JOURNAL OF APPLIED DEVELOPMENTAL PSYCHOLOGY 1, 135-l 48 (1980)

Using What Children Know

to Improve Their Learning*

SUSAN M. MCHALE AND MEREDITH J. WEST

The University of North Carolina at Chapel Hill

Eighty children from three to seven years of age were tested on two forms of o

matrix task, one of which was designed to take into account children’s limited

problem solving skills. The tasks involved seriating nine items (geometric shapes

or birds) ctcross two dimensions in a 3 x 3 matrix. The children were required to

replace items that had been removed from cr matrix board, to reproduce the

entire matrix when all items had been removed from the board, and to transpose

the matrix, that is, to reproduce the same spatial relations between the items,

rotated ninety degrees. Results showed that children performed better when

tested using common materials than when they were given standard materials.

Furthermore, a greater percentage of children were able to complete the tasks

and were able to respond correctly on the first trial of the tasks when using

common materials (bird families) than when using the standard geometric shapes.

The results were discussed in terms of task variables that influence children’s

performance and the problems resulting from generating theories of children’s

cognitive competence based on their performance in specific situations.

Parents and teachers of young children constantly confront the problem of how to facilitate children’s acquisition of a new concept or skill. This occurs on both a formal level, i.e., teaching a school-related skill, and on an informal level, answering children’s questions about new ideas or experiences. One way teach- ers and parents approach this task in both formal and informal contexts is to relate the topic at hand to some knowledge or skill already possessed by the child. For instance, a parent may describe death as similar to the state of sleep. In school, arithmetic may be taught through the use of word problems which make number concepts relevant to the child’s experience.

*This research was supported by a grant from Sigma Xi. The authors would like to thank the

staff and children of the Ephesus Church Preschool in Durham, North Carolina and the Carolina Friends School of Chapel Hill, North Carolina, for their cooperation. Requests for reprints should be

sent to Meredith J. West, Department of Psychology, University of North Carolina, Chapel Hill, N.C. 27514.

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136 MCHALE AND WESl

The assumption underlying these attempts is that children’s knowledge of the real world can facilitate their acquisition of more abstract relations or con- cepts. The research literature is copious with demonstrations that dimensions of tasks such as familiar stimuli (Borke, 1971), responses that are well-established in children’s repertoires (e.g., Chi, 1978), and clear, unambiguous instructions (Corsale & Omstein, 1977) drastically affect children’s ability to solve particular problems. Sigel (1974) has described numerous task variables that influence children’s performance on tests of cognitive development.

Although practitioners generally adopt these strategies in helping children learn new concepts, researchers in child development often ignore the need to make tasks meaningful for young children if they wish to test the extent of the child’s cognitive competence. Based on information acquired in isolated testing sessions, however, characterizations of the young child have been drawn that may have limited the paradigms used to study child development.

The awareness that children perform differently depending upon the way in which a task is presented may provide a new dimension to the study of children’s cognitive development (Gelman, 1979). The Piagetian system, for example, has been criticized for failing to account adequately for the construct of decalage, that is, the observation that children are able to use new cognitive operations at different times depending upon the kind of task that is presented (e.g., children may learn to conserve number prior to conserving mass). By studying particular task variables that enable children to use concepts more or less easily, we may be able to account for this phenomenon more systematically.

The purpose of this study is to explore some of the relationships between children’s current knowledge and their ability to learn a new but related concept. In this study we will demonstrate how the use of children’s existing knowledge aids in teaching them new, seemingly complex concepts. A test of children’s relational thinking was chosen from the research literature. This test has been administered to children of various ages and norms describing the children’s performance are available. Moreover, the components of this particular task have been analyzed by several investigators who have used the task to assess various aspects of children’s cognitive development.

The matrix task devised by Bruner and Kenney (1966) assesses children’s ability to order stimuli simultaneously along more than one dimension. This task involves arranging stimuli within a two-dimensional matrix and correct perfor- mance, according to Bruner and Kenney, requires that children attend to higher order features of the stimuli rather than considering each stimulus as an isolated object. This task assesses not only children’s ability to seriate, an operation thought to be lacking in preschoolers, but also their ability to decenter, to per- ceive relations among objects, and to formulate spontaneously rules for ordering stimuli. Theorists have traditionally claimed that such abilities are absent from the repertoire of the young child (Bruner, 1964; Inhelder & Piaget, 1969).

IMPROVING CHILDREN’S LEARNING 137

To test children’s ability to deal with two dimensions simultaneously and to

abstract those dimensions from perceptual stimuli, Bruner and Kenney presented children between the ages of three and seven years with a matrix board divided into nine squares and nine beakers varying in height and width. In their correct positions, the beakers increased in height from the lower to the upper side of the board and increased in width from the left to the right side of the board. The children were presented with three tasks: to replace one, two, or three beakers when these were removed from the board; to reproduce the matrix when all the pieces were scrambled; and to transpose the matrix, that is, to reproduce the matrix rotated ninety degrees.

Bruner and Kenney reported that not until age five could more than 20% of the children replace three beakers correctly or reproduce the matrix, and not until age seven could more than 25% of the children transpose the matrix. Thus, Bruner & Kenney concluded that these young children were stimulus-bound, i.e., that they attempted to solve the problem by copying a mental image of the matrix rather than formulating rules for building the matrix by abstracting out dimensions of the stimuli, a skill that older children possessed.

The purpose of the present study was to see if young children would show improvements in these cognitive skills if the task was modified by using common objects that were familiar to young children. Specifically, children between the ages three and seven years were tested on two forms of a matrix task, the standard task described by Bruner and Kenney (1966) and a task in which the stimuli and instructions were altered in order to make them appropriate for young children. Specifically, materials whose dimensions were meaningful and familiar to young children were employed. Bruner and Kenney (1966) asked children to seriate according to height and width, abstract dimensions with which children may have little experience. In the present study, another set of stimuli, bird families (i.e., father, mother, and baby) which also varied according to size, was also employed. It was expected, however, that young children would already understand the relationships between these stimuli and therefore be able to use this in performing the two-dimensional seriation task. Thus it was predicted that children’s performance would be better when they used common materials in the matrix task than when they solved the same matrix task using the standard materials.

METHOD

Subjects. Sixteen children from each of five age groups, 3-year-olds, (mean = 42 mos; range = 38 mos - 47 mos.), 4-year-olds, (mean = 53 mos; range = 48 mos - 59 mos;), 5-year-olds, (mean = 65 mos; range = 60 mos - 7 1 mos), 6-year-olds, (mean = 80 mos; range = 74 mos - 83 mos), and ‘I-year-olds,

138 MCHALE AND WEST

(mean = 90 mos; range = 84 mos - 95 mos) served as subjects. They were all middle class children living in a university town and enrolled in local nursery or elementary schools. Within each age group, half of the children were females and half were males.

Materials

Two sets of materials were employed, a standard set and a set of common materials chosen so that stimuli would be familiar to young children.

Standard Materials. The standard materials consisted of a cardboard ma- trix board, 22.56 square cm. in area, divided into nine squares, each 7.52 square cm. in area. The constituent pieces of the matrix were red cardboard rectangles ranging in height from two to six cm. (2, 4, and 6, cm., respectively) and in width from one to three cm. (1, 2, and 3 cm., respectively; see Figure Ia).

Common Materials. The age-appropriate materials consisted of a matrix board, 45 cm. x 60 cm. in area (Figure Ib) on which were drawn three trees (the columns of the matrix), with three branches extending from each tree (forming the rows of the matrix). At the intersection of each tree and branch, a nest was drawn. The constituent pieces of this matrix were nine cardboard birds graded in size and varying in form. There were three varieties or shapes of birds (families) which were graded in size (a large, medium and small family) as well as three sizes of birds within each family (a father, a mother, and a baby bird of each variety). The birds were held to the board by means of small pieces of velcro attached to the nests and the backs of the birds.

General Instructions. Upon entering the room, the experimenter stated to the child, “I’m going to put my toys on this board right here and then I’m going to ask you some questions about the toys. I want you to listen very carefully so you can answer all my questions. ”

After the experimenter put the shapes or the birds on the board she asked the children questions about the items in each row and columns. For example, “Can you tell me about all the birds in this row? Who are they?“; or, “Can you tell me about all the shapes in this row? What size are they?”

Procedure. Children were tested individually in a small room near their classrooms by a female experimenter. The length of the testing session varied depending on the children’s performance. The testing procedure was stepwise in nature, with the child’s performance (pass or fail) determining which questions were next asked. Half of the children in each age group received the’standard task first and half received the common materials first. Assignment to these Order Groups was randomly determined.

There were three levels of tasks tested using each set of materials, a replacement task, a reproduction task, and a transposition task. Because higher

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Figure 1. Standard (geometric shapes) and common (bird families) materials

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level tasks required the skills of the lower level (preceding) tasks, children’s failure on any task terminated the game. For each of the tasks children were given several chances to solve the problem. That is, upon initial failure children were presented with the same problem again but questioned in a decreasingly complex fashion. If children were unable to solve a particular task when it was presented in the simplest fashion, the game was terminated.

Replacement Task. The child was told, “I’m going to take some shapes/ birds off the board and I want you to put them back where they belong. First shut your eyes. Now open them. Where does this shape/bird belong?”

On the first trial three items were removed from the board, on the next trial two items, and on the final trial one item was removed from the board. After the child replaced each of the items s/he was asked, “What made you put that shape/bird there? How did you know where it belonged?” Next, the child was questioned about each row and column in the matrix to determine whether they would spontaneously correct themselves if they had made an error. Examples of spontaneous correction questions are: “Are all the daddy birds together? Is the little bird family together? Are all the tall shapes together? Are all the fat shapes together? ’ ’

If the child failed to replace all items on this task correctly even after the spontaneous correction questions, the game was terminated and the second ma- trix game begun.

Reproduction Task. The instructions were as follows: “Now I’m going to take all the shapes/birds off the board and I want you to put them back where they belong, ” (experimenter removes items from board). “Can you put all the shapes/birds back where they belong? Can you build something like there was before? Remember, the rule is that all the shapes/birds that belong together have to go next to one another.”

After the child reproduced the matrix s/he was asked, “What made you put all the shapes/birds like that? How did you know where they belonged?”

Children who reproduced the matrix were given the transposition task. Children who failed to do so received further questioning:

1. If the child correctly placed at least two rows or columns s/he was asked the spontaneous correction questions. Children who spontaneously corrected themselves were given the transposition task. Those who failed to do so received further questioning with verbal labels of the stimuli provided.

2. In this “label” procedure, items were given to the children individu- ally, in a standard order, and labeled by their dimensions by the experimenter

(e.g., “Here is the shortest, skinniest shape, where does it go?/ here is the biggest daddy bird, where does it go‘?“). If children correctly place all items they were given the transposition task. If not, the game was terminated and the second matrix task begun.

IMPROVING CHILDREN’S LEARNING 141

Transposition Task. The instructions for the transposition task varied, de- pending on the materials. For the standard set the instructions to the child were as follows: “Now we’re going to put this shape down here,” (experimenter moves shape from upper left to lower right comer), “and I want you to build something like there was before. But remember, all the skinny shapes still have to be together and all the tall shapes still have to be together, and this shape,” (exper- imenter points to lower right comer), “has to stay right here. Can you find where all the shapes belong now? Can you find the new places where they go?”

For the stimulus-appropriate set the instructions for the transposition task were as follows: “Now I’m going to tell you a story about the birds. One night when all the birds were sleeping in their nests, all of a sudden there was a big storm. And the rain fell and the wind blew so hard that all the birds were blown right out of their nests, just like this.” (Experimenter takes birds off board.j “They all landed on the ground. But do you know what? Since it was the middle of the night, it was so dark that the birds couldn’t see anything! They couldn’t get back to their old nests! But finally the biggest daddy decided to fly around and find a new nest. So he flew around and around till finally he did find a nest to sleep in, ” (experimenter places bird in lower right comer). “He was so tired by this time that he couldn’t move, he has to stay right where he is, but he wants all the other birds to find a new place to sleep too. He wants all his family to be together next to him like before. Do you think you could help all the birds fly back to where they belong now? Remember to put all the birds together that belong together. ’ ’

For both sets of materials, after the child placed all the items back on the board the experimenter asked, “How did you know where they belonged? What made you put them like that?” If the children placed all items correctly the game was terminated and the second matrix task begun. If the child failed to place all items correctly s/he was given further questioning:

1. If the child correctly placed at least two rows or columns s/he was asked the spontaneous correction questions. If children spontaneously corrected them- selves the game was terminated and the second matrix game begun. Those who failed to do so received further questioning in which verbal labels for the stimuli were provided.

2. In this procedure, items were given to the child individually, in a standard order and labeled as in the reproduction task. If children correctly placed all items the game was terminated and the second matrix task begun. If they failed to do so they received further questioning in a modified transposition task.

3. In this task the child was asked to perform a one-dimensional transposi- tion rather than a two-dimensional transposition problem. Thus, instead of mov- ing the reference item from the upper left to the lower right comer, the experi- menter moved the item to the lower left comer. The experimenter then presented the transposition problem in the same way it was done originally.

142 MCHALE AND WEST

If the child was able to place all items correctly the game was terminated and the second matrix task begun. If the child correctly placed at least two rows or columns, the spontaneous correction questions were asked, and subsequently the second matrix task begun. If the child failed to correctly place all items, the game was- terminated and the second matrix task begun.

The second task was introduced by the experimenter: “Now I’m going to ask you some more questions. This time we’re going to play with some different toys. ” The second task was then presented in the manner described above using the remaining set of materials.

Scoring. Children’s responses were scored differently across tasks. The total possible point score for the transposition task was eight, for the reproduction task, four, and for the replacement task, three. Scores for the particular tasks were determined in the following manner: Children began with the total possible number of points for each task, but lost one point for each successively simpler mode of questioning required for problem solution.

In the transposition task correct solution on the first trial resulted in a score of eight points; if spontaneous correction took place at this time, children re- ceived seven points; if children responded correctly to labeled placement they received six points; spontaneous correction here resulted in five points: one dimensional transposition was given a score of four; spontaneous correction received a score of three; if children responded correctly to labeled placement here, they received two points; and finally, spontaneous correction resulted in a score of one.

In the reproduction task, children who performed correctly on the first trial received a score of four; children who spontaneously corrected themselves at this point received a score of three; children who correctly responded to labeled placement received two points; and children who spontaneously corrected them- selves were given a score of one.

In the replacement task, children received three points if they were able to replace three items correctly; two points if they could only replace two items correctly; and one point if they replaced only one item correctly. Spontaneous corrections at any point in this procedure were given one half point.

RESULTS

The children performed better when tested with the common materials than with the standard materials. Across age, a greater percentage of children were able to complete the stepwise series of three tasks using the modified materials (56%) than when using the standard materials (24%). Because the data were ordinal in scale, non-parametric statistics were employed in all analyses. Analyses were first performed to assess differences across subject groups (sex and other effects).

IMPROVING CHILDREN’S LEARNING 143

Next, analyses were performed to measure the overall effects of materials, as well as the effects of materials on each of the tasks (replacement, reproduction, and transposition). Finally, differences in children’s performance across age were assessed.

Across age groups, there were no differences between the sexes on either the standard or the stimulus appropriate materials by the Mann Whitney U test (U = 29.5; Z = 1.246). Thus, the data for the boys and girls were collapsed for further analyses. No effect for order of presentation of the materials was found using the Mann Whitney U test (U = 846.5; Z = .447) and thus, further analyses were performed with the data collapsed across order.

Effects of Materials. When the data were collapsed across age groups no significant differences were found across materials on the replacement task: most children performed at ceiling level on both sets of materials. Differences between materials on the reproduction and transposition tasks however, were statistically significant by the Wilcoxon matched-pairs signed-ranks test (z = -5.75, p < .OOl; and z = -4.858, p < .OOl, respectively). Children’s scores were signifi- cantly higher when using the common materials than when using the standard materials.

Differences between the standard and common materials for each of the three tasks at each age were also assessed (Table 1). There were no differences between materials on any of the tasks for children in the three-year-old age group. There were also no statistically significant differences for any of the older age groups on the replacement task: the means for all age groups fell between 2.70 and 2.95. There were, however, statistically significant differences across materials on both the reproduction and transposition tasks for all of the older age groups (four, five, six, and seven-year-olds), except in the case of the seven-

TABLE 1

Comparison across standard (s) and common (c) materials

of mean task scores by age

Task Replacement Reprodocfion Transposition

AS= S C S C S C

3 1.8 2.2 0 .02 0 0

4 2.7 2.9 .9 2.7*‘* 1 3.5**

5 2.7 2.83 .75 2.82*** .5 3.5***

6 2.8 3.0 .9 3.4*** 1.23 6.45***

7 2.95 2.95 2.5 3.7f 5.2 7.25

*p < .os

**p < .Ol

***p < .005 by Wilcoxon matched-pair signed-ranks test

144 MCHALE AND WEST

year-old children on the transposition task. On each of these tasks children’s scores were significantly higher on the common materials than on the standard materials.

Age Differences. The data showed differences in children’s performance across age. The older children generally received higher scores (i.e., they re- quired fewer simplifications of the task for solution) on both sets of materials. In fact, children in the oldest age group performed close to ceiling level using the common materials on all three tasks, whereas the scores of children in the youngest age group (3 years) represented a floor effect. Other comparisons showed that the proportion of children who ultimately passed each task increased with age, as is illustrated in Table 2. Moreover, the proportion of children who responded correctly on the first trial of each of the three tasks also increased with age, as is illustrated in Table 3. In each of these comparisons children demon- strated superior performance at every age on the common materials. On the replacement task 100% of the children were able to respond correctly by the age

TABLE 2

Percentage of children by age completing each task

using standard (S) and common (C) materials

Task Replacemenf Reproduction Tmnsposifion

Age s C S C S C

3 81% 94% 0% 6% 0% 0%

4 100% 100% 37% 88% 25% 50%

5 100% 100% 26% 02% 13% 69%

6 100% 100% 32% 88% 18% 75%

7 100% 100% 75% 100% 69% 91% -

TABLE 3

Percentage of children by age responding correctly

on first trial of each task using standard (S) and common (C) materials

Task Replacement Reproduction Transposition

Age S C S C S C

3 12% 25% 0% 0% 0% 0%

5 69% 87% 6% 37% 0% 18%

5 69% 87% 0% 61% 6% 20%

6 74% 100% 12% 74% 6% 37%

7 94% 94% 39% 74% 50% 69%

Reproduction - Bruner &

Transposition - Kenney

Reproduction o-----o McHale & West

Transposition*----*

I I

5 6 7

AGE

in years

Figure 2. Comparison of the present results and those of Brunw and Kenney (1966)

Number of errors exhibited by children of three different ages on reproduction and

transposition tasks

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of 4 years, though the percentage of children responding correctly on the first trial (to the most difficult instructions) was much lower. In the reproduction and transposition tasks the proportion of children who could complete the tasks changed dramatically with age, from virtually no children completing the tasks at age 3 years to nearly 70% using the standard materials and to greater than 90% using the familiar materials at age 7 years. The percentage of children solving the tasks on the first trial was again, much lower even in the oldest age group, particularly with the children who were asked to use the standard materials.

Comparison to Bruner and Kenney (1966). The findings of the present study indicate that children were able to perform better on the matrix task when common materials were employed. Direct statistical comparisons with Bruner and Kenney’s (1966) data are not possible because the scoring procedures dif- fered across the two studies. However, a comparison of the mean number of errors made by children in Bruner and Kenney’s (1966) study and in the present study is illustrated in Figure 2. Bruner and Kenney’s study employed only 5, 6, and 7-year-olds. The results of the present study demonstrate that, on the aver- age, children in these three age groups made less than one error on the reproduc- tion task (using the common materials). In Bruner and Kenney’s study, on the other hand, only 7-year-old children achieved this level of performance. On the transposition task, children within each age group displayed twice as many errors on the standard task as did children of the same ages who used the common materials. On the replacement task, even the 5-year-olds performed better (using the common materials) than Bruner and Kenney ‘s 7-year-olds. On the transposi- tion task, Syear-old children made fewer errors using the common materials than the 5- and 6-year-old children who were given the standard materials in Bruner and Kenney’s study.

DISCUSSION

The present study demonstrates that children’s success on a particular problem varies as a function of how that problem is presented and offers some information about the task dimensions of a problem that affect a child’s performance. The results indicated that young children were able to solve a task designed to assess abstract and relational thought when that task was modified to make stimuli familiar and when instructions provided information to aid the children’s perfor- mance .

These findings have both practical and theoretical implications: they are relevant to characterizations of the child in theories of development and they point out variables that should be considered when studying or teaching young children. In making use of what children already know, teachers may enable

children to solve tasks they are otherwise incapable of solving. Furthermore, in

IMPROVING CHILDREN’S LEARNING 147

the process of instruction, teachers may be able to provide differing amounts of information to facilitate children’s performance (as in the levels of questioning within tasks, for example).

No practice effects were obtained in the present study. That is, children’s performance using standard materials was not facilitated by experience with the familiar materials. In this task children did not grasp the concept of seriation on the basis of the one example they were provided with. This may have been due to the brevity of children’s exposure to the modified task (one trial) or to the fact that children need more experience with the complex task materials themselves (i.e., the geometric shapes) before they are able to apply relational or operational thinking in using those materials. According to the former explanation, children do not learn new concepts all at once. Rather, they need numerous experiences with concrete and meaningful examples of potentially complex or novel concepts prior to solving problems with more abstract materials. In this case, the teacher’s role is to create instances of complex concepts that are relevant to individual children’s experiences (e.g., Borke, 1971) in promoting children’s understand- ing of a concept (i.e., an inductive approach). On the other hand, children’s difficulty may lie in the paucity of their information about the particular task materials and their dimensions. In the present study, children may have had little or no experience in identifying relative heights and widths of geometric figures whereas even the preschoolers could readily identify examples with alternative labels for the same concepts (i.e., the relative sizes of “daddy”, “mommy ’ ‘,

and “baby” birds). Children may have the ability to seriate, but they may need to learn about the particular contexts in which they apply this concept. In this case, the teacher’s role may be to provide children with experiences in identify- ing and labeling critical dimensions of task materials to aid in later solutions of complex problems (Gelman, 1969). Thus, children may find it easier to apply a concept or operation to new situations after they have been given additional experience or particular information about that new situation. The relative effi- cacy of these alternative strategies for facilitating children’s understanding and application of new concepts requires systematic investigation.

The results of the present study have theoretical implications, as well. Children’s cognitive stages and the existence of mental structures have typically been inferred from observations of performance in testing situations using stimuli comparable to the “standard” materials employed here. Theoretical conceptuali- zations which are based on the child’s performance with abstract materials (e.g., the standard stimuli) may, therefore, substantially underestimate the problem- solving capabilities of young children.

Certainly there are limits to the kinds of problems very young children can solve. Some tasks require specific abilities such as linguistic skills, for example, that young children have not yet acquired. As yet, however, theory and research in cognitive development do not define the limits of children’s cognitive compe- tence .

148 MCHALE AND WEST

REFERENCES

Borke, H. Interpersonal perception of young children: Egocentrism or empathy? Developmenral Psychology, 1971,5, 264-269.

Bonier, J. The course of cognitive growth. American Psychologisf, 1964, I9 1-15. Bruner, J. & Kenney, H. On multiple ordering. In J. Bruner, R. Oliver, and P. Greenfield (Eds.),

Studies in cognitive growth, New York: Wiley, 1966, 154-167. Chi, M. T. H. Knowledge structure and memory development. In R. Siegler (Ed.), Children’s

thinking: What develops? Thirteenth Annual Carnegie Symposium on Cognition. Hillsdale, N.J.: Lawrence Brlbaum Associates, 1978.

Corsale, K., & Grnstein, P. A. Developmental changes in the use of sematic information for recall. Paper presented at the Meetings of the Psychonomic Society, Washington, D.C., November,

1977. Gelman, R. Preschool thought. American Psychologist, 1979,34, 900-906. Gelman, R. Conservation acquisition: A problem of learning to attend to relevant attributes. Journal

of Experimental Child Psychology, 1969, 7, 167-187.

Inhelder, B., & Piaget, J. The early growth of logic in the child. New York: W. W. Norton & Co.,

Inc., 1969.

Sigel, I. E. When do we know what a child knows? Human Development, 1974, 17, 201-217.