Relationships among Piagetian, IQ,and Achievement Assessments

Rheta DeVries

University of Illinois at Chicago Circle

DEVRIES, RHETA. Relationships among Piagetian, lQ, and Achievement Assessments. CHILDDEVELOPMENT, 1974, 45, 746-756. Empirical relationships are explored among the theoreticallydifferent Piagetian and psychometric assessments of intelligence, and school achievement. Sswere 143 bright and average children chronologically aged 5, 6, and 7 years. Factor analysesof perfoniiance on the California Test of Mental Maturity (CTMM), Metropolitan Achieve-ment Test (MAT), Stanford-Binet, and 15 Guttman-scaled Piaget-type tasks indicated thatPiagetian, IQ, and achievement tests overlap to some degree, but also measure different aspectsof cognitive functioning.

Belief in psychometric intelligence is sothoroughly ingrained in American psychologyand education that hardly a school system orprofessional journal can command respect with-out taking account of IQ in educating or .study-ing children. Recently, however, McClelland(1973) challenged the validity of IQ tests asmeasures of intelligence. His review of theliterature led him to argue convincingly thatthe high correlations between IQ scores andvarious measures of occupational success orlife adjustment are likely due to social classrather than to intelligence.

School achievement tests have also re-cently been under attack. Kohlberg and Mayer(1973) reviewed the literature and found thatschool achievement onJy predicts further schooJachievement and fails to predict anything elseof value (such as occupational success).

The crumbling assumptions that an IQ

score represents intelligence and that schoolachievement prepares children for later suc-cess lead to a demand for alternatives in theoryand practice. Kohlberg and Mayer (1973)suggest that Piagetian "cognitive stage mea-sures provide a rational standard for educa-tional intervention where psychometricintelligence tests do not" (p. 489). This al-ternative suggestion is congruent withMcClelland's (1973) less specific advocacy oftests with scores which "change as the persongrows in experience, wisdom, and ability toperform effectively on various tasks that lifepresents to him" (p. 8). Therefore, the Piaget-ian alternative to psychometric methods seemsworth examining.

The issue with regard to inteUigence is:Are there theoretical and empirical differencesbetween psychometric and Piagetian concep-tions of intelligence? The issue with regard toschool achievement is: Are there theoretical

This article is based on a paper presented at the annual meeting of the American Educa-tional Research Association, New Orleans, March 1973. The study was supported by theDepartment of Program Development for Gifted Children, Illinois Office of Public Instruction,with supplemental support provided by the Office of Education, U.S. Department of Health,Education, and Welfare through the Chicago Early Education Research Center, a componentof the National Laboratory on Early Childhood Education, and by the Urban Education Re-search Program and the Research Board of the University of Illinois at Chicago Circle. Com-puting services used in this research were provided by the Computer Center of the Universityof Illinois at Chicago Circle. Their assistance is gratefully acknowledged. The author wouldlike to thank Dr. Arthur Turner and other personnel of the Unit 4 schools in Champaign,Illinois, for the many supportive services which facilitated the conduct of the study, and tothank the cooperating teachers, principals, and children of Champaign, Urbana, and SaintJoseph, Illinois. The author especially vnshes to acknowledge the invaluable criticism andsuggestions of Dr. Constance Kamii and Dr. Lawrence Kohlberg on earlier drafts of thisarticle. Author's address: College of Education, University of Illinois at Chicago Circle, Chicago,Illinois 60680.

[Child Development, 1974, 45, 746-756. © 1974 by the Society for Research in Child Development, Inc. Allrights reserved.]

and empirical differences between schoolachievenment and knowledge measured byPiagetian tasks? This study is therefore con-cerned with the empirical relationships amongthe theoretically different Piagetian and psycho-metric assessments of intelligence, and schoolachievement. Let us first consider theoreticaldifferences and related research findings.

Theoretical and Empirical Relationshipsbetween Psychometric and PiagetianConceptions of Intelligence

IQ tests are not derived from any theoryof intelligence but are based, instead, on cer-tain assumptions about intelligence. IQ test-makers assume that the more correct answersthe child gives relative to others of the samechronological age, the more intelligent he is.IQ is thus defined in terms of individualdifferences with regard to a wide variety ofitems which have no theoretical significance inthemselves (that is, one cannot conclude any-thing about a child's general intelligence fromhis response to a single item). To a largeextent, these items simply tap bits of surfaceinformation (such as the days of the week, thedifference between a baseball and an orange,and perceptual discrimination of similaritiesand differences). Their surface nature is indi-cated by the fact that psychologists try so hardto keep their test answers secret in order toprevent "spuriously high" scores by individualswho simply learn the answers.

In contrast, Piaget's tasks are derived from(and have contributed to) a research-basedtheory of intelligence. Concerned with findingout what intelligence is rather than withquantifying it, Piagetian research has demon-strated universal, qualitative changes in thereasoning of humans from birth through ado-lescence. The theory accounts for these changesin terms of a gradual development of basiccognitive structure. Piagetian tasks are con-cerned with how the individual views andreasons about reality (for example, whetherthere are more blocks or more blue blocks,whether a quantity changes in amount whenchanged in shape, and whether one is a sisterto one's sister). Each task has theoretical sig-nificance and in itself reveals something im-portant about the individual's general develop-ment of his intelligence. Assessment is notconcerned just with right answers but withkinds of wrong answers as well. Wrong answersare important for assessment because research

Rheta DeVries 747

has shown that a child must go through manyinstances of being wrong before he finallyconstructs adult-level knowledge and intelli-gence. Thus, intelligence is defined by Piagetin terms of an individual's place in a universalsequence of development toward formal opera-tional reasoning.

Research findings bearing on the relation-ship between psychometric and Piagetian in-telligence are mixed. Relationships reported be-tween Piagetian tasks and IQ are sometimeslow (Beard 1960; Dodwell 1960, 1962) andsometimes moderate (Almy 1966, 1970; Du-dek, Lester, Goldberg, & Dyer 1969; Elkind1961; A. S. Honig, personal communication).Moderate correlations are usually reported be-tween mental age and Piagetian performance(Freyberg 1966; Kohlberg 1963; MannixI960; Russell 1940a, 1940b). Factor-analyticstudies generally indicate that Piagetianmeasures define factors separate from psycho-metric intelligence factors. Kohlberg and De-V ries (in press) found three factors in theperformance of bright and average 6-year-olds:

1. General psychometric intelligence (11 tests orsubtests drawn from a variety of psycho-metric measures);

2. Conservation (Liquid, Leneth, Ring Segment);3. Classification (Sorting and Class Inclusion).

Stephens, McLaughlin, Miller, and Glass(1972) found five interpretable factors in theperformance of 150 normai and retarded chil-dren from 6 to IB years of age:

1. Verbal (13 WechsJer and three Wide RangeAchievement Test variables );

2. Piagetian reasoning (23 Piagetian measures),CA, MA;

3. CJa.ssification (four Class Inclusion tasks);4. Spatial reasoning;5. Performance (Wechsler Performance IQ and

Object Assembly).

In a second study of the same Ss 4 years later,Stephens (1972) found the following sevenfactors:

1. Verbal (six Wechsler verbal subtests and threeWide Range Achievement subscores );

2. Conservation (Substance, Weight, Volume,Length, Liquid);

3. Performance (five Wechsler performance sub-tests );

4. Flexibility of thought processes (MA, CA, fourPiagetian measures of spatial reasoning, rela-tion.ships, and classification );

5. Classification (three Class Inclusion of Ani-mals tests);

6. Mobility in dealing with concrete and abstractspatial relations (three tasks);

748 Child Development

7. Transition from concrete to abstract operationalthought (Dissolution of Sugar, Conservation ofWeight and Volume, Class Inclusion of Animals,Transfer from Two to Three Dimensions, andChanging Mobile Perspectives).

Hathaway (1973), analyzing data collected byDudek, Lester, and Goldberg, was able toidentify three independent factors among 100children 5—8 years of age:

1. Wise subtests;2. Seven Piagetian tasks;3. California Achievement Test subtests, some

Wise subtests, and four Piagetian tasks.

The general picture presented by thesefindings is not clear but does suggest some de-gree of overlap and some degree of nonover-lap of psychometric and Piagetian measures ofintelligence.

Theoretical and Empirical Relationshipsbetween School Achievement andPiagetian Conceptions of Knowledge

Piaget's view of knowledge is muchbroader than that reflected by school achieve-ment tests. In the larger sense, Piaget views thedevelopment of knowledge and the develop-ment of intelligence as the same. In the nar-row psychometric sense of achieving rightanswers to specific questions, Piaget (1964)points out that it is general cognitive develop-ment which makes specific learning possible.Since it is well known that achievement testsare highly correlated with IQ tests, the ques-tion arises of whether Piagetian and achieve-ment assessments overlap. For example, doesPiagetian number conservation predict arith-metic achievement?

The research literature contains little re-garding the relationships among Piagetianmeasures and measures of psychometricachievement, but a few studies suggest thatthese assess different kinds of knowledge. Inthe Hathaway study described above, anachiev.ement factor included some Piagetiantasks but was independent of a factor com-prised of other Piagetian tasks. E. Ross (re-viewed in Hathaway [1973]), studying 8- and9-year-olds, found four Piagetian classifica-tion tasks to form a factor separate from

Reading Comprehension, Slosson IQ, andParagraph Meaning. Hood (1962) studied therelationship between five grades of arithmeticcompetence (based on teachers' judgments)and three Piagetian stages on number-relatedtasks, and found that no child at the lowestlevel on one measure was at the highest levelon the other; between these extremes, however,the relationship was not linear. Almy (1966)reports that for children 5—7 years of age, con-servation of number and liquid are moderatelycorrelated with reading readiness but cor-related at a low or negative level with vocabu-lary. The general picture presented by thesefindings is also unclear but suggests some non-overlap between Piagetian and school achieve-ment measures.

In order to clarify further the relation-ships among performance of young children onPiagetian tasks and psychometric tests of in-telligence and achievement, the present studyconsiders the following two questions: (1) Towhat extent do IQ tests and Piaget-type tasksmeasure the same intelligence? Specifically,how does Stanford-Binet mental age^ (MA) re-late to performance on Piaget-type tasks? Also,how does IQ on the California Test of Men-tal Maturity (CTMM) relate to performanceon Piaget-type tasks? (2) To what extent doschool achievement tests and Piaget-type tasksmeasure the same knowledge? Specifically, howdoes performance on Piaget-type tasks relateto performance on the Metropolitan Achieve-ment Test (MAT)?

Method

Subjects.—The Ss were 143 white chil-dren, of bright, average, and retarded psycho-metric abilities (measured by performance onthe Stanford-Binet Intelligence Scale), enrolledin the public schools of Champaign, Illinois (in-cluding some retarded pupils in Urbana andSaint Joseph, Illinois). High-IQ and average-IQ children were chronologically aged 5-7years. Low-IQ Ss were mentally aged 5—7 yearsand chronologically aged 6-12 years. Table 1shows the distribution and characteristics ofthe sample.

Procedure.—Fifteen Piaget-type tasks^

1 Mental age is taken as the measure of psychometric intelligence on the Stanford-Binettest because it is defined in terms of increase with age and might therefore be assumed to cor-respond to Piagetian developmental changes.

2 The battery is referred to as "Piaget-type" because some tasks are included which

Rheta DeVries 749

TABLE 1

MEAN CA, MA, AND I Q OF BRIGHT, AVERAGE, AND RETARDED SUBJECTS (A^ = 143)

AGE GROUP BRIGHT AVERAGEAND —^

CHARACTERISTICS Boys Girls Total Boys Girls Total

5 years:N 8 8 16 9 8 17CAh S-S 5-8 5-7 5-6 5-6 5-6MA*' 6-10 7-5 7-2 5-10 5-9 5-9IQ 130 133 132 108 105 106

6 years:'N 8 8 16 8 9 17CA»> 6-6 6-6 6-6 6-7 6-5 6-6MAb 8-2 8-2 8-2 6-10 6-11 6-10IQ 129 129 129 104 107 105

7 years:N 8 8 16 8 8 16CAh 7-7 7-7 7-7 7-9 7-7 7-8MA'' 9-8 9-9 9-9 7-11 7-11 7-11IQ 130 130 130 101 105 103

Mean, all ages:A' 24 24 48 25 25 50CA'' 6-6 6-7 6-7 6-7 6-6 6-6MA' ' 8-3 8-5 8-4 6-10 6-10 6-10IQ 130 131 130 104 105 105

•> Age RTOup classification for this proup is mental age. rather than chronological age.'' Years and months.

RETARD ED«

Boys

87-105-6

69

88-66-4

74

89-117-5

75

248-96^5

72

Girls

57-45-3

67

88-96-5

72

810-17-6

74

218-116-7

72

Total

137-85-568

168-76-5

73

1610-07-675

458-106-6

72

were individually administered in three sessionstotaling about 2 hours, as follows: session 1:Guessing Game (DeVries 1970), Conserva-tion of Mass, Sibling Egocentrism, Left-RightPerspective Constancy of Generic Identity (re-vised photogi"aph form of the test described inDeVries [1969]), Class Inclusion; session 2:Conservation of Number, Constancy of SexIdentity (DeVries 1969; Kohlberg 1963), Con-servation of Mass in the context of the ring-seg-ment illusion (Jastrow effect). Dream Inter-view, Conservation of Length; session 3:Length Transitivity, Conservation of Liquid,Magic Interview (Kohlberg 1963), ObjectSorting (Kohlberg 1963).

Scores on the California Test of MentalMaturity and the Metropolitan AchievementTest were obtained from school records andinterpolated for time of Piagetian testing.

Analysis.—A Guttman scale was con-structed for each of the Piaget-tvpe tasks whichmet Green's (1956) criterion of an index ofconsistency greater than .50. Each scale alsomet Kohlberg's (1963) criteria for develop-

mental sequentiality. That is, mean scalescores increase with age, success on each scaleitem increases with age, and the sequence ofitems is justified by a logical rationale based onPiaget's theory. Each S w .s assigned a scalescore on each task.

Factor analyses, using both the principal-component method and the principal-factormethod, were performed with two groupingsof variables: (1) Stanford-Binet MA and 15Piagetian tasks {N = 122), and (2) Stanford-Binet MA, 15 Piagetian tasks, CTMM Lan-guage and Non-Language IQ, and four MATsubscores (N = 50). Both orthogonal andoblique rotations were performed. This wasnecessary because Piagetian tasks would beassumed to be related, and it is thus necessaryto ascertain whether the restriction of ortho-gonality (independence) of factors distorts thefactor picture.

Only Ss were included for whom data werecomplete on all variables. Since CTMM andMAT" data were available on only 50 brightand average Ss, the first factor analysis was

Piaget never studied (Guessing Game, Gonstancy of Generic and Sex Identity, Ring SegmentGonservation, and Magic). Nevertheless, these were inspired by Piaget's work and are similarin focus and method to Genevan tasks. Tasks and scoring are described in detail elsewhere(DeVries 1971).

750 Child Development

performed in order to establish the patterningof Piagetian and mental age variables with alarge sample which included the retardates.The second analysis could thus be validatedagainst the first.

Results

For both groupings of variables, theoblique rotations revealed factor structuresnearly identical with those of the orthogonalrotations. The principal-component and prin-cipal-factor methods also yielded essentially thesame results. Therefore, the results belowfocus primarily on the outcome of the princi-pal-component method with orthogonal rota-tions.

Factor analysis of Stanford-Binet MA andPiaget-type tasks.—Table 2 shows the inter-correlations among mental age and Piagetiantasks for the larger sample of 122 bright,average, and retarded Ss for whom all datawere available. Low to moderate correlationswere found between mental age and thesetasks. Table 3 shows the results of the factoranalysis. Three main factors emerged from theorthogonal rotation; a first conservation factor,accounting for one-third of the variance; asecond factor containing most of the remain-ing Piagetian variables and MA; and a thirdidentity factor. The oblique rotation showedthe identity factor to be closely related to theconservation factor (r = .36). Three tasks(Sibling Egocentrism, Length Transitivity, andObject Sorting) form two other weak factors.

These results suggest that Stanford-Binetmental age is a poor predictor of performanceon most of these Piaget-type tasks. Mental agerelated to performance on five tasks (GuessingGame, Left-Right Perspective, Magic, GlassInclusion, and Dream) but is independent ofperformance on Gonservation, Identity, Sorting,Sibling, and Transitivity tasks.

This evidence indicates that intelligenceas defined by Stanford-Binet mental age over-laps to a moderate degree with Piagetian in-telligence, but that they are not identical.Therefore, the theoretical differences betweenPiagetian and psychometric intelligence doseem to correspond to real differences in cogni-tive measurement.

Factor analysis of Stanford-Binet MA,Piaget-type tasks, CTMM, and MAT.—Table4 shows the intercorrelations among MA,Piagetian tasks, and MAT subtests for the sub-

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TABLE 3

FACTOR MATRIX RESULTING FROM VARIMAX ROTATION OF STANFORD-BINET MA

AND PIAGETIAN VARIABLES (TV := 50)

VARIANCE ACCOUNTED FOR BY:

Factor 1(34.4%)

Factor 2(11.1%)

Factor 3(8.0%)

Factor 4(7.3%)

Factor 5(6.7%)

Stanford-Binet MA 0.28Guessing Game 0.29Sibling Egocentrism 0.12Generic Identity 0.22Left-Right Perspective —0.04Mass Conservation 0.79"Number Conservation 0.84"Sex-Role Identity 0.19Class Inclusion 0.0.=5Liquid Conservation 0.80"Length Conservation 0.76"Length Transitivity 0.04Magic 0.18Ring Segment Conservation 0.58'*Object Sorting —0.02Dream 0.38

" The highest loading of the variable.^ Secondary loading > .40

sample of 50 bright and average 6- and 7-year-olds for whom all these data were available.Correlations are similar, though generallysomewhat lower, in comparison to the correla-tions reported in table 2 for the larger sample.Table 5 shows the result of the factor analysis.Essentially the same grouping of Piagetianvariables appeared as found for the largersample, a finding which engenders confidencein the relatioriships found for the smaller andmore restricted sample. The conservation andidentity factors were especially stable. Fourmain factors emerged which accounted for61.3% of the total variance. The first factor,accounting for one-third of the variance, in-cluded Stanford-Binet MA, CTMM Languageand xNon-Language IQ, Left-Right Perspective,Class Inclusion, and Magic (with substantialminor loadings of Ring Segment Conservation,Dream, and MAT Arithmetic). The secondfactor included all the conservation tasks andSibling Egocentrism (with substantial minorloadings of the two identity tasks). The thirdfactor was defined by the four MAT subtestsand Dream. The fourth factor included the twoidentity tasks and Object Sorting. The minorfifth and sixth factors were defined, respec-tively, by Guessing Game and Length Transi-tivity.

The oblique rotation indicated that thefirst and second factors were related (r = .33),primarily because of the loading of Ring Seg-ment Conservation on both factors. The first

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factor was also related to the third factor (r =.34), primarily because of the loading ofStanford-Binet' MA, MAT Arithmetic, andDream on both factors. Figure 1 represents therelationships among the three main factors.

These results confirm the general findingof the analysis with the larger sample. Someoverlap does exist between T>iagetian and psy-chometric assessments. However, the overlap islimited, and Conservation, Identity, Sorting,Guessing Game, and Transitivity stand out asparticularly different from psychometric men-tal age.

In addition, this result indicates that, withthe exception of the Dream measure, no over-lap exists between knowledge on Piaget-typetasks and school achievement knowledge asmeasured by the MAT. The correlation of only.20 between Number Conservation and Arith-metic achievement is particularly striking.Therefore, the theoretical differences betweenthese two measures of knowledge also corre-spond to real differences in cognitive measure-ment.

Discussion

The results of this study are in generalagreement with the findings of other factor-analytic studies of performance on Piagetian,IQ, and achievement tests. To a very large ex-tent, Piagetian tasks do appear to measure a

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TABLE 5

FACTOR MATRIX RESULTING FROM VARIMAX ROTATION OF STANFORD-BINET MA, PIAGETIANVARIABLES, C T M M NON-LANGUAGE AND LANGUAGE IQ, AND MAT SUBSCORES {N = 50)

Stanford-Binet MAGuessing GameSibling EgocentrismGeneric IdentityLeft-Right PerspectiveMass ConservationNumber ConservationSex IdentityClass InclusionLiquid ConservationLength ConservationLength TransitivityMagicRing Segment Conservation . .Object SortingDreamMAT Word KnowledgeMAT Word Discrimination . .M.AT ReadingMAT ArithmeticCTMM Non-LanguageCTMM Language

" The highest loading of the variable.^ Secondary loading > .40.

different intelligence and a different achieve-ment than do psychometric tests. This findingsuggests examination of the nature of thisdifference and the implications for assessmentof intelligence, for education, and for researchon children.

Two primary differences can be noted be-tween Piagetian and psychometric measures.First, they differ in their general perspective;and second, they differ specifically in how theyassess intelligence.

The psychometric perspective takes astandard of normal intelligence closely relatedto school success. Psychometric intelligence isdefined in terms of success on school-t)'pe items,and evidence of validity is frequently offered interms of high correlations with school achieve-ment. Cronbach (1960) even asserts that "theterm 'intelligence test' is being replaced bysuch terms as 'test of general mental abibty'or 'test of general scholastic ability' " (p. 164).Thus, the psychometric definition and per-spective of intelligence are very narrow, de-fined by educational expectations of children.

In contrast, Piaget's definition of intelli-gence is not limited to school-type success but

Factor 1

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takes the long-range perspective of the evolu-tion of knowledge and intelligence in the indi-vidual. This evolution is described in terms ofchanges with age in the structure of knowledge.Thus, the Piagetian perspective is a broaderone, defined by children's changing reasoningabout reality.

In ternis of how they try to measure in-telligence, psychometric IQ tests assess howmany correct answers a child can give in ahighly structured situation. Reality is structuredfor the child, and, as McClelland (1973) hasnoted, what is required is respondent behavior,not the operant kind of behavior necessary inlife situations where one cannot "choose be-tween defined-in-advance responses" (p. 11).Basically, IQ tests measure, as Inhelder ([1943]1968) pointed out, "the results of previous ac-tivities and acquisitions" (p. 44). These char-acteristics are also true of standardizedachievement tests.

In contrast, Piaget's tasks focus on thechild's reasoning behind his conclusions. Thesetasks confront the child with ambiguities ofreality and ask him to impose his ideas on theseambiguities. Basically, this is an assessment ofthe structure of the child's logic in terms of its

754 Child DevelopmentMAT Word KnovledgeAT Arithmetic

MAT Vord DiscriminationMAT ReadingDream

Conservation of MassConservation of NumberConservation of LengthConservation of LiquidConservation of Ring

SegmentSibling Egocentrism

CTMM Non-Language IQCTMM Language IQLeft-Right PerspectiveClass InclusionMagicStanford-Binet Mental Age

FIG. 1.—Diagram of primary factors defined by Piagetian, psychometric intelligence, and schoolachievement measures.

future development. The focus is upon theoperations which make possible many specificacquisitions.

McClelland (1973) emphasized that whatintelligence tests mainly predict are test-takingand symbol-manipulation competencies. In-helder' ([1943] 1968) commented that theBinet test gives a numerical sum of successesand failures, but that "it remains a very trickyproblem to go further and conclude from thissummation of results anything about the waythe child arrived at them, the intellectual con-structions that enabled him to do so, or thenature of the deficiencies from which his fail-ures stemmed" (p. 45). Inhelder concludedthat "although the Binet-Simon test is an excel-lent means for the rapid detection of mentalanomalies, it cannot meet the demands of apsychological 'diagnosis' of thought" (p. 44).

Given these differences in perspective and

method, let us consider the implications forassessment of intelligence. The question is.What is the most valid measure of intelligence?Many challenges to the validity of IQ testshave already been mentioned. In addition, In-helder ([1943] 1968) found that IQ tests areoften faulty even in their assessment of perrna-nent mental retardation, the purpose for whichthey were originally designed. Her study ofchildren (and some adults) classified as re-tarded on the basis of IQ revealed that theIQ measures were not sensitive to differencesbetween children who eventually became for-mal operational (but whose rate of develop-ment was slow) and true retardates who neverprogressed past the concrete operational stage.Piagetian tasks did differentiate between thesetwo groups, though in some cases a diagnosiscould not be made with certainty until adoles-cence. Later longitudinal study of retardatesby Stephens (1972) indicates that many re-

tardates continue to progress through Piagetianstages even past the age of 20.

These findings suggest that IQ assessmentoften categorizes individuals as permanentlyretarded when, in terms of the development ofreasoning, they are simply slow in their rate ofdevelopment. (It may be that such inappropri-ate labeling even contributes to creating per-manent retardation by relegating low-IQchildren to educational situations which pre-vent or fail to promote their continued de-velopment. )

Piaget's tasks do seem to provide atheoretically and empirically more valid assess-ment of intelligence than psychometric mea-sures. However, Piagetian tasks are notproposed as substitutes for psychometric tests.IQ tests probably do serve a purpose in pro-viding, as InheMer ([1943] 1968) suggested,a "first approximation" to assessment of achild's intelligence.

It should also be pointed out that evenPiagetian tasks are limited in their ability toassess an individual's intelligence. At levelsbelow the level of formal reasoning, it istempting to try to evaluate individual chil-dren's strengths and weaknesses on Piaget'svarious tasks. However, such attempts wouldbe mistaken primarily because particular pat-terns of comparative progress have no long-range predictive value. That is, the fact thata child is more advanced on physics problemsthan on mathematics problems has no long-range significance in terms of his general in-telligence. However, the fact that he is moreadvanced in some area of reasoning may besignificant. H. Sinclair (personal communica-tion) relates that while retardates generallyperform at the same level across all Piagetiantasks, normal children typically show advancesin some areas. Sinclair speculates that suchadvances may create a disequilibrium whichprompts dissatisfaction with lower-level think-ing in other areas. Such dissatisfaction withlower-level reasoning is necessary before achild feels the need to construct somethingdifferent. Sinclair also cautions that apparentlyestablished structures (pseudo-structures) maysometimes seem to disappear. For example, achild who previously conserved weight maygive nonconser\'ation responses when his focusshifts from weight to local pressure. We simplydo not know enough about decalages onPiagetian assessments to draw firm conclusionsabout the intelligence of a child relative to

Rheta DeVries 755

other children. Perhaps it is unrealistic to ex-pect to be able to make valid fine-grainedassessments of individual intelligence whichhave long-range predictive value.

Now let us tum to implications of thisstudy for education. The finding that schoolachievement is almost entirely unrelated to thedevelopment of reasoning on Piagetian taskssuggests a reassessment of the overall objec-tives of education. The Piagetian perspectiveleads to the view that the aim of educationshould be the long-range development of theindividual (not only cognitively, but emotion-ally, socially, and morally) (Kamii & DeVries,in press; Kohlberg & Mayer 1973). Academicachievement as an educational goal would thenbe reduced in proportion and placed in thelarger developmental perspective.

It is not suggested that Piaget's ta.sks sub-stitute for tests of a child's academic knowl-edge. Certainly tests of reading ability,computational skills, etc., have an appropriateplace. However, their meaning becomes clearerwhen placed in the broader context of Piaget'stheory of development.

Finally, what are the implications of thisstudy for research on children? Virtually allcontemporary studies take account of psycho-metric intelligence, and many studies actuallyare structured in such a way that other be-haviors of children are viewe 1 through the lensof the IQ. Such acceptance of the IQ as in-telligence may obscure our possibilities for ad-vancing our knowledge about child develop-ment. Serious reassessment of research methodsand interpretation of findings which rest onIQ measures seems warranted.

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