Paper-and-Pencil Inventory the Assessment …...341 A Paper-and-Pencil Inventory for the Assessment...

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A Paper-and-Pencil Inventory forthe Assessment of Piaget’s TasksHenry O. Patterson and Louis MilakofskyThe Pennsylvania State University

Although science educators conversant withPiaget’s work have recognized the importance ofadapting instruction and curricula to the cognitivelevel of their students, such attempts have been dif-ficult because of a lack of appropriate cognitive as-sessment instruments. To meet such a need, a com-prehensive, objective paper-and-pencil inventorywas investigated using 542 subjects, 8 years throughadulthood, in order to determine its usefulness fornormal and retarded students. The results showedthat the inventory was acceptably reliable and validand had advantages over other Piaget tests. Withsome suggested improvements, it was concludedthat the instrument had potential as an educationaland theoretical research tool.

The need for an easily administered standard-ized instrument to measure cognitive develop-ment in children and adults has been widely dis-cussed in the educational and psychological lit-erature. Althouh many Piagetians see attemptsat psychometrizing the tasks as invalid and use-less (e.g., Elkind, 1971; Herron, 1978), othershave advocated the development of objectivestandardized instruments (e.g., Bart, 1978;Kaufman, 1971; Tuddenham, 1971).

Several possible research and applied uses ofsuch a standardized instrument have been en-umerated well by Tuddenham (1971), but al-

APPLIED PSYCHOLOGICAL MEASUREMENTVol. 4, No. 3 Summer 1980 pp. 341-353© Copyright 1980 West Publishing Co.

ready researchers in the area of science educa-tion are working to develop a streamlined assess-ment tool to use in the identification of cognitivestages of students. A growing number of chem-ists, physicists, and mathematicians are involvedin this applied Piagetian research; but, unfor-tunately, some of these researchers-not wellversed in test construction, standardization, orPiaget’s theories and desiring a quick assess-ment instrument suitable for use with groups ofstudents-have reacted to the dearth of suitabletests by devising their own instruments. Thedanger with some of these applied research stud-ies by &dquo;naive&dquo; but well-intentioned science tea-chers, as pointed out by Herron (1976, 1977,1978), is that curricula will be prematurely al-tered and students unfairly categorized on thebasis of self-styled Piaget assessment deviceshaving questionable reliability or validity.Notwithstanding the theoretical discussions of

the usefulness and validity of paper-and-pencilPiaget tests, and the necessity of their properstandardization, a literature review showed thatsome 17 paper-and-pencil tests have alreadybeen reported (Patterson & Milakofsky, 1978).Almost all of these tests were designed to mea-sure formal thought; most require a high level ofverbal and reading ability; and all can be ad-ministered in groups. Although most are basedon tasks identified by Inhelder and Piaget(1958), different tests use vastly disparate num-

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342

bers of items and scoring techniques. Most im-portantly, and with few exceptions (e.g., Lawson,1977; Sheehan, 1970), very little has been pub-lished about both the reliability and validity ofthese tests.

If a conclusion can be drawn from the studiesthat have taken a psychometric approach to Pia-get’s tasks, it would be that it is possible to con-struct assessment instruments that (1) faithfullymeasure cognitive development and yield resultssimilar to the classic Piaget individual interviews(with the possible exception of the timing for for-mal thought) and that (2) greatly facilitate Pia-getian research. Of all the varied instruments re-ported, however, there appear to be some no-table gaps. No test clearly meets all of the follow-ing criteria:

1. Comprehensively covers concrete and for-mal tasks;

2. Requires minimal language and readingskills;

3. Can be administered to a wide range of

ages;4. Can be quickly and easily administered to

virtually any size group;S. Can be quickly and objectively scored; and6. Has been standardized and adequately

studied for reliability and validity.

A published but little known instrument thatseems to meet all but the last criterion doesexist. An Inventory of Piaget’s DevelopmentalTasks (IPDT), published by Furth (1970), is anexperimental instrument to be used in the studyof cognitive development with subjects 8 years ofage and older. Although 10 years have passedsince its publication, the existence of this inven-tory has not been widely reported; and despitelimited studies by Ross (1968), Filer (1972), andPatterson (1975), there still are no major pub-lished reports on reliability or validity.Because of the need for such a test, and be-

cause preliminary investigations with this inven-tory suggested that it had merit, a major re-search project was conducted to evaluate the re-liability, validity, and usefulness of the IPDT.

The initial results of this project have recentlybeen reported (Milakofsky & Patterson, 1977,1979; Patterson & Milakofsky, 1978). The pur-pose of this paper is to expand on these previousreports by presenting additional data on the re-liability, validity, and usefulness of the IPDTand by making suggestions for its improvementas an educational assessment instrument.

Method

The IPDT

The IPDT is a 72-item untimed multiple-choice paper-and-pencil inventory designedoriginally as part of a project involving the test-ing of cognitive development in Navaho Indianchildren. A sample page showing an item in theConservation of Volume Subtest is included as

Figure 1. It was designed to translate some ofPiaget’s concrete and formal operational tasksinto an objective, quick, standardized paper-and-pencil format requiring minimal readingability. Presented in illustrations are 18 sets oftasks, divided into subtests of 4 items each. Eachset is introduced by an example that is correctlyanswered in the test booklet. Five problem areasare covered in the test: conservation (4 subtests),images (4 subtests), relations (3 subtests), classi-fication (4 subtests), and laws (3 subtests). The18 subtests are identified in Table 1 with the ap-proximate ages for their mastery according tothe Piaget literature.In this study, the IPDT was administered in

four forms:

1. Group Test. Groups of students were givenanswer sheets with the IPDT test bookletand were read instructions on how to takethe inventory. Subjects were allowed as

much time as necessary to complete allitems. Approximately 45 minutes were re-quired for this administration.

2. Group Test, Part 1. The same procedurewas followed as with the Group Test exceptthat only half the test was given, i.e., sub-jects only answered Items 2 and 3 in each



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Figure 1Sample Page from the IPDT Showing the

Example and the Last Item on theConservation of Volume

Subtest (Courtesy Furth, 1970)

subtest. Items 1 and 4 in each subtest werecovered in the booklet and on the answersheet. This administration usually required25 minutes.

3. Group Test, Part 2. The same as GroupTest, Part 1, except that subjects answeredonly Items 1 and 4 in each subtest, andItems 2 and 3 were covered. Approximately25 minutes was required.

4. Individual Test. To determine if the paper-and-pencil format obscured subjects’ un-derstanding of the concepts tested, the sec-ond and third items in each test (same itemsas in Group Test, Part 1) were chosen topresent individually to subjects. Objects

similar or identical to those illustrated inthe IPDT booklet were collected or con-structed and spread out on tables. Subjectswere brought in individually, shown the ob-jects, and asked questions similar to those inthe booklet. Testers were trained not to ask

leading questions, but to make sure subjectsunderstood what was being asked. Testersrecorded responses on an answer sheet andwrote comments when appropriate. This ad-ministration required about 30 minutes persubject.

SubjectsA total of 542 subjects were tested in all during

1976 and 1977: 250 third-, sixth-, and ninth-grade students in a suburban school district; 210freshmen and sophomores at The Berks Campusof Penn State University; 60 adults in collegecontinuing education classes at Berks; 8 edu-cably retarded children at a special educationcenter; and 14 educably retarded adults at asheltered workshop. Informed consent was ob-tained for all participants in the study.For the major reliability-validity part of the

study, 4 groups of approximately 60 studentseach were used in the design shown in Table 2.In the public schools, classes were selected bythe respective school principals to participate inthe study, and individuals were assigned to agroup randomly. College students in psychologycourses were randomly assigned to one of thethree groups. Subjects not in the 12 groups usedfor the reliability-validity study were adults inselected continuing education psychologycourses, additional college freshmen and sopho-mores in selected chemistry and logic courses,and additional sixth graders from a class in thesame school as Groups 4 to 6. The retarded sub-jects were chosen on availability by the specialeducation teacher in the center and an adminis-trator in the sheltered workshop.The following background information, where

available, was obtained on subjects: age, sex,number of brothers and sisters, birth order,home neighborhood, father’s occupation, latest



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Table 1Content Summary of IPDT

Note. From Milakofsky and Patterson (1979). Copyright 1979 ,

by Journal of Chemical Education. Reprinted by permission.

IQ and achievement test scores (SAT scores forcollege students), and grade averages.

Testing Procedure

As Table 2 indicates, for the reliability-validitystudy there were three phases of testing with atleast a month elapsing between each phase. InPhase 1 students in each group took tests in oneof three orders: (1) one third took an IndividualTest first, followed by the Group Test a few dayslater (Groups 1, 4, 7, and 10); (2) a second thirdhad the Group Test first followed by the Indivi-

dual Test (Groups 2, 5, 8, and 11); and (3) a finalthird had only Group Test, Part 1 (Groups 3, 6,9, and 12).In the second phase, the first two groups in

each grade took retests of the Group Test, andthe third group took the Group Test Part 2. Thethird phase consisted of tape-recorded inter-

views with 30 randomly chosen students in

Groups 3, 6, and 9; they were asked to explaintheir answers to selected questions on whichtheir group had performed poorly. The omissionof Group 12 interviews was simply due to lack oftime before the subjects finished school.



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Table 2

Reliability-Validity Research Design

Note, From Milakofsky and Patterson (1979). Copyright 1979by Journal of Chemical Education. Reprinted by permission.

The above counterbalanced design was usedso that reliability and validity information couldbe assessed without contamination by prior ex-posure to the inventory. The testing sequencewithin each grade permitted uncontaminatedgroup scores to be compared with uncontam-inated individual scores, and test-retest correla-tions could be computed without administrationorder contamination. Only Groups 3, 6, and 9were interviewed because all other groups hadbeen contaminated by the individual test.The subjects who were not part of the above

design were administered the IPDT Group Test;the retarded subjects had to be given special in-dividual administrations where items were readto them out of the booklet.

Results and Discussion

Reliability

Three measures of reliability were computed:

1. Test-retest reliability (coefficient of stabil-ity) was determined by correlating total

IPDT Group Test scores for 8 groups on 2administrations of the Group Test, 1 monthapart. The results are shown in Table 3.

2. Internal consistency (split-half reliability)was assessed by correlating IPDT GroupTest, Part 1, scores with Group Test, Part 2,scores (corrected by the Spearman-BrownFormula) to yield reliability coefficients forthe test as a whole (Table 4).



346

Table 3Pearson Product-Moment Correlation

Coeff icients for IPDT Group Test-Retest Scores

*Q<.01 ; **~<.001

3. Total IPDT Group Test and retest scoreswere compared by an analysis of variance. Asignificant phase effect was found (F (1,120)= 6.242, p < .02); but a post hoc analysis in-dicated that the only significant differencein test-retest scores was for Group 2 (F(1,120) = 16.138, p < .001). Figure 2 clearlyshows the similarity of means for all groupsexcept two.

These data on reliability correspond closely toreliability studies on other Piaget tests (Lawson,1977; Sheehan, 1970). The lower test-retest cor-relations in Grade 6 can be explained and in-deed are actually predicted by Piaget’s theory.Students 11 to 12 years of age are in the transi-tional stage between concrete and formal opera-

Figure 2Mean Scores of IPDT Group

Tests and Retests 1 Month Later

(Courtesy Milakofsky & Patterson, 1979)

Table 4

Split-Half Reliability Coefficients for IPDT

aCorrected by Spearman-Brown formula.



347

tions, and their reasoning is not consistent. Thisis shown by the larger variances in scores forGrade 6 than for any other group (see Table 5).The significant test-retest difference found in

the scores of Group 2 is more difficult to ex-

plain. Since Phase 2 retest scores for Grades 1and 2 were virtually identical, and since Group 1

did not change significantly from test to retest,the most likely explanation for the Group 2change is that it is an artifact of the first GroupTest administration. A review of that particulartesting session revealed that there were indeedadministration abnormalities that could have

depressed the Group 2 scores.

Table 5

Mean Scores of Five M6st Difficult Subtestsof IPDT by Grade

aMaximum score = 4.bmaximum score = 72cIncludes subjects who were not part of the reliability study.



348

The general conclusions concerning reliability,therefore, are that the IPDT scores are reason-

ably stable over a short period for a wide rangeof age groups and that scores are not seriouslyaffected by situational testing variables. Fur-thermore, the inventory has considerable inter-nal consistency and appears to be measuring ageneral lasting trait rather than a specific tem-porary trait.

ValidityTo evaluate concurrent validity, an analysis of

variance was performed to determine if therewere any significant differences between the In-dividual Test and the identical items in the

Group Test. Figure 3 illustrates the finding thatthere was no significant difference in GroupTest scores and Individual Test scores at anygrade level (F (1,148) = .848, p > .20). Althoughthe difference for Grade 3 is large, it was not asignificant difference.Construct validity was investigated by compar-

ing mean scores for each group on the IPDT.

Figure 3Mean Scores of Identical Items on Group

Test, Part 1, and IndividualTest for Each Grade

(Courtesy Milakofsky & Patterson, 1979)

Additional analyses of variance showed a signifi-cant grade effect in both Group (F (3,120) =70.36, p < .001), and Individual (F (3,152) =72.518, p < .001) IPDT scores; however, a posthoc analysis revealed no significant difference ingroup or individual scores between ninth gradeand college (F (1,120) = .83, p> .20; and (F(1,152) = 1.24, p> .20). These results seem con-sistent with Piaget’s stage theory.The same pattern of increasing mean scores

on two different kinds of administration of theIPDT shown in Figures 2 and 3 is also evident ina breakdown of the 18 subtests by problem area,as seen in Table 6. If the criterion of 75% ormore correct responses on items in a subtest

(i.e., at least three out of the four items) achievedby 75% or more of a group is used to define mas-tery of a subtest concept (such a criterion hasbeen used by Elkind, 1962), the data show 15 outof 18 concepts (83%) were mastered by collegestudents, 12 out of 18 (67%) by ninth graders, 5out of 18 (28%) by sixth graders, and none bythird graders. Mastery clearly increases withage; and the big increments between Grades 3,6, and 9 are evident.When IPDT group scores were compared to

other standardized instruments, the resultsshowed significant correlations with achieve-ment tests and, with one exception, IQ tests(Table 7). For college students, the highest cor-relation with an achievement measure was with

high school grade-point average, e.g., for Groupll,r=.71,N=21,p<.001.The final and least objective indicator of valid-

ity was the Phase 3 informal interviews with thepublic school students. Ten subjects from eachgrade (Groups 3, 6, and 9) were randomly se-lected for interviews. They were shown andasked to explain their answer to the most fre-quently missed items on the IPDT. The un-equivocal finding of both investigators inter-

viewing separately was that the students whomissed items had not achieved the requisite cog-nitive structures; neither the paper-and-pencilmultiple-choice format of the inventory nor theway any individual items were presented ap-



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Table 6

Percentage of Subjects by Grade Attainingat Least Three Out of Four Items Correct

on Each Subtest

peared to significantly mislead the students intoan incorrect answer.The general conclusion concerning validity is

that the IPDT basically shows the development-al progression of reasoning found by Piaget andother researchers in the five major areas in-cluded on the inventory and that it yields a resultsimilar to the traditional individually admin-istered tasks even though using a paper-and-pencil format. These indicators, closely corre-sponding to similar validity studies of other tests(Bart, 1972; Lawson, 1977; Renner, 1977), offersome evidence that the IPDT has concurrentand construct validity.

Other Results

A few other findings are noteworthy. Table 5summarizes the results of scores obtained from

all students given the Group Test (excludingGroups 1, 4, 7, and 10) and lists the five mostdifficult subtests for each group. The data in Ta-ble 6 show that no group mastered Classes, Dis-tance, or Rotations and that only college stu-dents mastered Conservation (volume), Images(shadows), and Probability-and these were

barely mastered. These results clearly supportrecent studies showing that Piaget was incorrectabout the timing of the attainment of formalthought (e.g., Elkind, 1962; McKinnon & Ren-

ner, 1971; Towler & Wheatley, 1971); a largenumber of adolescents (including college stu-

dents) are not fully formal thinkers.An analysis of scores among full-time college

students (Table 8) revealed a slightly higherscore for science majors than for non-sciencemajors, but the difference was not statisticallysignificant. The administration of the IPDT to



350

Table 7Pearson Product-Moment Correlation

Coefficients for Group IPDTScores and Standardized Test Scores

aLorge-Thorndike Intelligence Test.biowa Tests of Basic Skills.

the two mentally retarded groups resulted inmeans of 21.5 for the 7- to 9-year-old group (N =8) and means of 25 for the 19- to 45-year-oldgroup (N = 14). Because of the small samplesize, and because individual IQs and back-

ground information could not be obtained forthese subjects, it is difficult to make any inter-

pretations of the results. It would appear, how-ever, that the IPDT could be of use in identify-ing particular strengths for mildly or moderatelyretarded adults.

Concerning correlates of scores with subjectbackground information, the comparisons of to-tal IPDT group scores with sex, number of sib-

lings, birth order, and neighborhood showed nosignificant trends. There clearly is a relationshipbetween age and score, but not within a grade. Acorrelation of -.50 (N = 53, p < .001) betweenIPDT group score and age for subjects over 22years is consistent with other findings on the de-cline of formal thought through adulthood(Coleman, 1973).

Usefulness

The IPDT proved to be a quick, easily ad-ministered test that can be given to normal sub-jects 8 years and older in groups and to mentallyretarded subjects on an individual basis. Sinceminimal reading proficiency is required, minor-

ity and culturally deprived students with readingproblems would not appear to be seriously dis-advantaged by the test, although this study doesnot deal with such samples. Most normal sub-jects from age 8 through adulthood immediatelyunderstood how to take the inventory, and most8-year-olds had little difficulty reading theitems. Most normal subjects required about 45minutes to complete the inventory; the mentallyretarded subjects generally needed more time.In addition, all ages seemed to find the inventoryintrinsically interesting and challenging, andmost found it enjoyable.

Several uses are foreseen. Piaget researcherscould use this inventory to further study cogni-tive development over a wide age range and withdifferent socioeconomic or minority groups. Ed-ucators could use the IPDT to aid in curriculum

assessment, especially in determining readinessand subsequent ordering for certain science andmath courses. In addition, educators who havedeveloped Piaget-based courses and either needan instrument to identify students with reason-ing difficulties or would like to assess pretest orposttest performance might find the IPDT use-ful.

Although there appears to be wide potentialfor this instrument, prospective users should beaware of the limitations to this inventory. Asmost Piagetians contend, a single score on a pa-



351

Table 8Mean Subtest Scores for College Science-Engineering

__________

and Non-Science Students

amaximum Score = 4.bmaximum Score = 72.

*E n.B. with df of 1,108per-and-pencil inventory cannot yield the samekind of qualitative information that an individ-ual interview can. The IPDT therefore would bebest used in situations where individual inter-views are impractical or impossible and where aquick gross measure of functioning is required.Even then, significant decisions on placement ofa student certainly should not be made entirelyon the strength of the IPDT score. Interpreta-tion of scores should only be made in light ofPiaget’s theory; the IPDT is not designed to beused as an IQ test or an achievement test.

Users should also keep in mind that the IPDTis directed more at concrete thought than at for-mal thought. As would be expected, therefore,

for junior high age and older there is a ceiling ef-fect on parts of the test, since 90% or more ofninth graders answered the same 35 items cor-rectly and 90% of college students answered thesame 40 items correctly. It appears that roughlyhalf of the test is too easy for subjects 14 to 15years and older; however, with recent evidenceof regression of thought in old age (Coleman,1973; Papalia, Kennedy, & Sheehan, 1973), theconcrete operational emphasis of the test wouldmake this inventory quite useful for life-spanstudies.For use with normal junior and senior high

school and college students, a new form of theinventory could be printed to omit the following



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eight subtests: Quantity (Subtest 1), Levels (Sub-test 2), Sequence (Subtest 3), Matrix (Subtest 5),Symbols (Subtest 6), Movement (Subtest 8),Seriation (Subtest 10), and Inferences (Subtest17). Possibly Weight (Subtest 4), Inclusion (Sub-test 16), and Perspective (Subtest 7) could alsobe eliminated. The resulting inventory, whilehalf as long, should be as reliable and valid asthe complete IPDT.

Conclusion

In light of the widespread search for standard-ized instruments to assess Piaget’s tasks, theIPDT is clearly a promising theoretical and ap-plied research instrument. The data presentedin this study on reliability and validity certainlyare a beginning at standardization of the instru-ment and provide the necessary initial back-

ground information for judicious use of theIPDT by researchers.Much more research needs to be done with the

instrument before it might be recommended forwidespread applied use. Norms for each age lev-el and various socioeconomic groups need to be

determined, and additional reliability and valid-ity studies using a more representative sampleneed to be done. A more comprehensive analysisof the items also might lead to a revision of theinventory beyond the suggestion of eliminatingcertain subtests for older subjects.This study has only been the beginning of a

long path of research to develop a highly effec-tive instrument for the assessment of cognitivedevelopment, a needed tool in the empirical in-vestigation of Piaget’s theories and in the im-provement of education.

’

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Tuddenham, R. D. Theoretical regularities and in-dividual idiosyncrasies. In D. R. Green, M. P.Ford, & G. B. Flamer (Eds.), Measurement andPiaget. New York: McGraw-Hill, 1971.

AcknowledgmentsParts of this study were funded under a grant from

The Pennsylvania State University CommonwealthCampus Scholarly Activity Fund (Phase III), TheBerks Campus Scholarly Activity Fund, and the Col-lege of Science and College of Liberal Arts ComputerFunds.The authors gratefully acknowledge the generous

cooperation and assistance of the following: StanleyT. Dubelle, Christ J. Bucolo, Stephen Gancar, andCalvin Bossler of the Governor Mifflin School Dis-trict ; Robert E. Brown, Berks Campus; Scott Schaef-fer, Cathy Plushanski, William Hockley, James Hen-ry, Joel Cleveland, Robin Juckem, Thomas Gerhard,and Nancy Miller, student assistants; and Nancy Pat-terson, Barbara Stutzman, Sandy Kreis, Kathy Lo-rah, and Judy Donahue.We also thank Carol H. Ammons, University of

Montana, for her review of an earlier draft of thismanuscript. An earlier version of this paper waspresented to the Division of Educational Psychologyat the 86th annual convention of the American Psy-chological Association, Toronto, Ontario, Canada,August 28, 1978.

Authors’ Address

Send requests for reprints or copies of the authors’other papers on this topic to Henry O. Patterson andLouis Milakofsky, The Pennsylvania State University,Berks Campus, R.D. #5, Tulpehocken Road, P.O.Box 2150, Reading, PA 19608.



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