young children's knowledge of balance scale problems
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This article was downloaded by: [New York University]On: 17 October 2014, At: 21:11Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH,UK
The Journal of GeneticPsychology: Research andTheory on Human DevelopmentPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/vgnt20
Young Children's Knowledge ofBalance Scale ProblemsGerald T. Mcfadden a , Annette Dufresne a & AkiraKobasigawa aa Department of Psychology , University of Windsor ,CanadaPublished online: 06 Jul 2010.
To cite this article: Gerald T. Mcfadden , Annette Dufresne & Akira Kobasigawa(1987) Young Children's Knowledge of Balance Scale Problems, The Journal of GeneticPsychology: Research and Theory on Human Development, 148:1, 79-94, DOI:10.1080/00221325.1987.9914539
To link to this article: http://dx.doi.org/10.1080/00221325.1987.9914539
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Journal of Genetic Psychology, 148( I ) , 79-94
Young Children’s Knowledge of Balance Scale Problems
GERALD T. McFADDEN ANNETTE DUFRESNE AKIRA KOBASIGAWA
Department of Psychology University of Windsor
ABSTRACT. Five- and 7-year-old children’s knowledge of balance scale problems was assessed in terms of Siegler’s (1976, 1981) rule-assessment techniques using two tasks: (a) Siegler’s tasks in which the experimenter placed weights in various configu- rations on the balance scale and asked children to predict the outcome (lefthight side down or balance) and (b) a construction task in which the experimenter placed weights on only one side of the balance scale and asked children to place a specific number of weights on the other side of the scale to generate a desired outcome (lefthight side down or balance). A majority of children at both age levels (75%) relied only on the weight dimension to solve Siegler’s tasks. When the construction problems were introduced, many of the 5-year-olds continued to use weight only, whereas many of the 7-year-olds placed the weight by relying on the distance dimen- sion, and still other 7-year-olds relied on both the weight and distance dimensions. The utility of Siegler’s rule-assessment technique for classifying children’s knowl- edge was also demonstrated.
THE PURPOSE OF THE PRESENT INVESTIGATION was to study young children’s knowledge of balance scale problems in terms of the rule- assessment procedure developed by Siegler (1976, 1981). Siegler’s rule- assessment approach has been described as a significant advance in the
We gratefully acknowledge the excellent cooperation of the staff. supervisors, and students at various City of Windsor Day Nurseries and Community Centers, and the administrative s tdx teachers, and students of the Essex County Separate School System. We are also grateful to Robert Siegler for sending us his original balance scale problems.
Requests for reprints should be sent to Akira Kobmigawa, Department of Psy- chology, University of Windsor, Ontario, Canada N9B 3P4.
79
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80 Journal of Generic Psychology
study of cognitive development (Flavell, 1985). In addition to relying on nonverbal patterns of responses as the primary indication of children’s ex- isting knowledge, the procedure has helped researchers clearly identify in- itial, intermediate, and mature forms of reasoning strategies in a develop- mental sequence.
The point of departure of our research was Siegler’s (1976) series of studies in which he assessed the rules children of different ages use to solve balance scale problems. Initially, Siegler generated four increasingly com- plex rules that children might use to solve such problems. He hypothesized that children using the most primitive rule (Rule 1) consider only the amount of weight on each side of the balance scale. These children predict that the scale will remain level if the weights are equal, regardless of the distance of the weights from the fulcrum, or that the side with the greater weight will go down if the weights are unequal. At the next level (Rule 2), if the weights on both sides are equal, children look for a difference in distance and predict that the side with the greater distance will go down. If the weights are unequal, however, Rule 2 users predict that the side with the greater weight will go down (the same as Rule 1). Children using Rule 3 always consider both weight and distance but do not know the precise rules for combining weight and distance. Finally, children using the most ad- vanced rule (Rule 4) multiply the distance by the weight for each side and compare the products to solve any type of problem.
To compare the hypothesized rule usage with children’s actual per- formance, Siegler (1976) presented subjects of different ages with six dif- ferent types of balance scale problems (see Table 1) that would produce dis- tinctive patterns of responses for each of the four rules. All of Siegler’s problems consisted of the experimenter placing various configurations of weights on a balance scale that had four equally spaced pegs on each side of the fulcrum and asking the children to predict whether the scale would re- main balanced or one side of the balance arm would go down. Of the 120 children Siegler tested, 107 (89%) were unambiguously classified as using one of the four rules. He also found age-related trends in the complexity of the rules used; virtually all of the 5- and 6-year-olds used Rule 1, the 9- and 10-year-olds used Rules 2 and 3 most frequently, and the 13- and 17-year- olds used Rule 3 most frequently.
Although Siegler’s (1976, 1981) work represented a well-articulated ex- ample of recent information-processing approaches to cognitive develop- ment (Flavell, 1985), his rule-assessment procedure has come under criti- cism (Strauss & Levin, 1981). One criticism centers on the limited response that a child is allowed to make in the Siegler tasks. The problems are pre- sented in a fixed fashion: A specific number of weights are placed on certain pegs. Children are asked only to indicate whether the scale will remain balanced or one side will go down. The limited choice involved in Siegler’s
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TABLE
1 Pr
edic
ted
Patte
rns
of R
espo
nses
for
Diff
eren
t Rul
es on
the
Var
ious
Bal
ance
-Sca
le P
robl
ems
Rul
es
Rul
es
Sieg
ler’
s tas
ks
1 2
LWD
C
onst
ruct
ion
task
s 1-
w
1-D
2-
W
2-D
3
Bal
ance
Wei
ght w
D
ista
nce w
w
Con
flict
wei
ght
Con
flict
dis
tanc
e
w
Con
flict
bal
ance
CN
-bal
ance
-
100
100
100 w
10
0 10
0 0 w
- C
N-w
eigh
t -
CN
-dis
tanc
e 0
100
0 C
N-c
onfli
c; &
stan
ce
-
w
100
100
0
CN
-con
flict
bal
ance
0
0 10
0
0 0
0
25
100
100
100
100
25
25
25
100
100
25
100
100
100
100
25
100
25
100
100
25
0 25
25
10
0
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82 Journal of Generic Psychology
rule assessment procedure, according to critics, forces a child to make judg- ments that may underestimate his or her existing knowledge.
In light of the above criticism, the present research was conducted to determine whether or not a more comprehensive picture of young children’s existing knowledge of balance scale could be obtained within the rule- assessment approach by using two different assessment conditions. Specific- ally, we were interested in determining whether children diagnosed as using Rule 1 in terms of Siegler’s (1976) task would continue to focus only on the weight dimension while solving problems of a new task we developed, use a new dimension (i.e., distance), or use both the distance and weight dimen- sions (Rule 2 or 3). By so doing, we were also able to assess the further util- ity of the rule-assessment technique with the new task.
Toward this end, 5- and 7-year-old children’s knowledge of the balance scale was assessed by using Siegler’s task and a construction task. Children of these two age levels were used in our initial study (Study 1) to determine whether or not children at different age levels, assessed as Rule 1 users with Siegler’s task, might demonstrate different knowledge when assessed by the construction problems. To determine the replicability of the data, a follow- up study (Study 2) was conducted with additional 7-year-old children. Find- ings from Study 2 will also be provided.
In Siegler’s task, weights were placed on both sides of the fulcrum. For the construction task, however, the experimenter manipulated weight and distance only on one side of the scale. The child was then given a fixed num- ber of weights and asked to place them at a point on the other side where he or she thought that the two sides would balance or that one side would go down. This construction procedure was selected for several reasons. As the Method section describes, this procedure allowed us to predict different pat- terns of responses by children using different rules. In addition, because the task required children to manipulate the amount of distance, the distance dimension presumably increased in salience. Furthermore, although all of Siegler’s problems could be solved by using Rule 1, some of the construc- tion problems were not solvable by adopting this rule. As a result, it was an- ticipated that at least some children might generate a new rule with the con- struction task that they might not use with Siegler’s task.
Method
Subjects
Subjects for Study 1 were thirty 5-year-old (M age = 5.3 years) and thirty 7-year-old (M age = 7.3 years) children, balanced within each age for sex. They were drawn from three day nurseries and two community day care facilities in predominantly lower-middle and middle-class areas of Windsor,
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McFadden, Dufresne, & Kobasigawa 83
Ontario. Subjects for Study 2 were twenty 7-year-old (M age = 7.4 years) boys, drawn from a predominantly middle-class parochial school located in the outskirts of Windsor, Ontario.
Apparatus
The balance scale consisted of a wooden crossbar (32 in.) with four equally spaced wooden pegs on each side of a fulcrum. Two aluminum posts were placed under the arms of the balance scale to prevent it from tipping when the weights were placed on the pegs. Every weight was circular and had a hole in its center so that it could be fitted on the pegs. Each weight weighed approximately 28 g with an outside diameter of 1 % in. and an inside diame- ter of 5/8 in. As many as six weights could be placed on any given peg.
Balance Scale Problems, Rules, and Predicted Response Patterns
Siegler’s problems. Twenty-four of Siegler’s problems were used, consisting of four examples of each of the following six problem types: balance prob- lems, with equal amounts of weight equidistant from the fulcrum; weight problems, with unequal amounts of weight equidistant from the fulcrum; distance problems, with equal amounts of weight different distances from the fulcrum; conflict-weight problems, with more weight on one side and more distance (i.e., occupied pegs farther from the fulcrum) on the other, arranged so that the side with more weight goes down; conflict-distance problems, similar to conflict-weight except that the side with greater dis- tance goes down; conflict-balance problems, like other conflict problems, except that the scale remains balanced. These items were used in Session 1. Examples of these problem-types and predicted patterns of correct answers for Rules 1 and 2 are presented in the left side of Table 1. (For predicted patterns of responses for Rules 3 and 4, see Siegler, 1976.)
In addition to the above 24 items,.four distance and four conflict- distance problems were selected from Siegler’s problems. These items were different from those used in Session 1 and were included in Session 2 to de- termine if the children continued to use Rule 1 or a more advanced rule prior to the administration of the construction task.
Construction problems. Twenty problems were used for the construction task, consisting of four examples of each of the following problem-types: construction (hereafter CN) balance problems for which the child was given the same number of weights as had been placed by the experimenter and was asked to place the weights on the empty side of the scale to create a balance; CN weight problems that required the child to place a predetermined number of weights on the empty side so that the heavier side would go
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84 Journal of Genetic Psychology
down; CN distance problems in which an identical number of weights was to be placed on the empty side so that the side with the weights farther from the fulcrum would go down; CN conflict-distance problems that required the child to place a given number of weights on the empty side to make the side with less weight go down; and CN conflict-balance problems in which the child was asked to create a balance situation by placing the weights on the empty side. The correct solution involved placing the weights farther from the fulcrum if given less weights or closer to the fulcrum if given more weights. These 20 items were used in Session 2. Examples of these problem- types are shown on the right side of Table 1 .
The predicted performance for the construction problems for children using various rules was based on a description of the rules (Siegler, 1976, 1981) and on certain assumptions. As will be indicated shortly, certain problem-types were impossible to solve with Rule 1 or Rule 2 knowledge. The predicted performance for such impossible problems was assumed to be at a chance level, or 25% correct, as the child was required to place the weights on one of the four pegs. Some problem-types were solvable from Rule 1 or Rule 2 users’ viewpoints by choosing any one of the four pegs. The predicted performance for such problems was also assumed to be at a chance level (i.e., 25% correct).
For the construction problems, Rule 1 was subdivided into two types, one that focused only on the weight dimension (Rule 1-W) and one that focused only on the distance dimension (Rule 1-D). Similarly, Rule 2 was subdivided into two types, Rule 2-W and Rule 2-D. Although these addi- tional rules (Rule 1-D and Rule 2-D) were equally applicable to the Siegler task, as will be shown in the Results, none of the children used such rules for solving Siegler’s problems. Consequently, no attempt was made to subdi- vide Rules 1 and 2 for analyzing children’s performance on the Siegler task.
Rule 1-W users think that the scale will always balance if both sides of the scale have the same weight, regardless of the distance, and that the side with the greater weight will go down (the same as Siegler’s Rule 1 ) . AS a result, these children believe that the choice of any peg represents a correct solution for CN balance and CN weight problems. In contrast, CN dis- tance, CN conflict-distance, and CN conflict-balance problems represent impossible problems for these children. Thus, their predicted performance was 25% across all problem-types (see Table I) .
Rule l-D children believe that the side with the greater distance will go down, regardless of the weight, and that the scale will balance if the distance is equal on both sides. These children were expected to solve CN balance, CN distance, and CN conflict-distance problems correctly because the cor- rect solution of these problems can be arrived at by using the distance di- mension only. CN weight problems were expected to be impossible for Rule 1-D users because the choice of pegs should result either in balance or the
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McFadden, Dufresne, & Kobasigawa 85
wrong side going down. The predicted rate of success was 25%. Similarly, Rule I-D children were expected to attempt to solve CN conflict-balance problems by equating the distance, which is never correct. The predicted rate of success for these problems was 0%.
Rule 2-W children pay attention only to weight, although they attend to distance when the weights are equal (the same as Siegler’s Rule 2). They were expected to solve CN balance and CN distance problems correctly be- cause, in both cases, they would be given the identical number of weights that the experimenter had placed on the scale. For these children, the choice of any peg would solve CN weight problem , whereas CN conflict-distance and CN conflict-balance problems were expected to be impossible (25% correct).
Rule 2-D children place weight by relying only on the distance dimen- sion except when the distances are equal, when they also pay attention to weight. These children were expected to solve all of the problem-types but CN conflict-balance problems. CN conflict-balance problems were expected to be impossible for Rule 2-D users because the choice of any peg will not result in balance according to this rule.
Rule 3 children always rely on both distance and weight to solve bal- ance scale problems. Because only the knowledge that a weight weighs more the farther it is from the fulcrum, and vice versa, is required to correctly solve all construction problems, a child with Rule 3 knowledge was expected to solve correctly all construction problems.
Procedure
The children were interviewed individually in two sessions in an isolated room at their day nursery, community center, or school. During Session 1, children’s rule usage was assessed with Siegler’s procedure. Session 2 began with the eight Siegler items followed by the 20 construction problems. The children were not given any feedback as to the correctness of their responses in either session. The identical assessment procedure was used for Studies 1 and 2.
Session I. In general, each child was asked to sit next to the experimenter at a table with the balance scale in front of them. After briefly establishing rapport with the child, the experimenter explained to the child the general nature of the game with the balance scale and encouraged him or her to hold some of the weights to see that they all weighed the same.
Each problem began with an empty balance, the arms of which were supported by the two aluminum posts. Then the metal weights were placed on the pegs on the two sides of the balance scale, and the child was asked to predict which side would go down or whether the scale would balance if the two supporting posts were not there. The 24 problems were ordered so that
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one item of each problem-type was included in the first six problems, one in the next six problems, and so on.
Session 2. One week after Session 1, all children were pretested with the eight Siegler items to determine if they continued to use Rule 1 during Session 2. These items were arranged so that one item of each problem-type was included in the first two problems, one in the next two problems, and so on.
The 20 construction problems were then presented. The child was told that he or she would play a different game with the balance scale toy. The child was instructed:
I will place some weights on only one peg, for example, on my side (ex- perimenter points to right side). Then I will give you some weights to place on your side (experimenter points to left side). Sometimes I will ask you to place the weights where you think it will make your side go down. But sometimes I will ask you to place the weights on your side where you think it will make my side go down. And sometimes I will ask you to place the weights where you think it will make the scale balance if these posts were taken away.
The experimenter then placed a number of weights on one peg on either the left or right side of the scale. The child was given some weights and asked to place them on one peg on the empty side to generate a specific out- come (e.g., right side down) if the supporting posts were not there. The 20 construction problems were also arranged in a random order as described previously.
Rule Assessment Criteria
For Siegler’s problems, Rules 1 and 2 were assessed if at least 20 of the 24 responses during Session 1, or at least six of the eight responses during Ses- sion 2 corresponded to the predictions made by that rule (see Table 1). Also for Rule 1, at least three predictions of balance in the four distance prob- lems were required.
For the construction problems, the rule assessment criteria were as follows: (a) at least 16 out of 20 responses corresponded to the predictions for that rule (see Table 1) and (b) there were at least three correct responses for the four CN conflict-balance problems for Rule 3, as this was the only problem-type discriminating Rule 3 from Rule 2-D.
Results
Classification by Rule Models
Siegler’s problems. Fifty-six children (93%) in Study 1 were judged to be rule users in terms of the criteria described previously. As expected, a ma-
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McFadden, Dufresne. & Kobasigawa 87
jority of the children (n = 43 or 72%) solved balance problems by attending only to the weight dimension (Rule 1). In contrast, only six children (10%) used both the weight and distance dimensions when the weights on both sides of the fulcrum were equal (Rule 2). Seven children’s (1 1%) perform- ance conformed to a special case of Rule 1 (rule of less weight down [LWD]), always predicting that the lighter side of the scale would go down. Although more of the older (n = 5 ) than younger children (n = 1) used a higher rule (Rule 2), this age-related trend was not statistically reliable. The findings of Study 1 were replicated in Study 2: 16 of the 20 children (80%) used Rule 1, 2 children (10%) used Rule 2, and 2 children (10%) used Rule LWD. No children were classified as using Rule 3 or Rule 4 in either study. In addi- tion, no child was found to use Rule 1-D or 2-D during the Siegler tasks.
The children classified as using a particular rule made at least 22 of the 24 responses (i.e,, better than the classification criteria set) in the way predicted by that rule model. Combining the data from the two studies, Figure 1 demonstrates this high degree of correspondence between the pre- dicted and actual patterns of correct answers and errors for Rule 1 , Rule LWD, and Rule 2 separately. Visual inspection of these data indicates that the fit of the rule models to actual performance was close in each case.
Construction problems. Children were assessed as using a specific rule ac- cording to the criteria described in the Method. The number of 5- and 7-year-old children classified into various rules in Study 1 were: 14 and 4 for Rule 1-W, 2 and 14 for Rule 1-D, 4 and 1 for Rule 2-W, 2 and 4 for Rule 2-D, and 0 and 2 for Rule 3. Thus, 47 of the 60 children (78%) in Study 1 were classified according to rule models for the construction problems (i.e., 1-W, 1-D, 2-W, 2-D, and 3). Unlike the findings for the Siegler problems, age-related trends emerged with the construction problems: Significantly more of the older (n = 21) than younger (n = 8) children utilized the distance dimension (Rules l-D, 2-W, 2-D & 3 combined), whereas signifi- cantly more of the younger (n = 14) than older (n = 4) children responded at a chance level (Rule 1-W), p < .01. (Mainland and Murray’s (1952) tables were applied to the data. Mainland and Murray’s tables substitute for direct computation of Yates’ corrections or Fisher’s exact probabilities. Thus, only p values are reported.) The number of children who used both the weight and distance dimensions (Rules 2-W, 2-D, & 3) did not differ sig- nificantly between the two age groups. Two of the 13 unclassified children, regardless of the type of problem, always placed the weights on the same peg that the experimenter had placed the weights (a rule of the same peg). When the criterion for rule usage was slightly adjusted, at least 14 of the 20 responses by nine unclassified children conformed to Rule l-W (n = 7), Rule l-D (n = I ) , or Rule 2-D (n = 1).
Sixteen of the 20 children (80%) in Study 2 were judged to be rule users
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Predicted
Actual
- 0 !! i 0
a m
a r n
-
Problem-Type
FIGURE 1. Correspondence between the predicted and actual patterns of responses: Siegler’s task. (B = balance; W = weight; D = distance; CW = conflict weight; CD = conflict distance; CB = conflict balance.)
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McFadden, Dufresne, & Kobasigawa 89
according to the rule models. Only 2 children (10%) were assessed as using Rule 1-W, whereas 14 children were assessed as using one of the higher rules (Rules 2-W, 2-D, and 3). Three of the four unclassified children used the rule of the same peg.
Recall that the children’s performances on the Siegler problems were quite comparable across Studies 1 and 2. In contrast, significantly more of the 7-year-olds in Study 2 (70%) than the 7-year-olds in Study 1 (23%) util- ized both the weight and distance dimensions (i.e., Rules 2 and 3) for solv- ing the construction problems, ~ ’ (1 ) = 8.90, p < .01.
To explain this puzzling difference between Study 1 and Study 2, we considered two possibilities. First, both boys and girls were used in Study 1 whereas only boys were included in Study 2. The finding concerned here cannot, however, be explained in terms of the sex-related difference because about an equal number of boys and girls used Rule 2. Second, a majority of the children in Study 1 came from lower-middle-class families whereas the children in Study 2 came from middle-class families. The observed differ- ence in rule usage between the two studies may have resulted from this social class variable; many researchers have shown that the development of children’s cognitive skills is related to socioeconomic factors (e.g., Minton & Schneider, 1980).
The actual and predicted performance in the construction problems is illustrated in Figure 2 for Rules 1-W, 1-D, and 2-W separately. The data from the two studies were combined. The fit was again close for each case.
Siegler’s problems versus construction problems. Prior to administering the construction problems in Session 2, Siegler’s distance and conflict distance problems were again given to the children. It was found that mainly the original distance users (i.e., Rule 2 users in Session 1) continued to use that dimension in Session 2 (5 and 2 children for Studies 1 and 2, respectively). Thus, the majority of the children were not solving balance scale problems by using the distance dimensions immediately prior to the presentation of the construction problems. It was unlikely, then, that any changes in rule usage indicating that children were using the distance dimension to solve construction problems were due to the experience children gained with the balance scale in Session 1.
We will now examine children’s tendency to change their rules during the construction procedure. We were interested in two shifts in rule usage: a shift from using the weight dimension only (Rule 1) to using the distance dimension, and a shift from using a simple Rule 1 to using a more complex Rule 2 or higher. Data that summarize both of these changes are set out in Table 2. The data are based on 75 children (94%) who were unambiguously classified as using Rules 1 (Rule LWD included) and 2 on the Siegler task. These changes from weight to distance, and from Rule 1 to Rule 2 or higher,
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I
C'N C'N CN CN CN B W D CD CB
Problem-Type
FIGURE 2. Correspondence between the predicted and actual patterns of re- sponses: Construction task. (CN-B = construction balance; CN-W = con- struction weight; CN-D construction distance; CN-CD = construction con- flict distance; CN-CB = construction conflict balance.)
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McFadden, Dufresne, & Kobasigawa 91
were examined by applying the binomial test (Siegel, 1956, p. 67) to these data. Regarding the first type of change, children were categorized as dis-
tance users (D in Table 2) on the Siegler problems if they had been classified as using Rule 2, and as distance users on the construction problems if they had been classified as using Rule 1-D, 2-W, 2-D, or 3. The remaining chil- dren were classified as nondistance users (ND in Table 2). Analyses indi- cated that children at each age level showed a significant tendency to change from the use of the weight dimension in Siegler’s task to the use of the distance dimension in the construction tasks, p c .01 or better (see upper half of Table 2). This shift in the use of distance is, however, more clearly shown in the data for the 7-year-olds (64%) than in those for the 5-year-olds (28%). Many of the 5-year-old nondistance users on the Siegler task were also nondistance users for the construction task (72%).
Regarding the second type of change, relatively small proportions of the 5- and 7-year-olds in Study 1 adopted a higher rule during the construc- tion procedure (n = 5 in both cases). This modest shift in rule usage from a lower to higher rule was significant only for the 5-year-olds, p c .01. In contrast, many of the 7-year-olds in Study 2 (66%) changed their rule usage from Rule 1 (Siegler task) to Rule 2 or 3 (construction task). This tendency to change their rules between the two tasks was statistically reliable, p c .001.
TABLE 2 Number of Children Showing Changes in the Use of the Distance
Dimension (upper half) and Rule 1 or 3 (lower half) between Siegler’s and Construction Tasks
Construction Tasks 5-yr-olds 7-yr-olds 7-yr-olds
Siegler’s Tasks Study 1 Study 1 Study 2
D ND
ND D ND D ND D 0 1 0 5 0 2
18 7a* 9 16‘** 6 12a**
Rule I Rule 2 N Rule 1 Rule 2/3 Rule I Rule 2 N Rule 2 0 1 3 2 0 2 Rule 1 20 5 b* 20 gb*** 6 12b**
Nore. D = Distance users; ND = nondistance users. ‘Number of children showing a shift from ND (Siegler task) to D (construction task). bNumber of children showing a shift from Rule 1 (Siegler task) to Rule 2 or 3 (construction task). *p < .01. * p < .001. ***ns.
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92 Journal of Generic Psvchology
Discussion
One aspect of the present study was concerned with the utility of Siegler’s rule-assessment technique for classifying children’s performance on balance scale tasks. The following three pieces of evidence are relevant to the first concern. First, outside Siegler’s laboratory, we have shown that approx- imately 80% to 90% of the children could be classified as using one of Siegler’s rule models to solve Siegler’s balance problems. Second, we gen- erated a rule model of “less weight down,’’ which was not identified by Siegler. Users of this rule predict on the basis of the weight dimension only, and consequently, this rule represents a special case of Rule 1. Once we specified this new rule, we were able to classify an additional 10% of the children. Third, the utility of the rule-assessment procedure was illustrated further by using novel balance scale problems (i.e., construction problems). When Siegler’s assessment method was extended to the construction prob- lems, about 80% of the children were classified according to newly for- mulated rule models (e.g., Rules l-D and 2-D) as well as Siegler’s original rule models. These three pieces of evidence converge to confirm the use- fulness of Siegler’s rule-assessment technique.
The second question posed in the present study was whether or not a more comprehensive picture of young children’s knowledge might emerge when broader assessment situations were used. Siegler (1976, 1981) has claimed that a majority of young children use Rule 1, a rule that involves a reliance on only one dimension, usually weight, to solve problems. Indeed, when the Siegler problems were presented, nearly 80% of the children at both age levels were classified as using Rule 1, making predictions solely on the basis of weight. Yet, when the construction problems were introduced, almost 70% of the 7-year-oIds who had been initially classified as using Rule 1 (weight only) apparently used the distance dimension (Study l), although many of the 5-year-old children continued to focus only on the weight dimension. Interestingly, a significant number of 7-year-old children in Study 2 who had been identified as using Rule 1 (weight only) with the Siegler items were assessed as using Rule 2 or 3 (both weight and distance dimensions) with the construction problems.
When broader assessment situations are used, then, a more complex picture of young children’s knowledge of balance scales emerges. When children begin to use rules to solve balance scale problems, as Siegler hypothesized, a majority of children attend only to the weight dimension. Children at this level, just as many of the 5-year-olds did in Study 1, apply this rule to a wide variety of situations (e.g., both Siegler’s and construction tasks). Children at the next level become aware of the importance of the dis- tance as well as the weight dimensions. These children, just as many of the 7-year-olds did in Study I , use the weight dimension only for one set of
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McFadden, Dufresne, & Kobasigawa 93
situations (e.g., Siegler’s task) and the distance dimension only for another set of situations (e.g., construction task). Children then move onto the Siegler’s Rule 2 level at which they can use the two dimensions simultane- ously but under limited task demands, as demonstrated with the construc- tion problems in Study 2. For some reason, however, these children use Rule 1 when Siegler’s problems are presented.
A great proportion of children seemed to benefit from being exposed to the construction problems-some by beginning to use the distance dimen- sion that they did not use in Siegler’s task, and some by adopting a higher rule using both the weight and distance dimensions for certain construction problems. The question that arises is why did exposure to the construction tasks benefit these children. The construction task required children to manipulate the amount of distance, and consequently, the distance dimen- sion of this task should have become more salient than for Siegler’s task. Considering this, it is not surprising that many of the 7-year-olds in Study 1 were assessed as using Rule 1-D (distance only) with the construction prob- lems. How does one account for children’s higher rule usage with the con- struction problems as opposed to the Siegler problems? The two types of problems differ in that a simple strategy (“If the same weight, then balance”; “If Side X more weight, then side X down”) is sufficient to solve all of the Siegler problems, whereas this simple Rule 1 strategy does not ap- ply to some of the construction problems. Consider, for instance, construc- tion conflict-distance problems that require children to place weights on the scale to make the lighter side go down. These problems represent impossible tasks if children rely only on Rule 1, which states that the heavier side always goes down. When a simpler strategy (Rule 1) is applicable to tasks, apparently young children may use that strategy even though they are able to use a more complex strategy. Alternatively, the construction problems may serve as a type of training, thereby enabling a new strategy to emerge. Allowing children to manipulate the distance only and not the weight, as well as asking the children in some problems to make the lighter side go down, may provide the children with the information that distance is also important for solving balance scale problems. Furthermore, some children learn that their existing framework (Le., Rule 1) is inadequate for dealing with some of the construction problems. As a result, a new strategy of using both weight and distance in solving some types of balance scale problems may emerge in children.
In summary, the present research findings indicate that young children’s existing knowledge of balance scale problems may be more com- plex than a simple rule that focuses only on the weight dimension, and that the use of Siegler’s task alone may underestimate such knowledge. Perhaps the conclusion of the research may be best stated in Siegler’s (1981) own words: “Numerous tasks with varying characteristics will need to be ex-
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94 Journol of’ Genetic Psychology
amined to build a comprehensive model of children’s rules for dealing with complex content domains” (p. 83).
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Flavell, J. H. (1985). Cognitive development. Englewood Cliffs, NJ: Prentice-Hall. Mainland, D., & Murray, I. M. (1952). Tables for use in fourfold contingency tables.
Minton, H. L., & Schneider, F. W. (1980). Differentialpsychology. Monterey, CA:
Siegel, S. (1956). Nonparametric statistics: For the behavioral sciences. New York:
Siegler, R. S. (1976). Three aspects of cognitive development. Cognitive Psychology,
Siegler, R. S . (1981). Developmental sequences within and between concepts. Mono- graphs of the Society for Research in Child Development, 46(2, Serial No. 189).
Strauss, S., & Levin, I. (1981). Commentary on Siegler’s “Developmental sequences within and between concepts.” Monographs of the Society for Research in Child Development, 46(2, Serial No. 189).
Science, 116, 591 -594.
Brooks Cole.
McGraw-Hill.
8, 481-520.
Received January 23, 1986
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