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The Use of Equivalence Concepts byChildren and AdultsR. Miller aa University of the Witwatersrand , USAPublished online: 04 Sep 2012.

To cite this article: R. Miller (1977) The Use of Equivalence Concepts by Children and Adults,The Journal of Genetic Psychology: Research and Theory on Human Development, 131:1,125-138, DOI: 10.1080/00221325.1977.10533281

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The Journal of Genetic Psychology, 1977, 131, 125-138.

THE USE OF EQUIVALENCE CONCEPTS BY CHILDREN AND ADULTS*

University of the Witwatersrand

R. MILLER

SUMMARY The general aim of the present study was to test the hypothesis that the

younger the child the more perceptible are the attributes used in equivalence tasks. Two questions were posed. First, is there a difference between chil- dren and adults in using both perceptible and functional attributes as op- posed to only one kind of attribute? Secondly, is there a difference between children and adults in using either perceptible or functional attributes for the first of two different kinds (perceptible or functional) of attributes used? In addition, various modes of presenting materials were considered. To test the use of perceptible and functional attributes, 7 2 grade one pupils (31 males, 41 females) and 7 2 first year university students (16 males, 56 females) were administered open-ended equivalence tasks. Only in one out of 18 tests was a significant difference obtained between children and adults regarding the use of both perceptible and functional attributes. None of the 18 tests yielded a significant difference between children and adults regarding the first of two different kinds of attributes used. The mode of presenting the materials did not appear to influence the results.

A. INTRODUCTION The notion that children tend to rely more on concrete or perceptible

rather than on abstract attributes when engaged in classification tasks or the sorting of objects into equivalence groups has long been accepted as a feature of cognitive development (1, 2, 4, 10, 12, 13). It is upon this largely undisputed hypothesis that Bruner’s theory of cognitive growth is predi- cated, as his central thesis is that the young child, using ikonic representa-

* Received in the Editorial Office, Provincetown, Massachusetts, on February 20, 1976. Copyright, 1977, by The Journal Press.

I This paper is based on part of a thesis submitted for the degree of M.A. to the University of the Witwatersrand. The work was carried out under the supervisior of Professor J. W. Mann to whom the writer expresses his gratitude.

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tion, groups objects according to perceptible attributes, whereas the older child, using symbolic representation, increasingly relies on functional attri- butes as the basis for equivalence concepts. Despite the impressive theoreti- cal embellishments which surround this hypothesis, the empirical evidence supporting it appears to be rather meagre. The evidence derives from a study by Bruner’s co-workers, Olver and Hornsby (8), who report that six-year-old children group objects according to perceptible properties to a greater extent than older children and that, with increasing age, there is a steady increase in functionally based equivalence. These findings provide the foundation for the thesis that children use different modes of represent- ing the world at various stages of development, and, indeed, most of the subsequent experimental results reported in Studies In Cognitive Growth are interpreted in these terms.

For example, in the experiment “On conceptual categories,” Olson argues as follows:

Surely the child’s mode of representation should affect his strategy, that is the pattern of hypotheses or decisions he makes en route to problem solution. The strategy used by a child who represents his world ikonically should be qualita- tively different from that of a child capable of symbolic representation (7, p. 136).

Olson’s Ss are tested, different strategies are identified for Ss at different ages, and the different strategies are attributed to different modes of rep- resentation. The problem, however, is that it is equally possible to argue theoretically that the strategy used by a child affects his mode of representa- tion. Similarly, in discussing the strategies used by children of different ages in the game of 2 0 questions, Mosher and Hornsby conclude as follows:

For, as the child increasingly relies on symbolic representation rather than on representation by action and image . . . he attains the structure of information necessary to follow through a constraint-seeking strategy, to guide his inquiry by cycles of questioning that narrow from the general to the specific. In contrast, the child relying on enactive and ikonic representation with the consequent com- plexive nature of his equivalence groupings lacks the prerequisite structure for such a constraint approach, and thus can do little more than use hypothesis scanning in seeking new information (6, p. 101).

Again, the various strategies used by the S s in this experiment are attrib- uted to the operation of different modes of representation. On the basis of the results, however, the opposite conclusion is equally compelling. Part of the problem is recognized by Olver and Hornsby.

Whether functionalism is made possible by the child’s ability to use new grouping principles, or the other way round, must remain a moot point (6, g. 73).

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R. MILLER 127

In a similar vein, whether the child’s ability to use new grouping princi- ples is made possible by a particular mode of representation, or the other way round, must also remain a moot point. What is required is persuasive evidence that modes of representation do indeed operate in the manner maintained by Bruner, and it is the finding by Olver and Hornsby that young children consistently base equivalence on perceptible properties and older children on functional properties which bears the burden of such evidence. At a more general level, the notion that cognitive development proceeds from the concrete to the abstract or from the perceptual to the conceptual is in need of clarification.

Although the weight of the evidence would, in general, appear to support the findings of Olver and Hornsby, the issue is by no means unanimous. For example, Stacey and Portnoy (11) found that the responses of mentally defective children to the words in the vocabulary section of the Wechsler Intelligence Scale for children were significantly more functional than those of borderline children, and Wolman and Barker (14) testing children’s defini- tions of words found that definitions in terms of use decreased with age. Price-Williams (9), working among the Tiv of Nigeria, found that abstract classifications occurred when children were interested in the task and that abstract classifications were most frequent for all age groups. A similar result was found in a previous study ( 5 ) specifically designed to test Bruner’s hypothesis, which required children and adults to sort eight sets of objects into equivalence groups. The major finding was the predominant use of functional rather than perceptible attributes by both the children and the adults. The most parsimonious explanation for what appear to be contradic- tory empirical findings is that the kind of attributes used in equivalence concepts depends on the task objects. This argument, however, is only of limited value, as it does not explain why some kinds of attributes are used rather than others in the formation of equivalence concepts. One method of investigating the factors which influence the choice of attributes is systemati- cally to vary the presentation of similar objects in equivalence tasks and in this way to isolate critical features influencing the use of various kinds of attributes. Consequently, in the present experiment Ss were presented with six different presentations of the same objects. In addition, to ensure that the results were not specific to a single set of objects, three different sets of objects were utilized.

A further complicating issue concerns the terms employed by various investigators. In the present experiment the terms “perceptible” and “func- tional” attributes are employed in accordance with Bruner’s usage. Previ-

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ously, terms such as “concrete concepts,” “perceptual concepts,” “abstract concepts,” and “functional concepts” have been used. These terms are confusing, as it is not the concept which is concrete, abstract, perceptual, or functional but the common attributes selected in an equivalence task. The notion of a concept implies an abstract entity rendering the term “abstract concept” redundant and that of “concrete concept” or “perceptual concept” a contradiction in terms. In much the same way, Piaget’s term “concrete operations” tends to be misleading, as it is not the operations but rather the problems to which the operations are directed which are concrete. Despite these semantic difficulties, what most investigators seem to be concerned with is the child’s ability to go “beyond the information given.” In this sense, it seems reasonable to distinguish between attributes which are immediately observable, such that an S is able to point to them, as opposed to those which cannot be directly perceived and require an inference of some kind, such as a common function.

It is also necessary to clarify specifically what is intended by the term to “use” an attribute in an equivalence task. Olver and Hornsby simply re- corded the kinds of attributes used by Ss. Garner (3), however, has em- phasized the difference between what S s do and what they are capable of doing, given the opportunity of repeated attempts and, as Price-Williams has also suggested, the necessary encouragement. Bearing these factors in mind, the present study was designed to employ open-ended tasks in which more than a single response was required and to answer questions relating to what theSs are capable of and what they spontaneously “do.”If children and adults differ as regards their ability to use both perceptible and functional attributes, then this would seem to provide evidence for Bruner’s hypothesis in what could be considered its strong form. If they differ only with respect to the kind of attributes they tend to use spontaneously, but not in terms of their ability to use other kinds of attributes, then this would lend support to a weak form of the hypothesis. If no differences are found, then clearly the hypothesis must be rejected and reasons found for Ss using one or other kind of attribute provided that their behavior does not appear completely random. Specifically, the questions posed in the present study were as follows:

In a task in which more than one classification for the same set of objects is requested, is there a difference between children and adults in using both perceptible and functional attributes or only one kind of attri- bute?

2 . In a task in which more than one classification for the same set of objects is requested, do children and adults using both kinds of attributes differ with respect to the kind of attribute used first?

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B. METHOD 1. Design

For both questions 1 and 2, a 2 X 2 design, for each of the presentations and each of the sets of materials, was employed. For question 1, the variables relate, on the one hand, to children and adults, and, on the other, to the use of both kinds of attributes (perceptible and functional) and the use of only one kind of attribute (perceptible or functional). For question 2, the variables relate to children and adults and the first kind of attribute used (either perceptible or functional) by those Ss who used both perceptible and functional attributes. An indirect comparison between the various modes of presentation was possible by comparing the results of each test. If one presentation yielded a significant difference between children and adults and another did not, then it could be assumed that the nature of the presentation of the test materials was responsible. In a similar way, if children (or adults) are more influenced by the specific nature of the test materials, then one would expect consistent differences between children and adults, for the same presentations, with different test materials.

2 . Subjects Seventy-two children and 7 2 adults were randomly selected from the

grade one pupils at a Johannesburg primary school and the first year psychology students at the University of the Witwatersrand, respectively. The mean age for the children was 6 years 6 months, and for the adults, 19 years. The children comprised 31 males and 41 females, and the adults, 16 males and 56 females.

3 . Materials Three sets of materials, each containing three objects, comprised the tests.

These were as follows: Animal test-elephant, camel, donkey; Fruit test- banana, apple, pear; Vehicle test-motor car, tractor, truck. The three sets of materials were presented in the following six different ways:

1. 2.

3.

Outline drawings of the objects. Outline drawings of the objects with a perceptible attribute included.

In all cases this was the color blue. Outline drawings of the objects with functional attributes included; for

the animal test, attributes suggestive of riding; for the fruit test, attributes suggestive of eating; for the vehicle test, attributes suggestive of transporting.

4. 5 .

A combination of 1, 2, and 3 above. Miniature toy models of the animals in the animal test and the

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vehicles in the vehicle test, and plastic imitations of the fruits in the fruit test.

6. Verbal presentation of the objects in each test, mentioning each object by name.

The pitures were all outlined in black on white paper cards approximately four inches square. For each of the three tests, the pictures were mounted side by side in a folder, allowing for simultaneous presentation of the three objects comprising each test. Presentations 1 and 3 are illustrated in Figure 1.

4. Procedure The children and adults were each randomly assigned to six groups with

one group of adults and one group of children receiving one of the six presentations. Each of the 12 groups comprised 12 Ss. All the Ss received the same instructions which were as follows:

I am going to show you three things and I want you to tell me what is the same about them but I don’t want you to use the name that we give them. If I showed you these pictures (table, chair, bed) then I wouldn’t want you to tell me that they are all furniture. Instead, we could say that they are all the same because they have the same color, or because they have the same shape, or because we find them in houses, or because we can sit on them, or because they all have four legs, or because they are all made of wood. So you see there are lots of ways in which these things are the same. Do you understand what I mean when I say I want you

TEST A

TEST F

TEST V

PRESENTAT ION

I

1 PRESENTATION 3

8 FIGURE 1

PICTURES COMPRISING THE THREE SETS OF MATERIALS FOR PRESENTATIONS 1 AND 3

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R. MILLER 13 1

to tell me what is the same about the things I’m going to show you? Also, I want you to tell me as many things as you can think of that are the same and not only one thing. Do you understand everything? Now there is one more thing to remember. I want you to tell me as soon as you think of something that is the same. It doesn’t matter even if you think it’s a silly thing but you must tell me as soon as you think of something because I want to see how quickly you can think of things that are the same. I don’t want you to think of a few things and then tell me which one you think is best but to tell me what is the same as soon as you think of something. Do you understand everything?”

The S s were asked to exclude the specific nominal or generic concept for the sets of objects, the reason being that they present a thorny problem for, as Olver and Hornsby point out, they may represent nothing other than “superfi- cial word labelling” (8, p. 82). Even very young children use nominal con- cepts, but it is not clear whether they are used as concepts or labels. If the terms “animals,” “fruits,” and “vehicles,” were used, the S was told of his error and asked to try again. In addition, the latter part of the instructions were included in an attempt to encourage adult S s to respond in a spontaneous manner and to refrain from selecting concepts which may appear more sophisticated. It was felt that children would respond as concepts occurred to them without regard for the impression created.

C. RESULTS

1. Question 1

The results are given in Figure 2. For the sake of clarity, Figure 2 contains only the number of Ss using both kinds of attributes (perceptible and functional), for each of the three tests and each of the six presentations. As equal numbers (12 children and 12 adults) were employed in all cases, the number of Ss using only one kind of attribute (perceptible or functional) is obvious from the data provided in Figure 2. The results were analyzed by means of a chi square test and in the case of small expected frequencies, a Fisher test, for each of the presentations and each of the tests. It was decided to reject the null hypothesis at or beyond the .05 level of significance, and in all cases two-tailed tests were used. Only one result, that of presentation 4 for the animal test, yielded a significant difference between children and adults (p < .05).

Figure 2 reveals that the results for the six different presentations are remarkably similar except perhaps for the animal test. For the fruit and vehicle tests, there is little to suggest that the different presentations influenced whether both perceptible and functional attributes were used, as

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C H I1 D R E N

ADULTS

Idi I 1 1 6

P R E S E N T A T I O N S

FIGURE 2

ATTRIBUTES, FOR EACH OF THE THREE TESTS AND EACH OF THE SIX PRESENTATIONS

NUMBER OF CHILDREN AND ADULTS USING BOTH PERCEPTIBLE AND FUNCTIONAL

opposed to only one kind of attribute. Furthermore, there is little consistency between the results for each presentation when compared over the three sets of materials. For example, the results for presentation 4, although yielding a significant difference between children and adults for the animal test, were very similar for the fruit and vehicle tests with 10 out of 1 2 children and eight out of 12 adults for the fruit test, and 11 out of 1 2 children and nine out of 12 adults for the vehicle test, using both kinds of attributes. In addition,

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for this presentation, the number of children using both kinds of attributes for the animal test was considerably less than the number of adults (four out of 12 children and nine out of 12 adults), whereas more children than adults used both kinds of attributes for the fruit and vehicle tests.

This lack of consistency over the three sets of materials is also illustrated by presentation 2. For the animal test, presentation 2 was the only case in which fewer children (three out of 12) and fewer adults (four out of 12) used both kinds of attributes as opposed to only one kind of attribute. However, with the fruit and vehicle tests, for the same presentation, the situation was reversed to the extent that for the vehicle test all of the children and 11 out of 12 of the adults used both kinds of attributes. Far from any consistency, it would appear from the results that, in general, there was a progressive increase in the number of Ss using both kinds of attributes. This is evident from a consideration of the total number of children and adults using both kinds of attributes for each of the three tests: for the animal test, 32 out of 72 (45 percent) children and 44 out of 72 (61 percent) adults; for the fruit test, SO out of 72 (70 percent) children and 55 out of 72 (76 percent) adults; for the vehicle test, 67 out of 72 (93 percent) children and 65 out of 72 (90 percent) adults. Only in the case of the children for the animal test were both kinds of attributes used to a lesser extent than one kind of attribute.

2. Question 2 The number of children and adults using either perceptible or functional

concepts for the first of more than one equivalence classification is given in Table 1. Because the total number of Ss is not equal, it is necessary to convert to proportions in order to compare the results of the different presentations and tests. The proportions of children and adults using func- tional attributes first are given in Figure 3. (The proportion of Ss not represented on the histograms used perceptible attributes first.) In some cases the actual number of Ss was small and by converting to proportions this fact is obscured. For this reason the actual numbers will be provided in brackets when discussing the various proportions. The raw data were analyzed by means of a Fisher test, for each presentation and each test, separately. It was decided to reject the null hypothesis at or beyond the .05 level of significance, and in all cases two-tailed tests were used. None of the 18 tests yielded a significant result (p < .05). As in question 1, there is little consistency between the more extreme results of the presentations over the three tests. For example, only for presentation 1 for the fruit test, and presentation 3 for the vehicle test, were proportionately more functional

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CHILDREN ADULTS

Lu

1 2 3 5 6

P R E S E N T A T I O N S FIGURE 3

PROPORTION OF CHILDREN AND ADULTS USING FUNCTIONAL ATTRIBUTES FIRST FOR EACH OF THE THREE TESTS

AND EACH OF THE SIX PRESENTATIONS

than perceptible attributes used by both children and adults. But for these two presentations the situation was reversed for the remaining two tests. Furthermore, whereas for presentation 1, proportionately fewer children than adults used functional concepts for the fruit and vehicle tests, the reverse is true for the animal test. In fact, for none of the six presentations did children and adults consistently use proportionately more of one kind of attribute than the other, over the three tests.

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If the first attributes used over the six presentations are considered, the picture for children and adults is different. For the children, the differences between the total proportion of functional attributes used were not large: .41 (13 out of 32) for the animal test; .36 (18 out of 59) for the fruit test; and .33 (22 out of 67) for the vehicle test. For the adults a more extreme difference was obtained, due mainly to the animal test: .23 (10 out of 44) for the animal test; .53 (29 out of 55) for the fruit test; and .48 (31 out of 65) for the vehicle test. Of the total number of attributes first used, the proportions of func- tional attributes used by the children and adults were .36 (53 out of 149) and .43 (70 out of 164), respectively.

D . DISCUSSION The results for question 1, which was concerned with the use of both kinds

of attributes as opposed to one kind of attribute, indicate that the differences

TABLE 1 NUMBER OF CHILDREN AND ADULTS USING EITHER PERCEPTIBLE OR

FUNCTIONAL ATTRIBUTES FOR THE FIRST OF MORE THAN ONE EQUNALENCE CLASSIFICATION, FOR EACH

PRESENTATION AND EACH OF THE SETS OF MATERIALS

Vehicles Animals Fruit Presentations Percept. Funct. Percept. Funct. Percept. Funct.

1. Child 4 3 2 4 7 3 Adult 6 1 1 8 5 6

L.

Child Adult

Child Adult

Child Adult

Child Adult

Child Adult

Child Adult

3.

4.

5 .

6 .

Total

3 3

0 1

6 7

1 2

10 10

2 1

3 6

4 4

7 4

3 4

4 5

7 7

3 8

1 1

6 5

4 3

7 4

4 5

3 4

2 6

2 1

6 5

3 5

8 6

4 5

3 2

5 4

3 7

9 4

3 8

22 31

19 34

13 10

32 26

18 29

45 34

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between children and adults in this respect are negligible. This would seem to suggest that, although significant differences between children and adults may occur, the limited extent of such differences is contrary to the hypothesis that children rely more on perceptible attributes than adults. It may be suggested that the reason for the close similarity between children and adults for the fruit and vehicle tests could have been due to adults using only functional attributes and children using only perceptible attributes, a differ- ence which would be masked by the category “only one kind of attribute.” Plausible as this argument may be, it was not the case. For the fruit test, 13 children and 13 adults used only perceptible attributes, and nine children and four adults used only functional attributes. For the vehicle test, one child and three adults used only perceptible attributes and four children and four adults used only functional attributes. In fact, taken together, more children used functional attributes only, than adults, and fewer children used perceptible attributes only, than adults. Only in the case of the animal test was this trend reversed. Again, this is contrary to the view that children use perceptible attributes to a greater extent than adults.

As regards the different presentations of the stimulus objects, it would appear that they do not influence the extent to which both kinds or only one kind of attribute is used. The fact that in only one case a significant difference between children and adults was obtained is contrary to the view that children are more “stimulus bound” than adults or that they have greater difficulty in changing from one mode of classification to another. Even when the nature of the presentation was suggestive of one or other kind of attribute, the children did not exhibit rigidity to a greater extent than adults. Perhaps, most important is the fact that no consistent effects were observed within a particular presentation over the three sets of materials, the very opposite being the case, indicating that the nature of the presentation of the stimulus objects is not an important variable in determining whether both perceptible and functional attributes are used in equivalence tasks.

As regards the second question, which was concerned with whether children and adults using both perceptible and functional attributes differ with respect to the first kind of attribute used, no significant differences were obtained. As mentioned in a previous study ( S ) , this is psychologically an even more significant result than that of the previous question. This is because, assuming a particular developmental mode of representation to be operative, it would be manifest in the initial attributes used by S s using both kinds of attributes. In other words, an S using only one kind of attribute may simply be unaware of others and so, despite the influence of a dominant mode of representation, may be constrained to use a particular kind of

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attribute. But in the case of Ss using both kinds of attributes, this argument is diminished, and considerable weight may be attached to the first attribute used. Similarly, the nature of the presentation of the stimulus objects could be expected to influence the kind of attribute first used. Even when the results for a particular presentation deviated markedly from the others, the effect was not consistent over the three sets of materials. In view of this fact, the nature of the presentation of the stimulus objects cannot be regarded as an important factor in determining the kind of attribute first used. In addition, the fact that in some cases the children used proportionately more functional attributes than the adults and in others less, indicates that even for the first attribute used, children cannot be regarded as more “perceptual” or “stimulus bound” than adults.

In general, what seems to emerge from the present experiment is that the difference between children and adults, in using perceptible and functional attributes, is negligible, and the nature of the presentation of the external stimulus does not seem to influence either the use of both kinds of attributes or the first of two different kinds of attributes used, to any great extent. Rather, the kinds of objects used in equivalence tasks seem to be important in determining the concepts used by both children and adults. The fact that, for most of the comparisons, the differences between the tests appear more extreme than the differences between children and adults and the different presentations, implies that it is the objects used in equivalence tasks which set the limits and not the level of cognitive development of the Ss.

There is reason to suspect that an interpretation based on experience or knowledge, rather than the more perceptual nature of the child, is worth investigation. Such an interpretation may be supplemented by a few infor- mal observations which are not mentioned by way of evidence but only as possible explanations. First, the children commonly used, as a functional attribute for the animal test, the fact that the three animals are found in the zoo whereas the suggested attribute of “rideability” was often excluded, on the basis that elephants could not be ridden. Secondly, the animal test seemed to provide more opportunities for perceptible attributes and many of the children, and for that matter the adults too, simply listed parts of the body-e.g., heads, tails, eyes, ears, noses, legs, etc.-as equivalence con- cepts. It may be noted that the number of adults using both kinds of attributes for the animal test was less than with the other tests. So it seems that provided the objects used in an equivalence task are within the range of the experience of all the Ss, if not directly by means of books, pictures, films, etc., no differences of any consequence are obtained as regards the use of both perceptible and functional attributes. While it is reasonable to assume

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that the S s were familiar with the materials used in the present experiment, it cannot be assumed that the equivalence functions, for each test, were equally known to all the Ss.

Further support for the above interpretation derives from a comparison of the results of the present experiment with those of the previous experiment. The results in both cases were similar as regards the two main questions posed but differed with respect to the overall use of perceptible and func- tional attributes which were used first by Ss using both kinds of attributes. In the present experiment, more perceptible than functional attributes were used by both children and adults, whereas in the previous experiment the opposite was the case. It is concluded that the use of perceptible and functional attributes is a function of experience or knowledge rather than a particular mode of representation.

1.

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3. 4.

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12.

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