basisof one criterion are subdividedaccordingto a second,stablecriterion
Childrenare, thus. able,by the end ofthe nongraphic collectionsphase, to form stable, nonoverlappingcollectionsandto dividetheseinto subcollectionsCanchildren,at thispoint, be saidto be
'able to classify?Inhelder and Piaget arguethat, almay be so
though thesechildren'sclassifications
differentiatedand hierarchizedas to closely resemhierarchies,they are still Weble class-inclusion
Accordingto InhelderandPiaget,"the
operational.
true criteriaby which we can distinguishsuchpreoperationsfrom true classificationare the ability of
'all' and
the subject to appreciatethe relations
'some,' andhis power to reasoncorrectlythat A < B
[i e., that the subclassis smallerthan the classin
which it is includedl" (lnhelder& Piaget,D6a' p'
child is stillunableto
54). Thatis, thepreoperational
grasp fulll' the logical relation of inclusion. When
shownI 2 rosesand6 tulips,for example,andasked,
"Are there more flowers or more roses?," the prechild typicallyanswers,"more roses."
operational
to form a larger
He is capableof adding subclasses
class(flowers : roses + tulips), but he is unableto
simultaneouslyperform the inverse tgansformation
(roses= flowers - tulips).As a result,he is unable
to makeaquantitativecomparisonof theclassandits
larger subclass.For sucha comparisonrequiresthat
to isothe classinto its subclasses
the child separate
whileat the sametime mainlatethelargersubclass.
taining the integrity or identityof the class,the other
term in the comparison.In other words, the child
must be able to attendat once to the part and to the
whole, and thatis preciselywhatthe preoperational
are isochild cannotdo. As soonas the subclasses
lated,the child losessightof the whole. As a result,
ratherthantheclass
he comparesthe two subclasses
when both operais
only
It
and the largersubclass.
are present
classes)
of
(addition
division
and
tions
thatthechild becomescapable
andfully coordinated
at oncethe classand the subclass
of contemplating
andof comparingthe t\\ o. At thispoint(thethird and
abilities)'
of classificatory
lastphaseof development
the child's groupsare no Iongersirnplyjuxtaposed
e e l l - a r t i c u l a t eIdo,g i c a lc. l a s s - i n c l u but constitutw
sion hierarchies
Vygotsky
Usingsomewhatdifferentprocedures.
( I 962) andBruneret al. ( I 966) havealsostudiedthe
developmentof classificationabiliries Although
there are many differencesin the tvpesof classificareportedacrossthethreeprogramsof
tory responses
in parresearch,therearealsostrikingsimilarities.
ticular,all threestudiessuggeslthat\oung children
go through an initial stagein which they arecaught
themselvesby relationshipsamongthe elernents
relations,or
thematic
arrangentents,
spatial
whether
idiosyncraticresemblancesFurther.all threestudies indicatethatchildrengo throughan intermediary
stage in which groups are formed on the basis of
similarityalone.but the criterionfor groupingfluctuates.During thelaststages,childrenprogressively
classes
learnto groupobjectsinto stable.exhaustive
and to organizethe classesthus formed into Iogical
hierarchies
Basis of Children's Groupings. Olver and
Hornsby(1966)maintainedthat children'sclassifipropercationsexhibit semanticas well assyntactrc
ties and that both setsof propertiesundergodevelopmental change. The syntax of classificationis
defined as the formal structureof the classor grouPing formed The semanticsof classificationare the
featuresof objectsor eventschildrenuseto establish
equivalences.
Working with the theory of cognitivedevelopment of Bruner et al. (1966)' Olver and Homsby
proposedthat in the early stage,s'henthe child's
mode of representationof the world is essentially
ikonic, childrenwould group objectssolelyon the
basis of perceptual properties Older children,
is s1'mbolic.were exwhose mode of representation
pectedto use more abstractcriteria. In particular' it
was aSsumedthat what usesobjectshave and what
functions they serveconstitutea more abstractnotion and require more "goine bevondthe infomlation given" thanwhat objectslook like Accordingly, it was predictedthat youngerchildrenwould
form conceptsbasedon perceptualattributesrvhereas older children would form conceptsbased on
functionalattributes.
Olver and Hornsby(1966)repon the resultsof
two experiments,one by each author' ln Olver's
study(seealsoBruner& Olver, 1963)childrenaged
6 to 19 were presentedwith a seriesof concrete
nounsand rvereaskedhor"'eachne\\'ltem \\'asslmllar to, anddifferentfrom. the itemspreviouslyintroduced. For example,the words bananaand peach
A REVIEWOF SOME PIAGETIANCONCEPTS
would be presented,and, then, the \\'ord potato
would be addedto the list At this point, the child
would be asked, "How is potatodifferentfrom bananaand pcach?" and "How are bananaand peach
wascontinued
andpotatoall alike?" This procedure
(e.g.,
until a list of nine items had beenpresented
banana, peach, potato, meat, milk. water, air,
wascloser
germs,andstones).Hornsby'sprocedure
to thatoflnhelderandPiaget(1964).Childrenof6 to
I 1 yearswere shown an alray of 42 drarvingsrepresenting familiar objects (e.g., doll, garage,bee,
pumpkin, sailboat,etc.). The children'stask was
simpll' to selecta group of pictures,Their grouping
completed, children were asked how the pictures
they had chosenwere alike. The pictureswere then
retumed to their original position in the array, and
children were askedto form anothergroup,The entire procedurewas repeatedl0 times.
In bothOlver's andHornsby'stasksit wasfound
that 6-year-oldsbased more of their groupingson
perceptualattributes(color, size,shape,positionin
space)than did older children. In Olver's verbal
task, the useof functionalattributesincreasedsteadily from4gVoat age6 to'l3Voat age 19.Conversely,
the use of perceptualattributesdecreasedsteadily
from roughly 25Vo to l)Vo. ln Hornsby's picture
task. therewas againa steadydeclinein perceptually
basedequivalencefrom 47Voat age6 to 20Voat age
I f. in contrast,the use of functionaland nominal
attributesincreasedfrom 307o and 6Vcrespectively
to 48Vc and 32Vorespectively. Comparing thesetwo
setsof findings, Olver and Hornsby notedthat the
same pattern of development obtained whether
words or pictureswere presentedand rvhetheritems
were presentedin random or predeterminedorder.
They describedthis pattern in the following terrns:
Equivalencefor the six-year-oldreflectsa basis.
in imagery, both in what he usesas a basis for
grouping and in how he forms his groups. . . '
With the development of symbolic representation, the child is freed from dependenceupon
moment-to-momentvariation in perceptualvividnessand is able to keepthe basisofequivalence
invariant.(1966, p. 8a)
We are not convincedthat Olver andHornsby's
progresdata supportthe notion of a stage-by-slage
sion from a perceptually based to a functionally
At no agewerechildren'sgroupbasedequivalence.
ings basedsolely on perceptualproPenies.To the
contrary.even Olver and Hornsby'slounger children produceda sizablePercentageof functionalre-
sponses.(Indeed.the largestcategoryof responses
producedby the 6-year-oldsin Olver's study was
functional l49Vc), not perceptual[25Vo)) What
theseresultssuggestto us is that if theredoesexista
differencebetweenyounger and older childrenwith
respectto the basisthey selectfor classifyingobjects, it is one of degreeand not of kind Younger
childrenmay useperceptualcriteriasomewhatmore
frequentlythando older children;but they clearlydo
not use perceptualcriteria to the exclusionof all
asbasisfor
others.What specificcriterionis selected
equivalencein any given situationapp€arsto reflect
lessa particularmodeof representingreality thanthe
interplayof a largenumberof factors Theseinclude
the modeof presentation(verbal versusvisual)of the
stimuli; the readinesswith which the stimuli Presented can be subsumedunder a single.conventional
label (both factorsseemto have influencedsubjects'
performancein Olver and Homsby's studies);the
(e.g., Kagan,
child's style of conceptualization
preference
Moss, & Sigel, 1963)or organizational
(Smiley& Brown. 1979);andso on. Supportfor this
comesfrom a studyby Miller (1973).
interpretation
Miller (1973)gave 6-year-oldsand collegestudentseightoddilt,problems.Eachprobleminvolved
a set of four objects(e.g., an orange,a plum' a
banana,and a ball), and subjectswere askedto remove "the thing that doesn't belong." The same
questionwas repeatedtwice, and subjectswere encouragedto take out a different object each time
The setsof four objectswere constructedin such a
way that removal of one object left a perceptualsubset(e.g., an orange,a plum, anda ball)andremoval
of a different object left an abstractsubset(e'g., an
orange,a banana,and a plum)' In general,the 6year-oldshad little difficulty forming both typesof
subsets.Indeed,in two of threeproblemswherereliable differencesrvereobtained betweenthe 6-yearolds and college students,the significantresultwas
due to the children's inability to generatea percePtual subset.Both children and adultstendedto form
abstract subsetson their first correct trial. Taken
together,theseresultssuggestthat: (l) 6-year-olds
can form categorieson the basisofboth concreteand
abstractcriteria and (2) 6-year-oldsdo not necessarily differ from collegestudentswith resPectto the
kind of criterion they Prefer to use.
A variable that may have contributedto the 6year-olds'superiorperformance,in lr4iller's(1973)
task, is the use of modeling' Miller took children
through two training problems prior to testingand
showedthem horr two different solutions(one perceptual, one more abstract)could be provided for
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
'l'herc
is little doubtthatsuchcarefulcoachirrg
cach,
nrusthavc left children in no uncertaitltyas to the
thatwere
naturcof thc taskor the typesof responses
expectedfrom thenr(Nash& Gelnran,cited in Gelm a n& G a l l i s t e l 1
, 9 7 8 ;S n r i l e y& B r o w n , 1 9 7 9 )
dclgartenand first-gradesubjectscouldsortobjccts
level.In contrast.thcrewereno
at the superordinate
developnrcntaldifferencesin the ability to sort
basic-levclobjects-basic-levelsortsrvercvirtualIy
perfectat all agelevels.In a secondexperiment,3and first-.
and 4-year-oldsas well as kindergartners
problerns
given
were
oddity
fifth-graders
and
third-.
Basic
Categories
and
Classification
relations
with either basic-levelor superordinate
The work of lnhelderandPiaget( I 964) gaverise
of
Again, basic sortswcre virtually perfectat all age
interestin thedevelopment
to rnuchexperimental
correct
By
levels For the 3-year-olds,the percentage
the structureof children'sfree classifications.
As
groups,
was
100%
it
age
for
all
older
wasggVo;
lnhelder
supPorted
and large,the evidencecollected
(55%
poorly
performed
the
3-year-olds
to
unable
expected,
are
young
children
that
claim
and Piaget's
coffect) on triads that could only be sorted at thc
sort objectsinto classes(see Flavell, 1970. for a
to note,howevlevel.lt is interesting
superordinate
researchpublished
review of the free-classification
was almost
performance
4-year-olds'
the
er, that
prior to 1969). However, recentwork by Rosch,
(1976)
with
conect
perfect,
967o
and
Johnson
Mervis, Gay, Boyes-Braem,
Recentfindings indicatethat even l'lz- to 3-year( i 979) indicatesthatevenvery young
andSugarman
old children may be capableof consistentsorting at
children can, and do, sort objectstaxonomically
t h e b a s i cl e v e l( e g . , N e l s o n ,1 9 7 3 ;R i c c i u t i ,1 9 6 5 ;
when presentedwith appropriatesets of stimuli
R o s s ,1 9 8 0 ;S t o t t ,1 9 6 1 ; S u g a r m a n1.9 7 9 ) I. n - S l g - l
Roschand her colleagues(1976)notedthat the
(1979)study, childrenbetweenl2 and 36
were
typarm-a4]s
experiments
stimuli usedin classification
agewere given six groupingtasks.Matethat
of
a
months
bed)
(e.g.,
a
dresser,
a
table,
ically stimuli
rials in each task were eight small objects evenly
could be groupedtaxonomicallyonly at the suPerordividedinto two classes,for example,four dollsand
dinatelevel (e.g., furniture).They pointedout that
four rings. Each task involved (1) a phaseof spontaxonomiesof concrete objects include a level of
and (2) a phaseduringwhich
is
manipttlation
that
taneous
(e.g., chairs, apples,shirts)
categorization
given
several grouping-elicitation
were
children
categories
level;
lessabstractthan the superordinate
of
classificatory activity were
types
probes.
Two
categoto
as
basic
are
referred
level
at
this
formed
examined:(l) the order in which objectswere maries. In a number of experiments,Rosch and her
nipulated (sequentialclassification)and (2) the arcolleaguesfound basic categoriesto be the most in(l)
possess
sigrangement of objects in space (spatial classificaclusive categorieswhose members
(2)
are
tion). Spontaneousand elicited performanceusually
common,
in
nificant numbers of attributes
(3)
coincided.In general,the resultssuggesteda shift in
and
movements,
motor
similar
of
means
usedby
children's classificationsfrom a sequential,stimpossesssimilarshapes.
ulus-boundorganizationofsingle classesto an antrcRosch and her colleagues(1976) predictedthat
ipatory representationand coordinationof the two
basic-levelcategorieswould be the first to develop.
in the array. The l2-month-olds showed a
classes
encode
Roschet al. reasonedthat if young children
(e.g'
tendency to manipulate identical objects
reliable
schemes
'
the world by meansof sensorimotor
successively:they repeatedlyselecteditems from
Piaget,1970)or images(e.g., Bruneret al., 1966),
one of the two classes,generally that with greater
then basic objects should be learnedeasily. In one
tactile-kinestheticsalience. Their anangementof
experiment, kindergartnersand first-, third', and
objects in space, however, was haphazard.Comfifth-graders were assignedto one of two sortine
(e' g. , all the
pletespatialgroupingsof singleclasses
mateconditions(basic or superordinate).Stimulus
l8 months
until
not
appear
did
the
rings)
all
(shoes'
dolls
or
clothing
photographs
of
rials were color
of similar
selection
of age.By 24 months,sequential
socks,shirts, pants), furniture (tables,chairs,beds,
within a
objects
and
classes
objectsextendedto both
dressers),vehicles (cars, trains, motorcycles, airFinally'
grouped.
sPatially
were
category
basic
planes),and people'sfaces (men, women' young
who
children
younger
the
of
all
but
one
whereas
condigirls, infants). Subjectsin the superordinate
expertment
the
in
any
at
grouped
two
classes
four
different
Point
of
the
picture
each
tion were given one
arrangedthe objectsone class at a time' more than
objectsin eachof the four superordinatecategories'
half the 30- and 36-month-olds shifted betleen
Subjectsin the basic condition receivedfour differclassesas they sorted.Thesechildren clearly could
ent pictures of a basic object in each of the four
attend to both classesat once. Whether they consuperordinatecategories.The resultswere straightbetweendistructed one-to-onecorrespondences
the
kinhalf
forward. As in previousstudies,only
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS
s i n r i l a ro b j e c t s( e . _ e. a d o l l i n e a c hr i n g ) o r s o r t e d
i d e n t i c aol b j e c t si n t o s p a t i a l l yd i s t i n c gt r o r r p st,h e i r
actions\\,erealrrays swift and deliberareIndeed,ir
often appearedro Su-earman
as if theolder childrcn
had rnentally constructedsome classificationin
which both classeswere represented
and. seizing
objcctsnroreor lessat random.wereanangingthenr
accordingto the schemethey had formed.
inhelderand Piaget(1964) thernselves
reported
havingobserved,alongu,iththe eraphic-collections
characteristic
of the first phaseof developmentof
free classification,
other, lessfrequentproductions
that arequitesiniilarto thosereportedby Sugarman
(1979) Specifically,Inhelder and Piaget (1964)
found that young children rvould at times successivblyselectsimilar objectsand then tossthem
into a pile or hold them in their handswithout attemptingto build them into a configurational
structure.InhelderandPiagetminimizedthesignificance
of theseproductions,which they viewedas a verv
primitive type of nongraphiccollection.They argued that the similar objectswere manipulatedsequentially on the basis of "successiveassimilations" and were not formed into a classification
(collection)proper.
Should the classificationsproduced by Sugarman's (1979)infantsalsobe construedas resulting
from successive
assimilations?
After all. eachof the
arrays Sugarmanused in her -eroupin_s
tasks contained two classesof identicalobjects,and Inhelder
and Piaget(1964) have never deniedthe fact that
children, even very young children, can discern
physical similaritiesbetweenobjects.One could argue that where such similarity is high, as was obviously the casein Sugarman's(1979)experiment.
the young child successivelyexplores similar objects preciselybecausethe perceivedresemblanceis
particularly salientand catchesand holds her attention. Conversely,where the similarity betweenobjectsis low, as wasthe casein Inhelderand Piaget's
(1964)own experiments
(recallthatthestimuliused
could only be sortedat the superordinatelevel), the
child becomes distracted by the configurational
propertiesof the objectsand as a resultbuilds without regardfor similarity.
We do not believethat the productionsSugarman
(1979) obtainedresultedsolely from sequenrial,
stimulus-bound
assimilations,
which mimic classificationsbasedon similarity. One might doubt that
successive
manipulations
of identicalobjectsunambiguouslyrevealclassificatory
behavior.But add to
this the ability to placethe -eroupsin rwo separare
locations.therebyusingspaceto keeprhetwo categories separate,and it becomeshard to deny a true
tJ/
classificator
y contpcrence
u'i(h basic-lc.r
el ob.jccts
S u g a r m a n 'dsa t ad e n r o n s t r atthea ts c q u e n r i a
classif i c a t i o n sr,v i t hn o s p a t i aal r r a n e e n t eonitt h eo b j e c t s .
o c c u ro n l y a t t h ee a r l i e
s y l 8 n r o n t hosf a s e .
s ta _ e e B
infantssuccessiveIv
selectedcrrrl,erouped
to*qether
spatiallyall of theobjectstharbelongedrooneof the
trvoclassesin tlie arra1,For us, suchtindinessupportthe notiontharsignificantclassificatcrrv
competenciesare presenrfrom the earliestages(rvhichis
not to say. obviously.that no developnrent
relnains
to take place).This conclusionis supponedby rhe
recentrepons of Cohen and Younger r I98l) and
R o s s( 1 9 8 0 ) .B o t h s t u d i e su s e dh a b i r u a i i oann dr e coverl,-f19--1'tabituation
responses
to showthat infantsdo categorizesomesetsof objects
The work of Roschet al. ( I 976) andrharof Sugarman( 1979)demonstrare
thatchildrenasyouns as
3 yearsof age can sort objectsaccordineto a consistentcriterionand without remainderor overlap.
indeed.thereis evidencetharstill youngerchildren
cando the same.Thesedemonstrations
clearlychallengelnhelderand Piaget's( 1964)descriprion
ofrhe
development
of freeclassification
. At thevery least,
they force us to abandonthe hotion thara sta_se
of
graphiccollectionsinvariablyprecedesthatof nongraphiccollections.In addition,they provideclues
about some of the processes
that conrributeto the
young child's acquisitionof knowled-ee-in both
factualand linguisticdomains.
Primacy of Basic Categorization
According to Roschand her colleagues(1976)
basiccategoriesaretheprimary cuts we makeon our
environment.We can and do establishequivalences
at higher and lower levels of abstraction.but the
basic level is the prina4 level at which we form
equivalences-the primary level at which we chunk
objects in our environment. There is somesupport
for the notion that our most spontaneous
or irnrnediate categorizationof the world is in termsof basic
categories.Experimentswith adult subiectshave
shownthat concreteobjectsaretypicalll iirst recognized as membersof their basic-levelcategoryand
are normally referred to by their basic-levelname
(Rosch et al., 1976; Shipley. Kuhn & Madden,
I 98 I ). Is thereevidencethat infantsandr oungchildren carve their u'orld into basic catesories?We
think so. First, there is the infant's oiien spontaneous(Sugarman.1979) sorting of anays into
second.thereis the infant'sdifferbasiccategories;
ential and appropriatereactionsto differentobjects;
and third, there is the young child's useof basiclevel termsfor basicobjects.
We have alreadydiscussedthe infant'ssorting
198
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
behavior Young childrenalso reveal their classificatory compcterlcethrough their actions---other
thansorting-upon objects'We nrightsay thatsortactionin the sensethat
irr-qis an object-indcpendent
all classesof objects-roses,books, cups, and so
on-{an bc sortedin the same rvay. By contrast,
actions,such as drinking' rolling. and so on, arq
object dependentor object specific' When we talk
hereaboutthe infant'sactionson objects,we havein
When givena
responses.
mind theseobject-specific
ne\\'instanceof a familiarcategory,for example,a
shoe,or a cup, l-year-oldchildrenmay try to put lt
on theirfeet, or bring it to their lips respectivelyln
other words, they behavedifferentially and approwith new examplesof prepriatelywhen presented
(Nelson,1977) Of
iuniablyknown basiccategories
of
course, there is the question what this capactty
means.lnhelderand Piaget(1964)maintainedthat
to
activityis only analogous
theinfant'sassimilatory
We believethat the infant'sassimilaclassification.
tion of novel objectsto existing sensorimotorschemas is in fact a printitivefonn of classification'
Roschet al. (1976)reasonedthat if by the time
the child begins to acquire words, he or she has
availablemostly basic-levelconcepts,then basicobject names should be the first nouns acquired'
Roschand her colleagues(1976) carefully analyzed
speech
Brown's(19?3)protocolsofthe spontaneous
period
of
initial
her
during
Sarah,
of his subject,
languageacquisition.Twojudges read Sarah'sprotocols, and utterancesof an item in any of the taxonomiesRoschet al. (1976) had studiedwere recorded. The results were straightforward. Basiclevel nameswereessentiallythe only namesusedby
Sarah at that stage. Similarly, vocabulary studies
reviewedby Clark (1978) suggestedthat ofthe first
50 or so object words that children learn, many of
them are basic-levelterms. Additional supportfor
the primacy of basic-levelnames in children's ac'
quisition of concretenounsis provided by the study
of Roschet al . ( I 976) of the names3-year-oldsgive
to picturesof objects. Of the 270 namescoilected,
all but one was a basic-levelname. True, not all of
the namesprovidedby the childrenwere colrect' but
elrors were typically basic-levelnamesfor objects
other than thosepictured (e.g., bluebenies instead
natesanrongobjectsin theircverydavcnvitottment
Roschet al (1976)alsonotedthat rvhatobjectsare
coincide
treatedas basic ievel doesnot necessarily
and
of
superordinates
definition
with the biological
who
think
individuals
an
example,
As
subordinates.
trees are those objects one sits under to avoid the
penetratingheat of the sun probablydo not know
whetherthe treesthey sit under are maples,oaks'
andso on For theseindividuals,the seenringsuperordinate is psychologicallya basic-levelconcept
(i.e., a treeis a treeis a tree).
of nouns
Young children'sovergeneralizations
view that
the
a-sainst
are sometimesheld asevidence
of basic
availability
the
reflects
early noun usage
concepts.Recent evidencepoints to a different inhowever'
of children'sgeneralizations
terpretation
Briefly, it appearsthat these reflect the child's attempt at using as meaningfula label as he can when
he doesnot yet know the appropriatelabel lnstead
of selectinga label at random, he selectsone from
within the same hierarchy. Two lines of evidence
supportthis hypothesis.First, 2- and 3-year-oldchildren who produceoverextensions,nevertheless,accurately comprehendadult terms (Gruendel, 1977;
Huttenlocher,l9?4; Thomson& Chapman'1977)'
Second, several investigators (Bloom, l9'13;
Gruendel,19?7; Rescorla,1980, 1981)have observed that a period of relatively accurateuse of
categoryname is often followed b1'overextenstons
to exemPlarsof a commonsuperordinate'For example, the initial accurateuse of the term car is foliowed by its use for many diverseobjectswithin the
broader category of vehicle. This overextenston
could signify either the formation of, or an alreadypresent,superordinatecategory' Recall that Rosch
et al. (1976) found that children's labeling enors
typically involved using inaccurate basic-level
names,such as bluebeniesinsteadof grapes' Both
names reflect basic level categoriesfrom the same
superordinatecategory. These resultssuggestthat
some early conceptsmay be more richly organized
than the basic-levelanalysissuggestsChildren of a
very young age may be capableof using hierarchical-classificationschemesto at leastrepresentand
organizetheir knowledgeabout objects' Put differently, what young children's overextenslonsmay
revealis their implicit useof an organizationscheme
of grapes).
long before that organizationcan be explicitly ac(1977)
found
test, Anglin
On a comprehension
cessedand used in sorting tasks'
that young children responded accurately when
We have reviewed evidence that indicatesthat
ln
animal'
or
to
collie
askedabouta dog as opposed
even very young children are capableof forming
seemingcontrast, more were accuratewhen asked
categoriesaccbrding to stable, consistentcriteria'
about an apple as opposedto fruit or food' Anglin
We iubmit that this f,rndingis surprisingonly in the
concludedthat young children tend to use telrns at
to
contextof an expectationto the contrary' It is hard
thar level of generalitywhich maximallydiscrimi-
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS
as
sec how the child could masterltcr environnren(
quickly and as efficiently as she does if shc rvere
incapable
of fomringstablecategoriesFor thc most
inecononricalnreansof nrasterynrustnecessarily
volve the generalization
to all novel, unfamiliarinstancesof what is known or what has been discovered to be true about a small set of familiar
instances.Clearly the formationof categoriesthat
if suchgenerareat leastconsistent
is indispensable
alizationis to bearfruit We wantthechild to beable
to generalizefrom old cup to new cup that which is
true aboutcupsand from old shoeto new shoethat
rvhichis trueaboutshoes.In eachcase,the recognition that the old and the new objectsbelongto the
samecategorycreatesa basisfor generalization.In
other words, the fact that the child can categorize
uponthe basisof similarity-however that similarity
may be recognized-means that she does have a
capacity for projecting or generalizinginformation
to appropriateinstances.A child who alwayscategorizedobjectson the basisof their spatialconfigurations would make one erroneousgeneralization
after the other.
We have also consideredevidencethat suggests
that the first categoriesthe child learns are basic
categories.Roschet al (1976) describecharacteristics of the basiccategorizationprocessthat help elucidate why it is that basic categoriesare primary,
why it is that so many ofour perceptionsandconceptions involve basic categories,and why-we addit is especiallyadaptivefor the young child to form
basic categoriesas opposed to categoriesat other
levels of abstraction.
Rosch and her colleagues(1976) arguethat, far
from being unstructured,the world we live in is
highly determined:real-world attributesdo nol occur independentlyfrom each other. Creatureswith
feathersare more likely to have wings than creatures
with fur; and objects that look like chairs are more
than
likely to have the property of sit-on-ableness
objectsthat look like birds. Given that combinations
of anributesdo not occur uniformly, it is to the individual's advantageto form classificationsthat mirror (at some level of abstraction)the conelational
structureof real-world objects. For such classifrcations would enable the individual to predict from
knowing any one property an objectpossesses
many
of the other propertiesthat may be present.
The level of abstractionat which categoriesare
formed that best delineatesthe correlationalstructure of the environmentis not the basiclevel but the
subordinatelevel. Objectsthat belongto the category ofrocking chair sharea largersetof attributesthan
do objectsbelonging to the basiccategoryof chair..
199
However,thegain in conelationalvaluebetweenthe
featuresof membersof a category,asone goesfrom
a basicto a subordrnate
category,is accompanied
by
a severelossin generalityor inclusiveness.
lt makes
intuitire goodsensethatoneshouldrvishone'scategoriesto be, on the whole, as inclusiveas possible
Clearll . the broader the category.the larger the
numberof itemsfor which a summarydescription
is
provided.Superordinate
categories
simultaneously
obviouslyare more inclusivethanbasiccategories.
Hower,er, their membersshare ferver attributesin
common Thus, Roschet al. (1976)arguefor the
prioritl.' of basic categories They are at the most
the correlational
inclusivelevel that still delineates
structureof the environment.
Put somewhatdifferently, the argumentis that
of two
basic categoriesdominateas a consequence
oppositeprinciples.On theone hand,categorization
must help reducethe near-infinitevarietyof the environmental array to behaviorally and cognitively
usableproportions. Attempts at fulfilling this goal
lead to the formation of a few very largecategories,
with the greatestpossiblenumber of discriminably
different objectsbeing assignedto the samecategory. On the other hand, it is obvious that the more
differentiatedan individual's categories,the greater
his ability to predict and, generally,control occurrencesin his environment Fulfillment of this particular goal calls for the formationof a largernumberof
small, distinct categoriesthat conespondto detailed
discriminationsamong stimuli. The basic level of
categorizationis the level that maximizesthe conflicting demandsof information richnessand cognitrve economy.
Thus, following Rosch et al. (1976), formation
ofcategoriesat the basiclevel, as opposedto higher
or lower levels of abstraction,presentssignificant
adaptiveadvantagesfor the young child. At birth, all
the objects,places,and eventsthat the child experiences are novel. The first years of life must be
largely devotedto resolvingthesenovelexperiences
into familiar, recognizableforms and predictable
events.A child who is inclined to form basiccategories is effectively breakingdown or parsinghis environment into the most functional units, units that
allow him to generalizethe iargestamountof information to the largestnumber of objects.
Classification and Hierarchies of Classes
Inhelderand Piaget(1964) recognizedthat were
one "to find a mixture of graphic and non-graphic
collectionsfrom the beginning . . onecould argue
that classificatorybehavior owes its origin to nongraphiccollectionsalone" (1964, p. 3l). The pre-
200
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
o f g ra p h i ca n d
t h a ta n r i x t u r e
v i o u ss c c t i o n isn d i c a t e
gollcctionsi.i foundfront the beginning
nongraphic
W h c t h c ly o u n gc h i l d r e rgt r o u po b j c c t so n t h e b a s i s
o f s i n r i i ai rt y i r l o n ct n o n e r a p h icco l l e cito n s) o r o n t l t e
basisof somc other critcrion, such as the objects'
j o i n tc o n t r i b u t i o nt so p l e a s i n sg p a t i acl o n f i g u r a t i o n s
( g r a p t r rcco l l e c t i o n s d
s e a ri l y u p o nt h e n a ) .e p e n d h
tule of thearraystheyget. Objectsthatcanbe solted
a t t h eb a s i cl e v e lo f c a t e g o l i z a t i oanr et v p i c a l l y a. n d
o f t e ns p o n t a n e o u s lsyo. r t c di n t oc o n s i s t e net .x h a u s objectsthatcan onlr be sortedat the
tive categorics:
level are not WhYl
superordinate
A s I n h e l c l earn d P i a g e (t 1 9 6 4 )c l a i n r e di.t c o u l d
is not fullt
be that the child's graspof classificatory
apfactors
extralogical
nrany
adequate.However.
pearto contributeto theeaseor ditTicultvu'ithwhich
t h e c h i l d b u i l d sh i e r a r c h i c acll a s s i f i c a t i o nlsn t h e
next sections.u,e discusssomeof thesefactors.
ConrpetingBehavioral Tendertcies. One possibility as to ',vhyyoungchildrendo poorly on hierby the *'ork of
archicalsorting tasksis suggested
R i c c i u t i .R i c c i u t i( 1 9 6 5 )t e s t e di n t a n t sb e t s e e nl 2
and 20 monthsof agewith a procedureverl' similar
to thatusedby Sugarman( I 979)andobtainedesserrtially the same results.He subsequentlyretested
subjectsrvhentheywere
someof his 2O-month-old
40 monthsold (Ricciuti& Johnson.1965).Not surprisingly.completespatialgroupingsofboth object
classeswere by then far more frequent.What was
surprising,however, was that children also producedgroupingsthatweredistinctlyillogicalfrom a
classificatorypoint of view. Thel' would. for ingroupings,eachcontainstance,form two separate
ing two objectsfrom eachclass.]r'loreover.the objects within each grouping would be anangedir,
such a way as to form, as Flavell (1970t put it.
"what looked suspiciouslylike a 3-year-old'sversion of an interestingdesignor pattern" (p. 993)
Ricciuti and Johnson's(1965) findings suggest
thatyoungchildrendevelop,aroundthe agesof 3 or
4. a tastefor interesting,novel configurations.lnsteadof simply groupingthe idenricalobjectsin an
anay in differentlocations.thechild combinesthem
in creative,fancifulways. Her groupingactivity,in
otherwords,is no longereovernedby a classificatory schemealone: other dispositionsor tendencies
competewith, and at timesprevent(as Ricciutiand
Johnsonhave shown), the formation of logical
c lassifications.
do prefer
Assumefor a momentthat 3-year-olds
to formingsymbuildingcreativedesignsor patterns
It seemsreasonable
metricallogicalclassifications.
the anay of
hetcrogeneous
to supposethat the morc
a
child
forming
of
greater
the
likelihood
objects,the
s o r u ei l l o g i c a lc o n f i g u r a t i oonr o t h e r .B o t h S u g a r n r a n( 1 9 7 9 )a n d R i c c i u t ia n d J o h n s o n( 1 9 6 5 )u s c d
an'avstl'latcontainedtwo differentclassesof identical objects Such arrays,it u'ould seenr.offer onll
linrited possibilitiesin the \\'ay of figural rrlasterpieces Were one to increasethe perceptual/r.ssinrilarity betrveenthe objects in the arra1" one
nrightexpectto find fewerand ferverlogicalclassifications.To put the matter differently,whether 3year-oldsgroupobjectstogetheron thebasisofcomor on the basisof theirjointcontriburnonattributes
tion to thecreationof pleasingspatialconfigurations
rnightdependon the natureof the objectsused Arrays that are composedof highly similar subsets
arrays commight elicit classificatoryresPonses;
posed of dissimilar objects. nright elicit varying
building responses.
that
RecallthatRoschet al.(1976)demonstrated
categoobjectsbelongingto the samesuperordinate
few perceptualattributesin comry tcnd to possess
mon to havehighly dissimilarshapes.Hence,a superordinatesortingtask confrontsthe young child
with perceptuallydissimilarobjects-the kind we
proposeas likely to elicit building as opposedto
Ifthis accounthasmerit' it
responses.
classificatory
to concludethartheyoungchild'swellis reasonable
documentedfailureto sort objectstaxonomicallyat
the superordinatelevel is due trot to an inadequate
graspofclassificatorylogic but rather,in part, to the
of compet(andcontinuedintervention),
emergence
ing behavioraldispositions(Bever, 1970).
One implicationof the precedingargumentis that
a reductionin the salienceof the perceptualcontrast
between objects would facilitate the production of
taxonomic sorts. Some suPPortfor this is provided
. h e ya s k e d3 , t a l . ( 1 9 8 1 )T
b y a s t u d yb y M a r k m a n e
and4-year-oldsto sort the samesetof objectstwice.
once on piecesof paperplacedon a table' and once
in transparentplastic bags The objectsto be sorted
fell into four superordinateclasses:furniture (kitchen chair,easychair, table,couch),vehicles(motorcycle,car, plane,truck),people(boy' woman,man'
fireman), and trees(evergreen,rust-coloredtrees' a
deciduoustree. and a tree with needlelikeleaves)
Markman et al. reasonedthat havin-ethe children
sort the objects into transparentbags that did not
readily allorv for spatialarrangementwould tend to
reducethe impact of perceptualand configurational
variables.The result would be to facilitate the forAs predicted,there
mationof Iogicalclassifications.
was a markedimprovementin both 3- and 4-yearolds' sortingwhenthey sortedinto plasticbags'The
authorsconcludedthat young childrenfail to sort
objectstaxonomicallyin part becausethey beconte
CONCEPTS
A R E V I E WO F S O M EP I A G E T I A N
d i s t r u c t cbc1l ' s p a t i avl l r i a b l e sa n d n o t b c c a u s et h e v
havc diff'clentprinciplesof classification.
CompetingHierarchical Organizatiotts. Until
no\\/.wc havc beenconcernedonly u,ith classifications based on rclations of similarity, assunring
(at'tcrlnhelderand Piaget,196,1)
thatclassifications
bascdon otherrelationswereprinritiveproductions
rr,hoseexistencewas due to the child's inadequate
graspof classificatorllogic. Recently,however.a
n u m b c ro f a u t h o r s( e g . N e l s o n . 1 9 7 8 ;M a n d l e r ,
1 9 7 9 ,s e c a l s o M a n d l e r .v o l I I I , c h a p . 7 . ) h a v e
the claim that the only, or eventhe most
challenged
rnrpor
tant,way in which our knowledgeis organized
ofclasses.Acis in termsofclassesand hierarchies
cordingto theseauthors,childrenand adultspossess
an alternativemode of conceptualorganizationone u,hich is basedon spatiotetnporalrelations.The
fundamentalunits in this type of organizationare not
categories
but schemas.The tendencyto use schenrasmight very well interferewith an ability to imposea classification
structureon the environment
psychology'suse of the concognitive
Modern
structsc/rerrais both like and unlike Piaget'suseof
s c h e m e .( S e e M a n d l e r , l 9 8 l ; M a n d l e r , v o l . I i l ,
of the differences.)
chap.7 for a detaileddiscussion
Both are takento be mental structuresthat organize
memory, perception.and action. However, for
Piaget,the emphasisis more on the logico-mathematical structures that underly and constrain
schemes.For schematheorists(e.g., Rumelhart,
1980,Rumelhart& Ortony, 1977,Schank& Abelson, 1977)the emphasisis more on the representations of everyday knowledge that are embodied in
the schemas-be they face schemas, restaurant
scriptsor gramnrarsfor folktales.Someevidencefor
inforyoungchildren'ssensitivityto spatiotemporal
mation . . . studiesof causalreasoningin young
children. Bullock and Gelman (1979) found that
children as youn-sas 3 selectas causethe event that
precedesratherthan the event that follows the effect
to be explained.Gelman, et al. (1980) also found
with picturesof
thatyoungchildren,whenpresented
an object and an instrument,have no difficulty selectinga third picturedepictingthe outcomeof applying the instrumentto the object.Theseand other
similar findings (see Bullock, Gelman, &
Baillargeon.1982,for a revierv)sugSestthat childrendevclopcausalschemasthat faithfully portray
the sequencingof eventsin causalsequencesand
can be appliedto
thatspecifyu,hattransformations
objectsand rvith what effects
A secondsourceof evidencethat children can
structure
detectand nrake use of temporal/spatial
conresfiom studiesthatexaminechildren'sdescrip-
201
t i o n s o l ' e v e n t s e q u e n c e sF o r e x a m p l e .N e l s o n
( 1 9 7 8 )a n a t y z e p
d r e s c h o o l e rdse' s c r i p t i o nosf s u c h
event sequcnces
as eatingdinner at home. havin,g
lunchat a daycarecerlter,andeatincat MacDonald's
restaurantShe found that the children generally
asreedon ivherethe sequencestanedand stopped
andon the order in which eventstook place To do
this. childrenrnusthave beenable to keeptrackof
e\/entorder. This conclusionwould seem to go
l f
a g a i n sPt i a g e t ' s( 1 9 5 9 )q , o r ko n c h i l d r e n ' sr e c a l o
stories.Piaget(1959)reportedthat his young subjects were very poor at maintainin-s
the conect sequenceof eventswhenretellingstories.As N'landler
(1981)pointedout, however,Piaget'ssubjectsmay
have had difficulty keeping track of sequencebecausethe storiesused were poorly motivatedand
When 5- and6-year-olds
hearstopoorlystructured.
riesthat containclearand temporalandcausalconnections,they have no troubleretellingthem correctly (e.g , Mandler & Johnson,1977; Stein &
Glenn,1979).
The existenceof an alternativemodeof concepspatialand
tual organization,one that emphasizes
temporalrelations,may well serveasanotherreason
why youngchildrenfail to producetaxbnonticclassifications.Recall,for example,the representative
constructions
Inhelderand Piaget(1964) obtained
(e.g., a train station);such productionscan be attributedto the child's use of an altemativemodeof
organizationratherthan to a fundamentalinability to
grasphierarchicalrelationsbetweenobjects.Some
support for this interpretationcomes from Smiley
and Brown (19'79),who found that preferencesfor
sortingmaterialsinto thematicor taxonomicgroupings shou,eda curvilinearrelationshipacrossage.
Younger children and older adults preferredthematic categories.It seemsreasonableto suPposethat
what is changingis not the ability to classifyobjects
logicallybut ratherthe choiceof a basisto usein a
taskthatallowsfor morethanonepossibleorganization. In otherwords, young children'stendencyto
producethematicgroupingsmay be due to in part to
their greaterpreferencefor organizationsthat rely on
spatialor temporalrelations(Markman, 1981).
In a u,ay, the two previousalternativeaccounts
regardingthe failure of a roung child to classify
reduceto one, that is, that the child's figural and
thematicconstructionsboth reflecta preferencefor a
part-wholeorganizationas opposedto a classorsanization (llarkman & Siebert, 1976). When the
objects,
youngchild is presentedwith nreaningless
such as building blocks and geometricshapes.he
usesthemto build creativedesignsor configurations
( e . g . , D e n n e y , 1 9 7 2 aI;n h e l d e ra n d P i a g e t ,1 9 6 4 ;
202
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
with
R i c c i u t i & J o h n s o n ,1 9 6 5 ) ;w h e n p r e s e n t e d
toyor
real
objects
as
such
moremeaningfulstimuli,
situaand
scenes
constructed
he
sizereproductions,
&
tions with which he is familiar 1eg" lnhelder
prervhen
and
Piaget,1964;Markmanet al ' l98l)l
senledwith verbalitemsandaskedaboutsimilarities
and differencesamong them' the 1'oungchild relates
or
the iten.rsin terms of a story that niay be inspired
part to
relationbetweenelementand totality is one of
subclass
or
to
class
member
class
whole ratherthan
to class.
in thiscontext'to considerMarkIt is interesting,
Rem a n ' s( e . g . , 1 9 7 3 a ,1 9 8 0 )w o r k o n c o l l e c t i o n s '
collective
of
referents
call that collections are the
their
sron.Finally. becauseof thesedifferencesin
to
expected
nright
be
collections
internalstructure,
have greaterpsychologicalstability'or coherence'
That is' it shouldbe simplerto corlceprhanclasses.
do
tualizccollectionsas organizedtotalitiesthan to
an
in
rvholes
only
are
classes
all,
After
soforclasses.
empirical'
are
collections
contrast,
ln
scnse
abstract
by specfinitc setsof elementsthatarecharacterized
to one another'
ifiablerelationships
chilAccordingto lnhelder and Piaget(1964)'
8
until
test
class-inclusion
the
pass
to
drenareunable
requisite
the
lack
they
because
age
of
years
or 9
lnsteadof comparingthesuperconcreteoperations.
(flowersandpeordinateclassto its largersubclass
the two
comPare
tunias),young children typically
andSie'
Markman
daisies)
and
(petunias
subclasses
the superbert ( 1976)suggestedthat this is because
oncett
coherence
psychological
Iacks
class
ordinate
have
collections
is divided into its subclasseslf
then
classes'
than
ereaterpsychologicalcoherence
in
whole
the
keep
to
able
better
lnitOr"n should be
thus'
and'
subparts
its
to
attending
nrind while
comparshouldperform betteron tasksthat requlre
Ir4arking the whole to its subparts Accordingly'
first-grade
and
min and Siebert gave kindergarten
children two different versions of the Piagetian
task.Only childrenwho faileda preclass-inclusion
are kinds of bouquetsor that they are instancesof
questionwas'
modeledafter the standardPiagetian
someone
with'
play
"Who would have more toys to
orvned
who
someone
or
who owned the blue blocks
quescollection
the
on
the blocks?" Performance
standard
the
on
that
to
superior
tions was reliably
relatedto eachother' For petuniasto form a bouquet'
for trees to form a forest, they must be in close
a
spatial proximity; for children and adults to form
biological/
family, they must be related by some
pur.niing bond. To determinemembershipin a.colIection, then, one must considerthe propertiesindi-
answerconectly.
structure
These resultsshow that the part-whole
uPonor
operate
to
children
for
easier
of collectionsis
CONCEPTS
A R E V I E WO F S O M EP I A G E T I A N
rcason with than the class-inclusionstructureof
c l a s s e sR. e c e n t l yN
, 4 a r k m aent a l ( 1 9 8 0 )h a v es u g gcstedthatpart-wholestructuresmi_sht
be easierfor
childrento fornr as well. If part-wholerelationsdo
reflecta psychologicallysimpler principleof hierarchicalorganization,then one might expectthat
children left relatively free to impose their own
structureon a novelhierarchyrvouldconstructa collectionratherthan a classhierarchl,.
To test this hypothesis.Markman et al. (1980)
taught subjects(aged 6 to l7 years) novel classinclusionhierarchiesFour categories(eachcomposedof two subcategories)
wereconstructed.
Nonsensesyllableswere usedto refer to the four categoriesandeightsubcategoriesChildrenin eachofthe
four agegroupswereassignedto one of two training
conditions,6stensionand inclusion.For childrenin
the ostensioncondition, the experimentersimply
pointedto andlabeledthe entirecategoryandeachof
(membersofeachsubcategory
thetwo subcategories
were grouped together, and the two subcategories
wereplaceda few inchesapart).Trainingcontinued
until subjectswere able to provide all three correct
labels. Children in the inclusion condition rvent
as
throughthesamepointingandlabelingprocedure
did children in the ostensioncondition. The only
differencewas that they were given additionalinformation about category membership. That is, they
weretold: "A's area kind of C"; "B's area kind of
C " ; a n d " A ' s a n dB ' s a r e t w o k i n d s o f C ' s "( w h e r e ,
obviously.A and B arethe labelsof thetwo subordinate categoriesthat comprise the categoryC). This
information was given immediately after the Iabeling and pointing.
Childrenin both conditionswere testedwith rhe
exact sameprocedure.Each child was askedquestions aboutan entire category(C) and its subcategories (A and B). For the entire category,the questions
were: "Show me a C"; "Put a C in the envelope";
"ls this a C?" (pointingto an A); and "ls thisa Cl)"
(pointingto a B). For the subcategories
the questions
were: "Show me an A"; "Put an A in the envelope"; "ls thisa B?" (pointingto an A); and "ls this
a B?" (pointingto a B). It wasexpectedthatchildren
in the inclusioncondition, who were given classinclusioninformation,would achieveclass-inclusion interpretations
of the material.In contrast.it
was predictedthat children in the ostensioncondition, who receivedminimal informationaboutthe
hierarchicalrelation,might (enoneously)imposea
part-wholecollectionorganizationupon it. The resultsconfirmedthe predictions.Subjectsin the inclusionconditioncorrectlyinterpreted
therelationas
onc ofclassinclusion.Subiectsin theostension
con-
203
dition nristakenlyinrposeda collectionstructureon
the inclusionhierarchiesChildrcnasold as l4 vears
of agcdeniedthatany singleelemcnt(A or B) rvasa
C andpickedup severalelementswhenaskedfor a C
or when askedto put a C in an envelope.
Theseresultsareespeciallysurprisingrvhenone
considersthat plural labelswere usedduringtraining, for example, "These are A's." "These are
''These
''
B's."
a r eC ' s
A n d s i n g u l a rl a b e l sw e r e
usedduringtesting,for example,"Show me a C."
(this is analogousto sa)ing, e.g., "These are pe"These are daisies." "These are
tunias"
on
flowers.") To imposea part-wholeorganization
igthe hierarchy,the subjecthad to systematically
nore the cuesprovidedb1'the syntax.
The fact that the l4-i,ear-oldsin the Markmanet
and enoneouslyimal. (1980)studyspontaneously
poseda part-wholeorganizationon the novel hierarchiesthey were taught certainly refutesany suggestionthattheyoungchild'sclassifications
reflecta
qualitativelydistinct,more primitiveoonceptual
organizationthat is basedon part-wholerelationsand
is replacedin time by an adult-typeconceptualorganization.Instead,it appearsthat both the collection
and class modes of hierarchicalorganizationare
availablefrom a very early age. Becausethe partsintwhole modeof organizationis psychologically
pler, it is the prefened mode of organization--one
alike will imposewhen
thatchildrenandadolescents
call for a classthesituationdoesnot unambiguously
inclusionhierarchy.Thus, theyoungchild'stendency to groupelementsinto wholes-stories, pattems,
or scenes-rather than class-inclusionhierarchies,
might be interpretedas indicativeof a systematicand
enduring preferencefor part-whole organizations.
This preferencemight be rooted in the psychological
characteristicsof this type of organization.that is,
the fact that it appearsto be easierto oPerateon, to
conceptualize,
to establish,and so on.
We are not suggestingthat very young children
arejust asgood asteenagersat solving problemsthat
involve part-wholeor class-inclusionhierarchies
Clearly,the older childrenwill be superioron most
tasks.What we are suggesting,though,is thatboth
types of organizationare available to younger and
older children and that all children may find it easier
to, and may preferto, imposepart-wholeasopposed
to class-inclusion
structureson hierarchies.Thus,
whateverdevelopmentthere is in termsof establishing, maintaining.and operatingon eachtypeof organization,would take place over a considerable
amountof time, and possiblywould representimprovementsin degreeratherthan kind.
Finding a Basisfor Classification. Why do
204
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
young childrenadhereto a criterion \\'hensortins
levell
objcctsat thc basicbut not at thesuperordinate
offeredaboveis thatthereis greater
Oneexplanation
perceptual
dissimilarityamongmembersof superorthananlongmembersof basiccatedinatecategories
gories(Roschet al , 1976) As the child takesin the
different propertiesof the objects before him. his
attentionswaysaway from the propertyinitiallyseand is capturedfirst
lectedasbasisfor classification
propertl', and so
by
anothcr
then
by one property.
on. In short, the child keepsswitchingcriteria ln
addition,young childrenmight fail to groupobjects
accordingto a consistentcriterionat the superordinate level, /?o,becausethey are incapableof adhering to the samecriterionthroughouttheirclassification, but becausethey areincapableof uncoveringa
criterionthat could serveas basisfor classification
By this account,the young child's failureto group
levelis due
at the suPerordinate
,objectsconsistently
up with a
in
coming
to the child's havingdifficulty
to sysunable
being
to
his
criterion-not
satisfactory
tematicallyappll' the criterionselected.This explathat once children haveselected
nation presupposes
or hit upon a criterionby which to classifyobjects.
Giventhis
theyalwaysknou'to applyit consistently.
groupings
are
haphazard
or
inconsistent
assumption,
naturally interpreted as reflecting the child's inability to discoverin the array before him a basisfor
of
bcennrainlyconcernedhave all beencategories
concreteobjects.But thesameargument
rcal-ri,orld,
regardingthe criterionselectedcouldbe extendedto
categoriesof blocks that vaD' along a numberof
dinrensionsFor instance,one might say that the
greaterthe nunrberof dimensionsthat must be ignored.the lessobviousor salientthebasisfor classificationand the more difficult the task. Panialsupport for this hypothesiscomes from traditional
experinientsthat have shorrnthat
concept-learning
the
addinginelevantstimulusdimensionsincreases
(Haygood
&
Stevendifficultyof learningfor adults
s o n .1 9 6 7 ; W a l k e r &B o u r n e ,l 9 6 l ) a n df o r n u r s e r y children (Osler &
school and elementary-school
K o f s k y ,1 9 6 5 )
Additional suPport for the above hypothesis
comes from Fischerand Roberts (1980) ttho aschildrenbetweenl5 and 75 monthsofage on
sessed
a developmentalsequenceof classificatonskills.
The sequencewas predictedfrom Fischer's( 1980)
skill theory.A totalof l2 distinctstepsweredifferentiatedand over 95Voof the childrentestedfit the
sequenceperfectly. Becausethe first 4 stepsof the
sequenceare the most relevantto our argument,we
exclusivell'ri'iththese.It \\ asPrewill beconcerned
dictedthat b)' l5 monthsof age childrenuould be
ableto handlesinglecategories(Step1), Whenpresentedwith blocksthat variedalonga singledimension(e.g., shape),childrenwould grouptogetherall
classification.
the blocks that belongedto the samecategory.For
rvould
have
It is easyto seewhy the young child
example, they would pick circles from triangles
criteria
up
with
satisfactory
little difficulty coming
when the blocks were all the same color and size
on when presentedwith objectsthat mustbe sortedat
(recall Sugarman's[19?9] finding that l8-monththe basic, as opposed to the suPerordinate,level.
olds will producecompletespatialgrouPingsof one
Children can group objectsinto basic categoriesacof the two classesin an arrav). At about2 lears of
cordingto any or all of a numberof criteria:shape.
age, children were expected to be able to handle
and
their
use,
in
programs
involved
function, motor
(Step2). For exseveralcategoriessimultaneously
as
easily
found
is
for
classification
A
basis
on.
so
in
Step I' children
those
ample, with blocks like
se'reralare availableand becausethe overall physitricategories----circles,
three
into
blocks
would sort
cal sinrilarityof membersof the samebasiccategory
(again,
Sugarman's
recall
squares
and
ansles.
is usuallyvery salient.The child who is presented
classes
I I 9?9] findingsthatby 24 monthsof ageboth
with an array containingobjectsthat belongto (two
At2ti: years.
grouped)
were
spatially
array
the
in
faced
is,
thus,
categories
different
basic
or three)
childrenwere expectedto sort blocks into threecatewith highly contrastingsubsetsof objectsthat have
gories,even if therewere variationswithin eachof
clear-cutboundaries.It is not difficult
perceptually
the categories.For example.differenttypesof trifor the child to identify the instancesof eachbasic
angles.circles.andsquaresmight makeup thethree
to
be
in the array.Thesetend
categoq,represented
(Step3). Finally.by 3 or 3 /r yearsof age'
categories
of
seParate
a
number
along
sinrilarto one another
the child was expectedto handle not onl\ simple
of
as well asdifferentfrom theinstances
dimensions
rvherethere\\ erevarlthe othercategoriesOn all thesecounts.it appears categoriesbut alsocategories
That is, u henthe
dimension.
interfering
ationson an
thatit rvouldbe easyfor thechild to selecta basisfor
simultaneousll'
shape
and
color
varied
in
both
blocks
andto carryout the groupingof basicclassification
as tn
variations
(but
within-category
no
presented
levcl objectsconsistentlyand exhaustivelv.
sort
-[he
to
able
Step3). thechild wasstill expectedto be
with whichwe have
categories
supcrordinate
CONCEPTS
A R E V I E WO F S O M EP I A G E T I A N
andthen subdivide
thenrinto threeshapccategorics
eachcate-9ory
into threccolor categories(Stcp 4).
Fischerand Roberts'(1980) subjectswere 70
childrenbetweentheagesof l5 and7-5months Each
of the four tasksrequiredthechild to sortblocksinto
(oneor rnorc)boxes Boxeswere usedto ntinimize
and to make the nathe needfor vcrbal instructions
tureof thetaskasobviousandassinrpleas possible.
A separatebox rvasusedfor eachcatesorv For tasks
thatinvolvedtwo or threecategoriesidenticalboxes
wereanangedin a line beforethe child.
how the
The experimenterfilst dernonstrated
blockswere to be sortedand describedhow he had
sortedthem. Then, he put them in a scrambledpile
before the child and said. "Put the blocks in the
boxesso they go togetherlike the rvay I put them
in " If the child ered in sortingthe blocks,the experirnenter
re-sortedthem correctll'andthen urged
the child Io try a secondtime (cf. Nash & Gelman
citedin Gelman& Gallistel.1978) After the second
wenton to the next task For
trial, the experinrenter
everystep,the child had to sort a// blocksconectly
to passthe step.
profilesof all70 childrenfit the
The performance
hypothesized
sequenceperfectly.The resultsfrom
later
this and a secondexperiment(which assessed
steps in the sequencepredictedfrom skill theory)
skillsin
indicatethat childrenacquireclassificatory
a gradualsequencethatstartsby t 5 monthsof age(if
notbefore).TheseresultsclearlycontradictInhelder
(1964)analysisof the developmentof
and Pia-set's
Otherattemptsat testingthe sequence
classification.
Inhelderand Piagetproposed(e.g.. Hooper et al.,
1979;Kofsky, 1966)havealsofailed to supportit.
However. the Iatterstudiesdid repon the samegeneral trend from poor, inconsistentclassificationto
skilled, consistentclassificationthat Inhelderand
Piagetfound. FischerandRoberts'( I 980) resultsare
particularlyinterestingin that ther indicate that
young preschool children possessfar more classificatoryability than the resultsof previousstudies
(whether or not they found the developmentalpatternpredictedby Inhelder& Piaget, 1964)led one to
expect.FischerandRoberts.( 1980)alsoshow-and
this is the point we wishedto make-that this ability
is somewhatdependenton the panicular anay of
objectswith which the child is presented.At first,
the child can only sort arraysthat arecomposedof
variationsalongonly
singlecategories
thatrepresent
one dimension.that is. the blocksare identicalexceptfor variationsin one dimension.suchas shape.
Lateron. the child cansortanaysinto singlecategoriesand ignoreinelevantvariationsrr ithin eachcat-
205
cgory. for cxample,dift-erentt1'pesof circles, tria n g l e s ,o r s q u a r e sL. a t e r s t i l l . t h e c h i l d b e c o m e s
of objects
able( I ) to tacklearraysthatarecontposed
that vary along two dimensionsand (2) to divide
them first accordingto one diruensionand then to
subdividethem accordingto the other dimension
It is hard to believethat the child learnsanew at
each stepof the sequencehow to sort objectsinto
consistent,exhaustiveclassesOn groundsof parsimonyalone.one would rvantto rejectsuchan assumption.Instead,one nrightsuggestthatthe child
quite well that one shouldsort accordunderstands
criterionanddoesso from
ing to a stable,consistent
the earliestages. What would changeover time.
then. is not the abilitl' to adhereto a criterion
but the ability to parse
throughouta classificatron,
more and morecomplexarrays-to uncoveramidst
the complexitya criterionor a set of criteriathat
would permit the child to sort lhe anay rvithoutremainderand without overlap
In other words,one might sa1'that the ability to
classesis thereverl'
exhaustive
constructconsistent,
earlyon andthatwhat improvesin time is theability
to moreandmorecomplex
to applythis competence
arrays.Anays that containobjectsthat vary simul(somereletaneouslyalonga numberof dimensions
vant, some inelevant) require more complex processing than do arrays that are composedof two
types of very distinct objects (such as thoseSugarman, i979, andRicciuti, 1965,used).The natureof
the psychologicalprocessesinvolved in the abstracin simplerand more
tion of a basisfor classification
complexanays still remainsto be specified.Once
we have some idea of the natureof theseProcesses
and how they developover time. we may have a
much betteridea of the natureof the young child's
difficulty with superordinatesortingtasks.
At this point, one might make the following
claim. If it is correct to assumethat a child aitval's
appliesa criterion consistentlyonce she has succeededin uncoveringir. then wererveto show or tell
the child what the criterionis, she shouldhave no
of thecategory
difficulty in pickingout theinstances
anddoingso consistentll.However.this strongprediction of the hypothesisis not borne out by the
facts. First, modelinga classificationis not sufficient to get a child to classifyobjectsconectly ln
Fischerand Roberts'(1980)experiment'theexperimenterfirst sortedthe objectsand then had the child
do the same.The childrencould not alwars sort the
blocks as the experimenterhad: they followed a
clear-cutdevelopmentalsequencein terms of the
they could imitate Thus. more is inclassifications
ZUO
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
volvcd than just the ability to use a criterion
consisrently.
Horton and Markman (1980)provideadditional
thecriterionis, is
evidencethattellingthechild
"vhat
not necessarilyhelpful to the child. Horton and
Markrnaninvestigated4-, 5-. and 6-year-olds'acThey found
quisitionof artificialanimalcatesories.
that ( I ) basic-levelcategoriesrvereacquired nrore
easill, than superordinatecategoriesfrom exposure
of thecriteto exemplarsalone;(2) the specification
rial featureswas beneficialfor the acquisitionof
thatis, basic-level
categories.
only rhesuperordinate
rvhen
criteriawere
were
not
learned
better
categories
specified;and (3) only the olderchildrenbenefited
from the specificationof the criteria, and then only
when learning superordinatecategories(this is the
The
resultthatis relevantto thepresentdiscussion).
4-year-oldchildren did not benefitfrom the specifilevel. In concationof criteriaat the superordinate
trast, both the 5- and the 6-year-oldchildrenwere
better able to learn superordinatecategorieswhen
the criteria were specified
Given that criterial informationcan be helpful in
the acquisitionof superordinatecate-eories-asthe
older 6hildren's performance demonstrates-why
the failure of younger children to use it? Horton and
Marknran( 1980)rule out a failure in understanding.
Children could understandthe descriptionsand
could sort objectsbasedon eachindividual criterion
when so instructed Horton and Markman arguethat
the informationprocessingdemandsof the taskwere
too great.In addition, it could havebeen a question
of poor strategicskills. There aremany instancesin
the literaturewhere young childrenfail to make use
of informationor skills thatare at their disposal.The
rehearsalliterature is a particularly good case in
point (e.g., Flavell & Wellman. 1977). There is
someevidencethat the samemight be going on here.
to
For instance,Anglin (1977)askedpreschoolers
define common nouns and later to classify objects
into categoriesdenotedby the terms they had been
asked to define. Anglin reportsthat when classifying, thechildrenoftenfailedto usetheir own definitions for the categorizationof the objects.
Factual Knowledge and Classification Abilities. Above we argued that the child may have
difficulty forming superordinatecategoriesbecause
is abstractand not immethe basisfor classification
diatell,accessibleto the young child. However, in
somecasesit may be the featuresthat characterizea
not because
hi-qherordercategoryare inaccessible,
they areabstractand difficult to discernbut because
or relethe child has not yet acquiredthe necessary
vant knowledge to appreciatetheir significance
Chi's (1980) study of preschoolersrvho are interestedin dinosaursmakesthis point.The more a
child knows about dinosaurs,the more complex a
classification
schemereflectedin his recall of the
namesof dinosaurs Carey's (1978) rvork on childrens' conceptof "animal" helps illustratehow
there could be an interactionbeNveenknowledge
and the useof a classificationstructure.
Careyhasdonea seriesof studieson thedevelopnlent (from 4 to 7 years)of the understandingof the
In
conceptof animal(Carey, 1978;in preparation).
rvitha number
thesestudies.childrenwerepresented
of animateandinanimateobjects,somefamiliarand
someunfamiliar.For exanrple,childrenwereshown
picturesof a person,a dog, an aardvark,a dodo, a
a fly, a worn, an orchid,a baobab,
hammerhead.
thesun,clouds,a bus,a harvestingmachine,a garlic
press,a hammer, and a rolltop desk. They were
askedseveralquestionsabout each picture Some
questionsinvolvedpropertiesofthe particularobject
("ls the sun hot?"); othersinvolvedpropeniesof
of an object("Does a
an immediatesuperordinate
live in water?"), or propertiesof anihammerhead
of living
mals("Does a worrn eat?"), or proPerties
things("Does a dodo grow?"). The animalproperties probed were, eats, breathes.has a heart, has
bones,sleeps,thinks,andhasbabiesThe properties
of living thingswere, is alive. grou's,and dies.
Animals that adults take as more peripheralexemplars of the class were systematicallyassigned
fewer animalcharacteristicsby the children In addition, there u'as a marked absenceof a clear differentiation among animal properties. Thus, Carey
found a stable ordering of the animals in terms of
how often they were attributed animal properties.
Roughly, this ordering was: people, mammals,
birds, insects, fish, and worrns. Even though the
most peripheralanimalswere creditedwith a particular animal property only 20Voto 407oof the time,
each child credited every animal u'ith at least one
animalproperty.That is, theorderingof the animals
does not seemto reflect some children's failure to
appreciatethat the peripheralanimalswere animals.
Although the animals were ordered.the properties
were not Subjects were no more likely to credit
animalswith eating than with havingbonesor thinking. Adults. on the contrary, attribute eating,
breathing,andhavingbabiesto allanimals,sleeping
and having heartsto fewer, having bonesto fewer
still,andthinkingto fewestofall. Thus,4- to 7-yearolds were likely to attributeonly oneor two animal
propertiesto the peripheralanimals.but thoseproperties were just as likely to be having bonesand
thinking as eating and having babies.The animal
A REVIEWOF SOME PIAGETIANCONCEPTS
propefiiesclearly were not differentiatedfrorn each
other in rhesubjccts'patrernsof responses.
Careytakesher resulrro suggesrthar the child's
concept of animal is enrbeddedin a very im_
poverished biological theory This follows from
both the rendenciesto underattributeanimal DroDerties to penpheralcasesof animalsand not todiiferentiateanimalpropertiesfrom eachother. We apree
with Carey'sinterpretation.
But more importanlin
thiscontext,her findingshaveconsiderable
implica.
tions for rhe way young children will behaveor,
classificarion
tasks.
If peripheralanimalsare not known to have a
heart, they presumablyu,ill not be classifiedto_
getherwirh animalswho areknown to have a heart.
Similarly. if childrendo nor know that not all ani_
mals havebones,they mal,endup classifyingitems
togetherthat they should not Children's erroneous
classifications
might be takenas evidenceof an in,,has_
ability to applycriteria(e._e.,.,has-a-heart,',
problems u,as virtually perfect at all ages tested.
Performanceon the superordinatelevel problems
was significanrlyworse,especiallyin the youngest
agegroup.Srill, the 3-year-olds,
meancorrectDer_
centase was 55Vo and the 4-year-olds' was 96Vo
Thesedatasuggestthatchildrenfind it easierto son
Itemsthat belongin the samebasic,as opposedto
superordinate,category-nor that they are funda_
mentallyunableto perform the latterkind of task.
Daehler.Lonardo, and Bukatko (1979) exam_
ined rhe difficulty very young children have in
matchingstimuli at severallevelsof perceptual
and
conceptualsimilarity. Four different types of rela_
tionshipsbetweenstimuli were tested:(l) identical
stimuli,(2) stimulibelongingto the samebasiccate_
gory, (3) stimuli belonging to the samesuperordi_
natecategory,and finally (4) stimulibearinsa com_
plementaryrelation to one anotherie.g.,-crayon_
coloringbook,hammer-nail).Subjectsrverel6 chil_
d r e na t e a c ho f 3 a g el e v e l s2 l t o 2 2 , 2 7 r o2 g , a n d3 l
bones") consistentlyBut, in fact, thiswould reflect
to 33 months.Stimuliconsisted
of realobiectsor tov
children'signoranceof biologicalfactsratherthan
objects.The exemplarsfor eachbasic-leu.l..t.go.y
an inabilityro maintaina hierarchical
classification
differed in sizeand color and, wherepossible,detail
scheme.
and shapeaswell. Stimuli were neverlabeledduring
We haveexplored a numberof reasonswhv the
testtrials; the experimentersimply held out the stanl
young child has difficulty sorring arrays thai are
dard to the child and instructedher to ..find the one
composedof objects that can only be sorted at the
(of four choices)thatgoeswith thisone.,' Any child
superordinatelevel. We havearguedrhatdespitehis
who failed to respondto the experimenter'sinstruc_
poor performancein superordinate
sortingtasks,the
tions was led to the table as the instructionswere
young child doespossess(ar leastsomeofl the rele_
repeated.A responsewas recorded whenever the
vant logical abilities.Actually, we believethereis
subject placed rhe standardbesideone of the four
enoughevidencein theyounechild of a capacityfor
alternativesor touchedor picked one of the alterna_
hierarchicalorganizationto su_sgest
that what needs
tives. Correctresponseswere verballyreinforced.If
explaining is the fact rhat this ability is not always
the child made an error, she was askedro respond
displayed-rather than rhe fact thar ir is not disagain. If she were still not correct, the correct replayed at all. This argumenrwas used to inrerpret
sponsewas modeled.At the completionof eachtri_
results from a variety of free-classificationstudies
al, the conect responsealternativewas removed,a
with preschoolers(e.g., Denney, 1972a, 1972b:
new item was added,and all four stimuli in the array
Fischer & Roberts, 1980; Nash & Gelman cited in
were rearranged.Thus, all stimuli in the arraywere
Gelman& Gallistel,1978).ft is buuressedby stud_
eventually relevant. Becausechildren *ere inuariies that usedsimplified classificationrasksas well as
ably attractedto eachnew item, they wereallowedto
memory studies.
play with it briefly as prior restingindicaredthat the
opportunity to becomefamiliar with eachnew item
before a trial helped reduce a substantialresponse
bias for selectingit on the subsequenrtrial. There
were 6 distinct trials for each rype of relationship
examined(24 altogether)
of elementsbelongto the samecaregory.
The results were straightforwafd. performance
We havealreadypresenred
oddity,datarhatsup_
improved with age in every condition. Moreover,
port the norionthat young childrenaresensitive
to,
the order of difficulty of conditions for each age
and can pair items on the basisof. superordinate group
was consistent-identity matchesrvereeasi_
relations.Recallthe studyofRosch et al. (1976)in
est, followed by basic-level,superordinate
level,
which children3 yearsof ageand olderwere qiven
andcomplemenrary
matches.Finally,childrenin all
oddity problems.performanceon rhe basic-'ievel
age groupsrespondedabovechancelevel in all four
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
acc
conditions.\\'ith thc exccptionof the youn-qest
group nriltchingconrplenlentar\stimuli. The fact
to superordithatpcrfornrance
on stiruulibelongin-e
rvasir ell abovechanceat
natetaxonomiccategories
all asesagainsuggests
thatfrom a very earlyage(in
this caselessthan2 years)childrenareableto detect
and rnakeuseof superordinate
reiations.However,
the equivalences
selectedby Daehlerand his colleagues( 1979)do lend themselves
to alternativeinpairswerecamelterpretations.
Their superordinate
cow. fork-spoon. boat-truck.apple-banana,and
panls-shirt.The underlinedpairsappearespecially
ambiguousas they represent
itemsthatthe child. no
doubt. nrust have had ample opportunitiesto see
togetherand so the basisof his nratching,or equivalencejudgment.is unclear.
Adults are better at rememberingwords from
lists that containsubsetsfronr the sametaxonomic
lists
categories
thanwordsfrom randomlygenerated
( e . g . ,C o f e r ,B r u c e ,& R e i c h e r 1
. 9 6 6 ) I. n a d d i t i o n ,
if the wordsthat aretaxonomicallyrelatedareseparatedin the list, adultstendto clusterthemby meani n g i n o u t p u t( e . g . , B o u s f i e l d .1 9 5 3 ) .I t h a s b e e n
reportedthat young childrendo not rememberwords
from lists with taxonomicallyrelatedsubsetsbetter
than words from unrelatedlists (e.g., Hasher &
Clifton, 1974;Nelson, 1969).In addition,the degree of clustering has been found to increasewith
age, from grade school through college (e.g.,
Bousfield,Esterson,& Whitmarsh,1958;Neimark,
Slotnick, & Ulrich, i971). The preschooler'salleged inability to detect and benefit from the hierarchicalorganizationof to-be-remembered
lists has
been thought to reveal a fundamentalinability to
appreciateor impose hierarchicalrelationson stimuli. Such conclusions, however. are beginning to
look unwananted(Huttenlocher& Lui, I979).
There is now evidencethat young children are
better at remembering items that are all from the
sametaxonomiccategorythanitemsthat areunrelated (e.g.,Cole,Frankel,& Sharp.l97l; Kobasigawa
& On, 1973).In the studyof Kobasigawaand On
(1973), for example, kindergarten subjects were
presentedwith 16 pictures in four category sets
(e.g., animals: zebra, lion, camel, and elephant;
vegetables:corn, onion, carrot, and pumpkin); or in
a random order with one item from each category
composing the four presentationsets. The categorically groupedpresentationfacilitatedfree-recall
performance,both in terms of number of items recalledandthe speedwith which items'wererecalled;
it also increasedthe amountof clusteringin recall.
Even 2-year-oldshavebeenfound to recall pairs
of objectsbetterwhen they are from the same,rather
than fronrdifferent,cateeoriesGoldbcrg.Perlnrutter, and Myers ( 1974)testedchildrenaged29 to 3-5
monthson a task requiringfree recallof trvo-itenr
lists Each of the threetrials consistedof the randomly orderedpresentation
of six boxes.eachcontaininga pair of objectsselectedfrom threecategories(food, animals,and utensils).For threeof these
pairs. the objectsbelongedto the sametaxonomic
category (e.g.. cookie-lollipop;elephant-_eiraffe:
fork-spoon).The threeremainingpairsrverefornred
of unrelateditems from the samecategories(e 9.,
M&M's-lion; apple-cup;dog-plate).(Pilot u'ork
showedthatlabelswerereadilyproducedfor all picturesand that althoughfork and spoonwereassociated responsesfor a few children, none of the other
items were given in responseto each other.) The
mean number of correct responseswas higher for
relateditemsthan for unrelateditems.
Additionalevidencethat youngchildrenimpose
hierarchical
organization
on objectsis Keil's (1977,
1979)findingthata hierarchical
structure
constrains
thedevelopment
of ontologicalknowledgeKeil had
judgmentsof whatpredchildrenmakeacceptability
icatescouldbe trueaboutcertainobjectsandevents.
Over and over againhe found children'sjudgments
reflectedan underlyinghierarchicalstructure.Thus,
for example,they failed to assignanimatepredicates
to inanimate objects and vice versa. Such results
indicatethatyoung childrencan makeimplicit useof
a hierarchicalclassification scheme. They do not
demonstrateexplicit use of the same structure-a
point to which we will return below.
Class Inclusion Revisited
For Inhelder and Piaget (1964), complete mastery of hierarchicalclassificationis indexedby the
mastery of the inclusion relation, and it is not attained until the stage of concreteoperations.The
preoperationalchild is incapableof class inclusion
becauseshe lacks the two reversibleoperationsof
classaddition(e.g., flowers= petunias+ begonias)
and class subtraction (petunias = flowers - begonias).Until sheacquiresthesetwo operations.the
to the class
child is unableto attendsimultaneously
and is, thus, incapableof making
and its subclasses
(e.g., "Are
quantitative
comparisons
class-subclass
there more flowers or more petunias?").
We do not believe that class-inclusiontests
shouldbe takenascriterial measuresof the ability to
classifyobjectshierarchically.Masteryof the classis a relainclusionrelation,with all its implications,
tively late development(Winer, 1980);hierarchical
classification,by contrast,emergesin the first few
yearsof life. We have seenevidenceof hierarchical
A H E V I E WO F S O M EP I A G E T I A N
CONCEPTS
o r g a n i z a t i o inn t h e 2 - y e a r - o i d ' s r o u p i n s o f o b jects-in his correctusageof supcrordinatcternts. in
209
D o e sa h a v et o b c a X l " ( r v l t e r_c
was
a realrvordchildrendid not know). Thcrewcrethree
his free recall perfornrance,and so on As nrorc
types of problenis.dcpendingon rvhethcrrhe iningeniousmethodsof investigatina
the prelineuistic
i.erences,asvalid (e g , "A pue is a kind of do_e
child'scognitionandknowledgearedeveloped.
D o c sa p u e h a v et o b e a n a n i m a l ? " ) :i n d e t e r m i n a t e
orre
nray find that evenyoungerchildrenare capableol
( . . 9 . , " A p u gi s a n a n i m a D
l . o e s a d u p l e x h arroeb e
constructingsirrrple,well-formedhierarchies
a f e n c e ? " ) ;o r i n v a l i d( c . g , " A p u e i s a n a n i r n a l
Winer( I 980) in an extensivereviewof theliteraDoesa pu_e
haveto be a cat?") The otherinference
tureon classinclusionnotesthat "the studiesshorvtaskwas a propertyinferencetask. Problernsq ereof
ing latedevelopmentfar outnumberthoseshorring
the form: 'All Xs have
Do all /s havero
" andconcludesthat "the resuhs
earlydevelopment,
(where_
have-"
was filled with a neu
clearly refute the claim of Piaget and othersthat
word for a property). Again, there were threerypes
class-inclusion
is developedby age7 or 8" (p 310)
of problems-where the inferencervasvalid (e g .
"All milk haslactose.Doesall chocolatemilk have
There is also evidence that children less than I I
yearsof agewho do passtheclass-inclusion
testmay
to have lactose?");wherethe inferencewas invalid
still haveonly an incompletegraspof the logic of
(e.g., "All milk haslacrose.Do all sneakers
havero
inclusion.Markman(1978)testedwhetherchildren
have lactose?");and, finally, where the inference
judgmentsdo so
who renderconectclass-inclusion
(e,g., "All milk haslactoseDo
was indeterminate
on the basisof logical or empiricalconsiderarions. all drinks haveto havelactose?").
Becauseher earlier work (Osherson & Markman
Smith reportsgroupas well as individualdatafoi
1974-1975) showed that children often trear raureachof the threetasks.However, the resultsthatare
ologicalstatements
as though they were empirical
most relevantto the presentdiscussionarethosethat
statements,Markman thought that children might
concernthe children'spatternsofrespondingacross
also treat the greaternumerosityof a class over its
the three tasks.Overall, 90Voof the 4-year-oldsand
subclassas an empirical fact ratherthan as a logical
all of the older children succeededon at leasrone of
consequence
of inclusion.
the tasks.As Smith pointsout, suchresultsdefiniteMarkman(1978)reasonedthat childrenwho do
ly argue against characterizingyoung children as
appreciatethe logical necessityof the class being
being unableto representand reasonaboutinclusion
( 1) shouldbe willing to make
largerthanits subclass
relations. For, if such a characterizationwere corthe class-subclass
comparison,evenwhen they have
rect, children would have failed all three inclusion
no empirical meansof judging the relative numertasks.The fact that almostall children met crirerion
osity ofthe two, (2) shouldunderstand
thatno addion at leastone task and many children on more than
tion of elementscould ever result in the subclass
one task suggeststhat children are able to represent
containingmore elementsthan the class,and finally
inclusionrelations.It also suggeststhatunderfavor(3) should be willing to comparea class to its subable conditionschildren can solve problemsthat reclass even when given only minimal information
quire them to evaluatesuch relations.
aboutthesubclass.A study wasdesignedto testeach
A subsequentexperiment was designedto exof thesehypotheses.Resultsindicatedthat children
plore further 4-year-olds'ability to draw inferences
take the greater numerosity of the class to be an
on the basis of inclusion relations. In this experiempirical fact until about 1I years.
ment, 10children,aged48 to 56 months,were_siven
Although performanceon the standardclassinfour valid and four invalid inference problems
clusion task points to a relatively late development,
These problems were slightly different from those
there is evidencethat even 4-year-olds are able to
used in the first experiment;they gave the children
representand implicitly evaluateinclusionrelations.
additional information that, presumably, made the
C. L. Smith (1979) tested4- to 7-year-oldson three
inferenceeasier,for example, "A yam is a kind of
different tasks. The first task involved quantified
food, but not meat. Is a yam a hamburger?" and "A
inclusion questionsof the form, "Are all Xs Is?"
pawpaw is a kind of fruit, but not a banana.Is a
''Are
and
someXs )'s?," whereX could be a subset
pawpaw food?" The results were quite strikin_s;
of .Y. No pictureswere used;children answeredon
children were correct 9lVo of the time, and 8 of the
the basis of their knowledge of the terms and the
l0 children made only one or fewer errors.
objects they denoted.
These results indicate that successon the stanThe other two tasks were inferencetasks One
dardPiagetianclass-inclusiontest shouldnot be held
was a class inference task. Children were given
up as the sine qua non condition of the ability to
problems of the form, "A is a kind of X.
embedclasseswithin one another.It is bestto think
210
R O C H E LG E L M A NA N O R E N E EB A I L L A R G E O N
than an1'of us antrcipatedtity and classification
despitethe nerv-found
Second,
ago.
y.orc
,uy l0
brillianceof the young child, thereis still much to
developrvithin the variousdonrainsof cognition
rvill be protracted,in somecases
The developnrent
t
o
l
4 y e a r s o fa g e T l r i r d 't h ey o u n g e r
I
3
t a k i n gu n t i l
the child, the ferverthe task seltingswith which he
cancope.That is' theirabilitiesareuncoveredwithin a ratherlimitedset of situations Fourth,what is
known early is often implicit. That is, the child's
governedby underlying
behavioris systematically
(e.g., thecountinsprinciples)thatare not
structures
known to the child. Thus, at leastin sonrecases,a
part of developmentis making explicit what was
initially implicit (for a similar argumentseeFlavell
& Wellman, 1977, on the developmentof metamemory).Finally,the evidenceon the relationships
amongabilitiesacrossdomainsis too weak to support a theory of overarchingstructures This leaves
tpen the possibility that there are domain-specific
structures rather than domain-independentstruct u r e s( c f . C h o m s k y ,i 9 6 5 ; K e i l , 1 9 8 1 ) '
We believethat many of the sameconclusions
will emerge as we gain further knowledge aboui
various domains of cognition lndeed, there is alto
ready sufficient evidence regarding the abilities
cause-effeci
physical
about
reason
and
seriate
relations.
We have already noted the strong tendency o:
very young children to impose an order relation on
objects(e.g., Bryant, l9?4; Bryant & Trabasso
tgU t). RaOitionalevidence on the abitity of young
anc
childrento seriatecomesfrom Cooper, Leitner'
Saltzmar'
and
Moore (1981), Greenfield'Nelson,
(lg'12),Koslowski ( 1980)' Greenfieldet al ' reportei
also develops.
a senes
that even3-year-oldchildren could construct
It seemsreasonableto suPPosethat as masteryof
a neu
insert
correctly
could
and
cups
out of stacking
hierarchicalclassificationis progressivelyachieved,
stack.
the
into
cup
thechild becomesbetterable to rePresentfor himself
As Koslowski (1980) notes, early demonstra'
the relationsthat exist between classesat the same
and different levels within hierarchies'Further, as
the child's ability to rePresentinteractionsamong
classesdeveloPs,so doeshis ability to reasonabout
such interactions.lt is in this light (it seemsto us)
that one can best make senseof the empirical work
on classinclusion. Quantitativecomparisonsof su4someoneeise. Koslowski (1980) tested 3- and
perordinateclassesand their subclassesare not sucth:
as
well
as
tasks
abbreviated
own
year-oldson her
cessfully performed until quite late-by contrast'
(196aI
traditionaltasksusedby lnhelder and Piaget
demanding
less
simpler,
involve
that
tasks
inclusion
u'as
The difference between the two sets of tasks
comparisonsare solved at an early age'
oi inclusionnot as a unitary,all-or-noneabilitv' but
to think of it as one doesclassification'nunlerlcal
reasoning,and so forth. One can devisetasksthat
rvrll result in a verl' broad range of perforntance
success-inclusion tasks that 4-year-olds solve
) nd
u , i t h o uat n yd i f f i c u l t y( e g . , C . L . S m i t h ,1 9 7 9 a
age
years
of
I
I
tharr
less
children
that
tasks
inclusion
fail. Recallalso the Markmanet al
s5,stenratically
l4-year-oldswill
1i980;un.xpectedresultthateven
for a collectiotr
hierarchy
mistakea class-inclusion
minimal inforprovides
situation
the
hierarchywhen
interpretatton'
their
constrain
guide
or
to
mation
that someinclusionabilThereis reasonto suPpose
ity is availableat anearlyagebut thatthis abilityis at
first relativelylimited and is only displayedunder
limited, favorableconditions(seeTrabasso'isen'
Dolecki,Mclanahan, Riley, & Tucker, 1978'for a
of limiting conditions)As the
carefulconsideration
child develops,he becomescapableof carryingout
on the inclumoreand more complexcomputations
Piagestandard
The
classes.
sion relation between
the
require
that
tests
many
ofthe
one
only
is
test
tian
child to evaluateand operateon inclusionrelations'
We do not mean to suggestthat the ability to
classify objects hierarchicallyis fully presentfrom
the start.The bulk of the experimentalevidencewe
have reviewed indicatesthat there is considerable
improvementwith age' However, the evidencealso
suggeststhat the improvementis one of degree,not
caof kind. As the child's information-processlng
ivorld
inthe
of
knowledge
as
his
pacitiesdevelop,
stratcognitive
and
perceptual
his
as
and
creases,
egiesbecomemore efficient, we find that his ability
to detect, and make use of, hierarchical structure
More on the Same Themes
Our review of some core concrete-oPerational
concepts highlighted several themes' First' preschool children have more knowledge about quan-
CONCEPTS
A R E V I E WO F S O M EP I A G E T I A N
the basisof their performance
on the lO-sticktasks,
Koslou,ski(1980)assignedchildrento the standard
three Piagetianstagesof seriationability. Of the
nranychildren who were classifiedas StageI (no
ability to seriate),75Vocouldconstructa systematic
seriesof 4 sticks,8 I 7ocould insert2 new sticksin a
4-stick series. and l00%ecould correct incorrectinsertions.What we seehereis a powertul effectof set
size---onethat yieldscontradictoryclassificationsof
the same children.It is hard to deny theseyoung
childrena seriationscheme,evenif it is appliedin a
restrictedrange.
Work by Cooperet al. (1981) leadsus to conviscludethatdespitetheyoungchild'scompetence
d-vis seriation, it is neverthelessfragile. These researchersfind 3-year-oldsable to discriminatebetween a seriatedand nonseriatedset of rods under
someconditions.Yet, they havedifficultydiscriminating betweenserieson the basis of the direction
lncrease.
The theme that "the young know more and that
the old know less" appliesto seriationas doesit to
other domains.Recentwork by Piaget(1980)supports this conclusionas well as the idea of development proceedingfrom the implicit to the explicit.
With Bullinger, Piaget (1980) studied the way
children between5 and l2 years solved a conflict
over what they saw. Children were shown a display
containing sevendiscs in a zigzag row. The thicknessesof all the discs were the same;the diameters
increasedprogressivelyby stepsof 0.2 mrn-a nondiscriminabledifference.Becausethe discswere arranged in a zigzag, the child could compare only
adjacentpairs of discs and, therefore, would conclude that eachpair of discssharedthe samediameter. However, becausethe last disc could be removedandcomparedwith the frst in thedisplay,the
child could seethat thesetwo did differ in diameter.
Children younger than I I years had difficulty resolving the conflict between their initial conclusion
that the f,irstand last discs were equal in diameterand
their perception that they were not. To resolve the
conflict, one hasto maintainthat the discshadto get
progressivelybigger, eveir if one could not physically seethis. That is, onehad to imposea presumed
orderingon the stimuli. It is hard to imaginehow one
could do this without an explicit understandingof
seriation and the principle of transitivity. Piaget
( I 980) reportsthat only the olderchildren(at leastI I
years old) could resolve the conflict successfully.
This leadsus to suggestthat an explicit understanding of the principle of transitivity is rather late in
developing, a conclusionthat is also supportedby
Moore's (1979)work.
Recentwork on the understandin-s
of phvsical
causalityreinforcesthe conclusionthat order relations are quite salientfor the young child Bullock
and Gelman (1979) had children watch the exact
sameevent-a ball rolling down a runwayanddisappearinginto a box-before and after Jackjumped
up from the box. When askedto chosethe ball that
madeJackjump, 3- to 5-year-oldchildrensystematically chosethe ball that was droppedfirst. The-vdid
this even when the order informationconflictedwith
a cue of spatialcontiguity, that is, when the beforeevent was in a runway that was separatedfrom the
jack-in-the-boxbut the after-eventwas not Bullock
and Gelman took thesefindings asevidencein favor
of the view that preschoolershonor a principle of
priority when reasoningabout physical cause-andeffect relations. That is, young children implicitly
apply the rule that causescannotfollow their effects
but can only precedeor coincide with their effects.
Other lines of convergingevidenceare reviewedin
Sedlak and Kurtz (1981) and Weiner and Kun
(1976).s
Bullock, Gelman,and Baillargeon(1982)go beyond granting preschoolersthe implicit principleof
priority. Bullock et al, maintain that preschoolers
also apply the principle that cause-effectrelations
are mediatedby mechanisms.Those familiar with
Piaget'searly (i930) and recentwork (e.g., 1974)
on physical causality will recognizethat this latter
conclusionis at odds with his ideasaboutthe development of the understandingof physical causality.
Piagetwas probably the first psychologistto investigate systematically the development of the
young child's conceptionof physical causality.He
and his collaboratorsaskedchildren to explaina variety of natural (e.g., the cycle of the moon, the
floating of boats) and mechanical(e.g., the operation of bicycles and steam engines) phenomena.
Analysesof the explanationscollected1edPiagetto
characterizethe young child's thoughtasfundamentally precausal.
According to Piaget, "immediacy of relations
and absenceof intermediaries. . are the two outstandingfeaturesofcausality aroundthe ageof4 to 5
(1930,p. 268).Thus, thepedalsofa bicyclearesaid
to make the wheels tum without being in any way
attachedto them. A fire lit alongsidean engineis
saidto make the wheelsof the engineturn, evenif it
is 2 ft. away; the sun is said to follow us as we walk
down the street. "Not a thoughtis given to the question of distanceor of how long the actionwould take
in travelling from causeto effect" (Piaget, 1930,p.
268).
In his early work on child causality, Piaget
212
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
. i v e n t h e i ra b i l i t Yt o r a k el n t o
f e c r sa t I d i s r a n c cC
accountchangesof conditionsrvhennlakingcausal
a t t r i b u t i o n si t.i s d i f f i c u l tt o d e n y4 - a n d5 - y e a r - o l d s
a n i m p l i c i tc o n c e r nf o r n t e c h a n i s mA s i n r i l a cr o n c l u s i o nf o l l o w s f o r e v e n y o u n g e rc h i l d r e n .g i v e n
rvorkby B aillargeon.Gelntan.andMeck ( I 98 t ) and
S h u l t z( I 9 8 2 )
ln two separateexperinlents.Barllargeonet al
( I 98 I ) shorvedchildrenthe rvorkingof a tltree-part
The initial piececonsistedof a long rod
apparatus,
that could be pushedthrougha hole in a post; the
piece',vasa setof five uprightblocks;
intermediate
theend partwas madeup of a leverand a toy rabbit
(Fred)sittingon a box nextto a toy bed.Childrenin
of
the experimentwere first given a demonstration
pushed
was
rod
ivhen
the
aPParatus:
working
the
throughthehole it hit the first block.The first block
fell andcreateda dominoeffect.The lastblock landed on the leverthat madeFred-the-rabbitfall into his
bed. After the demonstration,the children were
askedto predictwhetherFred wouid fall into his bed
and final
given variationsin the first, intermediate,
parts of the apparatus.Modificationswere of two
types'.relevant ones, those that disrupted the sequence,andirrelevantones,thosethat did not disrupt it. For example, a short stick was used and,
hence, co,uldnot reach the first block (a relevant
change) In contrast,a long glasstube could reach
notionof mediatetransmission
an
the first block, and, thus. whenused,constituted
is
mechanism
of
The idea that an assumption
inone
of
renioval
the
irrelevantchange.Similarly,
lacking in the preschooleris contradictedby several
termediateblock versusthe laying down of blocks
lines of research.Bullock (1979)adaptedher runwas relevant as opposed to inelevant' In the first
to givechildrena
aPparatus
way andjack-in-the-box
experiment,predictiontrialswererun on a fully visicauses.ln one
choicebetweentwo eventsasPossible
the secondexperiment,the block
experiment.childrensaw a ball and a li,ehtsource ble apparatus.In
and lever portion of the apparatuswas screened'
movc down parallel runways and disaPpearat the
as follows' If
et al. (1981)reasoned
Baillar-seon
sametime into the jack box (theperceptionof light
very occurthe
that
believe
wrongly
young
children
movementu'asdueto an inducedphi-phenomenon)'
is suffisequence
a
causal
in
event
first
the
of
ren.e
conln the experiment, 3-, 4- and 5-year-olds
treat
they
should
event,
final
the
about
bring
to
cient
as
runwa)'
tbe
sistentlychosethe ball runningdown
as
all modificationsof the first event Potentiallydisthatsteelballs
cause,presumablyon the assumption
ruptive and all modifications of the intermediary
aremorelikely to hit somethingandreleasetheJack'
eventsas nondisruptive.On the otherhand, if chil'
in-the-box Supportfor the conclusionthat4- and5dren do understandthat the intermediaryeventsin a
year-oldsmade such inferencesfollows f16p *'hat
causalsequenceeffectively connectthe first and last
happenedin Bullock's next experiment.
eventsin the sequence,they shouldregardall and
runu'ay
the
In the secondBullock experiment,
only the relev'antmodifications-whether of the inifrom thejackportion ofthe aPparatuswas separated
tial or intermediaryevents-as likely to disruptthe
in-the-boxportion. Otherwisethe experimenttvas
In the first experimentall 20 childrenin
wasoperated sequence.
exactlythe same (Thejack-in-the-box
were conect on at least15Voof rheir
experiment
the
by remote control.) ln this experiment,4- and 5Indeed. the averagecorrect repredictions.
23
Instead'
year-oldsdid not choosethe rolling ball.
4,ponr., for the 3-year-oldswas 8570;that for the
they attributedcausalityto the moving light Put
experrment'
second
the
ln
year-olds was 9Q.5Va
differently.childrenchosethat event as causethat
mechanism'
where the screenhid the intermediate
wasnrostplausible.Ballsdo not produceimpactat a
the'l5Va
19
met
well:
as
almost
did
children
the
distance;hog'ever,electricaldevicesoftencauseef-
( 1 9 - 1 0c)l a i n r e dt h e y o u n gc h i l d h a d t r o a s s u n r p t r o n
of contactbetrveencauseand elfect Thc idea \\ i'ls
of ntechattisnr
that the young lackedan assulllPtion
carrleto leam
child
young
the
With developnrent,
In Piagets
events
intenrrediary
of
chains
about
more recerlttrcatlllentof causality(e.g . Piaget'
1 9 7 4 ) . t h e a c c o u n to f d e v e l o p r n e ni ts d i f f e r e n t
as
However, the young child is still characterized
remost
his
By
nrechanisnr'
of
lacking a principle
cent accourtt.childrenhave to comc to attributcto
objectsthe operationsthey havemasteredAccording to Piaget."There is a remarkableconvergerlce
between the stagesof formation of operationsand
thoseof causalexplanation;the subjectunderstands
the phenomenaonly by attributingthe objects
operationsmore or lessisomorphicto his" (Piaget'
1 9 1 4 ,p . 4 ) . I n o n e e x p e r i m e nut s e dt o m a k et h i s
point.childrenwereaskedto explainwhy thelastof
a row of still marblesrolled away after the first u'as
hit by a moving marble.Childrenin the initial stage
(4 to 5 years)explainedthis as if they believedthe
moving marbleactedat a distance.Childrenin the
stage(6 years)assumedeachmarblein
subsequent
the row pushedthe one next to it Accordingto
Piaget(19?4).it was not until they reachedthe next
stage (i.e., until the advent of oPerationaltransitivity. 7 to 8 years)that childrenbeganto form a
CONCEPTS
A R E V I E WO F S O M E P I A G E T I A N
st this
c o n e c t c r i t e r i o n . D i f f c l c n t i a lp r e d r c t i o n a
l e v c l o f r c c u r a c yc o u l d o n l y h a v c o c c u n e di f t h c
c h i l d r e nr r e r eu s i n st h c i n t e r r n e d i aer yv e n t sa ss u c h
S h u l t z( 1 9 8 2 )h a s c o n c l u d c dt h a t e v e n 2 - y e a r olds assunrethat a causeproducesits effectsvia a
transnrission
of folce. be it eitherdirect (as in one
b a l l h i t t i n ga n o t h e ro) r t h r o u s ha n i n t e r m e d i a r yl n.
Shultz'siirst experinrent.aftera brief initialdemonstrationof a cause-effcctsequence.childrenwere
asked ro assigncausal attributionsto one of two
e n e r g ) ' s o u l c c s .A s a n e x a m p l e .c h i l d r e nr v e r e
shown that turning on a blorverhad the effect of
putting out a candle. They were then shown two
blowers(onewhite, the othersreen).eachof which
wassurrounded
on threesidesby a Plexiglass
shield.
The criticaldifferencebetweenthenvo blorverswas
whethertheopenside was facinga lit candle-and,
therefore.one could blorv out thecandle.If considerationsof mechanismdo not influenceyoungchilchooserandonrlybetweenblowers
dren,thel"should
chosethe
ascause.Theydid not; theysystematically
blowerrvhoseopeningfacedthe candle.Similareffects held for the transmissionof a sound source
from a tuningfork andthe transmission
of light from
a battery The consistentresult was that children
took noteof barriersthatwouldstopthetransmission
of light and sound when they madecausalattributions. Interestingly,a similarresultheld in Shultz's
(1982) study of Mali children in West Africawhetheror not they were in schoolenvironments.
If we acknowledgethat youngchildren'ssearch
for explanationsof their world is governedby the
inrplicit principlesof priority and mechanism,we
can accountfor the kinds of resultsreviewedhere.
But to grant these causalprinciplesis not to say
young childrenknow they are using them. In the
case of causal reasoning, we doubt rvhethermost
adults knou, they are using it. As before, we allow
for the implicit use of principles,just as psycholinguistsallow for the implicit useof rulesthatguide
the use and comprehensionof speech.
Again. to say the young child has somecompetenceis not to say shehas a complete.conect understanding of physical causality. As Baillargeon
(1981)shorvs,the developmentof the abilityto explain why a prediction is conect evolvesvery slowly. And as McCloskey. Caramazza. and Creen
(1980)shou'.evenundergraduates
atJohnsHopkins
Universitl, make erroneousassumptionsabout the
world. The kindsof predictionsmadearemoreconsistentrvithAristotle'swritingson physicsthananything Ne*ton ever wrotel Wrong theorieshave
aboundedin the history of science.But, whatever
musthavebeenmadeabout
the theory.assumptions
213
p r i o r i t y ,n r e c h a n i s ma,n d w e a k d e t e r n r i n i s (mB u l l o c k e t a l . 1 9 8 2 )o. t h e r w i s teh c r ec o u l dh a r d l l ' b ca
historyof science.
Like Carcy (1980) rve ascribeto the vieu' that
( I 974)recentexperirnents
on causalrcasonPia_eet's
ing shouldbe viewedasexperiments
on the acquisition and changeof explanationsystems.Looking
back to the Piaget(1974)experinienton rhechild's
of force.we susunderstanding
of the transmission
pect many of our readerswanted to knos' rvhatwas
wron-ewith the 6-year-olds'explanationof u,hy the
final marblemoved.lt certainlyincludedan assumption of possiblemechanism,albeita naiveone
antiOur precedingpointgoesbeyonda standard
Piagetianargument,that is,1,oungchildrenare bad
explainersWe do not meanthat causalunderstanding is simplya matterof beingableto provideexplaissueof whether
nationsper se.Thereis the separate
one understandsthe correct explanation.When
it is possibleto allo,vv
viewedfroni this perspective.
of physthattherearequalitativelydifferenttheories
ical reality as a function of developmentor even
schooling-just as Aristoteleanand Newtoniantheto deny the
ory are. It is not. however.necessary
youngor uneducated
a causalattitudethatis governed by principlesof causalreasoning.
There are further casesof earlier cognitivecompetencethan once expected---+itherwithin a Piagetian frameworkor not. Many of theseappearin other
chapters(e.g., see Brotttt, Bransford, Ferrara, &
Campione, vol. Ill, chap. 2; Mandler, r'ol. III,
c h a p . 7 : o r S h a t z ,v o l. I I I , c h a p . l 3 ) W e t r u s to u r
main point is clear by now Earlier competence?
Yes. Full competence?Certainh' not.
S U M M I N GU P
Structuresof Thought?
When we began our review we simply announcedour supportof the Piagetianview that what
we think, perceive,and remember is mediatedby
structuresof thought.We did so withoutevenjustifying this position.That we did not is a signof how
heavily Piaget /ras influencedall of us. Piaget's
ideasthat cognitivestructuresset the limits of problem-solvingabilitiesas well as influenceboth how
we perceivethe world "out there" and influencethe
contentsof memory, were either ignoredaltogether
or dismissedas unnecessary.As Flavell ( 1982)
determineour memonoted.the ideathatstructures
abilitiesis so
ries,perceptions,
andproblem-solving
pervasivein moderncognitivepsychologl'thatit is
almost a puzzleas to what the fuss rvasonce about
"Piaget, Newell and Simon. Chomsky and others
214
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
rnands Nervport( 1980)Ittakesa similarattempttn
just aboutcveryonethat adult
hnvenorv convincccl
by usinglinguisdornainof languageacquisitiLln
and child nrindsalike are inhabitedby exceedingly the
We suspectthis
units
structural
define
theory
to
tic
prorich structurcsof knorr'ledgeand cogllitive
theorizing
just
such
of
the
beginning
is
o
f
i
s
f
u
l
l
v
o
l
u
m
e
(
F
l
a
v
e
l
l
,
4
)
T
h
i
s
1 9 8 2 .p
cesses"
In any case.we trustthat Flarell (1982)is right
evidencein supportofthisvierv However'giventhe
and that the notion of structureis here to stay
s u b j e cot f t h i sr e v i e w .w e m u s tp o i n to u tt h a ti t i s n o t
Piaget'sinfluenceon this outconrein cognitivedetlue that ever)'oncaccePtsPiaget'sviews
velopnrentalcircleshas been, and will continueto
theofthe learning
First.therearestill advocates
be, ejnormousWe obviouslybelievethat the ultiory vieu'(e.g . Kendler' l9'r,9)'Second.we believe
will be difof thesestructures
trate characterizations
that Piagetstill rvouldhold that someof the current
we
particular.
In
Piaget
by
offered
than
those
ferent
traditiontendsto
rvorkin the infolnrationprocessing
arithmetic
underlying
structures
the
that
anticipate
losesightof the role of structurein cognitivedevelthought will not be the same onesunderlyingthe
oprnent(seesic.g1er,rol .I, chap 4, for a revierv
explanations'No
tendencyto form cause-and-effect
of theivork in thistradition).Whenrvearetold thata
is a needfor a
there
that
remains
matterwhat. thefact
child fails task.r,r', or : becauseof a memoryprobof reasoning
a
set
or
logic
it
structuralaccount-be
lem or a limit in shon-termmemoryor a failureto
to
knowledge
of
domains
those
principles-about
encodea crucialstimulus,the issueis, What exactly
attentron.
our
tumed
Piaget
which
is beingsaid?Therecouldbe theimplicitassumptlon
but we are
that the child has the requisitestructures
and
directly,
confronted
not
not sure.The questionis
Stages of CognitiveDeveloPment?
ln
mouth'
author's
an
rvords
in
put
to
so we hesitate
In our opinionthereis little evidenceto suppon
some cases it seems a legitimate inference(as tn
of
the
ideaof majorstagesin cognitivedevelopment
is
Trabasso's.1975.work); in othercasesthe issue
agaln'
and
over
the type describedby Piaget'Oier
more complex.
child hasmore
the evidenceis that the PreoPerational
what
(1981)
that
hypothesis
ConsiderSiegler's
evidenceis
the
Further,
exPected.
competencethan
is what is encoded'But why
changesin development
works
out conchild
concrete-oPeratronal
that the
doesrvhatis encodedchange?Piaget'sansweris that
kind of
the
using
without
domains
separate
in
cepts
the coenitive structureschange.And becausethe
integrative structuresthat would be required by a
structuresdeterminewhat is assimilable,it follows
generalstagetheory. In addition.thereis evidencein
that what is encodedwill change.Siegler (1981)
way a
some casesthat the structureunderlying the
might very well acceptthis interpretation'But if he
like
is
much
problem
a
about
reasons
oreschooler
did, then we would ask for a descriptionof the strucfor exadults,
even
and
children
older
by
used
ihat
ture. Sure,we areaskingfor a lot, perhapsmorethan
ample, the principles of causalreasoning'In other
yet can be accomplished (But see the recent pubcases,the evidenceis that there is structuralchange
licationby Siegler& Robinson,1982.)
reflectedin the developmentof a concept'The case
Our point simply is that we cannot be satisfied
of number concepts ls one clear example of the
with a zeitgeistthat acceptsthe notion of structure'
latter.
What is neededaredescriptionsof thesestructuresNone of the foregoing points eliminatesthe posall the more now that the evidence goes agalnst
sibility of therebeing within-domainstagesof develPiaget'sparticulardescriptions.Further,we needto
opment. It could even turn out that there are some
determinethe interactionbetweenstructuraland inrs
cognitive developmentaldomains wherein there
formation processingconstraintsas they influence
no
is
u'herein
there
others
and
stages
of
cognitivedevelopment.Suchthoughtsaremorethan
"uid.n." Flavell's(in press)recentwork on visual
evidence.
in the air. A variety of investigatorsand theoretiperspective-takingabilitiesis perhapsone suchcarrciansaretryingto accomplishthis(e.g.,Case,1978;
didate. And the domain of number concePtsmay De
Fischer,1980; Halford & Wilson, 1980;Pascual(1978)
yet another,althoughGelmanandGallistel's
Leone, 1970).The Halford and Wilson paperis inmodit-rcation'
needs
stages
version of the
terestingbecauseit offers an a priori definition of a
Recall Gelman and Gallistel'shypothesis'The
unit of inforntationprocessing.To do this they work
could only reasonaboutspecificnumerpreschooler
with categorytheory.6We reservejudgment on the
ical values.ln contrast.the elementaryschool-aged
descriptiveadequacyof this theory. As Halford and
child could reason about nonspecified numbers'
Wilson (1980) point out. it needsfurtherempirical
The proposed stageswere that Stage 1' reflected
support.Still, we seeherean effort to usea known
2 rearithmetic comPetencewith countables;Stage
nlathenlaticalstructureto define a uni( and then to
about
reasoning
algebraic
to
advance
an
flected
make predictionsabout information processingde-
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS
nunlbcrs Unfbrtunately,the datacontradictthe hypothesis-Undercertainconditions.preschoolers
carr
anddo usea principleof one-to-one
conespondence
to reasonabout nurnber.And they do this with set
sizesthey cannot count accuratel\'.Evans (1982)
further finds no conelationbetweenthe developrnentof the conceptsof zero,infinity, and negative
numbersin elernentary
school-aged
children.Indeed
the seeminglyrelatedconceptsof foreverand infinity fail to shorva within-subject
correlation.So even
in the caseof numberconcepts,the evidencefor a
transtaskstagedevelopntent
is weak at best.
There is one possibleway to retrievethe stage
argunrent for within-cognitive-domaindevelopments,This involvesrepresenting
a given level of
competencein terms of hierarchiesof related conceptsand thencharacterizing
eachstagein termsof
the dominanttendencies
at a given tinre. A similar
strategyhasbeenusedby Kohlberg( 1969).We hesitate to guesswhetherthis or other efforts to characterize cognitive development in rerms of stages
( e . g . ,C a s e ,1 9 7 8 ;F e l d m a n& T o u l m i n , 1 9 7 5 ;H a l ford & Wilson, 1980; Pascual-Leone,
1970) will
prove more successful.
Oneof Piaget'sbetterknownpositionsis thatthe
courseofcognitivedevelopment
mustbe paced,that
is, thereis little that can be doneto engineera truly
accelerated
rateofdevelopment(Piaget,1966),Althoughthe many successfultrainingstudiesserveas
evidenceagainstthis position,norionsof readiness
still abound-and we suspectthe1,always will.
Siegler(1978)reportsthat a 5-year-oldwho usesrhe
samerule as does an older child does not benefit as
much from the sametrainingasdoesrheolder child.
This is in partdue to a weakertendencyon the part of
the younger child to encode the relevant information; the latter fact raises the question of whether
time itself must passbefore the training is effective
or whether differences involving encoding strategies,processingspace,knowledge,andso on, need
to be modified during this time. More generally,the
questionis what happensduring a given time period
to enable learning to go forward (see Siegler &
Klahr, 1981,for an extendeddiscussion).
How Does DevelopmentHappen?
Up to this point we have focusedalmost exclusivelyon mattersof structure.We now turn to
mattersof function.How do an individual'scognitive structures
operate(i.e., How do theyrespondto
inputsfrom the environment?)?
The centralnotions
in Piaget's(e g., 1970) accountare assimilation,
accommodation,and equilibration And which
functional mechanismsare resDonsiblefor the
cnlergenccof eachstageof developrnentl)
l-he crucial notionshere are thoseof abstraction
rdflechissanteand iquilibrationnrajoranreiPiaget. 1975b;
For Pta_get,
all co-gnitivc
functioninsinvolvesthe
two fundanrental,
complententary
processes
of assimilationand accommodationPiasetdefinesassimilationas the incorporation
of externalelenrenrs
(ob.1ects
or events)into sensorimotor
or conceptual
schemesThus, for example,thumb suckingin the
infant is describedas the assimilationof a novel
elenrent,the infant'sthumb, into the existinesucking scheme. Similarly, rhe concrere-operarional
child who ordersa setof rodsis saidto haveassimilatedthe rods into a seriationscheme.
In his book,l'r'quilibrarion desstructurescognirlves,Piaget(1975b)postulatesrhat every scheme
tendsto feeditself, thatis, to incorporateinto itself
externalelementsthatarecompatiblewith irsnature.
The child's schemesare, thus. seenas consriruting
the motivationalsource,or the motor of development. Schemesdo not merelyconstrainthe nature
and range of exchangesthe child has with her environment,but they activelybring aboutsuch exchangesin their effort to feed or actualizethemselves.The child's activity is, rhus, necessary,in
that it aloneprovidesinputsto the child's assimilation schemes.
Many considertheforegoingnotionsvague.Yet,
as indicatedin our openingremarks,we said we
acceptedthe idea that developmentproceedsas a
function of assimilationand accommodation.To
show why, we apply thesenotionsto someof our
work.
An exampleof the way in which schemesguide
as well as motivate behavior comes from Gelman
and Gallistel(1978).Theseautborsfoundthateven
very young children obey the how-to-countprinciplesthatunderliecountingbehaviorin olderchildren
and adults.Consider,for instance,thecaseof a2Vzyear-oldchild who said, "2, 6, 10, 16" when engaging in what appeared to be counting, When
shown one object and askedhow many there were,
the child answered"2." When shown two objects
and askedhow many therewere,the child said, "2,
6, 6" (emphasison the last digit). Finally, when
shown three objects and asked to counr them, the
child counted "2, 6, 10," and when askedhow
many therewere, simply replied "10." This child
can be said to have appliedall of the ho"v-to-count
principles becausehe assignedone unique tag to
eachobject,he usedthe samelist over trials,andhe
repeatedthe last tag in a count u,henaskedthe cardinal-numberquestion.
Accordingto Gellnanand Gallistel,the child's
adherenceto the how-to-countprinciplesrevealsthe
216
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
her actionto thc specificcontour'*'eight' size' and
so on. of the object shc is attcrlptineto grasp'The
young child who uses an idiosvncraticcount list
to the conventlonal
eventuallywill accomnrodate
c o m m u n i c a t i o ni nsv o l v i n gc o u n t l n g
o n e .O t h e r w i s e
and numberswill be exceedinglrdifficult
Another example of schemesaccomnlodatlng
comesfrom Saxe's(1980)work rviththe
thenrselves
use a
in
Papuans PapuaNerv Cuinea-The Papuans
in
embodied
53-itemcountlist that hasno baserules
foundto
theonecitedabove(childrenhavealsobeen
has
to
monev
men
some
it. With recentexposureof
children
countrvith lettersas rveliasnumbers)The
to
conre the shift to a base-20systenl-Presumabl5'
have
they
because
who use such lists do not do so
numbers
rvith
large
to
deal
possible
make it
To summarize,for Piaget,the child's schemes
arethe motivationalsourceof derelopmentbecause
the
they activelyassimilateand accommodateBut
tne
constraln
than
more
does
of assimilation
Drocess
have
rvill
child
a
that
exchanges
of
range
natureand
with his environment The processof assimilation
asalso involvesthe seekingout of stimulithat are
schene
the
As
such'
similableto a given scheme'
obtains the necessaryinputs that feed the.scheme
that
items
searchof a list. The schemeassimilates
is alwal s Partot theasslmBecauseaccommodation
can then be stably orderedto create an acceptable
the eventualchange tn
guides
it
process,
ilation
with the
count list, that is, a list that is compatible
of
structures.We have illustratedhorvthe processes
schemeitself
the
in
work
might
assimilationand accommodation
The second source of evidence that countlng
By
developmentof countingskiil and knowled^ge'
frequency
the
schemesservea motivatingfunction is
a
form
principles
counting
the
that
postul;ting
countingis observedin the
with which spontaneous
we can
accommodates'
and
assimilates
that
scheme
of unusualcountlists' the
accountfor the appearance
enrbodies
availabilityof a countinsscherlle'u'hich
The
these(arrclpossiblyother)countingprinciples
child's
the
trotivates
and
counting,ih.n',. guides
ho*'
behavior,lt must be clearfrom the foregoing
items that can De readily assimilated?Because
young children are not instructedto practicecountto
Ing. u ,tt.ory that requiredextrinsic (as opposed
grounds'
int"rinsic)motivation would be on difficult
the
ln their theory, the motivationwould come from
would
the
schemes
is,
schemesthemselves,that
to
continuallyhave to assimilateextemalelements
chilpress
would
hence,
and.
develop,
subsistand
will be
dren to engage in activities whose results
comPatiblewith the schemesthemselves'
ln an assimilation,externalelementsare strucln
turedb1'.or adjustedto, theindividual'sschemes'
individual's
the
contrast,
b)'
an accommodation.
of
schemesmust adjust themselvesto the demands
accommothg snvironment.A schememustalways
the
tal developmental processes'Indeed' because
behavcounting
children's
of young
characteriitics
iors areubiquitous in otherdomainsof development
that
(e.g., languageaquisition),it seemsplausible
ubiqassimilationand accommodationare likewise
and later
uitous during the courseof development
A B E V I E WO F S O M EP I A G E T I A NC O N C E P T S
prcserveor restolethc existinSstateof equilibriunr
In cases rvhere accommodationis unsuccessful.
however,andassimilation
ofa givenelenrentproves
impossiblewithout significanrmodificationsof rhe
individual's schcmesor cognitivesystems,piager
talksof equilibrations
ntajoranres
or nrajorimprovernentsthat _senerate
qualitativelydistinct, superior
statesof cognitiveequilibrium
Obviously the latter situations-those unsuccessfulaccommodations
that call for an improved
(majorante)equilibration-are the nlost important
ones from a developmental
point of view. Exactly
how doesthe major equilibrarion
happen?It is hard
to find a clear accountin Piaget'swritings. One
thing is clear, this is that Piaget thought that
qualitativelynew conceptscould emergefrom the
processof reflectiveabstraction.T
We admit to havingbeenlessthansuccessfulin
our efforts to understandfulli' the notion of reflective abstraction.Again, rr,eresort to air example
from Evans' (1982)work on rhe acquisitionof the
conceptof infinity. Evanssu_lgests
that some childrenacquire,on theirown,thenotionthatthereis no
largestnumber on the basisof their self-initiated
countingtrials. The idea is that some children set
themselVesthe task of countingup to rhe largesr
numberand eventuallycometo recognizethat they
will never get therebecausethereis no largestnumber. Piaget would say the child who reachesthis
conclusion does so via the processof a reflective
abstractionfrom the setof counttrialsthat were selfgenerated.Parenthetically,the self-generatedcount
trials areexamplesof what Piasetmeansby logical
as opposedro physicalabstraccion
(Piaget,1975b).
We suspectthatpart of theresistance
to accepting
the idea that schemesassimilareand accommodateis
due to the absenceof detailedaccountsof how the
assimilationand accommodationprocesses
yield development.Piaget (1975b) tried to do this in his
more recenttreatmentsof the processes
of equilibration and reflective abstraction.We seethis work as
part ofPiaget's continuingeffons to derailthe nature
of assimilationand accommodation.
However, we
confessthat we still are far from a full understandine
of the variousprocesses
postulated
in piaget'streai
mentof reflectiveabstraction
andequilibration.yet,
we do not think it necessaryto rhrow up our handsin
despair. Perhapswork by Rumelha.rtand Norman
( 1978)on schemadevelopmenr
or Sieglerand Klahr
(198l) on developmentaltransirionprocesseswill
servethis end. And Rozin's(1976)norionof accessi n g h a sm u c h i n c o m m o nr r , i t hP i a g e t ' s( 1 9 7 5 b )n o tion of reflective abstraction Further. to repeat.
therecan be no denyingsonte(hing
like assimilation
217
a n d a c c o n t n l o d a t i oans b e i n ei n v o l r e di n l e a r n i n g
and developmentThosefamiliaru,iththe theoreti_
cal work of Rumelhartand his colleagues(e.g.,
Rumelhartand Norman. 1978; Rumelhart& Or_
t o n y , I 9 7 7 )r v i l lr e c o g n i zrch eu s eo f s i m i l a r l ya c t i v c
processesin their accountof horv schemataare
formed and developedWherherpiaget'spanicular
versionof horvschemes
developwill standthetestof
tlme, we do not know. But rveare surethat notions
akin to assimilationand accomntodarion
wili And
by now, they are no more mvsrenousIo us tnanare
the processes
of association
and selecriveattention.
Whence Come Structures?
The issueofwhenceconceptswasrakenuo in the
Pia-set-Chonrsky
debateheld in Francein 1975and
publishedin Englishwith Piatelli-palmarini
09g0)
servingas editor and commentator\ot only were
Piaget and Chomsky present,so \\ere Bateson,
Fodor, Inhelder, Jacob, lr{ehler, Monod. paoert.
and Premack-ro list bur someof the distinguiihed
participantsThe debatewas supposedto focuson
the Piagetianand Chomskianaccounrsof language
acquisitionbut was, in fact. a broaderdebateabout
Piaget's constructivismversus Chomsky's and
Fodor's innatism. Piaget defendedhis view that
structures are constructed and not inherited. He
maintainedrhat cognirivefunctions,but not cosnitive structures,were innate,Fodor and Chomsky
wereon the side of innateideas.
The nub of the disagreementbetu'eenChomsky
and Piaget concernsthe origin of mental structure.
Chomsky and Fodor maintain that structurebegets
structureandthatthisis logicallynecessary.
Fodor's
ar-qument
is that leaming inr.olveshlpothesistesting; hypothesesare either rejectedor accepted.For
one to inducethe correcthtpotheses.one must be
able to formulate those hypotheses.Therefore,the
hypotheses must already be available to the
organlsm.
To let sucha device[a learningdevicejdo whatit
is supposedto do, you havs 16 presuppose
rhe
field of hypotheses,the t'ield of conceptson
which the inductive loeic operates In other
words,to let this theorydo rvhatit is supposed
to
do you haveto be in effecra nativisr.You haveto
bea nativistabouttheconceptual
rescrurces
ofthe
organismbecausethe inductivethecrn.of leami n e . s i m p l v , d o e s n ' t e l l r o u a n r . r h i n ga b o u t
t h a t ( F o d o ri n P i a t e l l i - P a l m a r i n
1 i9, S 0p. p . 1 4 6 t47)
218
R O C H E LG E L M A NA N D R E N E EB A I L L A R G E O N
As notedby thc biologistsat thedebate,the nativist position (outlinedhere) does not. of course,
nreanthat the adult's Inentalstructuresare present
fronrtheoutsctany morethanit means-to translate
the argumentto a purely biologicalexample-that
adult sexualorgansare presentin the newly fertilprovidesampleeviized ovum Work in etholo-e)'
and nativistpositionsneed
dencethat constructivist
not be contradictory.The acquisitionof bird song
providesa lovelyexample The adultwhite-crowned
sparow has a characteristicsong. By varying the
kind of environnrentavailableto the young whitecrorvnedsparrow, Marler (1970) has been able to
shou,thatexperienceplays a centralrole in the deof the
velopmentof the song that is characteristic
regionin which thebird lives.For, ifa babyspalrow
is raisedin isolation,it will singa distinctlyoddsong
as an adult. Experts agreethat this odd song is the
basicform of the adultsong.It is odd becauseit is
neverheardin natureand lacksthosecharacteristics
that give it the statusof one dialector another.If the
young bird is exposedto the adult song during its
first l0 to 50 days of life, but never again, the bird
will sing the adult characteristicsong. This is true,
evenif the young bird is deafenedafter theexposure.
What matters is not the opportunity to sing the
song-the young cannot-but the opPortunity to
hearthe songof the region. Thereis a critical period
during which the bird must hearthe adult model. If
the isolatedbird hearsthe songfor the first time at
100 days, the experiencewill have no effect, Likewise. if the acousticinput is providedduring the first
days of life, it does not take. Subsequentdeafening
does inhibit acquisition. Marler argues from such
findingsthat the white-crownedsparrowis born with
template for the basic song. Experienceservesto
tune that templateto allow the young bird to learnits
panicular dialect. The bird bringsto the interaction
with the environment a structural advantagethat
oneset
helpsit focusattentionon, thatis, assimilate
of songsas opposedto another.In interactingwith
the environment, the bird develops the particular
song of its locale, that is, the basic templateis accommodated.The idea is nor that developmentinvolves a bit of innate structureand a bit of leaming
but llrdt developmentis a funcrion of the organism's
interaction with its environnten!.The potential for
structuralchangeis not reachedunlessthereis develand
betweenstructure
opment,thatis, an interaction
thepotentialis innately
environment.Nevertheless.
grven
For Chomsky and Fodor. the complexity and
power of the final structureis preordainedby the
complexityof the initial stnrcture.This is precisely
wherePiagetdisagrees.
Piagetinsiststhateachsuccessivestructurein the stagelikecourseof development is not only different from, but more complex
and powerful than, the precedingstructure.Piaget
fosters a notion of developmentalprocess as divorced from structure He grantsthat the processes
or developmentalfunctions are innate, but he does
not grant that complex processespresupposea complex structurefor their realization.Piagetarguesthat
cognitive functions foster the emergenceof structures more complex than prior ones Carrying this
argument back to the very beginning of development, he maintainsthere is only processor function
and no structure: "l have my doubts . . . [that the
point of departureis innate], becauseI am satisfied
with just a functioningthat is innate" (Piagetin
Piatelli-Palmarini,
1980,p. 157).The tendencyof
the subjectto assimilateand accommodateis enough
to bring him into interaction with his environment
and this interactionyields cognitive structures.
Piaget's distinctly Lamarkian hypothesis was
criticized by the biologists at the debate.For example, Jacobpointedout:
In the caseof the small animalsfrom the bottom
6f Lake Geneva, the observedvariationsare always those allowed by their genotype.One always remainswithin the working margin authorized by the genes. . . .There is regulationonly
on structures and with structures that exist and
tlnt are there to regulate.. . . They adjust,of
course, the allowed working margin, but it is,
once more, the genotypethat prescribesthe limits. (Jacobin Piatelli-Palmarini,p. 62)
Despite persistentefforts by the biologists, Piaget
stoodby his view that structuresare not determined
innately.RatherthangrantingFodor'sview thatsucin prior struccessivestructuresmustbe represented
tures, he maintainedthat a prior structurecan contain the subsequentstructure only as possibilities,
possibilitiesthat do not get formed until they are
constructedor createdin the courseof an interaction
with the environment. The interactionitself alters
the prior structuresand, thus, more complex structuresdevelop.
We agreewith Chomsky andFodorregardingthe
ultimateorigin of the structuresmediatingthe kinds
of conceptPiaget describesas being presentduring
the early school years First, we cannotmake sense
of the notion of a functioning divorcedfrom a stnrcture. If structuresdo not guide functioning,then we
fail to seehow the developmentalprocessgetsstarted on the snmedevelopmentalcoursefor a// normal
A R E V I E WO F S O M EP I A G E T I A N
CONCEPTS
children. But, if we alloq' innatestructuralconstraintson the courseof development,
then rvecan
begin to make senseof the fact thatchildren all over
the world seem to develop the same conceptsin
about the samesequenceup to aroundthe beginning
of the concrete-operational
period.Further,rheevidencepoints to innatestrucruraldispositions
in inf a n r s( e g . , H a i t h , 1 9 8 0 ;S p e l k e ,1 9 8 0 ) .L i k e w i s e ,
much of the recentevidenceregardingthe cognitive
capacitiesof preschoolerspoints to the early availability of rich and complexreasoning
structuresAs
more evidencelike this coniesin, it becomesharder
and harder to escape the argument that there are
innatestructuralconstraintson thecourseandnature
ofcognitivedevelopment.
(1978)andKeil
Osherson
(1981) have made some progressin characrerizing
theseconstraints
To say that young children'sreasoningstructures
are rich is not to say that they are the same as the
adult structures.Indeed,we notedthe many conceptual domains where (despitethe presenceof early
capacities)young children'sreasoningstructuresa.re
nowherenearthoseof older children, which, in turn,
seemimpoverishedcomparedto adult's capacities.
As far as we are concemed, to say there are rich
cognitive structuresro start is just the beginning.
There remain the questionsof what thosestructures
are and how they determinethe emergenceof advancedstructures,given an appropriaterangeofexperience.And, of course, the accountof what the
appropriaterangeof experiencesarehasto be related
to the nature of the structuresthat set the range.
Finally, the obvious fact that humanshaveconsiderable conceptualplasticity, hasto be reconciledwith
the idea that thereareinnatestructuralconstraintson
the courseof cognitive development.For an example of how this might be accomplishedwe turn to
Rozin's Accessing theory of intellectual development.
Rozin ( 1976)has attemptedto deal with the facts
that(1) highly''intelligent" behavioral
mechanisms
are availableto specieslow down on the phylogenetic scale and (2) even though more "intelligent"
organismshave geneticallyspecifiedbehaviorprograms, they are lessconstrainedby theseprograms
or are more open to environmentalvariations.
Rozin begins by calling arrentionro the highly
"intelligent" nature of many special-purpose
behavioral mechanismsin animals.Foragingbees,for
example,recordthe locationof food sourcesin polar
coordinates,with the home nestas the origin of the
coordinatesystemandthe sun asthe point of angular
reference.It is now known that almost all of such
"intelligent" behavior is foundedon generically
219
specifiedcomputationalmachinen'thatprepares
rhe
beesto leam the locationofa food source The learning here does not reflect some general-purpose
faculty of association.Instead,the learningability appears within genetically consrrainedbehavioral
cucumstances
and the becs' "kno*,ledge" ofcelestial mechanics,which is implicit in thebees'behavior and is unavailablefor use in orheraspects
of the
bees'behavior.
Accordingto Rozin, the genericallydetermined
behavioralmachineryin lowly creaturesis unaccessiblefor use in contexts other than the specifiic
contextthat shapethe evolution of the requisiteneural machineryin the first place. Rozin's thesisis that
the evolution of general-purposeintelligence in
higher mammalshas involved the evolutionof more
generalaccessto computationalprocesses
that originally served specializedbehavioralpurposes.Still,
he stressesthe fact that even in humans,there are
many computationalroutineswhoseoutputsare not
generallyaccessible.For example,our visual system makes extensive computationsthat draw on a
greatdeal of implicit knowledgeof trigonometryand
optics. The end result, our perceptionof the world
around us, is generally accessible.But the intermediate computations are not. Likewise, humans
appearto possessgenetically specifiedneural machinery for computing phonetic representations
of
the speechthey hear (Eimas, i974) This phoneric
representationis an intermediatestagein the computation of a semantic representationof what humanshear. The evidenceindicatesthat the phonetic
representationis not consciouslyavailableto preschool-agedchildren(Gleitman& Rozin, 19"1'l;Liberman, Shankweiler,Liberman, Fowler, & Fischer,
1977;Rozin & Gleitman, 1977).
Rozin and Gleitman(1977)hypothesize
that the
ability to read restsheavily on the ability of humans
eventually to gain consciousaccessto the phonetic
representationof what they hear. Spellingrules relate written English to a phonetic representarion
of
spokenEnglish. Every fluent readercan give decidedly nonarbitrary pronunciationsof words she has
never seen (Baron, 1977). Thus, it seemshard to
deny that an important aspectof learningto read is
learning to compute a phonetic representationof
written material by using the lawful relations between spelling and pronunciation.Leaming to compute such phonetic representations
of visual inputs
mustbe very difficult if one doesnot haveconscious
accessto the phonetic representationof what one
hears. But it is known (see above) that the young
child has limited accessto the phoneticrepresentation. Hence, the Rozin and Gleitman(1977)argu-
220
R O C H E LG E L M A NA N D R E N E EB A I L L A B G E O N
of
mentthatreadingabilityrequircsthedeveloprrtent
consciousaccessto the phoneticrepresclltatlL)I]
Note that Rozin doesnot contendthat the ability
to read per se is codedin the genesbut that related
abilitiesaswell asa generalaccessing
ability(reflective abstraction?)
are The notion of accessingby
itselfdoesnot constitutea solutionto the de\elopnrentalproblem, that is, how to accountfor new
conceptswithin a nativist frame of reference Instead,it points to the fornr such a solutionmight
take.If the notion is to be takenseriously,onemust
What is it
raiseand answerthefollowingquestions:
aboutthe early representation
of a givensetof experiencesthat preventstheir being worked on by a
givenpieceof computational
machinery?Hoq,must
this representationbe altered for the machineryto
operateon it? What are the processesthat produce
such alterations and what experiencesbring these
processes
into play?
We introduceRozin'stheorybecauseit hasthe
form of the theory that is neededto deal with the
facts about the conceptsthat Piaget has studied.
Their developmentis more domainspecificthannot.
Very young children have considerablecognitive
abilities.Still, some, if not most, are exceedingly
hard to demonstrate.and the rangeof applicationof
these abilities is oftentimes remarkably restricted
compared to that in older children. Hence. their
ubiquitous tendency to fail may rdlated tasks.
Eventually,what arerigid, undergeneralized
capacities become fluid, generalizedcapacities.
A Concluding Remark
There are at leastthree importantways in rvhich
Piaget'swork has influencedthe field ofchild cognitive psychology. First, Piaget was among the first
modernpsychologiststo insist on the activerole the
child plays as a learner.Traditional learningtheory
tendedto characterizedevelopmentin terms of the
passiveregisteringand gradualaccumulationof environmentalcontiguities.In markedcontrast,Piaget
ponrayed the young child as one who continually
engagesin the selectionand interpretation,asrvellas
the storage,of information.Second,Piagetwasalso
amongthe first modernpsychologiststo underscore
the role cognitive struituresplay in young children's
reasoning.Again andagainPiagetdemonstrated
that
young children's cognitive structures determine
their perceptionand understandingof the world and
delimit the nature and rangeof knowledgethey acquire at each point in their development. Third,
Piagetis undoubtedlythe psychologistwho hasmost
contributedto our knowledgeof the facts of cogni-
tive developnrent.
His rvorkcoversthedevcJopnrc-nr
of a rcrnarkablywide and vari.'J set of conceprs:
nurnberconsen,ation.
objectperrnanence,
class-inclusion,length,distance.and so ('rn As we repearedly pointedout in thc chapter.invcstigators
nrar
not alwaysagreewith Piaget'sinierprctation
of rhe
developmental
phenonrena
he reported-butthevdo
not deny their reliabilityor interesr
On the debit side, we would arsuethat Piagets
ivorkpresents
Throughouthis
two majordrawbacks.
career,Piagetmaintainedthatall cognitiondevelops
throughfour successive
stages,u itheachstagecharacterizedby the emergenceof qualitativelydistinct
structures.It seemsto us that Piaeet'sstrongcommitmentto this view, thoughpraiseworthy
in sonre
respects,also had someunfortunateconsequences
In particular, it appearsto have led him to disregard-and even at times summarily dismiss-alternativeaccountsof his findings thatwereat leastas
plausibleas thosehe proposedhimself.The second
drawbackis analogousto the first Having commited
are achimselfto the view that cognitivestructures
tively constructedby the child, Piagetseemsnever
to haveseriouslyconsideredalternativeviews of the
developmentof these stnlctures.True, Piaget's
treatmentof developmentalissuesalmostinvariabll'
of therationalistandempiricist
includesa dis'cussion
of these
standpoints.However, his presentations
views are usually so simplistic as to border on the
charicatural.One lessonof modem researchin child
psychology is that accounts of how development
proceedscan no longer ignore the possibility that at
leastsomeof the structuresthat underlieour systems
of knowledge are innate. Another lesson is that in
order to do justice to the richnessandcomplexity of
the learningprocessesinvolved in the acquisitionof
cognitive structures,far more sophisticatedinvestigativeand descriptivetools than sere hithertoavailable must be developed. Piaget's account of the
manner in which cognitive structuresemerge appearsextremelylimited. But then.it is alwayseasy
to examine the past in terms of the present.What is
more difficult is to createthe future It will be hard.
very hard, to do as well as Piaget.
NOTES
l. Osherson(1974) providesa proof that the
groupings themselves are either inconsistent or
tautological.
2. Gold provided the information about subjects' agesupon requestfrom the authors.Theseare
not in his text.
3. Shultz et al. (1979) make as good a caseas
CONCEPTS
A R E V I E WO F S O M EP I A G E T I A N
anyoncfor treltin-gscparatelyissucsof a belieI in
of rnany
logical necessitl'and the understanding
conserVanons
4 For a conrpletelist of the propertiesofclassificatorl systemssecInhelder& Piaget' I 964' p. 48.
5 Our comntentsaboutcausalreasoningarerestrictedto thedomainof physicalcausalitySeeGelm a n & S p e l k c( 1 9 8 1 )f o r a d i s c u s s i oonf p o s s i b l e
in reasoningaboutphysicalcausalityand
differences
c
a
u
s
ality.
social
6 An exampleof thedifficultyin defininga unit
of M-spaceis takenup in Trabassoand Foellinger
( 1e9 7 8 )c o n s i d e rtsh ec r i t i q u e
(1978)Pascual-Leon
However,therestill recounts.
unjustifiedon many
to
definea unit on a priori
question
horv
of
the
mains
grounds.
?. This is but oneof Piaget'susesof theconcept
of reflectiveabstraction.See Vyuk (1981) for an
excellentcoverageof this and relatedconcepts.
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