Development of analogical reasoning in 4- and 5-year-old children

Cognitive

Development,

4, 65-88

Development

(1989)

of Analogical Reasoning in 4and s-year-old Children Patricia A. Alexander Victor L. Willson Texas

A&M

University

C. Stephen

White

University

of Georgia

J. Diane James

Madison

Gregory Digital

Equipment

Psychological

Jonna

D. Clark Corporation

Alice The

Fuqua University

F. Wilson Corporation

M. Kulikowich

Texas

A&M

University

This study assessed the development of analogical reasoning of 4- and 5-year-olds. Subjects were 60 preschoolers, ages 48 months to 71 months. Performance of geometric analogy problems was measured at monthly intervals with the Test of Analogical Reasoning in Children. Results indicated that the children were generally stable in their reasoning performance. There was a significant linear upward trend in performance for less proficient, nontrained reasoners, but post hoc analysis indicated a significant difference only between the first testing and all other testings. Generally, less proficient reasoners used a naive, nonanalogical strategy in completing the geometric analogy problems. Explicit training of the less proficient reasoners had a significant, positive effect on performance that was maintained for several months. Finally, it was determined that the nontrained children who became more proficient in analogical reasoning were significantly older than those who did not. Correspondence and requests for reprints should be sent to Patricia A. Alexander, Department of Educational Curriculum and Instruction, College of Education. Texas A&M University, College Station, TX 77843. The authors wish to thank Robert Stemberg for his comments on an earlier version of this manuscript. 65

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Fuqua,

Clark,

Wilson,

and Kulikowich

Within the past decade, there has been an increasing interest in the nature and development of analogical reasoning in young children. Researchers have sought to identify the processes underlying analogical reasoning (Holyoak, 1984; Mulholland, Pellegrino. & Glaser, 1980; Stemberg, 1977). to specify the stages of its development (Case, 198.5; Piaget. Montangero, & Billeter, cited in Gallagher, 1978; Wagner, 1983). and to assess its susceptibility to training (Alexander, White, Haensly, & Crimmins-Jeanes. 1987; Stemberg, Ketron, & Powell, 1982). As an information-processing task, analogical reasoning has long been considered an essential cognitive ability (Stemberg, 1977). and its importance is attested to by the consistent presence of analogies on intelligence and aptitude measures (Kaufman & Kaufman. 1983; Raven, 1973). Although the importance of analogical reasoning has been firmly established, the nature and development of this ability, particularly as it pertains to the very young, warrants further examination. For instance, in our search of the literature, we found no studies that had systematically investigated the development of young children’s analogical reasoning over an extended period of time. This absence of more long-term investigations of young children’s reasoning abilities seems of particular concern in light of significant cognitive changes that can occur during the preschool years (Carey, 1985; Flavell, Flavell, & Green, 1983; Holyoak, 1984). In the literature, the term, analogy, has been applied to a variety of cognitive activities; from a global learning strategy (Rumelhart & Ortony. 1977) to a specific problem set (Glaser & Pellegrino, 1982). The focus of our research with young children has been related to the latter in that it involves performance of geometric analogy problems of the type A:B::C:D (Alexander, Willson, White, & Fuqua, 1987; Alexander, Wilson, White, Willson, Tallent, & Shutes. 1987). In this previous research, we investigated the emergence of analogical reasoning among preschool populations (Alexander, Willson, et al., 1987; White & Alexander, 1988), the levels of reasoning competence demonstrated by these preschoolers, and reasoning strategies exhibited by young analogical and nonanalogical reasoners (Alexander, Willson, et al., 1987; White & Alexander, 1986). Furthermore, we evaluated the effects that explicit training had on the reasoning performance of preschoolers (Alexander, Wilson, et al., 1987). Our research, as with that of others, has suggested that: 1.

2. 3.

Even very young children may have the capacity to reason analogically (Alexander, Willson, et al., 1987; Crisafi & Brown, 1986; Vosniadou & Schommer, 1986; White & Alexander, 1988). Less proficient reasoners seem to employ a naive, albeit logical, strategy in analogy performance (Alexander, Willson, et al., 1987). Less proficient reasoners can be trained to perform significantly better on analogy tasks (Alexander, Wilson, et al., 1987; Stemberg, et al., 1982).

Development

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In addition, while several theories of analogical reasoning exist (e.g., Case, 1985; Holyoak, 1984), our research program has focused on the componential theory of analogical reasoning as articulated by Stemberg (1977; 1985). In accordance with this theory, we perceive competence in analogical reasoning to be based on the understanding and performance of essential cognitive components that underlie analogy tasks. Stemberg describes components as elementary information processes that operate “upon internal representations of objects or symbols” (1982, p. 227), and identifies five types based upon the function they perform. According to Stemberg, cognitive tasks can be decomposed into metacomponents, and perfomtance, acquisition, retention, and transfer components. Our research program in analogical reasoning has centered specifically on the assessment and training of the performance components of encoding, inferring, mapping, and applying. Although our analogy research and that of others has been informative, several important questions remain unanswered. Perhaps most importantly, prior research has been cross-sectional rather than longitudinal. Important questions about analogical reasoning development might be effectively addressed by examining change in the same sample over an extended period of time. It is possible, for instance, that young children have direct or indirect experiences within their preschool environments that stimulate the development of analogical reasoning. Therefore, more extended investigations of analogical reasoning would complement existing cross-sectional studies by identifying conditions associated with changes in reasoning performance and by contributing to the development of programs that enhance reasoning abilities. Because the length of study is an important variable in extended investigations, we decided to follow our children throughout the course of a preschool year, beginning in early October and running through May of the school year. Certainly an even longer period of study would have been preferable. However, in view of apparent differences in reasoning capability between younger and older preschoolers (Alexander, Willson, et al., 1987; Crisafi & Brown, 1986; Flavell, Green, & Flavell. 1986), we felt that this period of study would be adequate. In addition, we decided to incorporate a training component in this investigation for several reasons. First, although we have some understanding of the immediate effects of explicit analogy instruction on preschoolers, these training studies are very limited in number (e.g., Alexander, Wilson, et al., 1987). The present study would serve to confirm prior research findings and would allow us to compare the spontaneous development of analogical reasoning with that induced by a training program. Moreover, this current study would provide the opportunity to assessthe durability of training effects over a period of several months. Finally, we wanted to profile the reasoning patterns and characteristics of those children who become more proficient during the course of the study with-

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Wilson,

and Kulikowich

out direct intervention. It is likely that over the seven-month period there would be less proficient reasoners who would attain proficiency in analogical reasoning without the benefit of explicit instruction. We wanted to see if those children who spontaneously achieved proficiency could be differentiated in any way from those children who remained less proficient. In order to evaluate analogical reasoning performance in the young, we developed the Test of Analogical Reasoning in Children or TARC (Alexander, Willson, et al., 1987). In the analysis of analogy research, we found disparities between the natural play and school behaviors of young children and the procedures employed to assessanalogical reasoning in this population. For instance, early childhood instruction stresses the concrete manipulation of objects, yet young children are most often tested using abstract, nonmanipulative materials. Furthermore, these young children are often asked to take part in an unfamiliar test-taking routine, usually by adults with whom they are also unfamiliar (Gelman, 1979; Gentner, 1977). In essence, we wanted to avoid what Bronfenbrenner described as “the science of the strange behavior of children in strange situations with strange adults for the briefest possible periods of time” (1979, p. 19). The TARC remedies this situation in several ways. First, its analogy problems are constructed from attribute blocks that are common objects in preschools. Second, we structured these problems into a game-playing routine that we found to be familiar and motivating to young children. Finally, we conducted our assessment in a comfortable setting, the child’s preschool classroom. METHOD Subjects

For the purpose of this study, we tested 60 young children from two private preschools in a city in south central Texas. Parental permission to participate was secured for all children in the sample. Although the sample was racially mixed, the children were generally from middle and upper-middle class families. At the time of initial testing, the children ranged in age from 48 months to 71 months with 25 children 60 months of age or older. There were 33 males and 27 females in the sample. During the course of this extended study, 4 of the original sample discontinued testing. In the schools that we selected as sites for this study, the majority of the preschool time was spent in self-directed, discovery learning activities. Large group or whole class activities occurred on a very limited basis and generally involved only creative movement and expression. The children were free to move about the classrooms engaging in small group or individual play activities often at centers located around the room. The classrooms contained a wide variety of manipulative toys and art supplies that children were encouraged to use independently. The pupil/teacher ratio ranged from 1 : 8 to 1 : 12.

Development

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Instruments We assessed analogical reasoning development with the Test of Analogical Reasoning in Children. The original TARC was a manipulative cognitive task that used a wooden gameboard and colored attribute blocks common in preschool and primary grade classrooms (Alexander, Willson, et al., 1987). Because of the repeated testings required in the current study, we found it necessary to develop alternate forms (Forms B, C, D, and E) and alternate versions (life-size and reduced paper versions) of the TARC. As can be seen in the descriptions which follow, form refers to the specific sets of problems included in the TARC, while version refers to the mode of presentation of those problems. Each of the five forms of the TARC contains 16 geometric analogy problems of the type A:B::C:D, with the first two problems serving as practice items. These analogy problems are composed of geometric terms that vary on the attributes of color (red-R, blue-B, yellow-Y), shape (rectangle-R, square-S, circle-C, triangle-T), and size (large-L, small-S). We constructed the four additional forms of the TARC by randomly permuting either the color, shape, or size of the terms in Form A. Specifically, we transformed the color of the terms in Form B (B-Y, R-B, and Y-R), shape in Form C (R-*C, C+T, T+S, and S-R) and in Form E (T-C, C-R, S+T, and R+S), and size in Form D (L-G, S+L). A sample item from Form A and its permutations across forms are displayed in Figure 1. In the game version of the TARC, the examiner places three attribute blocks on a (76.2 cm X 25.4 cm) wooden gameboard to form the A:B::C stem of the geometric analogy problems. Four response options from which the appropriate D term is to be selected are then arranged vertically to the right of the gameboard. The examiner carefully explains the rules of the game to the child for the first two practice items and then briefly repeats the rule for each subsequent item. Administrative procedures for the life-size and reduced paper versions are similar to those for the game version. For the life-size version, which consists of cardboard constructions having the same dimensions and colors as the game version, the children use a game piece to mark their selections during testing. For the reduced version, which was first constructed using high resolution computer graphics and then photographed onto Polaroid film, the children mark their answers with a colored marking pen. In our opinion, this reduced version more closely resembles the analogy problems found on intelligence and aptitude measures. For all forms and versions used, the reliabilities were found to be strong, typically over 0.8. (The reliabilities and validities for the different forms and versions are extensively discussed in Willson, Alexander, White, Fuqua, Clark, & Wilson, 1986.) Testing Procedure At monthly intervals, we individually tested the preschoolers in accordance with their group placements. We conducted the initial testing and all subsequent

Alexander,

Willson,

White,

Fuqua,

Form A - Item 4

Clark,

Wilson,

and

Kulikowich

Form B - Item 4

0

‘000

B

l

R 0

A 0

Form C - Item 4

Form D - Item 4

Form E - Item 4 Figure 1. Sample item from the TARC, through E.

Form A, and permutations

from Forms B

testings in the children’s preschool. Pairs of examiners, who were experienced in administering the TARC, conducted the testing. Prior to giving the first test, the examiners spent time with the children acquainting them with the testing materials and procedures. One of the two investigators in each pair administered the analogy test, while the second coded relevant verbal and nonverbal behaviors.

Development

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During testing, children were required to select the missing D term to complete the A:B::C:D analogy problem from the four response options provided. Once the children had made their selections, the examiner asked them to explain the reasons for their choices. The second examiner coded the selections the children made and noted their justifications for those selections. The specific directions given to the children and the coding procedures that were followed are more extensively discussed elsewhere (Alexander. Willson, et al., 1987). For the purposes of this investigation, only the quantitative data from the TARC in terms of number correct and response option selection will be considered in analysis. Study Design In the current study, we originally assigned the preschoolers to one of five groups based on their initial performance on the TARC. We established the five-group design to examine the effects of proficiency level, various forms and versions, and training on the children’s analogy performance. Group’ 1 was composed of more proficient reasoners, Groups 2, 3, and 4 consisted of less proficient reasoners who received systematically varied forms and versions of the TARC but no explicit training, and Group 5 was comprised of less proficient reasoners who were given explicit analogy instruction. A preliminary test of the effects of different forms and versions indicated no significant variation for Groups 2, 3, or 4. Therefore, these three groups were collapsed without regard for the different task conditions. Thus, the three groups to be analyzed and discussed in this study are as follows: more proficient reasoners; less proficient reasoners, nontrained; and, less proficient reasoners, trained. Because of their importance to this study, the classification of proficiency level and the nature of explicit training will be described further. Proficiency Level. Proficiency level refers to the classification of the preschoolers as more or less accurate analogical reasoners. As in our previous research (Alexander, Willson, et al., 1987), this classification was made in relation to chance level performance. Chance level for the 14 nonpractice items, each having 4 response options, was determined to be a score of 6 or less, including 2 standard errors of the binomial. Fifty children received a score of 6 or less on the initial testing and were categorized as less proficient reasoners. Twenty of these less proficient reasoners, all 4-year-olds, were randomly selected to receive training. The other 30 were placed in the less proficient, nontrained group. The remaining 10 children, who scored better than 6 on the initial TARC testing, constituted the more proficient reasoners group. Because we found that the performance differences between more and less proficient analogical reasoners, as measured by the TARC, were rather dramatic (i.e., near-ceiling to near-floor effects), we felt that neither the repeated testing nor the explicit training of the more proficient group would prove informative. Therefore, we chose to train only less proficient reasoners and to monitor the consistency of more proficient reasoners’ performance periodically during the

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and Kulikowich

course of this investigation. Furthemrore, our decision to select only less proficient 4-year-olds for training was motivated by our perception (Alexander, Willson, et al., 1987) and that of others (Flavell, Green, & Flavell, 1986) that this age is pivotal in reasoning development. Explicit Training. Since the nature of the explicit training the children received is presented elsewhere (Alexander, Wilson, et al., 1987; White & Alexander, 1986). we will only summarize it here. As we noted, the content of the training was based on the component processes of encoding, inferring, mapping, and applying, as articulated by Stemberg (1977, 1982, 1985). In order to accentuate these component processes, we chose to deliver our training via a direct or explicit instruction model (Rosenshine, 1983). In accordance with the direct instruction model, instructional procedures emphasized explicit teacher explanation of each of the component processes, student participation in problem solution, continual teacher feedback, and independent student practice. Training materials, in the fomr of analogy problems, were also sequenced from concrete to abstract and from simpler to more complex. This instructional sequence is represented in the sample training problems displayed in Figure 2. For this study, we structured the training, which was delivered between the first and second testings. into three 20-25 minute sessions delivered on three consecutive days. We conducted these training sessions in small groups of four preschoolers each. Although one might have wished for more intensive training, previous research has shown that between 60 and 75 minutes of explicit instruction for most 4- and 5-year-olds was adequate to ensure understanding of the component processes. In the first session of training, we used familiar toy objects, such as metal cars and plastic farm animals, to teach the component processes of analogical reasoning (see Figure 2a). We began the session with an explicit explanation of each of the component processes and then modeled how those component processes were used in the solution of an analogy problem composed of the toys positioned on the gameboard. (An excerpt of the explanation of the component processes given the children during the first session is provided in the appendix.) The children then collectively participated in the solution of additional problems we created with the toys. Following this group practice, each child was individually asked to solve one or more of these concrete analogy problems and to explain his or her answer to the instructor. We gave each child immediate corrective feedback and reinforcement on his or her problem solving performance. Individual practice was continuea until each child successfully solved an analogy problem. We concluded the first training session with a brief review of the component processes. The second session of training included an initial review of the previous day’s instruction and progressed quickly to the solution of problems composed of more abstract manipulatives, such as the tree shapes shown in Figure 2b. Generally,

Development of Analogical Reasoning

73

a>

b)

c>

0 R

I 0

B

R n

0

Y

B cl Y A

Figure 2. Sample problems explicit analogy training.

for Sessions One (2a), Two (2b), and Three (2~) of the

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and

Kulikowich

we followed the same instructional procedures used in Session I of the training but employed different instructional materials. That is, teacher modeling, group participation, and individual practice focused on the application of the component processes to analogy problems constructed on the gameboard with the somewhat more abstract manipulatives. As with all sessions, we concluded the day’s instruction with a review. In Session 3 of training we reviewed, explained, demonstrated, and practiced solving analogy problems composed of even more abstract manipulatives, like parquetry blocks or the attribute blocks like those shown in Figure 2c. It is important to stress that while identical attribute blocks were used in training and assessment, all problems used in explicit instruction were different from those included on the TARC. The children in the nontrained groups received no explicit instruction in analogical reasoning during the course of this investigation. Rather, these children continued to participate in the normal preschool activities we described earlier and, with the exception of the repeated testing, had no direct exposure to analogy problem solving. To ascertain the effects of training over time, we tested a randomly selected subset of the trained children beginning with Testing 4. Originally, it had been our intention to retest all trained subjects for each month of the study. However, due to time constraints and logistical problems only a portion (n = 5) of these children could be monitored for Testings 4 and 5. We felt that by tracking the performance of this randomly chosen subset of the trained group we would satisfy our initial objective of analyzing the more long-term effects of explicit instruction and we would provide information that was previously lacking in the research literature. RESULTS Our primary interest in this investigation was the development of analogical reasoning of 4- and 5-year-olds over seven months of preschool. Means and standard deviations for the TARC, our measure of analogical reasoning, are displayed in Table 1 by group (more proficient; less proficient, nontrained; less proficient, trained) and by testing (Testing 1 to 6). In our analysis, we sought to: (a) assess the stability of performance for more and less proficient reasoners; (b) ascertain the immediate and more long-term effects of explicit training on analogy performance; and, (c) differentiate the less proficient, nontrained preschoolers who subsequently achieved proficiency, as defined in this study, from those who did not. Each of these empirical issues will now be examined. Performance Stability The means and standard deviations presented in Table 1 convey some interesting data about the development of analogical reasoning in 4- and 5-year-olds during the course of this investigation. We chose to examine these data in two ways:

Development

Table 1.

of Analogical

Reasoning

75

Means and (Standard

Deviations)

on the TARC

by Group by Testing

Testing

Group

More

10

MW)

MW)

M(SD)

M(SD)

9.30~~ (2.21)

-

7.10 (5.04)

-

9.90 (3.20)

IO.11 (3.62)

2.13 (1.85)

3.00 (2.84)

3.83 (3.95)

4.07 (4.25)

4.39 (4.29)

4.29 (4.33)

2.60 (2.48)

9.15 (2.56)

IO.55 (3.05)

I I .40h (1.95)

10.80 (1.92)

3

4

5

6

MSD)

MW)

proficicnl

Nontrained

n = 30 Less

2

proficient

II =

Less

I

proficient

Trained

n = 20 “out

of a possible

14

hrl = 5

first, by assessing trends within groups over time; and, second, by making comparisons across groups at designated points in time. In addressing the issue of performance stability, we will consider the within-group trends only for the more proficient and the less proficient, nontrained reasoners. Changes in the less proficient, trained group will be addressed in the section on explicit training. We analyzed the TARC scores for more proficient reasoners across testings by a one-way analysis of variance procedure. Results of the ANOVA demonstrated that these children’s scores did not change markedly over the study period, indicating a nonsignificant linear trend, F( 1, 26) = 1.47, p > .2, MS, = 8.49. Thus, it would appear that analogical reasoning performance for those children initially identified as more proficient remained rather stable during the 7 months of this study. This performance pattern for the more proficient group is graphically displayed in Figure 3. We conducted a similar trend analysis on the TARC scores for less proficient, nontrained reasoners. These results, also displayed in Figure 2, demonstrated a significant upward linear trend in analogy performance, F(1, 127) = 19.05, p < .OOOl, MS, = 4.68. In order to interpret this significant finding, we performed post hoc analyses of the six testings. Specifically, we compared each of the TARC testings for the less proficient, nontrained group using Tukey’s studentized range tests. The results of these analyses showed that there was a significant difference @ < .05) only between Testing 1 and all other testings. The significant difference only between Testing 1 and all other testings may appear surprising in light of the means presented in Table 1 for the less proficient, nontrained reasoners. However, the lack of a significant difference be-

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Alexander,

Table 2. Variables

Willson,

Means and (Standard of School and Age

White,

Deviations)

Fuqua,

on the

Clark,

Wilson,

and

Kulikowich

TARC by the Categorical

Testing Category

School School

1

2

MGD)

MW)

3

4

M(SD)

MW)

5 WW

6 M(.W

I

l, = 33 School 2 1, = 27

Age 48-53 n=6

3.480

5.38

(6.68)

(4.31)

7.15 (5.01)

6.85 (5.29)

7.81 (4.66)

6.71 (5.19)

3.48 (3.00)

5.65 (3.89)

6.04 (4.71)

2.71 (2.43)

4.06 (3.94)

(4.11)

5.33 (4.23)

6.33 (5.51)

4.83 (5.12)

5.89 (5.45)

6.15 (6.08)

6.25 (6.08)

3.19 (3.27)

6.92 (3.87)

8.07 (4.65)

5.69 (5.12)

6.93 (4.45)

(4.12)

3.14 (3.16)

4.64 (4.25)

7.23 (5.18)

5.56 (4.82)

6.18

6.36

(5.46)

(5.52)

3.62 (3.50)

3.09 (3.02)

4.00 (4.02)

4.55 (4.72)

5.92

6.15

(4.54)

(4.62)

4.37

54-59 n = 27 60-65 n = 14 66-7

I

II=

I3

“out

of a possible

4.00

14

tween other testings may be hugely the result of the increased variability evidenced in these children’s performances from Testing 1 (SD = 1.85) to Testing 6 (SD = 4.33). We will discuss the issue of subject variability later in this section. As it relates to the significant increase in analogy performance following Testing 1, we felt that this may have been partially attributable to test sensitization. That is, the initial exposure to the TARC tended to reduce the novelty of this analogical reasoning task, leading to improved performance on subsequent testings. In addition to the within-group trend analyses, we selected three specific testings (Testings 1, 3, and 5) for cross-sectional analysis. These 3 testings were chosen for particular reasons. First, the examination of TARC performance at Testing I would allow us to compare individuals at the outset of the study period, prior to any intervention. Second, Testing 3 was selected for cross-sectional analysis because it permitted us to examine the three groups at a point approximately midway in the study period. Further, Testing 3 was the last point in the study in which all children in the sample were tested. Finally, because of its occurrence nearer the conclusion of the study period, and because it allowed for

Development

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77

Reasoning

12

9

8

-L

I

I

1

2

I 3

I 4

I 5

1 6

TESTING Figure 3. Within-group trends for the more proficient, and less proficient trained groups by TARC testing.

less proficient

nontrained,

comparisons across all three groups, Testing 5 was chosen as a point for crosssectional analysis. In the analyses of Testings 1,3, and 5, we considered not only the effects for group (more proficient; less proficient, nontrained; less proficient, trained), but also for school (School 1; School 2) and for age (48-53 months; 54-59 months; 60-65 months; 66-71 months). The means and standard deviations for these three testings by school and by age are presented in Table 2. For Testing 1, a 3 (group) X 2 (school) X 4 (age) analysis of variance was conducted. Only the main effect for group was found to be significant, F (2,44) = 37.13, p < .OOOl, MS, = 5.50. All other main effects and interactions were nonsignificant, F c 2, p > .2. Post hoc analysis of group differences was

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performed by Tukey’s studentized range tests. As would be expected by the grouping procedure employed, the more proficient group was significantly different from both of the less proficient groups. No significant differences existed among the less proficient, trained and nontrained groups on Testing 1; that is, prior to intervention. These results indicate that at the outset of the study: (a) younger 4-year-olds to older Syear-olds were performing similarly on the TARC; (b) children from the two school sites were performing at comparable levels; (c) the three groups did not differ significantly by age; and (d) only the more proficient group differed from the others with regard to analogical reasoning ability. To assessgroup differences at Testing 3, we initially performed a 3 (group) X 2 (school) x 4 (age) analysis of convariance, with Testing I as the covariate. By employing this procedure, we sought to compensate for any differential effects among groups that might have existed at initial testing. However, Testing 1 was not a significant covariate, so an analysis of variance procedure was employed. Results of the ANOVA indicated that group, F (2,43) = 22.23, p < .OOOl,MS, = 12.08. and age, F (3, 43) = 3.47, p < .03, MS, = 12.08, were significant variables. The effect for school and all interactions were nonsignificant, F <

2.40. p > .05. To determine the source of the significant main effects for group and for age, we conducted Tukey’s studentized range tests. On the basis of the post hoc comparisons of group differences, it was determined that: (a) the more proficient group performed significantly better at Testing 3 than did the less proficient, nontrained; (b) the less proficient, trained were significantly better than their nontrained counterparts; and, (c) the less proficient, trained outperformed the more proficient group. The post hoc comparisons of age differences showed that children in the 54-59-month category performed significantly better than did the children 66-7 1 months of age. Again, this age pattern is likely to be an artifact of the large number of 4-year-olds receiving training. As the final point in the cross-sectional analyses, we examined children’s performance on the fifth testing. As with the previous analyses, an initial analysis of covariance was performed. When we determined that Testing 1 was not a suitable covariate, a 3 (group) X 2 (school) X 4 (age) analysis of variance was conducted. As was true for the analysis of Testing 1, only the effect for group was found to be significant, F (2, 30) = 11.39, p < .0002, MS, = 14.57. Although the effect for school did approach significance, the main effects for school and for age and all interactions were nonsignificant, F < 4, p > .05. Results of Tukey’s range tests revealed that on the fifth testing, the less proficient, trained and the more proficient groups performed significantly better than the less proficient, nontrained group. No significant differences were demonstrated between the trained and the initially proficient groups. However, it should be remembered that only a subset of the trained group was tested at this point in the study, and, although randomly selected, their scores may not be representative of the entire group.

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Explicit Training As noted, our intention in designing this study was to assessboth the immediate and more lasting effects of explicit training on the analogy performance of 4year-olds. We selected to examine the immediate effects of training by comparing the mean performance of the less proficient, nontrained groups against that for the less proficient, trained group on Testing 2. Testing 2 was selected for this comparison because explicit training was delivered between the first and second testings. As the means displayed in Table I suggest, the training these 4-yearolds received had a marked effect on TARC performance on Testing 2. The difference between the trained group and their nontrained counterparts on Testing 2 was significant, t( I, 47) = 7.90, p < .OOOl. Thus, the immediate effects for explicit training on the analogical reasoning performance of the 4-year-olds was determined to be strong. The more long-term effects of training were then assessed via trend analysis. Specifically, we examined the mean scores of the trained children over the six testings to establish the scoring pattern for that group. The results for the trend analysis, graphically displayed in Figure 2, showed that the scores for the trained group demonstrated a significant upward linear trend when Testing 1 was included, F (I, 46) = 43.25, p > ,001, MS, = 5.10. When only those testings following training were incorporated in the trend analysis (i.e., Testing 2-5), however, the linear trend was nonsignificant, F (1, 23) = 2.09, p > . 10, MS, = 5.10. This suggests that after explicit instruction, the scores for the trained group remained quite stable. (Additional analyses are presented in White & Alexander, 1986.) Together the results of these cross-sectional and trend analyses demonstrated that explicit training in analogical reasoning had an immediate and positive effect on the performance of less proficient 4-year-olds, and that this training effect was well maintained for months. As stated earlier, our examination of the means and standard deviations for the less proficient, trained and the less proficient, nontrained groups presented in Table I raised questions about subject variability. Specifically, we observed that along with a slight rise in mean performance, there was a noticeable increase in the variability of TARC performance for the less proficient, nontrained group over the seven months. This pattern was in sharp contrast to that for the trained group, who exhibited a sharp increase in mean performance following Testing 1 and a gradual decrease in variability over time. By testing for differential performance patterns between the trained and nontrained groups, we would be better able to describe the effects of explicit training on the development of analogical reasoning in the young. Thus, to understand the nature of the variability across groups, we compared the variances for the less proficient, nontrained group to those for the trained group by means of a Box Scheffe Test. In this analysis, the trained and nontrained groups are partitioned into three randomly-selected subgroups. The logarithms of each subgroup’s variance are then entered into a 6 (testing) X 2 (group) analysis of variance with three replications. As expected, the result of

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this test indicated that the variance trends of the trained versus nontrained groups were significantly different, F (1, 24) = 18.16, p < .ooO3, MS, = .29. Variantes for the nontrained children were significantly higher than those for the trained children. This finding demonstrates that, as predicted, explicit training not only had the effect of increasing mean TARC performance but of reducing subject variability among trained subjects. In addition to variability across groups, we were concerned with differential performance patterns exhibited by children within the less proficient, nontrained group. We felt that the increasing variability we described earlier may have been attributable to differential growth rates within that group. That is to say, some children who were initially characterized as less proficient may have come to understand the nature of the task. As a result, their performance would have continued to improve systematically over time. By comparison, other individuals in the less proficient, nontrained group may have failed to achieve an understanding of the geometric analogy task; thus, their performance would have remained consistently low across all testings. The result of this condition should be a widening gap in performance within the nontrained group that would account for both the improved mean performance and increased variability (Bryk & Weisberg, 1977). To test for differential growth rates of performance within the less proficient, nontrained group, therefore, we performed a fan spread analysis on their TARC scores. The fan spread test is essentially a gain-score analysis where the pretest and posttest scores are divided by their respective pooled within-group variances (Kenny, 1975). For the purpose of this analysis, we divided the less proficient, nontrained children into two subgroups: those who became more proficient over the course of this investigation, and those who did not. That is, there were individuals in the nontrained group who initially scored below 7 on the TARC, and who achieved a score of 7 or better on at least one subsequent testing without the aid of explicit training. For the purpose of this study, we labeled these children as the improved subgroup (n = 10; 36%). All other children in the less proficient, nontrained group whose performance remained at or below chance level constituted the nonimproved subgroup (n = 18; 64%). Two subjects who did not complete all testings were not included in this analysis. We performed a fan spread analysis on the improved and nonimproved subgroups for Testings 2, 3, and 5, with Testing 1 serving as the pretest. Testing 2 was selected for analysis because it was the first point at which a fan spread test could be conducted. Testings 3 and 5 were chosen for those reasons discussed earlier in this section. The results of the fan spread test, displayed in Figure 4, demonstrated that the gain scores for the improved children, adjusted by the pooled within-group variances, was significantly higher than that for the nonimproved children on Testing 2, F (1, 47) = 57.16, p < .OOOl, MS, = 7.34, Testing 3, F (I, 27) = 33.70, p < .OOOl, MS, = 6.98, and Testing 5, F (1, 26) = 74.34, p < .OOOl,MS, = 4.76. These results suggest that members within the

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10 9

(8.79)

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6

I

I

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vs. nonimproved

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nontrained group exhibited differential cognitive growth patterns as related to the TARC task and that the differences in performance between improved and nonimproved subgroups became greater as the study progressed. Performance

Characteristics

As mentioned, there were individuals, assigned to the group containing less proficient, nontrained analogical reasoners, who achieved proficiency over the course of this investigation without direct intervention. In addition to the question of variability, just discussed, we were interested in subject characteristics or response patterns that might differentiate preschoolers who showed marked improvement from those who did not. In this analysis, we used the variables of age, school, and gender to compare the improved and nonimproved groups. Although the effect for school was determined to be nonsignificant, a r-test analysis indicated that the mean age of the improved and nonimproved groups did differ

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significantly, f (I, 26) = 2.90. p < .02. The mean age was 66.8 months for the improved group and 60.5 months for the nonimproved group. A XI test for independence demonstrated no significant differences in the distribution of males and females in the improved and nonimproved groups. x2 (I) = .03, p > .OS. There were 2 females and 5 males in the improved group and 8 females and I I males in the nonimproved group. We then assessed the children’s response patterns (i.e.. the response option selected) in our attempt to differentiate the improved from the nonimproved groups. We analyzed student responses on the six testings of the TARC against a hierarchical rule structure for geometric analogy reasoning outlined by Alexander, Willson, et al. (1987). According to their findings, less proficient reasoners employ an identifiable, albeit naive, reasoning strategy in solving the geometric A:B::C:? analogy problems on the TARC. In short. this nonanalogic strategy entails the child’s search for an exact match for the third or C term of the analogy problem. Should an exact match be unavailable, the less proficient analogical reasoner seeks a term that resembles the C term in shape and color. followed by one that shares its same size and color, and so on until no similarity between the third term and options remain. The response patterns of improved and nonimproved preschoolers were examined by individual in relation to this hierarchical rule structure. Analysis clearly demonstrated that the shift in reasoning proficiency from less to more proficient was accompanied by an abandonment of the rule structure. For example, Subject 2, a less proficient nontrained reasoner, obtained the following scores (i.e.. number correct out of 14) on Testings 1 through 6. respectively: 4, 2. 12, I I, 14, and 13. On the initial testing. Subject 2 adhered to the rule structure on 9 of the IO items missed. Similarly, on Testing 2, she followed the rule structure on IO out of the 12 errors made. However, OII the remaining testings (3-6). that represent a shift to more proficient performance, Subject 2 adhered to the rule structure on 2 out of 2.0 out of 3, 0 out of 0. and 0 out of I errors she made. It also should be noted that the response pattern exhibited by Subject 2 is quite representative of the patterns for the improved groups. It is also representative of those children making the shift from less to more proficient in that the improvement in perforniance was often dramatic (i.e., from 2 at Testing 2 to I2 at Testing 3) rather than gradual in nature. By comparison, those children in the less proficient, nontrained group who did not achieve a higher level of proficiency continued to employ the hierarchical rule structure on the majority of errors made across all testings. Subject 4, for instance, received scores of 2. I, 2. 0, 0. and 0 on the six testings of the TARC, and he adhered to the rule structure on IO. 9. IO, 13. 13, and IO errors on each of those testings. As with our previous example, Subject 4’s response profile is quite typical of the performance for the nonimproved group. It would appear, therefore. that the adherence or abandonment of the hierarchical rule structure

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described by Alexander, Willson, et al. (1987) differentiated well between those who markedly improved in their analogical reasoning proficiency on the TARC and those who did not. Observational Data In addition to the more empirical concerns we have just addressed, we would like to offer several observations about the effectiveness of the testing and training procedures we employed. Overall, the efficacy of the explicit training program evidenced in the quantitative findings of this study was substantiated by our observations of the children’s behaviors. Yet, we did note some variability in the children’s general behavior and in their understanding and performance of the component processes both during assessment and instruction. To be more specific, there was some difficulty in keeping the children on task. The 20 to 25 minutes it took to administer the TARC or to conduct a training session appeared to tax the limits of some children’s attention. Furthermore, the novelty of the task and the attractiveness of the manipulatives, while motivating, were occasionally distracting. Also, although we provided individual practice during training until mastery was demonstrated, we found that the mapping component presented the greatest difficulty to the children. After explicit explanation and modeling by the instructor, it seemed that most children found it relatively easy to describe the terms presented (encode) and to explain the relationship between the adjacent A:B pairing (infer). By comparison, the ability to relate the first to the second pairing (mapping) appeared far more difficult. Indeed, we sensed that the children’s understanding and performance of the mapping component in problem solution was a major distinction between more proficient and less proficient reasoners. This confirms earlier research (Alexander, Willson, et al., 1987; Stemberg & Rifkin, 1979) that has suggested a pivotal role for mapping in ascertaining analogical reasoning proficiency. DISCUSSION The ability to reason analogically appears to be an essential tool in the acquisition (Rumelhart & Ortony, 1977) and organization of knowledge (Vosniadou & Brewer, 1987). As a consequence of the emerging literature, we have come to understand more about the nature and development of analogical reasoning. The major contribution of the current study to the existing literature is that it provided an extended examination of analogical reasoning in young children. In this study, we evaluated changes that occurred in 4- and 5-year-olds’ analogical reasoning proficiency either as a consequence of natural development or as the result of direct intervention. Further, to answer the questions posed in this investigation, we relied on both within-group trend analyses and cross-sectional

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procedures. Finally, we sought to differentiate between young children who eventually attained proficiency in analogical reasoning without direct intervention from those who did not. On the basis of our findings, we would describe the geometric analogy performance of the 4- and Syear-olds in our study as rather stable. Those children initially identified as more proficient maintained that level of performance for the duration of this study. For the nontrained, less proficient reasoners, we did identify a linear increase in mean test performance over time. However, a significant increase in performance occurred only after the Testing 1 for this nontrained group, and it would appear that task familiarity may partially explain such an initial gain. We also determined that explicit instruction in the component processes of analogical reasoning had a significant effect on the performance of the trained 4year-olds. This finding replicates the very limited number of training studies found in the literature that focused on young children (e.g., Alexander, Wilson, et al., 1987). As we noted in our introduction, a search of the literature revealed no studies have assessedthe durability of analogy training in the young over any extended period of time. Not only were the immediate effects of explicit training in analogical reasoning evident on test performance in this study, but the effects of that training were maintained for months afterward. Both the susceptibility of 4-year-olds to training, and the durability of that training should be viewed as encouraging. The implications of these findings for preschool instruction should be carefully considered. The contrast between the less proficient, trained and the less proficient, nontrained groups was also apparent in the variability of their performance over time. The diversity among the nontrained children increased over time, whereas the performance of the trained children was marked by great similarity. In other words, explicit instruction in this study had the effect of not only increasing mean performance but also of reducing subject variability. Finally, we turned our attention to those 4- and Syear-olds who began the study performing at or below chance level, but who progressed to a more proficient level without the benefit of explicit training. When we compared those children in the less proficient, nontrained group who markedly improved to those who did not, we found that age and the reasoning strategies employed differentiated these two groups. More specifically, those in the nontrained group who failed to progress from less proficient to more proficient over the seven months (a) were significantly younger, and (b) continued to adhere to a naive rulegenerated strategy characteristic of nonanalogical reasoners. In summary, the current study furnished important information about the stability of analogical reasoning performance among 4- and 5-year-olds. Additionally, it incorporated elements of both cross-sectional and more longitudinal investigations in the assessment of young children’s reasoning performance. Additional developmental studies of analogical reasoning are clearly required to

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replicate and extend the findings of this study. The present study traced the reasoning performance of these preschoolers for a seven-month period; that is, throughout a preschool year. A longitudinal study that assessesanalogical reasoning for a period of years and evaluates the impact of more forma1 schooling on the reasoning abilities of young children seems warranted. Further, by systematically combining cross-sectional and longitudinal investigations, we will continue to achieve a greater understanding of analogical reasoning development in young children. REFERENCES Alexander, P. A., White, C. S.. Haensly, P. A., & Crimmins-Jeanes, M. (1987). Training in analogy reasoning. American Educarionol Research Journal, 24. 387-404. Alexander, P. A.. Wilson, A. F., White, C. S., Willson, V. L., Tallent, M. K., & Shutcs, R. E. (1987). Effects of teacher training on children’s analogical reasoning performance. Teaching and Teacher

Education,

3. 275-285.

Alexander, P. A., Willson, V. L., White, C. S.. & Fuqua. J. D. (1987). Analogical reasoning in young children. Journal of Educational Psychology, 79. 401-408. Bronfenbrenner. U. (1979). The ecology of haman development: Experiments by nature and design. Cambridge: Harvard University Press. Bryk, A. S., & Weisberg. H. I. (1977). Use of the nonequivalent conrrol group design when subjects are growing. Psychological Bullerin, 85. 950-962. Carey, S. (1985). Conceprual change in childhood. Cambridge, MA: MIT Press. Case, R. (1985). lnrellecrual developmenr: Birrh IO adulthood. Orlando: Academic. Crisafi. M. A., & Brown, A. L. (1986). Analogical transfer in very young children: Combining two separately learned solutions to reach a goal. Child Developmenr. 57, 953-968. Flavell, J. H., Flavell, E. R., & Green, F. L. (1983). Development of the appearance-reality distinction. Cognitive Development. IS. 95-120. Flavell, J. H., Green, F. L.. & Flavell. E. R. (1986). Development of knowledge about the appearance-reality distinction. Monographs of rhe Society for Research in Child Developmenr.

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(1, SerialNo. 212).

Gallagher, J. M. (1978). Reflexive abstraction and education: The meaning of activity in Piaget’s theory. In J. M. Gallagher & J. A. Easley(Eds.),Knowledge and development: (Vol. 2). Piagef and education (pp. I-20). New York: Plenum. Gelman, R. (1979). Preschool thought. American Psychologisl, 34. 900-905. Gentner, D. (1977). Children’s performance on a spatial analogies task. Child Developmenr. 48, 1034-1039. Glaser, R., & Pellegrino, J. (1982). Improving the skills of learning. In D. K. Detterman & R. J. Stemberg (Eds.), How and how math can intelligence be increased? (pp. 197-212). Norwood, NJ: Ablex. Holyoak, K. J. (1984). Analogical thinking and human intelligence. In R. J. Stemberg (Ed.), Advances in rhe psychology of human inrelligence: Vol 2 (pp. 199-230). Hillsdale, NJ: Erlbaum. Kaufman, A. S., & Kaufman, N. L. (1983). Kaufman assessment battery for children: Interpretive manual. Circle Pines, MN: American Guidance Service.

Kenny, D. A. (1975). A quasi-experimental approachto assessing treatmenteffectsin the nonequivalent

control

group

design.

Psychological

Balletin,

82, 345-362.

Mulholland,T. M., Pellegrino.J. W., & Glaser,R. (1980).Componentsof geometricanalogy solution.

Cognifive

Psychology,

12. 252-284.

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Raven. I. C. ( 1973). Co/our& /?ro~r~.~.~ir~~ marrices. London: Rosenshinc. R. R. (1983). Teaching functions in instructional

Clark,

Wilson,

H. K. Lewis. programs. nrc

and

Elernmra~

Journal. 83. W-3.5 I. Rumelhart. D. E.. & Orfony, A. (1977). The rcprescnration of knowledge in memory. Anderson. R. J. Spiro, & W. E. Montague (Eds.). Schooling ond the ucquisirion ed
R. J. (1982). Reasoning. problem Handbook of humon ink~lli~errce (pp. Stemberg. R. J. ( 1985). Beyond IQ: A rriurchic

Kulikowich

School In R. C. of know/The com-

solving. and intclligcncc. In R. J. Stemberg (Ed.). 27-5-307). New York: Cambridge University Press. rhrorv o/humnn infellipnce. New York: Cambridge

University Press. Stemberg. R. J., Kctron, I. L.. & Powell. J. S. (1987). Componcmial approaches to the training of inrcllectual performance. In D. K. Dettennan & R. J. Stembcrg (Eds.). How and how much con infe~ligmre be increased? (pp. 15% 172). Norwood. NJ: Ablex. Stembcrg. R. J.. & Ritlcin. B. (1979). The dcvelopmcnt of analogical reasoning proccsscs. Jortmcrl of E.rperimenral Child Psychology. 27. 195-232. Vosniadou, S., & Brewer. W. F. (1987). Theories of knowledge restructuring in development. Review of Edrrcorional Research, 57. 5 l-67. Vosniadou, S.. & Schommer. M. (1986. April). The efivv cf explonaro~ annlogies on ymrng children’s comprehension q/ e.rposirory re.vf. Paper presented at the annual meeting of the American Educational Research Association. San Francisco. Wagner, J. ( 1983, April). Some prerequisires in leurning fo solve onolop problems. Paper presented al the annual meeting of the American Educational Research Association, Montreal. White. C. S.. & Alexander. P. A. (1986). Effects of training on four-year olds’ ability to solve White,

Willson,

geometric analogy problems. Copirion urrd Insrrucriorr. 3. 26 I-268. C. S.. & Alexander. P. A. (1988. April). Eflecrs of age. wcubulary knowledge. gender. socioeconomic sunus. and erhnicity on young children’s unolo~~vpv-formunce. Paper presented at the annual meeting of the American Educational Research Association, New Orleans. V. L., Alexander, P. A.. White. C. S.. Fuqua. J. D.. Clark. G. D.. & Wilson, A. F. (1986. April). Form and presenrarion variation in D lest of geometric analogies. Paper presented at the annual meeting of the American Educational Research Association. San Francisco.

APPENDIX Sample Instructional

Script

This sample script represents the investigators’ use of concrete toy objects represented in Figure 2a to explain and to model each of the component processes emphasized in the training program during Session One. General Directions We are playing a game today and in this game we have some different toys and a gameboard that we will be using. When we play this game, 1 am going to put some of these toys on the gameboard and some toys on the side. The first thing I am going to do is to put this here (placing a toy car in Box A of the gameboard), and this here (putting a second toy car in Box B), and this one here (placing a third car in Box C), but I’m not going to put anything here (pointing to the fourth box). Instead, I’m going to put some other toys over here (placing the four

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choices alongside the gameboard). Now, when we play this game, you need to find the car from over here (indicating the four options) that goes with this one (Box C) the same way that these two (pointing to Boxes A and B) go together. Let me tell you how 1 decide which one to choose. Encode First, I have to look very closely at the toys on the gameboard. This one (Box A) is a car. It’s a red car, and it is open. Do you know what we call cars like this that are open and don’t have a roof? Right, we call them convertibles. So in this box (A) I have a red convertible. Now in this box (B) I have another car, don’t I? It’s a convertible, a red convertible. Good. Infer Now that 1 have looked closely at these two cars, I need to ask myself how this one (A) and this one (B) go together. How is this car (B) like the first one. Well, they both have four tires, and a wheel, and they are both . . . red. Right! There is also something else about them that is the same. They are both . . open. What was that word we used for an open car? Convertibles! Good for you! But, if we look very carefully we will see that these cars are not exactly the same. There are some things about these cars that are different, aren’t there. Can you see how these cars are different‘? 1 can see that the cars are not exactly the same shape. What name can we give cars that look like this one (A)? Have you ever seen a car like this one? What name did we call it’?A sports car’?That’s a good name for this car. And what about this car’? What name can we give to cars that have this shape (B)? How about hot rod? We can call this kind of car a hot rod. So these cars are both red and they are both convertibles, but this one is a sports car (A) and this one is a hot rod (B). Encode What I do now is to look closely at this toy (Box C). I see that I have another car.. . another convertible. Good! What color is this convertible’? Blue. Good! And what kind of convertible is this one? This is a sports car, isn’t it?

Map Now I have to go back and look at the first car and think about how this car (A) and this car(C) go together. What about this car (A) and this car(C) is the same, and what about them is different? Well, they are both sports cars, and they are both convertibles, aren’t they? But, this one (A) is red and this one (C) is blue, so they are the same kind of car but they are different colors, aren’t they? APPLY Remember that when we play the game, 1 have to find the toy from over here that goes with this one (C) the same way these two (A and B) go together. Remember

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we said that these two (A and B) went together because they were both the same color and they were both convertibles, but they were different kinds of cars. We called this one a sports car, right? And we called this one a hot rod, good. So, 1 need to find the car over here (pointing to the four choices) that is the lance color car as this one (C) and a convertible, but I want a hot rod because this one (b) is a hot rod. So, I pick this one (picking up the second option and placing it in the fourth box), because it’s blue just like this one (C) and it’s also a convertible. It’s a hot rod, so it goes with this one (C) the same way these two go together. They are the same color but they are not the same shape. This one (A) is a sports car and this one (B) is a hot rod, and this one (C) is a sports car and this one (D) is a hot rod. This one (A) is red, and this one (B) is red, too, and this one (C) is blue just like this one (D). Let’s do another problem now and this time you can help me play the game. You can help me decide which toys go together.