AN INVESTIGATION or me RELA'HONSHW sew/Em CATEGORIZING BEHAVIOR AND INTELLIGENCE IN SCHOOL CHILDREN ' Them for the Dog“ of Ph. D. “KW STATE COLLEGE Lewd Coleman: 1955- WESIS .l I ‘ Illfllllll'Hl NW N WWW Illflflflflmllml IL, 3 1293 01905 0790_ This is to certify that the thesis entitled An Investigation of the Relationship Between Cetegorizin; Behnvior 4nd Intelligence School Children presented by Leonard Coleman has been accepted towards fulfillment of the requirements for Ph.D. . Psychology degree 1n __ M77. W Major professor 0-169 AN INVESTIGATION OF THE RELATIONSHIP BETWEEN CATEGORIZING BEHAVIOR AND INTELLIGENCE IN SCHOOL CHILDR EN BY LEONARD COLEMAN A. THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of P sychology 1955 Titans as ABSTRACT An attempt was made to substantiate the hypothesis that con- ceptualization is primarily a differential function of intellectual ca- pacity rather than purely a function of exPerience, specifically, that categorizing behavior is more highly related to mental age than it is to chronological age. A. concept—formation task of the categoriz- ing type and the Wechsler Intelligence Scale for Childrn were accord- ingly administered to 150 children. This included fifty children each at ages seven, nine, and eleven. Both mental age and chronological age were correlated with four conceptualization scores: (a) number of concepts, (b) mean time per concept, (c) degree of dimensionality, and (d) number of nonfunc— tional concepts These four scores were likewise compared to the mental ages derived from the full-scale, verbal-scale, and performance- scale scores of the WISC. Obtained results substantiated our hypotheses with reference to three of the four variables: the number of concepts achieved, the mean time necessary to produce a concept, and the number of non- functional concepts are all significantly related to mental age. Coef— ficients of contingency from 0.35 to 0.50 were obtained. Similarly, ii 860059 these three variables are more highly related to mental age than to chronological age as such, the differences being most pronounced with full-scale mental age. Analysis of individual age group rela- tionships indicate the differences are more pronounced in the eleven- year-old group with respect to number of concepts and number of nonfunctional concepts, while the differences are more pronounced in the seven-year-old group with respect to the time scores. The obtained results make possible the conclusion that mental age is a better predictor of categorizing ability (as measured by a nonverbal, categorical sorting type of concept-realization task) than is chronological age. Concept realization of this type is more highly correlated with general intelligence than with the verbal or perform- ance ability measured by the WISC. Future studies involving concept formation should include rigid control of intellectual factors. It is also suggested that results with the categorical concept-formation task be compared with other types of concept formation. iii ACKNOWLEDGMENTS The author wishes to express his sincere thanks to Dr. G. M. Gilbert, under whose inSpiration, supervision, and unfailing interest this investigation was undertaken, and to whom the results are here- with dedicated. He is also greatly indebted to Doctors Donald M. Johnson and Albert G. Dietze for their kind guidance and invaluable advice. Grateful acknowledgment is due to Mrs. Ozelma Lockwood, Principal, and the teachers of the Stoner School, Lansing, Michigan, for permission to carry on the study in their school. iv TABLE OF CONTENTS . INTRODUCTION ............................... Types of Concept Formation Which Have Been Investigated With Reference to Intelligence .......... ' Concepts of time .......................... Concepts of space ......... ‘ ................ Concepts of number ........................ Studies involving form discrimination and form analysis, including the use of sorting tests ........ Concepts of causal relationships ............... Social concepts ........................... Studies involving the use of abstract reasoning, including learning .......................... Studies involving specific intelligence tests and items customarily used in such tests ............ Discussion ................................. THE PROBLEM ............................... Hypotheses ................................ Definitions ............................... The Experimental Tasks ....................... The catego rizing task ....................... 14 16 16 23 26 35 35 35 36 36 Page The intelligence test ........................ 39 Subjects .................................. 40 RESULTS ................................... 44 DISCUSSION AND CONCLUSIONS ................... 55 SUMMARY ................................... 60 APPENDIX .................................. 62. BIBLIOGRAPHY ............................... 65 vi TABLE II. III. III-A. IV. IV—A. VI. LIST OF TABLES Age, Grade, Sex, and Intelligence Test (WISC) Results for the Three Groups . Means, Standard Deviations, and Ranges of the Scores on the Categorizing Task ........................ Coefficients of Contingency for Mental Age and Chronological Age and Number of Concepts, and Chi Square of the Difference .................... Intra-Age Group Relationships Between Intelligence Quotient and Number of Concepts ..................... Coefficients of Contingency for Mental Age and Chronological Age and Mean Time per Concept, and Chi Square Of the Difference ................. Intra-Age Group Relationships Between Intelligence Quotient and Time Scores Coefficients of Contingency Between Mental Age and Chronological Age and Degree Of Dimensionality ......... . Intra-Age Group Relationships Between Intelligence Quotient and Degree of Dimensionality ................. Coefficients Of Contingency Between Mental Age and Chronological Age and Number of Nonfunctional Concepts . . . vii 0000000000 IIIIIIIIII oooooooooo Page 42 46 47 47 50 50 52. 52 53 TABLE Page VI-A. Intra-Age Group Relationships Between Intelligence Quotient and Number Of Nonfunctional Concepts ..................... 53 viii INTRODUCTION Various kinds of concept formation have been dealt with in the literature. These include abstraction, analysis, synthesis, gener- alization of ideas, the grasping of general principles, and so on. Likewise, the investigations purporting to measure or determine the nature of concept formation have been as varied as the exPerimenters' I own conceptions and definitions. Only comparatively recently have such problems as concept formation been subject to exact investiga- tion and analysis. The purpose of this paper is to present a study Of a circum- scribed area of concept formation and its relationship to general intellectual functioning or ability. After a general consideration of the relationships between concept formation and intelligence based on a review Of the pertinent literature, a series of hypotheses and a methodology to test them will be presented. Types Of Concept Formation Which Have Been Investigated With Reference to Intelligence Many conditions related to the study of concept formation in children have been investigated. These conditions include chronological age, sex, training and experience, socioeconomic status, and vocabu- lary level, as well as intelligence or mental age. The types of con- cept formation which have been studied in relation to these conditions are more numerous; they include concepts of time, Space, cause—effect, part—whole, and number. A. large group of studies, more remotely related to concept formation, are those dealing with abstract thinking or reasoning. Still another type Of concept formation might be cata- logued under social concepts. However, the largest proportion of studies in this context are concerned with what we might call form analysis and/or form discrimination. These studies, represented by the Hanfmann-Kasanin (Vigotsky) Test, the Weigl Test, and the Goldstein-Scheerer type of test, involve sorting tasks in which com- mon elements are to be found among the stimuli presented. This type of test is now widely used in differentiating between so—called abstract and concrete behavior in psychopathology. Concepts Of time. Studies of time concepts in which the fac- tor Of intelligence was considered were carried out by Friedman (9, 10) and Grigsby (16). Friedman administered a battery of tests which he calls ”tests Of time understanding" to large groups of elementary school, junior high school, and senior high school stu- dents, as well as to a group Of adults. His time tests included personal and historical time lines, time words and dates, and tests of chronological sequence. He gives no information as to the origin of his intelligence measures, although it is likely that they were ob- tained by means Of group intelligence tests. At any rate, his results indicate little relationship between his tests and I.Q. in elementary school children. Correlations ranging from 0.31 to 0.55 between I.Q. and time concepts were Obtained among junior high school children, and correlations from 0.28 to 0.49 were obtained among senior high school students and adults. He also found insignificant correlations \ between his tests and socioeconomic status. Grigsby's study yielded results which generally parallel those of Friedman, although the sense of time relationships‘seems to level Off earlier in the latter study. Therefore, the results indicate that although there appears to be some relationship between the concept of time and intelligence, the develop- ment is highly disProportional. The concept of time deve10ps slowly at first but accelerates more rapidly during the early school years, then levels Off in the early high school years. Other possible fac— tors which were not investigated extensively by the above authors include training and experience, although socioeconomic status had no apparent effect on the formation Of concepts of time. The major criticism of these studies in terms of intelligence is the possible unreliability of the intelligence measures which were used. Concepts of space. Studies in this area involve the percep- tion of spatial relationships. Two representative studies are cited. Welch and Long (50) administered a battery of nine reasoning tests to -children in two groups aged four to six and six to eight. Some Of these tests were concerned with the ability to discover general principles in Spatial figures. The examiners were also interested in comparing the two age groups with respect to their ability to profit by hints, and to generalize to other reasoning problems which might be solved by using the same principles. Although little dif— ference was noted between these two age groups, the Older group seemed better able to profit from hints, and they were also superior with those problems involving the use Of words. Although no infor— mation is given relative to the intelligence Of the children involved, it may be inferred that the influence of education (i.e., exPerience) was primary. Grigsby's study (16), mentioned above, confirms the general expectation that such concepts become more explicit with increasing age, as does the ability to consider objects in relation to themselves without interposing the self as a point of reference. Graham and others (14) presented a discrimination problem consisting of circles varying in density and squares varying both in area and density to seventy-five children of ages seven to nine years. They were presented three squares varying in area and rewarded only when the square of middle area was. selected. If the middle square was selected on twelve consecutive trials, a critical series was presented with all reSponses being rewarded. The critical series consisted of both the circles and the squares. The results indicated that the ability to form a generalized concept Of "middle- ness" increases during the age interval from seven to nine. The authors also found a definite relationship between the first choice in the critical series and'later performance in this series. The authors state that this investigation was carried out in order to con- trol for the possibility that the child might be learning to respond to a specific stimulus rather than to the generalized feature of the stimulus. This experiment is notable for its methodology and con- trol, and it might be profitably applied to children on whom meas- ures of intelligence have been obtained. Concepts of number. Arithmetical ability, as well as the gen- eral formation of concepts of number, have long been considered as aspects of intellectual functioning, and as such arithmetical ability has played a part in the construction Of test batteries designed to measure general intelligence. In the WechslereBellevue Intelligence 6 Scale for Adults, for example, scores on the arithmetic subtest cor- relate from 0.63 to 0.67 with the total score. Wilson and Flemming (54) administered 106 different educational measures to twenty—five first-grade pupils, all of whom had also been given the Revised Stanford—Binet. One of the highest correlations found in this study was that between mental age and the numbers subtest of the Metro— politan Readiness Tests. Some of the lowest correlations were be- tween the authors' tests and chronological age. Since the effect Of formal education may be assumed to be at a minimum with these first-grade children, the authors' findings are more meaningful. Welch and Long (51), using tests involving their own conception of hierarchies of concepts with a wider age range of child subjects (42 to 83 months), found that those who failed to pass any of the "hierarchyH tests were also inferior in tests of number discrimina- tion and number matching, among others; whereas those children who passed their tests at any hierarchy were about equal in their ability to discriminate numbers, match numbers, and remember digits. These authors conclude that age differences between those groups passing and failing any of the tests contribute to the superiority of one group over the other. Using a higher and wider age range, Stuart (41) administered a varied battery of reasoning tests to 1,400 children Of ages nine to sixteen years. The battery included one test which purported to measure mathematical judgment. He used the Otis Self Administering Test of Mental Ability to Obtain an intel- ligence measure, and the Stone Reasoning Test in Arithmetic. The correlation between the two scores was 0.25. The highest correlation found between I.Q. and the nine tests given was 0.49 (reliabilities ranging from 0.72 to 0.93) for a test of ”ethical discrimination." Although Stuart concludes that I.Q. has little relationship to the capacities which he measured, he criticizes the use of group intel-l ligence tests in such research. He feels that the relationships would have been much higher if more—adequate measures Of intelligence had been used. This is a criticism which can be leveled at many studies in this area. Studies involving form discrimination and form analysis, in- cluding the use of sortirg tests. Most of the studies involving con- ceptualizing ability as usually defined are included in this section. It is likely that these investigators were attempting to tap a "pure" intellectual or abstract function. By the same token, the type Of conceptualizing ability measured by these procedures not only allows detailed analysis of the qualitative processes in the formation of concepts, but it also makes the final product more amenable to quan- tification. One of the most complete studies utilizing this type Of cate- gorizing ability is that of Reichard, Schneider, and Rapaport (36), who used the tests devised by Weigl (48) and Goldstein (13). The subjects were 234 normal white children aged four to fourteen. The authors' professed aim in this study was to provide normative data on the tests and subjects in question, so as to make these tests more ef- fective in studies of abnormality. A quantitative scoring method was used, as well as the usual qualitative evaluation of responses. The qualitative evaluation was based on the subjects' verbal behavior which the authors classify as: (a) concretistic (nonessential, inci- dental features); (b) functional description (function Or use); and (c) abstract conceptual definition. The results are specified as follows: 1. Weigl Color-Form Test. a. Children below five do not shift from a grouping principle they have once conceived. b. At seven to eight years the ability to perform two groupings becomes predominant. c. Above eight years 75 per cent or more are able to form both color and form groupings and are able to shift. d. Groupings on this test occur more frequently in terms of form. 2. Goldstein-Scheerer Sorting Test. a. There is a steady increase in the number of correct re5ponses and conceptual definitions in the first part where the child makes his own groupings; this appears to approximate the normal growth curve. b. In the second part where the child must define the groups formed by the examiner ("to meet the con- ceptual standards set by our civilization") the de- velopment is less regular. c. Grouping ability develops much faster than the ability to give verbal explanation for one's own groupings. Thompson (42), also using the Weigl test, as well as a modi- fied form Of it (“The BRL Test") and the Vigotsky Test (used by Goldstein and Scheerer), classified sixty children of average intelli- gence into two groups (grades four to six and grades one to three). Her results briefly indicate that generalizing ability increases within the age range studied, but she also notes a wide range of variability. Dickinson and Tyler (8) attempted to investigate the relationship be- tween this type of concept formation and intelligence more explicitly. They administered Smoke's (15) concept-formation cards (reliability of 0.87 to 0.92) to four groups Of second-grade pupils who were roughly comparable in mental and chronological age. The results indicated low, positive, and nonsignificant correlations with intelli- gence, this being measured by the Otis Group Intelligence Scale, Primary Examination, Form A. The authors conclude: 10 In general, the pupils at this level obtain higher gener- alizing scores when they are required to recall past experiences than when the memory factor is eliminated. The criticism of the use of group intelligence tests with children is also valid here. Using an adult population of fifty—three white male prisoner patients in Lexington, Kentucky, Aldrich (1) administered the Vigotsky Test along with the Wechsler-Bellevue and Rorschach Tests. He Ob- tained fairly high, significant correlations between the former two tests: Correlations Of the Vigotsky with the Wechsler-Bellevue: Information ........... 0.59 i: 0.07 P.E. Comprehension ......... 0.46 :I: 0.09 Arithmetic ............ 0.42 :I: 0.09 Similarities ........... . 0.62 :l: 0.07 Verbal Scale .......... 0.63 :l: 0.07 Picture Arrangement ..... 0.73 :1: 0.05 Picture Completion ...... 0.56 :l: 0.08 ' Block Design .......... 0.56 :l: 0.08 Object Assembly ........ 0.22 :l: 0.11 Digit Symbol .......... 0.38 :l: 0.10 Performance Scale ...... 0.66 :h 0.07 Full Scale ............ 0.67 :1: 0.06 In this same vein, Semeonoff and Laird (37) investigated the possi— bility of using the Vigotsky Test as a measure of general intelligence. Their analysis yielded correlations of 0.4 and 0.5 with a reasoning 11 test and the Progressive Matrices, a British group test. The Vigotsky Test correlated 0.57 (£0.04 P.E.) with‘the Kohs blocks. On the basis of these results, the authors conclude: While the Vigotsky Test cannot be regarded as a suitable alternative to commonly accepted intelligence tests, it has possi— bilities as an instrument for the study of at least the qualitative aspects of intelligent performance. Prothro (34) compared the intellectual performances of a group Of adult aments with children Of similar mental age (mental ages of five and six) on. sorting and digit tests. While both groups exhibited animistic thinking, much variability was noted, indicating that individuals of a given mental age do not stand exclusively at any single stage. Furthermore, the aments seemed to experience some difficulty in shifting from one aspect Of a situation to another, although they could explain the bases Of the groupings after they had been shifted by the examiner. The general results indicate that the aments were significantly poorer than the children on both the sort- ing and digit tests. Although the range Of chronological ages Of the subjects in this study is very wide, the results tend to support the argument that mental age is the better determiner of performance on a concept formation test than is chronological age as such. Colby and Robertson (4), who were primarily interested in the comparative development of form and color concepts, administered 12 the Vigotsky Test to 158 children aged 3-1/2 to 9—1/2. They con- clude that ”both constitutional and chronological factors are present in the formation Of concepts at these age levels,” and they state further: The Vigotsky Test is essentially a multiple unit abstrac- tion test. In it, color abstraction supposedly reveals a more primitive, i.e., a more concrete perceptual mind; form, an ap- perceptional or conceptual mind. The latter correlated with high intelligence and high scholastic achievement. Although these authors promise more-explicit analysis of their data later in terms of intelligence, apparently this has never been carried out. Also primarily concerned with color-form dominance at vari— ous age levels and Offering no information regarding intelligence, .Heald (19) found regular improvement associated with chronological age on this sorting—type of concept formation task. Stacey and Cantor (40) used Zaslow's test in their research. This test consists of fourteen cards on each of which is reproduced a figure. The fourteen figures range on a regular continuum from a circle to an equilateral triangle. The subject is asked to arrange the cards according to whether they belong to the ‘circle or the tri- angle, or the subject may be asked to arrange all of the cards along the continuum from circle to triangle. Stacey and Cantor presented 13 this test to four groups of fifteen subjects each, aged thirteen to fifteen. The mental ages of the subjects ranged from moron to borderline levels (I.Q. 49 to 79), determined by the Revised Stanford- Binet, Form L. With reference to intelligence, the results indicate that the borderlines tend to perform on a higher conceptual level than the morons. When the examiner selected the extremes of the continuum (pure circle and triangle) and the subjects were asked to place the rest of the cards along the continuum, the borderlines were clearly superior to the morons in their ability to do this. A study involving the more classical methodology was carried out by Crudden (5). He presented various series of complicated figures, in which had been imbedded symmetrical geometric figures to sixty-five subjects aged sixty—five months to seventy-eight months. The task ofothe subjects was to find previously learned simple fig- ures within the complicated figures. In terms of intelligence and age, the results indicate a definite relationship between ability on this test and I.Q., while no significant differences. were found between the ages used in the study. The authors conclude that abstraction as measured by means of their test is a significant function of intelli- gence. 14 Concepts Of causal relationships. The child's conception of causality has been investigated largely from the standpoint of natural versus supernatural causality. Most of the studies (20, 25) show parallels between this type Of concept formation and the other types, especially in terms of development or maturation. Lacey and Dallen— bach (25) state that concepts of causal relationship are probably not fully grasped until the eighth or ninth years of life. Until this time, most writers agree, such concepts are characterized by various de- grees of animistic or magical thinking, in which the child has diffi— culty in separating himself from his conception of the external world. Piaget (32) particularly emphasized the egocentric aspect Of children's concepts of causality. Hazlitt (18) takes issue with this conception, asking how the child manages to master his environment as well as he does. Hazlitt feels, furthermore, that great care must be exer- cized in the interpretation of Piaget's investigations due to the nec— essity in these studies for the child to exPress his concepts verbally. Hazlitt also feels that the difference between adult and child thinking is that of degree. He points out the fact that the adult is likely to make the same mistakes as the child when dealing with wholly un- familiar material, and that the adult is superior mainly in his verbal facility. 15 At any rate, Deutsche's (7) classic experiment is of interest to us in this connection because she also investigated the relation- ship between cause and effect concept formation and intelligence. She administered two sets of questions dealing with phenomena of nature to 732 subjects between the ages of eight and sixteen years. The first set was preceded by simple demonstrations about which the children wrote their comments concerning cause. Intelligence quotients were available from routine school examinations with the Kuhlmann-Anderson, the Army Alpha, and the Unit Aptitude Test. Her results indicate an increase in mean score with age, with a greater rise between the ages of eleven and twelve than between any other two consecutive ages. With children of age twelve only, cor— relations of 0.405 for Form I and 0.265 for Form II were obtained between her tests and school grade. Both forms combined correlated with school grade tO the extent Of 0.445. Kuhlmann—Anderson I.Q.‘s correlated 0.265 (Form 1), 0.129 (Form II), and 0.182 (combined forms). Deutsche concludes on the basis of her study: The higher relationship of quantitative scores to school grade than to age, and the low relationship between quantitative scores and intelligence and socio-economic status, suggest that training or experience, as acquired through the schools, out- weighs intellectual or innate maturational factors in determining the ability of children to answer the questions included in this test. 16 The use of "routine” group tests of intelligence is one of our major points of criticism of Deutsche's study. Social concepts. In a study of the developmental aspects of social concepts, Ordan (30) found a steady increase in abstractness from grade to grade, although concepts in the different social prob- lem areas differ in this respect. Furthermore, recognition of social problems is not great before the sixth or seventh grade. By using a personal interview test adapted for group use, Shaffer (38) had groups of children write the meanings of words involving social concepts. These words were presented on the black- board, and the children were asked to write everything they could about them. The responses were rated on a ten-point scale scale from complete misconception to very superior response. A. relia- bility coefficient of 0.90 was obtained with the word test with close agreement between the group and individual forms. Scores on the word test correlated 0.23 with an unsPecified group intelligence test. Studies involving the use of abstract reasonin& including learning. Welch (49) and Welch and Long (52) point out the hierarchi- cal nature of concept formation, indicating from their studies that the development of abstraction proceeds from lower to high levels in a l7 species—genus relationship: "Classes include other classes down a line to nine or more hierarchies" (49). Therefore, concepts are learned in hierarchical orders. For example, the class of human necessities (third order) includes the class of food (second order), which in turn includes the class vegetables (first order), composed of ”this potato" or ”that carrot” (authors' examples). Thus, this type of concept formation can be described in terms of "vertical" and ”horizontal" develOpment. The former proceeds from the level of proper names upward to the first- and second-order concepts, and the latter involves relational transitions ”which permit the individual to think of certain visual data as members of different classes at the same hierarchical level. . . . the shift in identity from one classificatory sense to another is an essential phenomenon of the higher processes of human thinking" (52). On the basis of their studies, these authors conclude that "discrimination, generalization and memory are the major fac- tors involved in the genetic development of abstract thinking." Al— though offering no specific material pertinent to intelligence as it is usually measured, it can be seen that many of the same factors which these authors consider important in concept formation are also usually considered as contributing to general intelligence. An attempt was made by Peterson (31), however, to investi- gate quantitatively the relationship between different levels of 18 abstraction and scores on an intelligence test. He devised an appa- ratus consisting of a lever with different positions along each arm for placing weights of different magnitudes. The subjects were given demonstrations with this apparatus. They were then required to find the general principle involved in determining specific weights which will balance at different positions along the arms of the lever. This test was presented to 539 subjects in school grades SE to 12B. In- telligence scores were obtained by administering the Terman Group Test of Mental Abilities for Grades 7 to 12, Form A. The results are tabulated as follows: r (Age and Intelligence) ...... 0.5363 :1: 0.031 P.E. r (Age and Generalizing) . . . . . 0.4587 2*: 0.034 r (Intelligence and Generalizing) 0.4049 :h 0.036 r (Age and Grade) . . . . . . . .. 0.8670 :h 0.011 r (Intelligence and Grade) . . . . 0.7573 :1: 0.018 r (Generalizing and Grade) . . . 0.5584 i 0.030 The author summarizes his conclusions as follows: There is no relationship between age and the ability to I solve general principle problems when grade is held constant; I there is no relationship between intelligence scores and ability to solve general principle problems when grade is held constant (partial correlation). The correlation between problem scores and intelligence scores for each age is positive but not high enough to indicate much similarity between the two tests. It would appear, therefore, that the generalizing task, while being an ability which is commonly thought of as intellectual, was neglected in the intelligence test used in the study. It would also appear that 19 school grade is more closely related to the task under consideration than is intelligence, another argument in favor of training and ex- perience. Husband (21), in a study primarily designed to relate various types of learning to general intelligence, administered some learn- ing tasks to fifty-three children with I.Q.‘s ranging from 81 to 162. The tasks included maze learning and the mental maze. He obtained correlations of 0.38 with maze learning and 0.34 with the mental maze in relation to I.Q. No information is given as to the origin of the intelligence score. The highest correlation of his battery with I.Q. was that with reading. On the basis of this study, the author concludes that these learning abilities are specific rather than general. The question arises, however, as to the type of conceptu- alization ability which is measured by using mazes; this question may also be asked about the work. Of Crudden (5), previously cited. Johnson (23), in considering this general area, also casts her lot with those who favor experience and training as the primary factors in the formation of concepts. She also sees many relationships be— tween the conceptual thinking Of adults and children, especially when both are faced with an apparently insolvable problem. She states: 20 The comparative analysis of the conceptual thinking of children and adults in unfamiliar situations shows similarity in individual differences in the selection Of procedure. This proc— ess is determined in part by previous experiences in develop— ment of concepts and in application of principles in the solution of problems. The studies of children give evidence of the early development of concepts and the ability to respond to the rela— tive differences or similarities in situations presented. The child is less hide bound by traditional forms of response. In unfamiliar situations the adult often reverts to habitual forms of response which are repeated though previously found unsatisfactory. With repetition, more logical modes of attack are. made. It is difficult to classify the various studies according to types of conceptualization ability studied, since, for example, those studies which utilize learning procedures predominantly may also use form discrimination or sorting methods as the stimulus material. Long and Welch (28), working within the framework of their hierarchical formulation, state that correlations between tests of syllogistic rea- soning and intelligence tests vary from 0.58 to 0.81. This latter figure is the highest claimed in any study, and it is regrettable that the authors do not substantiate it. At any rate, the authors presented a group Of four reasoning tests which were all solvable by some general principle to forty children aged 8 to 11-1/2. All of these subjects were also given the Revised Stanford-Binet. The authors conclude: 21 For the solution of any standard reasoning problem a minimal level of develOpment or maturation must have been attained in abilities which are only partially measured in stand- ard intelligence tests. It is apparent, therefore, that these authors consider chronological age at least as important as mental age in the ability to deal with abstract concepts. In a similar type of study, Ray (35) found a much higher relationship with intelligence. He administered a bat- tery of twenty-one tests designed to measure generalizing ability to eighteen lZ-year-old children. These subjects were divided into three groups on the basis of intelligence, as measured by the Binet. A. rank difference correlation of 0.89 was found between the complete solution of the problems (represented by the elimination of errors and correct statements of generalization) and intelligence. Further- more, low scores on the Binet showed a positive relationship with the frequency of a trial-and-error type of solution. It is likely, therefore, that the reasoning tests used in this study were tapping much of the same material as does the Binet. It might prove fruit- ful for this reason to break down the reasoning test battery in order to perform a subtest analysis. Brody (2) also used four subtests in making up a battery purporting to measure reasoning. These tests were designed to measure “verbal concrete reasoning" (VC), "verbal abstract 22 reasoning" (VA), ”nonverbal concrete reasoning" (NVC), and "non- verbal abstract reasoning" (NVA). The tests were administered to 1,301 children in grades four to twelve. Intelligence measures were also available from an unspecified source. Brody computed many different intercorrelations, including partial and multiple correlations, attempting to hold statistically constant single or multiple variables. Intelligence quotient correlated with NVC 0.40, with NVA. 0.45, with VC 0.52, with VA 0.54, and with the total battery 0.53. On the basis of these results, he concludes: The four types of reasoning tests do not individually seem to involve the same things measured by ordinary verbal intelli- gence tests. . . . VA and VC combined best approach this. Brody further suggests the possibility that verbal and nonverbal abil- ities may not be as independent as is sometimes claimed, and that there is the tendency to verbalize nonverbal items. The two studies to be cited next relate concept formation to vocabulary level. The first, by Noffsinger and Louttit (29), claims that the development of vocabulary is an important factor in the process of concept formation, a conclusion which seems quite rea— sonable if one considers only the verbal aspects. The other study, by Wilson (53), involved the presentation of twenty so-called "action- agent words” to college students and kindergarten and first-grade 23 children. The results indicated much less difference between these groups than anticipated. Although the older group was more variable, a greater variety of specific concept re8ponses was elicited in the younger groups. The college students also showed an ”appreciable percentage" of general and loose and incorrect reSponses to the fa- miliar words. Studies involving specific intelligence tests and items custom- arily used in such tests. As Wechsler points out (45), ”The concept of intelligence includes several factors: the cognitive abilities such as abstract reasoning, verbal, Spatial, numerical and other Specific factors, and the conative functions like drive, persistence, will and/or some aspects of temperament." Some of the studies reviewed in this section attempt to relate conceptualizing ability to one or more of these factors, as well as a general factor. The following studies were mainly carried out with the purpose of identifying a general factor, as well as the number and nature of Specific factors which go to make up total intellectual functioning. As Wechsler infers above, such undertakings may well be doomed to failure unless the "non—intellective" factors are also considered. At any rate, since many subtests of standard intelligence test batteries involve types of conceptualizing ability, the contributions of such subtests to the total 24 score or I.Q. should cast some light on the relationship between con— ceptualizing ability and intelligence. As pointed out previously, the block design and similarities subtests of the Wechsler-Bellevue Adult Scale Show the highest re- lationships to the total score; these are the subtests which might be best considered as measuring conceptualizing ability. Goldfarb (12) noted this possibility and found that the block design test also best measured intelligence when compared with the Otis Twenty Minute Test. He feels that the block design test measures the higher forms of synthetic or analytic ability, but he criticizes its manner of ad- ministration in the Wechsler-Bellevue. Since credit on this sub- test is partially dependent upon Speed, Goldfarb feels that its full potentialities are not being realized. Therefore, he administered his modified block design test to thirty adolescents of ten to four- teen years Of age He devised a broader scoring system and allowed a five-minute time limit in order to detect finer nuances of quali— tative performance. Each subject was also given the usual block design test as well as the Vigotsky and Weigl tests, which were scored in a manner devised by Zubin and Thompson (56). The ob- tained correlations are: 25 W-B Block Design Revised BD W-B Block Design - 0.90 W-B Similarities 0.56 0.65 Vigotsky 0.47 0.60 Weigl 0.52 0.57 It can be seen that, although the relationship between the original and revised block design tests is very high, in all instances there is a higher relationship between the other tests and the revised block design test. The altered method of scoring may provide an answer to the seemingly lesser contribution of the block design sub- test in the Wechsler Intelligence Scale for Children. Studies involving factor analysis are extremely numerous. One representative study of this type is that of Burt and John (3), who analyzed the Revised Stanford-Binet. As in most such studies, a general factor and five specific factors were identified; the gen- eral factor contributed 40 per cent of the total variance. The spe- cific factors were verbal, Spatial and numerical, immediate memory, understanding words, and understanding situatiOns. The authors feel that the Specific factors reflect the effects of test difficulty or age. Jones (24) did a similar analysis. also differentiating between four age levels (ages seven, nine, eleven, and thirteen). While he finds some factors common to all of these ages, he also identifies some which seem to be characteristic of one or the others. Reasoning 26 and ”visualization” seem to be more important at the upper age level. Jones did not find a general factor, stating, "Items on the Revised Stanford—Binet do not measure a unitary factor; the relations among the items can be explained most efficiently and consistently in terms of group factors, each contributing to a subject's total score or I.Q." Furthermore, it seems that the battery of items included at one age level of the Stanford-Binet is not factorially identical to the battery of items at other age levels. In a somewhat different vein, Laycock and Clark (26) analyzed Stanford-Binet performance in groups of old—dull and young-bright children of the same mental age. The wide differences found between these two groups are explained by the authors on the baSis of en- vironmental influences and the effects of experience. Tsao (43), using a modified factorial method, found that '‘variability in a men- tal or scholastic function was constant from grade to grade or from age to age,” but increasing age increases variability. He criticizes most factorial studies on this basis. Discussion It has been seen that the problem of defining what a concept is and how it is formed has been a recurrent source of discussion. 27 Early studies, using _intrOSpection as an experimental technique, tended toward definitions in terms of subjects' descriptions of the self-per- ceived processes which they used. Later work involved a marked change in direction and technique, and since that time definition has been based on overt behavioral acts. Regardless of the methodology involved, however, two major theories have been offered in explana- tion of the process. These are summed up by Woodworth (55) as follows: 1. Composite photograph theory: the features common to a class of objects summate their impressions on the observer, who thus gradually acquires a picture in which the common fea- tures stand out strongly while the variable characteristics are washed out. 2. Active search theory: the concept is supposed to originate as a hypothesis, which the observer proceeds to test by trying it on fresh specimens of the class. It will be noted that the first of the above theories assumes that conceptualization ability is a process Of abstraction of common char- acteristics or relationships, while the second assumes that a process of generalization is involved. Probably neither of these theories provides a complete explanation of the process, since both abstrac- tion and generalization seem to occur. In the course of attaining a concept, subjects almost invariably develop hypotheses or ideas about the factor common to all the stimuli. While testing these hypotheses, the pertinent elements of the stimulus field gradually 28 come into sharper focus. Although it is possible to conceive of situ— ations in which concepts are attained solely through abstraction or solely through generalization, the artificiality of such situations makes them unrepresentative of the process of concept formation in every- day life. It would appear, therefore, that both Of these approaches and their interaction are needed and utilized by the organism. How- ever, we are more concerned here with the conditions related to the formation of concepts than with the processes involved. With reference to children specifically, the study of conceptualiz- ing ability can be classified into two major groups: those which attempt to specify the characteristics of children's concepts and those which attempt to define the nature Of the conditions related to the formation of concepts. With regard to the latter, chronological age and intelligence are major considerations. Piaget's work opened up the area for extensive experimentation in the attempt to define the nature of conditions related to the formation of concepts and to describe the developmental formation of conceptual thinking. Pia- get's descriptions, arrived at by means of his "clinical method,” which mainly involves an interview-questionnaire procedure, specifies conceptual age levels and stages at which specific types of concepts may be expected to emerge. For example, in reference to the child's 29 conception of physical causality he postulates three main stages: up to age five or six the child's thinking is largely animistic and magical or ”precausal"; at about ages seven to eight the precausal thinking is still predominant, but many of the magical features have disappeared. The final stage, which is completed at about ages eleven to twelve, is characterized by more-rational adult-type thinking. Thus, accord— ing to Piaget, almost all of the conceptual experience of children progresses from diffuse, prelogical, and subjective forms through definite stages to more-differentiated, logical, and objective forms. The question which arises in our present context is whether there might also be such a relationship between concept formation and mental age as well as chronological age, and which factor is likely to be more important. It is possible to distinguish three major methods which have been used in the study'of conceptualizing ability. The first, the intro— spective method, we have noted was in greatest use during early in- vestigations of the problem. With this technique, the subject was usually faced with a task that called for some sort of conceptual behavior and he was asked to continue working with this task until he was able to report on his mental processes. Without going into detail on the merits and defects of this method, note should be taken 30 of the obvious unreliability and idiosyncratic nature of the reports that result. It is likewise obvious that application of this method to children is e5pecially unreliable since it places much weight on the verbal ability of the child or his ability to eXpress verbally his thought processes. The use of this method, while it may furnish some information concerning concept formation in a single individ- ual, is not of much value in the study of conceptualization as a uni- Versal function. The second method has been called "the learning method," and it consists of situations something like the one in which the sub- jects are required to learn the names of a series of stimuli, say by the anticipation method. They are then shown a second series of stimuli each of which has something in common with the first series with the problem of determining this common element. Un- fortunately, the use Of this approach is objectionable in that the concept formation process may be distorted by factors which are peculiar to the learning situation per se; e.g., retroactive inhibition. Consequently, any results must be viewed with skepticism if this method is used, at least so far as concept formation is concerned. The "problem-solving method" is the name given to the third kind of methodological procedure. Although similar to the learning 31 method, this technique does not require the subject to go through a preliminary learning period. Instead, he is presented with a collec— tion of stimuli, either simultaneously or successively, and asked to determine what they have in common or to classify them in some way. The categorizing tasks used by Hanfmann and Kasanin and Weigl are typical of this method. From this discussion, it would appear that, of the three methods described above, the last (i.e., the problem-solving method) is the one which permits the most successful investigation of concep- tualizing ability as an isolated phenomenon, especially in children. Furthermore, it will be seen later that this method lends itself to operational definition of certain generalized hypotheses. Finally, it permits quantification of the subjects' responses, thus enabling the obtained results to be put to statistical test. For the above reasons the problem-solving method is to be preferred. Studies aimed at determining and designating conditions related to concept formation arose in response to the necessity for quantify- ing general intelligence. Early intelligence scale constructors were faced with the problem of determining those specific functions which go to make up general intelligence. After devising specific tests which were thought to measure aspects of intelligence, these were 32 combined into batteries, administered to large populations, and then analyzed statistically in order to ferret out the ”factors," or those aspects which appeared to be primary in determining the total score. Studies of this type have isolated factors which seem to be related to the general area of conceptualizing ability, but the tasks utilized have been so varied and the statistical manipulation so devious that few definite conclusions have been possible. For example, Garrett (11), using factorial methods, concludes, "Abstract or symbol intelli— gence changes in its organization as age increases from a fairly unified and general ability to a loosely organized group of abilities or factors." 'Curtis (6) attempted to verify Garrett's hypothesis and found the opposite to be true. He states, in referring to the above hypothesis, ". . . as age increases, the general factor should have contributed less to the variance of the tests, but as found here be— tween ages nine and twelve there was an increase in the contribution of the general factors." However, Curtis also suggests the possibility that the differences between these two age levels might be due to the relative difficulty of the materials. Be that as it may, the processes of generalization and abstraction have subsumed many of the items in intelligence scales, and these subtests seem to correlate highest with the total scores. It follows, therefore, that conceptualizing ability should likewise be related to intelligence as we commonly measure it. 33 On this question, Vinacke writes (44): It is probably safe to say that psychologists have assumed that intelligence and concept formation are related, although they have not yet worked out the relationship explicitly. There are two assumptions really: (I) that one of the variables of intelli- gence is the ability to form and use concepts, and (2) that part, at least, of the reason why mental age increases during the pe- riod of growth is that the ability to conceptualize increases. Relatively little has been reported in the literature concerning the relationship between cognitive functioning and intellectual level. It has been seen that Deutsche found low relationships between scores on tests Of causal relations and intelligence test scores. The studies of Long and Welch also indicate that chronological age is at least as important as mental age in the formation of concepts. Most of these studies are deficient in one or more respects: number of subjects too few; intelligence criterion based on unreliable measures such as group tests; inadequate or inappropriate statistical procedures. While it might be assumed that the development of intelligence parallels general physical and mental development, it stands to reason that conceptualization ability as an area of intellectual ability should increase proportionately with that ability. Similarly, just as educa- tion, general experience, possibly socioeconomic status, and other factors influence the intellectual development of the child, so might 34 these factors influence conceptualizing ability, although this has been inadequately demonstrated in the past. From Piaget, Long and Welch, and others referred to previ— ously, we find that in addition to the increase of conceptualization ability with age there are also changes in dimensionality and com- plexity. Conceptualization proceeds from prelogical and magical to logical and objective, or possibly from concrete to abstract. Long and Welch have defined this also in terms of levels of abstraction. The parts which maturational factors and/or general intellectual factors play in this continuum have never been adequately investi- gated. THE PROBLEM It is evident from the review of the literature that the relation- ship between conceptualizing ability and intelligence has not been ade- quately investigated with reference to children. Almost universally, psychologists have assumed an intimate relationship between concept formation, as defined as abstraction and generalization, and intelli— gence. However, experiments have been either inconclusive or they have yielded results to the contrary, tending to support a conclusion that conceptualizing ability is primarily a function of training and ex— perience as represented by chronological age. Previous studies have been criticized on the following grounds: inadequate number of sub- jects, dependence on verbal responses with young children, narrow age range, inadequate control of the effects of exPerience Of educa— tion, and use of unreliable or inapprOpriate measures of intelligence. I Hypotheses 1 Definitions. For the purpose of this study, "categorizing be- havior" is defined as a process in which an individual, confronted with the task of classifying a group of objects, proceeds to discriminate 35 36 the essential common properties of the various Objects and to group them accordingly. Wechsler's definition of intelligence as "the ag- gregate or global capacity of the individual to act purposefully, to think rationally and to deal effectively with his environment" (46) is acceptable for our purposes. Based on the previous discussion and the review of the per- tinent literature, the following hypotheses are offered in order to test some of -the‘implications: Hypothesis I: There is a positive relationship between intel- ligence and the various aspects of conceptual functioning. Hypothesis II: Categorizing behavior is more highly related to intelligence than it is to chronological age. The Expe rimental Tasks The categorizing task. This task was designed on the basis of one used by Heald (19) and ultimately patterned after Weigl (48), Goldstein (l3), and others. It consists of a series of plastic pieces of three different forms (circle, equilateral triangle, and square), three different colors (red, yellow, and green), and three different sizes, for al-total of twenty—seven pieces. The different forms of the same size were made equal in size by equating Surface 37 areas. It was determined that if the sides of the figures were equated, the resulting perceptual differences between the sizes were so great as to virtually force a classification according to this dimension. By equating areas rather than sides, the size difference is still well above the threshold but requires the perception of relationship rather than absolute size. A standard set of directions for administration was devised (see Appendix). After it is certain that the child knows the names of the colors involved, he is asked to place all of the pieces into different groups so that a common principle governs his placement of the pieces. In other words, the subject is told to place all of the pieces into piles so that all of the pieces in each pile belong together in some way. Essentially the same directions are repeated with systematic hints until the subject can no longer classify the pieces in any way. The categorizing task was constructed and used for the follow- ing reasons: It provides a range of difficulty from simple to complex. It has more than one solution in a problem which is po- tentially solvable by individuals with a wide range of ability . - I-‘e- — ._ 1". The 38 It makes possible illogical or inapprOpriate solutions. It is relatively free from the effects of past experience. The results are easily quantifiable in various dimensions. It lends itself to an operational definition of concept forma- tion cited on page 43. categorizing task is scored on six different variables: Score for time: the mean time necessary to achieve a concept which is obtained by dividing the total time by the number of logical concepts achieved. Number of logical concepts: With the twenty-seven pieces of the categorizing task, six logical concepts are possible: classifications based on color, shape, and size, each yielding three groupings, and combinations of these: color-shape, shapecsize, and color-size, each making nine groupings. The first three concepts are referred to as unidimensional since they require a single common principle, and the second three are referred to as bidi- mensional since they require a double principle in their solution. Number of unidimensional concepts. Number of bidimensional concepts. Number of illogical or alogical concepts: these are de- fined as those concepts which the subject derives which ; 39 do not conform to the instructions in that pieces are mis- placed, or there are other than three or nine groupings. 6. Number of repetitive concepts: During the course of the administration any concept which is repeated is called a repetitive concept. Numbers 2, 3, and 4 are called functional concepts, while numbers 5 and 6 for this purpose are termed nonfunctional concepts. The intelligence test. The Wechsler Intelligence Scale for Children (47) was selected as the intellectual criterion for the fol- lowing reasons: 1. The test is now in wide clinical use and any conclusions derived from its use in this study may prove applicable to other areas. 2. The test is demonstrably a reliable measure of intelli- gence at the age levels in question. It is especially appropriate with children since motivational factors can be controlled to some extent through the individual ad- ministration. 3. The test yields scores in many different areas of intel- lectual functioning. 40 4. The scores derived from this test are readily subjected to appropriate statistical analysis. The Wechsler Intelligence Scale for Children has been stand- ardized on children of ages five to fifteen years, eleven months. In addition to a full-scale intelligence quotient, this scale yields a verbal intelligence quotient based on five subtests consisting of infor— mation, comprehension, arithmetic, similarities, and vocabulary; there is also an Optional digit-span subtest. A performance I.Q. is also obtained, this score being made up of picture completion, picture arrangement, block design, object assembly and coding, and the Op- tional maze subtest. In order to make comparisons between age groups, the verbal, performance, and full—scale scores were con- verted to mental ages. In comparing children within a single age group the usual I.Q. was used. Subjects Subjects were selected from the "normal" population of school children. For this purpose, normal is interpreted as those children who do not have a history of emotional or behavior disorder as far as could be determined, and who in the estimation of the teachers do not Show such a condition at the time of testing. The criterion 41 of academic normalcy was the usual grade placement according to age. The age levels of seven, nine, and eleven were selected (school grades two, four, and six). Selection was random through the class rolls, and in some cases an entire class met the criteria and all of the children in it were tested. For purposes of adequate statistical treatment as well as practical considerations of economy of time, fifty subjects at each of the three age levels were selected (total, 150). The categorizing task and the Wechsler Intelligence Scale for Children were administered to each subject. The order of pres— entation of the two tasks was alternated in order to eliminate constant errors due to practice. Data pertinent to the three age and grade groups are presented in Table I. The obtained I.Q.‘s range from the dull average through average, bright average, and superior levels, ranging from 78 to 150. Checked by means of a critical ratio, the mean I.Q.‘s of the three age groups do not differ from one another to any significant degree. The chronological ages correspond to grade level, since only those subjects who were normally grade—placed were used. The mental ages are roughly proportionate to the chronological ages, although the high degree of overlap should be noted between grade levels. Finally, the sample is composed of seventy-two boys and seventy-eight girls. "1 -———--—v TABLE I 42 AGE, GRADE, SEX, AND INTELLIGENCE TEST (WISC) RESULTS FOR THE THREE GROUPS Grade Item Total 11 IV VI Age .................. 7 9 11 Number ............... 50 50 50 150 Chronological age (months): Range .............. 84-95 108-119 132-143 Mean ............... 89.34 113.38 137.56 Intelligence quotient: Range .............. 78-134 80-125 88-150 Mean ............... 107.56 106.62 109.62 107.73 Mental age (months): Range .............. 74-134 90-150 119-189 Mean ............... 98.32 124.14 152.98 Sex Male ............... 26 20 26 72 Female ............. 24 30 24 78 43 With reference to the procedure and the general hypotheses stated on page 36, the hypotheses may now be restated in ope rational terms: A. The number of logical concepts produced is more highly related to mental age than it is to chronological age. The mean time necessary to produce a concept is more highly related to mental age than it is to chronological age; this is an inverse relationship. The degree of dimensionality of the concepts produced is more highly related to mental age than it is to chrono- logical age. The formation of nonfunctional concepts is more highly related to mental age than it is to chronological age; this is an inverse relationship. RESULTS In general, the results confirm our hypotheses; categorizing behavior as measured by the present method is highly related to intelligence as measured by the standard intelligence test. Further- more, although categorizing behavior is also highly related to chrono- logical age, the results indicate that there is a significantly greater relationship between the categorization measures and mental age than with chronological age. The problem which presents itself in the analysis of the data is twofold: to determine the degree of relationship between the vari- ous scores obtained on the categorizing task and measures of in- telligence represented on the WISC by full-scale, verbal-scale, and performance-scale I.Q.‘s, and to determine the differences between these relationships and those with chronological age. It is imme- diately apparent that, in comparing the three age levels with one another, the use of the I.Q. is unacceptable, since chronological age is inherent in such a score. Consequently, it is necessary to con- vert I.Q. scores to mental ages. Although this procedure is not rec- ommended in ordinary practice using the WISC, Wechsler himself furnishes tables for such conversions (47). This procedure is 44 45 defensible in a study such as this, since one, in essence, is using raw scores rather than the converted scores represented by the I.Q. Table II presents data concerning the performance of the three age levels on the categorizing task. Although the ranges on all of the measures are fairly uniform for the three ages, the means and standard deviations show some variability. Because Of the na- ture of these distributions, computation of t's for the differences can- not be justified. However, the magnitude of these relationships as well as those involving mental age are to be determined subsequently by means of the chi-square test. In Table III the comparisons between the number of concepts achieved by the subjects and the three mental age scores are pre- sented. The analysis represented here is the one used as well in most of the subsequent treatments, and a note of explanation is in order. The coefficients presented in Table III are essentially chi squares which have been converted into coefficients of contingency (C) for the sake of clarity. It can be seen that all of the comparisons are significant at least at the 0.01 level of confidence. It can be concluded, therefore, that there is a significant relationship between the absolute number of concepts achieved by the subjects and their mental and chronological ages. However, there are apparent differences TABLE II ON THE CATEGORIZING TASK 46 MEANS, STANDARD DEVIATIONS, AND RANGES OF THE SCORES Age Item 7 9 ll Ranges Number of concepts ............... 1—6 1-6 1-6 Mean time per concept ............. 104.0— 67.8- 55.0- 1766.0 881.0 921.0 Number of nonfunctional conCepts ...... 2—8 0-8 0-7 Number of unidimensional concepts ..... 0—3 0-3 0-3 Number of bidimensional concepts ..... 0-3 0—3 0—3 Means Number of concepts ............... 2.48 3.30 3.38 Mean time per concept ............. 550.54 322.02 261.18 Number of nonfunctional concepts ...... 4.90 4.08 3.94 Number of unidimensional concepts ..... 1.20 1.82 1.88 Number of bidimensional concepts ..... 1.28 1.48 1.50 Standard Deviations Number of concepts ............... 1.17 1.08 1.30 Mean time per concept ............. 344.92 190.20 177.52 Number of nonfunctional concepts ...... 1.43 1.91 1.44 Number of unidimensional concepts ..... 0.85 0.89 0.91 Number of bidimensional concepts ..... 0.66 0.61 0.67 TABLE III 47 COEFFICIENTS OF CONTINGENCY FOR MENTAL AGE AND CHRONOLOGICAL AGE AND NUMBER OF CONCEPTS, AND CHI SQUARE OF THE DIFFERENCE Coeffi- cient of It 2 em Contin- p X diff. Pdiff. gency Chronological age ............ .35 0.01 Mental age (full scale) Chronological age ............ Mental age (verbal scale) Chronological age ............ Mental age (performance scale) Mental age (verbal scale) Mental age (performance scale) 29.65 0.01 .50 0.01 .35 0.01 20.50 (N.S.) .45 0.01 .35 0.01 .41 0.01 25.20 0.03 .4 0.01 5 5.11 (N.S.) .41 0.01 TABLE III-A INTRA—AGE GROUP RELATIONSHIPS BETWEEN INTELLIGENCE QUOTIENT AND NUMBER OF CONCEPTS Item Age 9 11 x2 p x2 p Numbe r of c oncepts 5.03 (N.S.) 4.61 (N.S.) 38.63 0.01 fl 48 between the contingency coefficients. In other words, the data indi— cate higher relationships in favor of mental age in all three cate- gories: full-scale, verbal-scale, and performance—scale, which is in the direction predicted by our hypotheses. However, in order to determine whether this apparent difference is a significant one, some method was needed to test the significance of the difference between chi squares or contingency coefficients. To the writer's knowledge no such test has been devised. Therefore, a method was found to determine the chi square of the difference. This was carried out as follows: The original chi square contingency tables were adjusted so that the number of cells were equal, for both chronological age and mental age. Then a third contingency array was constructed so that the chi square of the difference between each cell frequency could be computed. This chi square is given along with its signifi- cance in Table III for the number of concepts, and in succeeding tables for the other measures where applicable. Therefore, this table indicates that, although both mental age and chronological age are significantly related to the number of con- cepts achieved, the full-scale mental age score and the performance- scale mental age score are more highly related to the number of concepts than is the verbal-scale mental age score. It is also noted, wr- 49 however, that the verbal-scale scores are not significantly better predictors of the number of concepts achieved than are chronological age and performance-scale scores. In view of the significant results in favor of full-scale mental age as opposed to chronological age, an analysis in terms of separate ages is presented in Table III-A. The results indicate that within the separate age levels the relationship is only significant in the eleven- year-old group. Tables IV and IV-A represent the same analysis applied to the time scores. These scores represent the mean time necessary to achieve each concept. Almost identical results were obtained here as were indicated above. There is a significant relationship between the three mental age scores and the mean time necessary to produce a concept. In other words, as mental age and chronological age in— crease, the time necessary to produce a concept decreases. The chi square of the difference between mental age and chronological age is significant with the full-scale and the performance-scale meas- ures, indicating significantly greater relationships than with chrono- logical age alone. Similarly, the verbal-scale scores are not sig- nificantly different from chronological age or from the performance- scale scores. The analysis within the individual age levels, as 50 TABLE IV COEFFICIENTS OF CONTINGENCY FOR MENTAL AGE AND CHRONOLOGICAL AGE AND MEAN TIME PER CONCEPT, AND CHI SQUARE OF THE DIFFERENCE Coefficient It f 2 em .0 p X diff. pdiff. Contingency Chronological age .......... 0.44 0.01 27. . Mental age (full scale) ...... 0.47 0.01 00 0 01 Chronological age .......... 0.44 0.01 18. , Mental age (verbal scale) 0.46 0.01 97 (NS) ' ....... 0.44 , Chronological age . . . 0 01 21.37 0.03 Mental age (performance scale). 0.45 0.01 Mental age (verbal scale) 0.46 0.01 1 43 (N 5) Mental age (performance scale). 0.45 0.01 ° ' ' TABLE IV-A INTRA-AGE GROUP RELATIONSHIPS BETWEEN INTELLIGENCE QUOTIENT AND TIME SCORES Item 7 9 11 x2 p x2 p x2 P Intelligence Quotient (full scale) Time per concept . . 10.64 0.02 0.50 (N.S.) 6.65 0.04 Intelligence Quotient (verbal scale) Time per concept . . 8.81 0.04 5.73 (N.S.) 2.82 (N.S.) Intelligence Quotient (performance scale) Time per concept . . 8.50 0.04 0.54 (N.S.) 4.31 (N.S.) 51 presented in Table IV-A, indicates that the seven-year—olds contribute most of the significance seen on the total analysis, although the eleven- year-old group shows significant relationships with full-scale I.Q. only. In other words, although there is a significantly greater relationship between mean time per concept and mental age, the seven-year-old group is more likely to show such relationship, although the eleven— year-old group is significantly related in terms of full-scale I.Q. The third categorizing measure produces scores for unidimensional or bidimensional concepts. By definition the unidi- mensional concepts are the most "abstract"; that is, these concepts represent a higher order of sorting, a principle encompassing a finer discrimination. As such, a positive relationship with intelligence is hypothesized. As indicated in Tables V and V-A, this hypothesis cannot be substantiated with the present data. By the same token, however, the production of uni- or bidimensional concepts is not related to chronological age. The chi squares reproduced in Table V—A indicate that the seven-year—olds are just as likely to produce unidimensional concepts as the nine- and eleven-year-olds. Tables VI and VI-A summarize the relationships between mental age and the formation of nonfunctional concepts. (As previ- ously described, nonfunctional concepts are defined as the total of 3a.“...— TABLE V COEFFICIENTS OF CONTINGENCY BETWEEN MENTAL AGE AND CHRONOLOGICAL AGE AND DEGREE OF DIMENSIONALITY Coefficient Item of p Contingency Chronological age .................... 0.06 (N.S.) Mental age (full scale) ................ 0.05 (N.S.) TABLE V—A INTRA—AGE GROUP RELATIONSHIPS BETWEEN INTELLIGENCE QUOTIENT AND DEGREE OF DIMENSIONALITY Age Item 7 9 11 x2 p x2 p x2 P Choice of unidimen— sional or bidimen— sional concepts . . . . 2.50 (N.S.) 0.85 (N.S.) 0.74 (N.S.) 53 TABLE VI COEFFICIENTS OF CONTINGENCY BETWEEN MENTAL AGE AND CHRONOLOGICAL AGE AND NUMBER OF NONFUNCTIONAL CONCEPTS Coefficient It 2 em .Of P X diff. pdiff. ContIngency Chronological age .......... 0.15 (N.S.) Mental age (full scale) ...... 0.42 0.01 Mental age (verbal scale) . . . . 0.45 0.01 6 50 (N S) Mental age (performance scale). 0.45 0.01 ' ' ' TABLE VI—A INTRA-AGE GROUP RELATIONSHIPS BETWEEN INTELLIGENCE QUOTIENT AND NUMBER OF NONFUNCTIONAL CONCEPTS Age Item 7 9 11 x2 p x2 p x2 p Intelligence Quotient (full scale) Nonfunct. concepts . 12.70 (N.S.) 5.88 (N.S.) 18.01 0.01 Intelliggnce Quotient (verbal scale) Nonfunct. concepts . 11.83 (N.S.) 14.95 0.03 15.60 0.02 Intelligence Quotient (performance scale) Nonfunct. concepts . 10.48 (N.S.) 7.29 (N.S.) 13.21 0.04 54 the number of times the subject repeats a concept once produced, the number of sorts which did not coincide to the directions or in which a common element could not be distinguished, and the number of failures to reSpond to a given step in the directions.) The con- tingency coefficient between the number of nonfunctional concepts and chronological age for the total sample is not significant. How- ever, as predicted, the relationship between the number of nonfunc- tional concepts and mental age is significant at the 0.01 level. In the further breakdown, both the verbal and performance mental age scores are significantly related to this measure. The chi square of the difference indicates, however, that the apparently greater magni— tude of the contingency coefficient between the performance and ver- bal scores is not significant. Apparently the performance scores do not predict the formation of nonfunctional concepts any better than do the verbal scores. Although not apparent from the chi squares or contingency coefficients, inspection of the scatter pat- terns indicates the relationship to be negative: as mental age in- creases, the tendency to produce nonfunctional concepts decreases. DISCUSSION AND CONCLUSIONS The results obtained support our hypotheses: that conceptualiz- ing ability as measured by means of a sorting-type task is more highly related to mental age than to chronological age. This is summarized in Tables 111 through VI. Pursuant to the stated hy- , potheses, the following conclusions may be drawn: A. As mental age increases, the ability to categorize ob— ject attributes also increases. Similarly, as presented in Table III, there is a significantly high relationship be— tween the absolute number of concepts produced and chronological age. However, mental age is the better predictor, yielding a significantly higher coefficient of contingency. B. Similar results are obtained with reference to the mean time necessary to produce a concept. Although this meas— ure is significantly related to both mental age and chrono- logical age, its relationship to the former is significantly greater. As mental age increases, the mean time neces— sary to produce a concept decreases. 55 56 C. The degree of dimensionality; that is, whether the subject produced a uni— or a bidimensional concept, is not sig- nificantly related to mental age. For example, the seven— year—old child was just as likely to produce a uni- or bidimensional response as the nine— or eleven-year—old. Therefore, on the basis of this measure, neither of the hypotheses can be substantiated; mental age is not related to degree of dimensionality any more or less than is chronological age. D. The results with reference to what we have called non— functional concepts are clear cut. Table VI indicates that, whereas the number of nonfunctional concepts pro- duced is not significantly related to chronological age, it is related to mental age at the 0.01 level of confidence. Therefore, the hypotheses are substantiated; age as such bears little relationship to the production of nonfunctional concepts, but as mental age increases, the production of nonfunctional concepts dec rease s. Since the scores obtained on the categorizing task are indicative that this task is a function of intelligence, the question arises as to the relationship between this and the verbal-performance 5.7 dichotomy on the WISC. As seen in Table III, for example, the per- formance—scale mental age score is significantly more related to the number of concepts achieved than to chronological age. How- ever, the differences between the verbal and performance scores are not significant within the same reference. This is also true with respect to the mean times and the number of nonfunctional concepts. It can be concluded, therefore, that although the performance scale is a better predictor of the various categorization measures than is chronological age, this is not true when compared with the verbal scale. Even though the nature of the categorizing task suggests similarity to the timed sensorimotor performance part of the WISC, it does not actually yield higher correlations with the performance scale. The higher correlations yielded with full-scale scores sug- gest instead that the categorizing task taps a more highly complex function of general intelligence. Results pertinent to the individual age and grade levels are presented in Tables III-A. through VI—A. It appears that much of the relationship found in the case of number of concepts and number \ of nonfunctional concepts is contributed by-lltlhe eleven—year—old group. This is the only one of the three groups which shows a significant relationship between these measures and intelligence quotient. With 58 respect to the time scores, on the other hand, the seven-year—old group as well as the eleven—year—old group shows significant rela— tionships. Also, in regard to these scores, the seven-year-olds show significant relationships with the verbal- and performance- scale scores as well as the full scale. The other categorization measure (unidimensional—bidimensional) shows no significant rela— tionships with the total group, and it is not expected to show any within the individual age levels. Finally, in substantiating our hypotheses, the findings are con- trary to many which have been published claiming that concept forma- tion is primarily a function of education and experience and other possible factors. By utilizing a measure of categorizing behavior which is relatively free from the effects of experience including verbal factors, a reliable measure of intelligence and a sufficiently large sample, it is felt that most of the criticism leveled at previous studies has been overcome. Furthermore, the present results clearly indicate that the factor of intelligence should be more rigorously con— trolled in studies purporting to investigate the relationships between conceptualizing ability and other variables such as thinking, reasoning, and personality characteristics. How much one may generalize from sorting tasks such as were used in the present study to concept 59 formation utilizing different media or tasks, such as verbal concepts, temporal concepts, or concepts of causality could be the subject of another study. SUMMAR Y An attempt was made to substantiate the hypothesis that con— ceptualization is primarily a differential function of intellectual ca- pacity rather than purely a function of experience, specifically, that categorizing behavior is more highly related to mental age than it is to chronological age. A concept-formation task of the categoriz— ing type and the Wechsler Intelligence Scale for Children were ac— cordingly administered to 150 children. This included fifty children each at ages seven, nine, and eleven. Both mental age and chronological age were correlated with four conceptualization scores: (a) number of concepts, (b) mean time per concept, (c) degree of dimensionality, and (d) number of nonfunc— tional concepts. These four scores were likewise compared to the mental ages derived from the full-scale, verbal-scale, and performance— scale scores of the WISC. Obtained results Substantiated our hypotheses with reference to three of the four variables: the'number of concepts achieved, the mean time necessary to produce a concept, and the number of non— functional concepts are all significantly related to mental age. Coef- ficients of contingency from 0.35 to 0.50 were obtained. Similarly, 60 61 these three variables are more highly related to mental age than to chronological age as such, the differences being most pronounced with full—scale mental age. Analysis of individual age group rela- tionships indicate the differences are more pronounced in the eleven- year—old-group with respect to number of concepts and number of nonfunctional concepts, while the differences are more pronounced in the seven-year—old group with respect to the time scores. The obtained results make possible the conclusion that mental age is a better predictor of categorization ability (as measured by a nonverbal, categorical sorting type of concept-formation task) than is chronological age. Categorization ability of this type is more highly correlated with general intelligence than with the verbal or performance ability measured by the WISC. Future studies involving concept formation should include rigid control of intellectual factors. It is also suggested that results with the categorical concept-forma- tion task be compared with other types of concept formation. . ....-7-—.__. . APPENDIX Directions for Administration of the Categorizing Task The blocks are scattered randomly in both color and shape before the subject. Do you know what color this is? [Show large red tri- angle] And what color this is? [Show medium yellow circle.] And this? [Show small green square.] I want you to put these pieces into different piles so that all of the pieces in each pile are the same or belong together. You may do this any way that you like, but be sure that all of the pieces in each pile are the same as each other in some way. Use all of the pieces. These same directions may be repeated if the subject does not understand, or if he fails to respond. After the first concept is achieved, the pieces are again Scat- tered randomly. That was very good. Now I want you to put the pieces into piles again, but this time make the pieces belong together in a different way; make the pieces in each pile the same but in a different way than you did it before. These directions are repeated if the subject produces the sec- ond concept, and they are used as long as the subject continues to produce a new concept. As soon as he repeats, cannot reSpond after a reasonable length of time, or produces an illogical concept, then 62 63 Hint I is presented. If a concept is forthcoming, then the above di- rections are repeated until the subject cannot respond, and Hint II is presented. This is continued until either six concepts have been achieved or all the hints have been presented. If the subject fails to produce a concept with the above direc- tions: Last time you put all of the pieces of the same color [or appropriate sort] in one pile, and all of another color [or apprOpriate sort] in another pile. This time I want you to put the pieces into piles So that the pieces are alike in another way. Repetition of the directions and hints are presented as de— _scribed above. 1 Hint 1: Place src, mgs, and lyt in a row in front of the subject. Put all of the pieces into piles like this. Remember, all of the pieces in one pile should be the same, but don't make them the same as you did the last times. Hint _I_I_: If the first concept was color, or color and shape, place lgt, mgs, sgc in front of subject. Put them into piles like this. The designation "src" means small red circle. The first letter refers to size, the second letter to color, and the last to the shape. 64 If the first concept was shape, or shape and size, place lys, mgs, srs in front of subject. Put them into piles like this. If the first concept was size, place lrt, lyc, lgs in front of subject. Put them into piles like this. Hint III: If the first two concepts were color and shape, or combinations of these, place lgs, mgs, sgs in front of subject. Put the pieces into piles like this. Although you can put them into three piles, you can also put them into more than three piles. If the first two concepts were color and size, or combinations of these, place Sgt, sgc, sgs in front of subject and repeat directions. If the first two concepts were size and shape, or combinations of these, place lgt, lyt, lrt in front of subject and repeat directions. 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