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Children's expressions of spatial knowledge
JOURNAL
OF EXPERIMENTAL
CHILD
Children’s
48, 114-130 (1989)
PSYCHOLOGY
Expressions
of Spatial Knowledge
GARY L. ALLEN University of South Carolina
KATHLEEN
C. KIRASIC AND REBECCA L. BEARD Old Dominion University
Different expressions of spatial knowledge were examined by having groups of first-, fourth-, and sixth-grade children perform model construction, verbal description, and route reversal tasks after they learned the correct path through a pedestrian maze. Age-related improvement was found in the rate of learning the maze and in the accuracy of verbal descriptions, suggesting that maze learning may be verbally mediated. All children performed well in sequencing intersections in the model but performed poorly in choosing path options in the model. Route reversal after learning was accurate and equivalent across groups. Overall, results suggest that both general and task-specific skills are involved in different products of spatial knowledge. o 1989 Academic PXSS, IIK.
Much of the research on children’s representation of spatial knowledge has been concerned either implicity or explicitly with the question of how best to measure such knowledge (see Newcombe, 1985; Siegel, 1981). In addressing the extent to which research in the area became driven by method rather than by theory, Liben (1982) made important distinctions among the following three connotations of spatial representation: storage of spatial information, spatial thought, and spatial products. Over the past decade, many researchers have sought to examine spatial storage and spatial thought as free as possible from the “confounding” effects of spatial products. However, such efforts have been problematic in the sense that evidence of developmental change in spatial cognition is necessarily inferred from spatial products. Furthermore, there is far more speculation than evidence regarding the interrelationships among different The second author’s current address is the Department of Psychology, University of South Carolina. Reprints may be obtained from Gary L. Allen, Department of Psychology, University of South Carolina, Columbia, SC 29208. 114 0022-0965189 $3.00 Copyright All rights
0 1989 by Academic Press. Inc. of reproduction in any form reserved.
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115
products of spatial knowledge. Consequently, it would be profitable to study such products in more detail in order to obtain a more comprehensive view of developmental change in spatial memory and behavior. The current literature provides little insight into the extent to which age-related differences in a variety of spatial tasks should be attributed to differences in acquisition (that is, the encoding and storage of spatial information for future reference) and the extent to which they should be attributed to cognitive operations required to produce certain products (for example, maps, distance estimates, and verbal instructions) after acquisition. The present study was designed as an initial step toward addressing this issue. The procedure involved an acquisition phase, during which elementary-school-age children learned a path through a pedestrian maze, and a test phase, during which they performed model construction, verbal description, and route reversal tasks. Children in this range of ages were selected because (a) interesting developmental changes have been documented over this range (e.g., Anooshian & Young, 1981; Cohen, Weatherford, & Byrd, 1980; Cousins, Siegel, & Maxwell, 1983), and (b) although no pretest of symbolic functioning in the Piagetian sense was administered, all children could be assumed capable of such functioning since early childhood (see Piaget, 1962). The tasks were selected for investigation because they represent rather disparate points along a concrete-to-abstract dimension. It was assumed that after they learned the maze to criterion all children would be at an operationally defined, behaviorally indexed, roughly equivalent level of procedural knowledge. Unnecessary assumptions regarding the format of this knowledge (i.e., propositional versus analog) and the relationship of procedural to declarative knowledge were not made. Consistent with this assumption, subsequent age-related differences in task performance could be attributed largely to operations required to produce particular spatial products rather than to availability of information per se. The model construction and verbal description tasks involved symbolic operations in the sense that children had to invoke “stand for“ relationships, the various components of the model maze “stood for” the corresponding components in the full-scale maze, and words in their descriptions “stood for” specific features and actions. In general, greater age-related differences in performance would be expected for these tasks than for the route reversal task, in which knowledge of the maze was expressed perceptual-motorically rather than symbolically. Children at different age levels were expected to perform similarly in the route reversal task not only because perceptual-motor expressions of knowledge may be considered developmentally more primitive than symbolic expressions (e.g., Fischer, 1980; Piaget, 1954; Wapner, Kaplan, & Ciottone, 1981), but also because knowledge of the maze was originally attained by means of perceptual-motor experience.
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Although symbolic operations were involved in both the model construction and verbal description tasks, the tasks were differentiated by the presence of a concrete task object (in the model construction task) and the need for access to a lexicon of spatial terms (in the verbal description task). It was expected that older children would perform both of these tasks more accurately than would younger children, but the age difference was expected to be greater for the verbal task because it involved a relatively abstract translation of experience into words. Predictions about the interrelationships among measures of spatial learning and the different means of expressing spatial knowledge could not be rooted firmly in theory or evidence from past research. One possibility was to base expectations on the distinction between perceptualmotor and symbolic tasks, in which case behavior in the original maze learning task would correlate most highly with performance on the route reversal task, both of which required maze navigation. Somewhat lower correlations would then be expected between the number of trials required in the maze learning task and measures of accuracy in the model construction and verbal description tasks, which required symbolic operations. Another possibility was that the correlations between rate of learning per se and task performance would reflect the application of certain encoding and retrieval strategies useful in both situations. For example, if verbal encoding of moves resulted in rapid (or slow) maze learning, then a high correlation between learning rate and performance on the verbal task would be expected. The distinction between perceptual-motoric and symbolic expressions of spatial knowledge could also serve as the basis for predictions concerning relationships between expressions of spatial knowledge. According to this distinction, it would be expected that the correlation between performance measures on the model construction and verbal description tasks would be higher than the one involving performance measures on the route reversal and model construction tasks or the one involving performance measures on the route reversal and verbal description tasks. In contrast, it is plausible that, as implied by Siegel (1981) and others, verbal and nonverbal expressions of spatial knowledge would not be highly correlated. If this is the case, then correlations between measures from the model construction and route reversal tasks would be higher than those between measures from the model construction and verbal description tasks or between measures from the verbal description and route reversal tasks. METHOD
Subjects Data were collected from 10 boys and 10 girls from each of the following grade levels: first grade (mean age = 6 years, 7 months; range = 6
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years, 0 months to 7 years, 9 months), fourth grade (mean age = 9 years, 6 months; range = 8 years, 11 months to 10 years, 3 months), and sixth grade (mean = 11 years, 4 months; range = 11 years, 2 months to 12 years, 4 months). All professional guidelines regarding the treatment of children in psychological research were followed explicitly. Apparatus
A pedestrian maze was constructed of cardboard in a 7.3 x 9.4-m laboratory. The walls of the maze were 1.8 m high and the pathways 45.7 cm wide. The maze contained four choice points, each an intersection providing the subject with the options of turning left, going straight ahead, or turning right (see Fig. 1). The design of the maze prevented the children
FIG. 1. Diagram of the four-choice pedestrian maze, with color of intersections labeled and locations of animal pictures indicated by small squares (approximate scale: 1 cm = 0.5 m).
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from seeing which two of the three options led to cul-de-sacs. Each intersection was color-coded using 30-cm* sheets of paper; the colors were experienced in the sequence orange, red, blue, and green. Pictures of animals were located on the floor at each of the four branches of the intersections. Each of these 16 pictures was a color photograph of an animal mounted on a 20-cm* sheet of yellow paper. These pictures were included to allow subjects the opportunity to learn the route through the maze by relying on intersection-landmark associations in addition to or instead of associations between intersections and direction of movement. Translucent white nylon fabric was draped over the top of the entire maze to eliminate room cues during maze navigation. The model construction task involved a sectionalized line drawing of the maze with color-coded intersections corresponding to those in the maze itself, 12-cm* replicas of the 16 animal pictures located at intersections, and a 5-cm tall plastic figure to represent an individual traversing the maze. The sectionalized line drawing, which was approximately 50 cm2 when assembled, included four separate color-coded intersections and 15 pathways. An audio tape recorder was to record children’s responses in the verbal description task. Procedure
The maze was described to children as a tunnel, and they were told that they were supposed to learn the way through the tunnel from beginning to end. Each child was told to imagine himself or herself as a scout who was sent ahead to learn the correct path through the tunnel; the experimenter was described as an assistant scout who would follow him or her through the tunnel and ask questions about which way to go. It was emphasized that each child had to learn the path through the tunnel so that he or she could later tell and show the other people which way to go. On each learning trial, the child led the experimenter through the maze. At each intersection, the experimenter asked the child which way to go, and on trials subsequent to the initial one, the experimenter also asked the child how he or she knew which way was correct. Learning trials continued until the child made three successive trips through the maze without making an incorrect choice at an intersection. The experimenter recorded the number of trials to criterion and the child’s response to the question of how he or she knew which choice was correct at each intersection. Model construction. For this task, children were presented the sectionalized line drawing of the maze consisting of the four color-coded intersections and 15 pathways. Each color-coded intersection also contained replicas of the animal pictures that were located at each branch of the intersections in the maze. The sections of the maze were spread out like pieces of a puzzle on a large table that was screened off from the maze
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itself. The construction task was oriented so that the maze and the line drawing assembled by the child were in correspondence with regard to the room as a frame of reference (that is, the child entered the maze with his or her back to the east wall of the room and constructed the model with his or her back to the east wall of the room). Children were told that the sections of the drawing could make an accurate map of the tunnel so that people looking at the map could make it through without making a wrong turn. To initiate the task, the experimenter selected the first segment of the model, moved the plastic figure to the end of this segment, and then told the child that a person walking through the tunnel would arrive at an intersection at this point in the tunnel. The child was asked to select which intersection would be seen at that point. After a selection was made, the intersection was put into place; if it was the correct intersection for that location, the experimenter oriented it properly with respect to the animal pictures. Then the child was asked to indicate the correct path through the intersection using the plastic figure. After a choice was indicated, the experimenter asked the child why he or she had selected the chosen path. This procedure was repeated for each intersection, with the experimenter providing all of the correct pathways connecting the intersections in the model. It is important to point out that the children were responsible only for selecting the intersections and indicating the correct path of travel at those intersections; the 15 pathways used in the model were placed by the experimenter. Dependent measures from the task included the number of intersections chosen in proper order, the number of correct turns indicated at properly oriented intersections, and children’s responses to the question of how they knew which was the proper choice at each intersection. Verbal description. In this task, children were given the following instructions: “Now that you know the correct path through the tunnel, I want you to describe to me how to follow that path. Tell me how to go through the tunnel from start to finish without making a wrong turn. It is important to give me as much information as you can.” The children’s responses were tape-recorded and subsequently transcribed. Two raters were used to judge how many of the four intersections would be navigated successfully if each child’s instructions were followed. Interrater reliability was 32; disagreements were submitted to a third judge, whose decision prevailed. The number of correct choices at intersections and the children’s indications of how they knew which choice was correct at each intersection were recorded for analyses. Route reversal. In this task, the child was led to the end of the maze and was asked to lead the experimenter to the beginning of the tunnel without making any wrong turns. The experimenter followed the child through the maze and asked at each intersection why the child chose
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the particular path that he or she did. The experimenter recorded the number of errors made during reversal and the children’s responses to the question of how they knew which choice was correct at each intersectiou. Order of tusk presentations. All subjects learned the maze first and performed the route reversal task last. The reversal task was presented as the final task because it permitted updating of information from the test environment; it also served as an indication of how robust navigational knowledge of the maze was after two intervening symbolic tasks. The order of the model construction and verbal description tasks was counterbalanced so that five boys and five girls at each age level performed the model construction task before the verbal description task and five boys and five girls at each age level performed the verbal description task before the model construction task. RESULTS
Table 1 presents the means and standard deviations by grade level for the principal dependent measures resulting from the method. Analyses of these measures are described by task in the sections that follow. Maze Learning The number of trials required to achieve a criterion of three successive errorless trips through the maze was analyzed in a 3 (grade level) x 2 (sex) ANOVA with 10 subjects per cell, which yielded a significant main
TABLE MEANS
AND
STANDARD
DEVIATIONS LEVEL
Task Maze
Learning
Model
Construction
Verbal
Description
(n
Grade
level 1 4 6 1 4 6 I 4 6 I 4 6
Route
Reversal
I 4 6
I
FOR T.HE PRINCIPAL = 20 PER GRADE
Dependent
DEPENDENT
MEASURES
BY GRADE
LEVEL)
Measure
Trials to Criterion Trials to Criterion Trials to Criterion Correct Intersections Correct Intersections Correct Intersections Correct Path Choices Correct Path Choices Correct Path Choices Correct Intersections Correct Intersections Correct Intersections Correct Path Choices Correct Path Choices Correct Path Choices
M
SD
7.8 4.6 4.3
3.3 1.9
2.1
0.6
2.6
1.5 2.1 I.0 I.1
2.5 0.9
0.9 1.2 I.7 2.7 2.8 3.0
2.7 3.3
2.1
0.8
1.5 I.5 2.2 1.3 I .9 I .h
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KNOWLEDGE
effect for grade level, F (2, 54) = 23.52, MSe = 3.11. (The .05 criterion for statistical significance was applied consistently through the experiment.) The main effect for sex and the grade level x sex interaction did not achieve significance, both F’s < 1.00. Scheffe comparisons showed that first graders required more trials to criterion than did either the fourth graders or the sixth graders, with the older children not differing from each other. Children’s responses to the question of how they knew which way to go at each intersection readily fit into three categories: (a) a general sense of knowing (such as “I know,” “I remember,” or “I just think so”); (b) references to animal pictures at each intersection (an object-based frame of reference); and (c) reference to the directional terms “left,” “right,” and “straight” (an action-based frame of reference). To determine the types of responses that were associated with successful navigation of the maze, the number of children relying on each type of response during the third successful trip through the maze was calculated. Interestingly, children were very consistent in their responses; only three children produced responses that fit more than one category, and in each of these cases, only one response was different from the others categorically. Thus, children could be categorized in a straightforward manner (see Table 2). TABLE NUMBER OF CHILDREN AT EACH LEARNING TASK (ERRORLESS TRIAL), AND ROUTE REVERSAL TASK 02 =
2
GRADE LEVEL CLASSIFIED BY TYPE OF RESPONSE: MODEL CONSTRUCTION TASK, VERBAL DESCRIPTION 20 PER GRADE LEVEL) _____-
MAZE TASK.
Type of Response Reference to general knowing Maze Learning Grade I 4 6 Model Construction Grade 1 4 6 Verbal Description Grade 1 4 6 Route Reversal Grade I 4 6
Reference to pictures
Reference to directional terms
I2 8 4
8 12 I4
0 0 2
16 6 6
4 12 14
0 0 2
3 1 I
17 19 19
9 14 14
16 6 6
4 I4 12
0 0 2
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A x2 analysis revealed that children from different grade levels were not distributed proportionately across categories, x2 (4) = 8.63. As shown in Table 2, the number of children reporting a vague, unspecified sense of knowing decreased with grade level, and the number of children making reference to pictures as orientation cues increased. Two children in the highest grade level were the only ones who used directional terminology. Model Construction
Two aspects of performance on the model construction task were analyzed separately: the number of color-coded intersections placed correctly and the number of correct path choices at the intersections. A 3 (grade level) x 2 (sex) ANOVA performed on the number of intersections placed correctly revealed no significant effects or interactions, all F’s < 1.00. The ANOVA performed on the number of correct path choices at the intersections also yielded no significant effects or interactions, all F’s < 1.00. The number of children whose responses fit into each of the three categories in answering the question of how they knew which way was the correct path at each intersection in the model is shown in Table 2. As in the case of maze learning, children were remarkably consistent in their responses; only two children produced responses in more than one category, and in these cases all but one response was in the same category. A x2 analysis indicated an unequal distribution of children from the three grade levels across categories, x2 (4) = 15.78. As indicated in Table 2, the number of children reporting undifferentiated feelings of knowing decreased across grade levels, and the number of children who used pictures as orienting cues increased. Only two children in the highest grade level used directional terminology in their responses. Verbal Description
The number of intersections described correctly as determined through interrater agreement was analyzed in a 3 (grade level) x 2 (sex) ANOVA, which yielded a significant effect of grade level, F(2, 54) = 3.46, MSe = 1.60. Neither the main effect for sex nor the interaction were significant, both F’s < 1.00. Scheffe comparisons revealed that the mean number of intersections described accurately by sixth graders was greater than that described accurately by first graders. Fourth graders’ performance was very similar to that of the oldest children, but the difference between the fourth and first graders was slightly less than that required for statistical significance. The number of children who made reference to no specific frame of reference, to pictures, and to directional terms is portrayed in Table 2. In contrast to other tasks, the verbal task resulted in children using more than one such frame of reference in describing the correct path through
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the maze. Accordingly, an effort was made to determine differences between the proportion of children at each grade level who made statements that fit these categories; pairwise comparisons of proportions were made using an approximation to the normal distribution. Results indicated that the age groups did not differ with regard to the proportion of children mentioning no frame of reference (. 15, .05, and .05 for first, fourth, and sixth graders, respectively), mentioning animal pictures (.85, .95, and .95 for first, fourth, and sixth graders, respectively), and mentioning directional movements (.45, .70, and .70 for first, fourth, and sixth graders, respectively). A greater proportion of first graders mentioned animal pictures than mentioned directional terms, and a greater proportion of these young children mentioned directional terms than mentioned no frame of reference at all. For the fourth and sixth graders, the proportion who mentioned animal pictures did not differ from the proportion who mentioned directional movements; for both of the older groups, a greater proportion mentioned either animal pictures or directional movements than mentioned no frame of reference. Route Reversal
A 3 (grade level) x 2 (sex) ANOVA performed on the number of intersections that children navigated correctly while traversing the maze in the direction opposite to that in which it was learned revealed no significant effects or interactions, all F’s < 1.00. Despite the fact that many children used different types of responses in the verbal task, 57 of the 60 children responded consistently with a single category of response when asked how they knew which choice was correct at each intersection. Of the remaining three, each made one response of a type different from their most common answer. Table 2 shows the categorization of children by response. A x2 analysis revealed the pattern of responding to differ across grade levels, x2 (4) = 15.78. As in the case of the learning task and the model construction task, the youngest children tended to express general feelings of knowing while the two groups of older children tended to refer to objects in the maze. The only children who mentioned directional terms were in the oldest group of subjects. Relations
among Tasks
Correlations among tasks are shown in Table 3. Despite the fact that both maze learning and route reversal involved navigation of the maze, the correlation between the two measures was nonsignificant. However, significant correlations were found between trials to criterion and the number of correct choices at intersection in the model construction task and between trials to criterion and the number of intersections described correctly. The correlation between trials to criterion and number of in-
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CORRELATIONS
1. Maze 2. Model 3. Model 4. Verbal 5. Route
Learning Intersections Path Choice Description Reversal
BETWEEN
PRINCIPAL
AND BEARD 3
MEASURES
FROM TASKS
(n
=
60)
1
2
3
4
- .21 ~ .32* - .36* -.I5
- .Ol .25* .25*
-.I3 .07
- .Ol
* Significant.
tersections correct in the model construction task did not achieve statistical significance. It had been expected that the two measures from the model construction task would correlate with each other more highly than either would correlate with the measure of verbal description. This expectation was not fulfilled; the number of intersections placed correctly and the number of correct choices at these intersections in the model yielded a correlation near zero. The correlation between the number of correct intersections and performance on the verbal description task was significant, but this was not the case for the correlation between the number of correct choices at intersections in the model and performance on the verbal description task. The correlations between performance on the route reversal task and performance on the two measures from the model construction task paralleled those mentioned above between performance on the verbal description and model construction tasks. The correlation between performance on the route reversal task and the number of intersections placed correctly was significant, but not so the correlation between performance on the route reversal task and the number of correct choices at intersections in the model. Interestingly, performance on the route reversal and verbal description tasks were uncorrelated. Performance on the Maze Learning Task as a Covariate
Grade level and performance on the maze learning task were highly correlated (r = - S6). Accordingly, a series of analyses of covariance was performed to determine the effect of grade level and sex on task measures with the trials to criterion measure serving as a covariate. (Caveat: Tests of the heterogeneity of slopes across independent variablecovariate combinations revealed violations of the strict assumption that such slopes must be equal in ANCOVA; thus inferences based on these analyses depend on the robustness of the procedure in the case of similar rather than identical slopes). Results were the same as with the ANOVAs for the two measures from the model construction task and for the
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measure from the route reversal task, all F < 1.00. The ANCOVA performed on the number of intersections described accurately in the verbal description task revealed no main effects or interactions among the independent variables, all F < 1.00. Employing trials to criterion as a covariate eliminated the main effect of grade level in the analysis of performance on the verbal description task. DISCUSSION
The results may be discussed in terms of four major findings. The first of these involves the verbal expression of spatial knowledge. After learning a route to a specified criterion, children from different grade levels provided evidence of age-related differences in the ability to describe that route. In contrast, no such differences were found in the ability to construct a model of the route or the ability to navigate the route in the direction opposite of that in which it was learned originally. These findings are consistent with the prediction that the absence of a concrete task object (such as the model) and the need to use spatial terminology would yield developmental differences in the verbal expression of spatial knowledge. As children grow older, they function more effectively in this abstract task that requires implicit knowledge of linguistic conventions for communicating spatial information (Klein, 1983; Scotton, 1987). This conclusion is further supported by the findings of Gauvain and Rogoff (1987), who found that although groups of 6- and 8-year-old children demonstrated equivalent spatial knowledge of the layout of a funhouse constructed in a large laboratory, the older children were more adult-like in the way they described the funhouse. Gauvain and Rogoff attributed the differences in verbal description to increased skill in the pragmatic conventions used to organize spatial descriptions. It is interesting to note that children’s descriptions of the maze intersections in the context of the verbal description task varied considerably from their explanations of choices at maze intersections in the other tasks. The youngest children referred to animal pictures and self-referenced movements (e.g., right and left) in the verbal task when they failed to do so in the context of the other tasks. This finding further indicates that the description task was qualitatively different from the others and that children responded to this difference behaviorally by describing features and movements. In the nonverbal tasks, the large majority of the youngest children consistently made no mention of these features and movements in explaining their choices at intersections, the large majority of the children in the two older groups consistently referred to features within the maze in explaining their choices, and two of the sixth graders always used directional terminology in all tasks. The second major finding was concerned with the two different tasks involved in model construction. Age-related differences had been antic-
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ipated for the model construction task. However, it appears that the three age groups were at the same relatively high level of performance in producing the correct sequence of intersections in the model and at the same very poor level of performance in making the correct choice of direction at intersections in the model. Fundamental to the children’s success in constructing a relatively accurate succession of intersections was their ability to invoke a “stands for” relationship between the maze and the model; previous studies demonstrated that many preschool children are capable of understanding this type of spatial corespondence (Hazen, Lockman, & Pick, 1978; Liben, Moore, & Golbeck, 1982; Siegel & Schadler, 1977). In addition, building the model one intersection at a time required the construction of temporal succession, an ability that also emerges in children younger than those included in this study (Brown, 1976). Consequently, the finding of no age differences in 6- to ll-yearolds on this measure of sequential memory does not violate expectations based on related findings. The difficulty experienced by children in selecting the correct direction of movement at intersections in the model was reminiscent of the problems encountered by some children (Hazen et al., 1978; Liben et al., 1982; Presson, 1982) and adults (Levine, Jankovic, & Palij, 1982) in model construction and map reading situations. Applying a systematic, generalizable frame of reference is critical to coordinating one’s perspective of a model or map with one’s view or memory of an environment. In the current task, the younger children’s poor performance may be interpreted as a result of their failure to apply such a frame of reference. However, the older children tended to base their directional responses on the animal pictures at the intersections in the model. This objectbased frame of reference could have resulted in more accurate performance; however, either the children’s memory for which animal picture was an appropriate cue at each intersection proved unreliable, or the children could not coordinate the animal pictures with their impressions of the shape of the maze. As Hazen et al. (1978) noted, the ability to traverse a route, to anticipate landmarks along that route, and to understand the general shape of a route is necessary but insufficient for children to construct a model accurately. The skill to coordinate all of this information within the context of a model seems essential to success. Before the experiment, it had been predicted that the two measures from the model construction task would be significantly correlated. On the contrary, the results showed these measures to be virtually unrelated. Clearly, the relatedness of measures should be predicted on the basis of shared task demands (mnemonic and conceptual) rather than task of origin. The third major finding from the present study concerned the two maze navigation tasks. An age-related decrease in the number of trials
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to criterion and little difference between age groups in route reversal performance were observed in both the present study and in Hazen et al. (1978), even though the earlier study involved 3-, 4-, and Syear-olds. Together, these findings suggest that the skills involved in the acquisition of navigational knowledge of a large-scale environment improve rather steadily from age 3 to age 9 and that the ability to reverse a route once it is learned changes very little over the same period. In the present study, a high correlation had been predicted between the measures of route learning and route reversal because they both were perceptual-motor, nonverbal expressions of route knowledge. In fact, the correlation was not significant, suggesting only a weak relationship between the speed of route acquisition and the ability to reverse the route once it is acquired. In general, two bases for correlational predictions had been presented prior to the study, one based on a distinction between perceptual-motor and symbolic processes and one based on a distinction between verbal and nonverbal processes. Unfortunately, the results did not indicate one basis to be more valid than the other. A wholesale distinction between perceptual-motor (route reversal) and symbolic (verbal description and model construction) expressions of spatial knowledge was not revealed, but a clear distinction emerged between perceptual-motor and verbal expressions. Measures from the route reversal and verbal description tasks were uncorrelated. However, performance on both of these tasks was significantly correlated with the number of intersections placed correctly-but not the number of correct choices at intersections-in the model construction task. This pattern of results leads to speculation that model construction, a task that itself has both symbolic and motoric aspects, taps both symbolic and perceptual-motoric resources. The fourth major finding involved the relationship among grade level, performance in the maze learning task, and performance in the verbal description task. Age-related differences in task performance were found only for the number of trials to criterion in the learning task and the number of intersections described correctly in the verbal description task. When speed of learning was covaried in analyses of performance measures, the only analysis affected was that involving performance on the verbal description task; covarying trials to criterion eliminated the grade level effect for the number of intersections described accurately. This finding permits cautious speculation that verbal mediation facilitates the rate of maze learning. It seems reasonable to posit, for example, that rehearsal of appropriate cues and associated movements would contribute to rapid learning, and improvement in this rehearsal per se over the age span 3-9 years has been well documented (e.g., Ornstein & Naus, 1978). No doubt, verbal mediation is of central importance in providing a description of a route, and perhaps it plays a useful role in constructing a model of a spatial layout. Consistent with this line of data-
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based speculation, however, verbal mediation may be peripheral to the ability to execute or reverse a route after it is learned. While it is true that one or more age-related cognitive advancements not yet considered could be responsible for the improvement in both the rate of maze learning and accuracy of verbal description, it is also true that the factors that would influence these two tasks to a much greater extent than the others is rather limited. At the very least, the speculation that verbal rehearsal is a source of common variance provides a testable hypothesis for future experiments. To date, relatively little attention has been directed to how processes that are basically verbal and processes that are basically spatial interact as children and adults construct representations (spatial products) of their experience in large-scale environments. Future studies focusing on the application of mnemonic skills in the service of spatial cognition and on the development of linguistic conventions for describing such experience will very likely provide valuable insight into this interaction of processes in everyday cognition. Theoretical
Considerations
Although many of the experimental procedures used in the study of the development of spatial cognition can be traced to Piagetian origins, most of the research in this area has been methodologically driven rather than theoretically motivated (Allen, 1985; Liben, 1982; Newcombe, 1985). The present study arguably represents something of a middle ground in this regard, concentrating on the concept of spatial product rather than on the methodological issue of how to best measure a state of knowledge. With regard to spatial products as spatial representations, Liben (1982, 1988) is one of the few investigators to interpret available evidence consistently in terms of an explicit theoretical approach. Employing a Piagetianbased approach, she has focused on the role of conceptual growth in distinguishing between “doing,” which implies activity in the surrounding environment, and “knowing,” which implies an internal cognitive state (Liben, 1988). This distinction brings to bear on the issue of different expression of spatial knowledge the well-established themes of developmental transitions from concrete to abstract, simple to complex, and action to thought. The results of the present study can support a distinction between “doing” (a relatively simple, concrete series of actions, such as executing a route) and “knowing” (a relatively complex, abstract product of thought, such as a route description). Even after all subjects could navigate the maze flawlessly, the older children described the route more accurately. However, the relationship between “doing” and “knowing” must be much more complex than can be described in terms of a general developmental transition from one to the other. First, we must consider the much-discussed fact that our window on any state of knowing necessitates
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specific actions on the part of the subject (e.g., verbal description and model construction in the present study) Consequently, spatial products carry two distinct connotations of knowing: information regarding a specific environment and skills for expressing this knowledge. In addition, we must acknowledge that the acquisition of information regarding a specific environment is probably not strictly a “bottom-up” affair; the very skills used to express spatial knowledge no doubt exert an influence on acquisition. Consider, for example, a mobility instructor for blind individuals who teaches her clients to use a “map-in-the-head” metaphor to organize their movements. The verbal descriptions produced by these individuals would contain many more references to cardinal directions than would those produced by many sighted individuals learning the same environment. In the final analysis, the study of the skills involved in expressing spatial knowledge must be considered an important factor in understanding what spatial information is acquired through experience. A skill theory (Corrigan & Fischer, 1985; Fischer, 1980) approach to spatial products may have important application in this regard. Such an approach is based on the propositions that various expressions of spatial knowledge involve multiple task domains and that the skills in different domains may be developed independently of each other and be task-specific (see Corrigan & Fischer, 1985). As with Piagetian theory, the cognitive or representational capabilities of the individual are critically important, but the specific demands of the task-in-context play a considerably more important role in skill theory as compared to Piagetian theory. A skill theory approach has particular appeal because of the variety of task domains that can be involved in expressions of spatial knowledge. Contemporary research on the skills involved in map interpretation (Downs & Liben, 1987) and the comprehension of route directions (Klein, 1983) may yield useful means for assessing skill levels in these domains. The integration of such assessment techniques into future studies that control environmental experience and provide multiple means for expressing spatial knowledge would make important strides toward the goal of understanding developmental and individual differences in spatial cognition. REFERENCES Allen, G. L. (1985). Strengthening weak links in the study of the development of spatial cognition. In R. Cohen (Ed.), The development of spatial cognition (pp. 301-321). Hillsdale, NJ: Erlbaum. Anooshian, L. J., & Young, D. (1981). Developmental changes in cognitive maps of a familiar neighborhood. Child Development, 52, 341-348. Brown, A. L. (1976). The construction of temporal succession by preoperational children. In A. Pick (Ed.), Minnesota Symposiu on Child Psychology (Vol. 10). Minneapolis: Univ. of Minnesota Press. Cohen, R., Weatherford, D. L., & Byrd, D. (1980). Distance estimates of children as a function of acquisition and response activities. Journal ofExperimental Child Psychology, 30,
444-472.
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AND BEARD
Corrigan, R., & Fischer, K. (198.5). Controlling sources of variation in search tasks: A skill theory approach. In H. Wellman (Ed.), Children’s searching (pp. 287-318). Hillsdale, NJ: Erlbaum. Cousins, J. H., Siegel, A. W., & Maxwell, S. (1983). Wayfinding and cognitive mapping in large-scale environments: A test of a developmental model. Journal of Experimental Child Psychology, 35, I-20. Downs, R. M., & Liben, L. S. (1987). Children’s understanding of maps. In P. Ellen & C. Thinus-Blanc (Eds), Cognitive Processes and spatial orientation in animal and man (Vol. 2, pp. 202-219). Dordrecht: Martinus Nijhoff. Fischer, K. (1980). A theory of cognitive development: The control and construction of hierarchies of skills. Psychological Review, 87, 477-531. Gauvain, M., & Rogoff, B. (1987, April). Ways of speaking about space: The development of children’s skill at communicating spatial knowledge. Paper presented at the meeting of the Society for Research in Child Development, Baltimore. Hazen, N. L., Lockman, J. J., & Pick, H. L.. Jr. (1978). The development of children’s representations of large-scale environments. Child Development, 49, 623-636. Klein, W. (1983). Deixis and spatial orientation in route directions. In H. Pick & L. Acredolo (Eds.), Spatial orientation: Theory, research, and application (pp. 283-31 I). New York: Plenum. Levine, M., Jankovic, I., & Palij, A. (1982). Principles of spatial problem solving. Journal of Experimental
Psychology:
General.
111, 157-175.
Liben, L. S. (1982). Children’s large-scale spatial cognition: Is the measure the message? In R. Cohen (Ed.), New directions for child development: Children’s conceptions of spatial relationships. 15, 51-64. San Francisco: Jossey-Bass. Liben, L. S. (1988). Conceptual issues in the development of spatial cognition. In J. StilesDavis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain buses and development (pp. 167-194). Hillsdale, NJ: Erlbaum. Liben, L. S., Moore, M. L., & Golbeck, S. L. (1982). Preschoolers’ knowledge of their classroom environments: Evidence from small-scale and life-size spatial tasks. Child Development, 53, 1275-1284. Newcombe, N. (1985). Methods for the study of spatial cognition. In R. Cohen (Ed.), The development of spatial cognition (pp. 277-300). Hillsdale, NJ: Erlbaum. Ornstein, P. A., & Naus, M. J. (1978). Rehearsal processes in children’s memory. In P. Ornstein (Ed.), Memory development in children (pp. 69-99). Hillsdale, NJ: Erlbaum. Piaget, J. (1954). The construction of reality in the child. New York: Basic Books. Piaget, J. (1962). Play, dreams, and imitation in childhood. New York: Norton. Presson, C. C. (1982). The development of map-reading skills. Child Development, 53, 196-199. Scotton. C. M. (1987, August). In what ways are conversations conventionalized? Paper presented at the meeting of the International Pragmatics Association, Antwerp. Siegel, A. W. (1981). The externalization of cognitive maps by children and adults: In search of ways to ask better questions. In L. Liben, A. Patterson, & N. Newcombe (Eds.), Spatial representation and behavior across the life span (pp. 167-194). New York: Academic Press. Siegel, A. W., & Schadler, M. (1977). Young children’s cognitive maps of their classroom. Child
Development,
48, 388-394.
Wapner, S., Kaplan, B., & Ciottone, R. (1981). Self-world relationships in critical environmental transitions: Childhood and beyond. In L. Liben, A. Patterson, & N. Newcombe (Eds.), Spatial representation and behavior across the life span (pp. 251-282). New York: Academic Press. RECEIVED:
April
18,
1988;
REVISED:
October 25, 1988.
OF EXPERIMENTAL
CHILD
Children’s
48, 114-130 (1989)
PSYCHOLOGY
Expressions
of Spatial Knowledge
GARY L. ALLEN University of South Carolina
KATHLEEN
C. KIRASIC AND REBECCA L. BEARD Old Dominion University
Different expressions of spatial knowledge were examined by having groups of first-, fourth-, and sixth-grade children perform model construction, verbal description, and route reversal tasks after they learned the correct path through a pedestrian maze. Age-related improvement was found in the rate of learning the maze and in the accuracy of verbal descriptions, suggesting that maze learning may be verbally mediated. All children performed well in sequencing intersections in the model but performed poorly in choosing path options in the model. Route reversal after learning was accurate and equivalent across groups. Overall, results suggest that both general and task-specific skills are involved in different products of spatial knowledge. o 1989 Academic PXSS, IIK.
Much of the research on children’s representation of spatial knowledge has been concerned either implicity or explicitly with the question of how best to measure such knowledge (see Newcombe, 1985; Siegel, 1981). In addressing the extent to which research in the area became driven by method rather than by theory, Liben (1982) made important distinctions among the following three connotations of spatial representation: storage of spatial information, spatial thought, and spatial products. Over the past decade, many researchers have sought to examine spatial storage and spatial thought as free as possible from the “confounding” effects of spatial products. However, such efforts have been problematic in the sense that evidence of developmental change in spatial cognition is necessarily inferred from spatial products. Furthermore, there is far more speculation than evidence regarding the interrelationships among different The second author’s current address is the Department of Psychology, University of South Carolina. Reprints may be obtained from Gary L. Allen, Department of Psychology, University of South Carolina, Columbia, SC 29208. 114 0022-0965189 $3.00 Copyright All rights
0 1989 by Academic Press. Inc. of reproduction in any form reserved.
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115
products of spatial knowledge. Consequently, it would be profitable to study such products in more detail in order to obtain a more comprehensive view of developmental change in spatial memory and behavior. The current literature provides little insight into the extent to which age-related differences in a variety of spatial tasks should be attributed to differences in acquisition (that is, the encoding and storage of spatial information for future reference) and the extent to which they should be attributed to cognitive operations required to produce certain products (for example, maps, distance estimates, and verbal instructions) after acquisition. The present study was designed as an initial step toward addressing this issue. The procedure involved an acquisition phase, during which elementary-school-age children learned a path through a pedestrian maze, and a test phase, during which they performed model construction, verbal description, and route reversal tasks. Children in this range of ages were selected because (a) interesting developmental changes have been documented over this range (e.g., Anooshian & Young, 1981; Cohen, Weatherford, & Byrd, 1980; Cousins, Siegel, & Maxwell, 1983), and (b) although no pretest of symbolic functioning in the Piagetian sense was administered, all children could be assumed capable of such functioning since early childhood (see Piaget, 1962). The tasks were selected for investigation because they represent rather disparate points along a concrete-to-abstract dimension. It was assumed that after they learned the maze to criterion all children would be at an operationally defined, behaviorally indexed, roughly equivalent level of procedural knowledge. Unnecessary assumptions regarding the format of this knowledge (i.e., propositional versus analog) and the relationship of procedural to declarative knowledge were not made. Consistent with this assumption, subsequent age-related differences in task performance could be attributed largely to operations required to produce particular spatial products rather than to availability of information per se. The model construction and verbal description tasks involved symbolic operations in the sense that children had to invoke “stand for“ relationships, the various components of the model maze “stood for” the corresponding components in the full-scale maze, and words in their descriptions “stood for” specific features and actions. In general, greater age-related differences in performance would be expected for these tasks than for the route reversal task, in which knowledge of the maze was expressed perceptual-motorically rather than symbolically. Children at different age levels were expected to perform similarly in the route reversal task not only because perceptual-motor expressions of knowledge may be considered developmentally more primitive than symbolic expressions (e.g., Fischer, 1980; Piaget, 1954; Wapner, Kaplan, & Ciottone, 1981), but also because knowledge of the maze was originally attained by means of perceptual-motor experience.
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Although symbolic operations were involved in both the model construction and verbal description tasks, the tasks were differentiated by the presence of a concrete task object (in the model construction task) and the need for access to a lexicon of spatial terms (in the verbal description task). It was expected that older children would perform both of these tasks more accurately than would younger children, but the age difference was expected to be greater for the verbal task because it involved a relatively abstract translation of experience into words. Predictions about the interrelationships among measures of spatial learning and the different means of expressing spatial knowledge could not be rooted firmly in theory or evidence from past research. One possibility was to base expectations on the distinction between perceptualmotor and symbolic tasks, in which case behavior in the original maze learning task would correlate most highly with performance on the route reversal task, both of which required maze navigation. Somewhat lower correlations would then be expected between the number of trials required in the maze learning task and measures of accuracy in the model construction and verbal description tasks, which required symbolic operations. Another possibility was that the correlations between rate of learning per se and task performance would reflect the application of certain encoding and retrieval strategies useful in both situations. For example, if verbal encoding of moves resulted in rapid (or slow) maze learning, then a high correlation between learning rate and performance on the verbal task would be expected. The distinction between perceptual-motoric and symbolic expressions of spatial knowledge could also serve as the basis for predictions concerning relationships between expressions of spatial knowledge. According to this distinction, it would be expected that the correlation between performance measures on the model construction and verbal description tasks would be higher than the one involving performance measures on the route reversal and model construction tasks or the one involving performance measures on the route reversal and verbal description tasks. In contrast, it is plausible that, as implied by Siegel (1981) and others, verbal and nonverbal expressions of spatial knowledge would not be highly correlated. If this is the case, then correlations between measures from the model construction and route reversal tasks would be higher than those between measures from the model construction and verbal description tasks or between measures from the verbal description and route reversal tasks. METHOD
Subjects Data were collected from 10 boys and 10 girls from each of the following grade levels: first grade (mean age = 6 years, 7 months; range = 6
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117
years, 0 months to 7 years, 9 months), fourth grade (mean age = 9 years, 6 months; range = 8 years, 11 months to 10 years, 3 months), and sixth grade (mean = 11 years, 4 months; range = 11 years, 2 months to 12 years, 4 months). All professional guidelines regarding the treatment of children in psychological research were followed explicitly. Apparatus
A pedestrian maze was constructed of cardboard in a 7.3 x 9.4-m laboratory. The walls of the maze were 1.8 m high and the pathways 45.7 cm wide. The maze contained four choice points, each an intersection providing the subject with the options of turning left, going straight ahead, or turning right (see Fig. 1). The design of the maze prevented the children
FIG. 1. Diagram of the four-choice pedestrian maze, with color of intersections labeled and locations of animal pictures indicated by small squares (approximate scale: 1 cm = 0.5 m).
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from seeing which two of the three options led to cul-de-sacs. Each intersection was color-coded using 30-cm* sheets of paper; the colors were experienced in the sequence orange, red, blue, and green. Pictures of animals were located on the floor at each of the four branches of the intersections. Each of these 16 pictures was a color photograph of an animal mounted on a 20-cm* sheet of yellow paper. These pictures were included to allow subjects the opportunity to learn the route through the maze by relying on intersection-landmark associations in addition to or instead of associations between intersections and direction of movement. Translucent white nylon fabric was draped over the top of the entire maze to eliminate room cues during maze navigation. The model construction task involved a sectionalized line drawing of the maze with color-coded intersections corresponding to those in the maze itself, 12-cm* replicas of the 16 animal pictures located at intersections, and a 5-cm tall plastic figure to represent an individual traversing the maze. The sectionalized line drawing, which was approximately 50 cm2 when assembled, included four separate color-coded intersections and 15 pathways. An audio tape recorder was to record children’s responses in the verbal description task. Procedure
The maze was described to children as a tunnel, and they were told that they were supposed to learn the way through the tunnel from beginning to end. Each child was told to imagine himself or herself as a scout who was sent ahead to learn the correct path through the tunnel; the experimenter was described as an assistant scout who would follow him or her through the tunnel and ask questions about which way to go. It was emphasized that each child had to learn the path through the tunnel so that he or she could later tell and show the other people which way to go. On each learning trial, the child led the experimenter through the maze. At each intersection, the experimenter asked the child which way to go, and on trials subsequent to the initial one, the experimenter also asked the child how he or she knew which way was correct. Learning trials continued until the child made three successive trips through the maze without making an incorrect choice at an intersection. The experimenter recorded the number of trials to criterion and the child’s response to the question of how he or she knew which choice was correct at each intersection. Model construction. For this task, children were presented the sectionalized line drawing of the maze consisting of the four color-coded intersections and 15 pathways. Each color-coded intersection also contained replicas of the animal pictures that were located at each branch of the intersections in the maze. The sections of the maze were spread out like pieces of a puzzle on a large table that was screened off from the maze
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119
itself. The construction task was oriented so that the maze and the line drawing assembled by the child were in correspondence with regard to the room as a frame of reference (that is, the child entered the maze with his or her back to the east wall of the room and constructed the model with his or her back to the east wall of the room). Children were told that the sections of the drawing could make an accurate map of the tunnel so that people looking at the map could make it through without making a wrong turn. To initiate the task, the experimenter selected the first segment of the model, moved the plastic figure to the end of this segment, and then told the child that a person walking through the tunnel would arrive at an intersection at this point in the tunnel. The child was asked to select which intersection would be seen at that point. After a selection was made, the intersection was put into place; if it was the correct intersection for that location, the experimenter oriented it properly with respect to the animal pictures. Then the child was asked to indicate the correct path through the intersection using the plastic figure. After a choice was indicated, the experimenter asked the child why he or she had selected the chosen path. This procedure was repeated for each intersection, with the experimenter providing all of the correct pathways connecting the intersections in the model. It is important to point out that the children were responsible only for selecting the intersections and indicating the correct path of travel at those intersections; the 15 pathways used in the model were placed by the experimenter. Dependent measures from the task included the number of intersections chosen in proper order, the number of correct turns indicated at properly oriented intersections, and children’s responses to the question of how they knew which was the proper choice at each intersection. Verbal description. In this task, children were given the following instructions: “Now that you know the correct path through the tunnel, I want you to describe to me how to follow that path. Tell me how to go through the tunnel from start to finish without making a wrong turn. It is important to give me as much information as you can.” The children’s responses were tape-recorded and subsequently transcribed. Two raters were used to judge how many of the four intersections would be navigated successfully if each child’s instructions were followed. Interrater reliability was 32; disagreements were submitted to a third judge, whose decision prevailed. The number of correct choices at intersections and the children’s indications of how they knew which choice was correct at each intersection were recorded for analyses. Route reversal. In this task, the child was led to the end of the maze and was asked to lead the experimenter to the beginning of the tunnel without making any wrong turns. The experimenter followed the child through the maze and asked at each intersection why the child chose
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the particular path that he or she did. The experimenter recorded the number of errors made during reversal and the children’s responses to the question of how they knew which choice was correct at each intersectiou. Order of tusk presentations. All subjects learned the maze first and performed the route reversal task last. The reversal task was presented as the final task because it permitted updating of information from the test environment; it also served as an indication of how robust navigational knowledge of the maze was after two intervening symbolic tasks. The order of the model construction and verbal description tasks was counterbalanced so that five boys and five girls at each age level performed the model construction task before the verbal description task and five boys and five girls at each age level performed the verbal description task before the model construction task. RESULTS
Table 1 presents the means and standard deviations by grade level for the principal dependent measures resulting from the method. Analyses of these measures are described by task in the sections that follow. Maze Learning The number of trials required to achieve a criterion of three successive errorless trips through the maze was analyzed in a 3 (grade level) x 2 (sex) ANOVA with 10 subjects per cell, which yielded a significant main
TABLE MEANS
AND
STANDARD
DEVIATIONS LEVEL
Task Maze
Learning
Model
Construction
Verbal
Description
(n
Grade
level 1 4 6 1 4 6 I 4 6 I 4 6
Route
Reversal
I 4 6
I
FOR T.HE PRINCIPAL = 20 PER GRADE
Dependent
DEPENDENT
MEASURES
BY GRADE
LEVEL)
Measure
Trials to Criterion Trials to Criterion Trials to Criterion Correct Intersections Correct Intersections Correct Intersections Correct Path Choices Correct Path Choices Correct Path Choices Correct Intersections Correct Intersections Correct Intersections Correct Path Choices Correct Path Choices Correct Path Choices
M
SD
7.8 4.6 4.3
3.3 1.9
2.1
0.6
2.6
1.5 2.1 I.0 I.1
2.5 0.9
0.9 1.2 I.7 2.7 2.8 3.0
2.7 3.3
2.1
0.8
1.5 I.5 2.2 1.3 I .9 I .h
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121
KNOWLEDGE
effect for grade level, F (2, 54) = 23.52, MSe = 3.11. (The .05 criterion for statistical significance was applied consistently through the experiment.) The main effect for sex and the grade level x sex interaction did not achieve significance, both F’s < 1.00. Scheffe comparisons showed that first graders required more trials to criterion than did either the fourth graders or the sixth graders, with the older children not differing from each other. Children’s responses to the question of how they knew which way to go at each intersection readily fit into three categories: (a) a general sense of knowing (such as “I know,” “I remember,” or “I just think so”); (b) references to animal pictures at each intersection (an object-based frame of reference); and (c) reference to the directional terms “left,” “right,” and “straight” (an action-based frame of reference). To determine the types of responses that were associated with successful navigation of the maze, the number of children relying on each type of response during the third successful trip through the maze was calculated. Interestingly, children were very consistent in their responses; only three children produced responses that fit more than one category, and in each of these cases, only one response was different from the others categorically. Thus, children could be categorized in a straightforward manner (see Table 2). TABLE NUMBER OF CHILDREN AT EACH LEARNING TASK (ERRORLESS TRIAL), AND ROUTE REVERSAL TASK 02 =
2
GRADE LEVEL CLASSIFIED BY TYPE OF RESPONSE: MODEL CONSTRUCTION TASK, VERBAL DESCRIPTION 20 PER GRADE LEVEL) _____-
MAZE TASK.
Type of Response Reference to general knowing Maze Learning Grade I 4 6 Model Construction Grade 1 4 6 Verbal Description Grade 1 4 6 Route Reversal Grade I 4 6
Reference to pictures
Reference to directional terms
I2 8 4
8 12 I4
0 0 2
16 6 6
4 12 14
0 0 2
3 1 I
17 19 19
9 14 14
16 6 6
4 I4 12
0 0 2
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A x2 analysis revealed that children from different grade levels were not distributed proportionately across categories, x2 (4) = 8.63. As shown in Table 2, the number of children reporting a vague, unspecified sense of knowing decreased with grade level, and the number of children making reference to pictures as orientation cues increased. Two children in the highest grade level were the only ones who used directional terminology. Model Construction
Two aspects of performance on the model construction task were analyzed separately: the number of color-coded intersections placed correctly and the number of correct path choices at the intersections. A 3 (grade level) x 2 (sex) ANOVA performed on the number of intersections placed correctly revealed no significant effects or interactions, all F’s < 1.00. The ANOVA performed on the number of correct path choices at the intersections also yielded no significant effects or interactions, all F’s < 1.00. The number of children whose responses fit into each of the three categories in answering the question of how they knew which way was the correct path at each intersection in the model is shown in Table 2. As in the case of maze learning, children were remarkably consistent in their responses; only two children produced responses in more than one category, and in these cases all but one response was in the same category. A x2 analysis indicated an unequal distribution of children from the three grade levels across categories, x2 (4) = 15.78. As indicated in Table 2, the number of children reporting undifferentiated feelings of knowing decreased across grade levels, and the number of children who used pictures as orienting cues increased. Only two children in the highest grade level used directional terminology in their responses. Verbal Description
The number of intersections described correctly as determined through interrater agreement was analyzed in a 3 (grade level) x 2 (sex) ANOVA, which yielded a significant effect of grade level, F(2, 54) = 3.46, MSe = 1.60. Neither the main effect for sex nor the interaction were significant, both F’s < 1.00. Scheffe comparisons revealed that the mean number of intersections described accurately by sixth graders was greater than that described accurately by first graders. Fourth graders’ performance was very similar to that of the oldest children, but the difference between the fourth and first graders was slightly less than that required for statistical significance. The number of children who made reference to no specific frame of reference, to pictures, and to directional terms is portrayed in Table 2. In contrast to other tasks, the verbal task resulted in children using more than one such frame of reference in describing the correct path through
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KNOWLEDGE
123
the maze. Accordingly, an effort was made to determine differences between the proportion of children at each grade level who made statements that fit these categories; pairwise comparisons of proportions were made using an approximation to the normal distribution. Results indicated that the age groups did not differ with regard to the proportion of children mentioning no frame of reference (. 15, .05, and .05 for first, fourth, and sixth graders, respectively), mentioning animal pictures (.85, .95, and .95 for first, fourth, and sixth graders, respectively), and mentioning directional movements (.45, .70, and .70 for first, fourth, and sixth graders, respectively). A greater proportion of first graders mentioned animal pictures than mentioned directional terms, and a greater proportion of these young children mentioned directional terms than mentioned no frame of reference at all. For the fourth and sixth graders, the proportion who mentioned animal pictures did not differ from the proportion who mentioned directional movements; for both of the older groups, a greater proportion mentioned either animal pictures or directional movements than mentioned no frame of reference. Route Reversal
A 3 (grade level) x 2 (sex) ANOVA performed on the number of intersections that children navigated correctly while traversing the maze in the direction opposite to that in which it was learned revealed no significant effects or interactions, all F’s < 1.00. Despite the fact that many children used different types of responses in the verbal task, 57 of the 60 children responded consistently with a single category of response when asked how they knew which choice was correct at each intersection. Of the remaining three, each made one response of a type different from their most common answer. Table 2 shows the categorization of children by response. A x2 analysis revealed the pattern of responding to differ across grade levels, x2 (4) = 15.78. As in the case of the learning task and the model construction task, the youngest children tended to express general feelings of knowing while the two groups of older children tended to refer to objects in the maze. The only children who mentioned directional terms were in the oldest group of subjects. Relations
among Tasks
Correlations among tasks are shown in Table 3. Despite the fact that both maze learning and route reversal involved navigation of the maze, the correlation between the two measures was nonsignificant. However, significant correlations were found between trials to criterion and the number of correct choices at intersection in the model construction task and between trials to criterion and the number of intersections described correctly. The correlation between trials to criterion and number of in-
124
ALLEN,
KIRASIC, TABLE
CORRELATIONS
1. Maze 2. Model 3. Model 4. Verbal 5. Route
Learning Intersections Path Choice Description Reversal
BETWEEN
PRINCIPAL
AND BEARD 3
MEASURES
FROM TASKS
(n
=
60)
1
2
3
4
- .21 ~ .32* - .36* -.I5
- .Ol .25* .25*
-.I3 .07
- .Ol
* Significant.
tersections correct in the model construction task did not achieve statistical significance. It had been expected that the two measures from the model construction task would correlate with each other more highly than either would correlate with the measure of verbal description. This expectation was not fulfilled; the number of intersections placed correctly and the number of correct choices at these intersections in the model yielded a correlation near zero. The correlation between the number of correct intersections and performance on the verbal description task was significant, but this was not the case for the correlation between the number of correct choices at intersections in the model and performance on the verbal description task. The correlations between performance on the route reversal task and performance on the two measures from the model construction task paralleled those mentioned above between performance on the verbal description and model construction tasks. The correlation between performance on the route reversal task and the number of intersections placed correctly was significant, but not so the correlation between performance on the route reversal task and the number of correct choices at intersections in the model. Interestingly, performance on the route reversal and verbal description tasks were uncorrelated. Performance on the Maze Learning Task as a Covariate
Grade level and performance on the maze learning task were highly correlated (r = - S6). Accordingly, a series of analyses of covariance was performed to determine the effect of grade level and sex on task measures with the trials to criterion measure serving as a covariate. (Caveat: Tests of the heterogeneity of slopes across independent variablecovariate combinations revealed violations of the strict assumption that such slopes must be equal in ANCOVA; thus inferences based on these analyses depend on the robustness of the procedure in the case of similar rather than identical slopes). Results were the same as with the ANOVAs for the two measures from the model construction task and for the
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KNOWLEDGE
125
measure from the route reversal task, all F < 1.00. The ANCOVA performed on the number of intersections described accurately in the verbal description task revealed no main effects or interactions among the independent variables, all F < 1.00. Employing trials to criterion as a covariate eliminated the main effect of grade level in the analysis of performance on the verbal description task. DISCUSSION
The results may be discussed in terms of four major findings. The first of these involves the verbal expression of spatial knowledge. After learning a route to a specified criterion, children from different grade levels provided evidence of age-related differences in the ability to describe that route. In contrast, no such differences were found in the ability to construct a model of the route or the ability to navigate the route in the direction opposite of that in which it was learned originally. These findings are consistent with the prediction that the absence of a concrete task object (such as the model) and the need to use spatial terminology would yield developmental differences in the verbal expression of spatial knowledge. As children grow older, they function more effectively in this abstract task that requires implicit knowledge of linguistic conventions for communicating spatial information (Klein, 1983; Scotton, 1987). This conclusion is further supported by the findings of Gauvain and Rogoff (1987), who found that although groups of 6- and 8-year-old children demonstrated equivalent spatial knowledge of the layout of a funhouse constructed in a large laboratory, the older children were more adult-like in the way they described the funhouse. Gauvain and Rogoff attributed the differences in verbal description to increased skill in the pragmatic conventions used to organize spatial descriptions. It is interesting to note that children’s descriptions of the maze intersections in the context of the verbal description task varied considerably from their explanations of choices at maze intersections in the other tasks. The youngest children referred to animal pictures and self-referenced movements (e.g., right and left) in the verbal task when they failed to do so in the context of the other tasks. This finding further indicates that the description task was qualitatively different from the others and that children responded to this difference behaviorally by describing features and movements. In the nonverbal tasks, the large majority of the youngest children consistently made no mention of these features and movements in explaining their choices at intersections, the large majority of the children in the two older groups consistently referred to features within the maze in explaining their choices, and two of the sixth graders always used directional terminology in all tasks. The second major finding was concerned with the two different tasks involved in model construction. Age-related differences had been antic-
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ipated for the model construction task. However, it appears that the three age groups were at the same relatively high level of performance in producing the correct sequence of intersections in the model and at the same very poor level of performance in making the correct choice of direction at intersections in the model. Fundamental to the children’s success in constructing a relatively accurate succession of intersections was their ability to invoke a “stands for” relationship between the maze and the model; previous studies demonstrated that many preschool children are capable of understanding this type of spatial corespondence (Hazen, Lockman, & Pick, 1978; Liben, Moore, & Golbeck, 1982; Siegel & Schadler, 1977). In addition, building the model one intersection at a time required the construction of temporal succession, an ability that also emerges in children younger than those included in this study (Brown, 1976). Consequently, the finding of no age differences in 6- to ll-yearolds on this measure of sequential memory does not violate expectations based on related findings. The difficulty experienced by children in selecting the correct direction of movement at intersections in the model was reminiscent of the problems encountered by some children (Hazen et al., 1978; Liben et al., 1982; Presson, 1982) and adults (Levine, Jankovic, & Palij, 1982) in model construction and map reading situations. Applying a systematic, generalizable frame of reference is critical to coordinating one’s perspective of a model or map with one’s view or memory of an environment. In the current task, the younger children’s poor performance may be interpreted as a result of their failure to apply such a frame of reference. However, the older children tended to base their directional responses on the animal pictures at the intersections in the model. This objectbased frame of reference could have resulted in more accurate performance; however, either the children’s memory for which animal picture was an appropriate cue at each intersection proved unreliable, or the children could not coordinate the animal pictures with their impressions of the shape of the maze. As Hazen et al. (1978) noted, the ability to traverse a route, to anticipate landmarks along that route, and to understand the general shape of a route is necessary but insufficient for children to construct a model accurately. The skill to coordinate all of this information within the context of a model seems essential to success. Before the experiment, it had been predicted that the two measures from the model construction task would be significantly correlated. On the contrary, the results showed these measures to be virtually unrelated. Clearly, the relatedness of measures should be predicted on the basis of shared task demands (mnemonic and conceptual) rather than task of origin. The third major finding from the present study concerned the two maze navigation tasks. An age-related decrease in the number of trials
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to criterion and little difference between age groups in route reversal performance were observed in both the present study and in Hazen et al. (1978), even though the earlier study involved 3-, 4-, and Syear-olds. Together, these findings suggest that the skills involved in the acquisition of navigational knowledge of a large-scale environment improve rather steadily from age 3 to age 9 and that the ability to reverse a route once it is learned changes very little over the same period. In the present study, a high correlation had been predicted between the measures of route learning and route reversal because they both were perceptual-motor, nonverbal expressions of route knowledge. In fact, the correlation was not significant, suggesting only a weak relationship between the speed of route acquisition and the ability to reverse the route once it is acquired. In general, two bases for correlational predictions had been presented prior to the study, one based on a distinction between perceptual-motor and symbolic processes and one based on a distinction between verbal and nonverbal processes. Unfortunately, the results did not indicate one basis to be more valid than the other. A wholesale distinction between perceptual-motor (route reversal) and symbolic (verbal description and model construction) expressions of spatial knowledge was not revealed, but a clear distinction emerged between perceptual-motor and verbal expressions. Measures from the route reversal and verbal description tasks were uncorrelated. However, performance on both of these tasks was significantly correlated with the number of intersections placed correctly-but not the number of correct choices at intersections-in the model construction task. This pattern of results leads to speculation that model construction, a task that itself has both symbolic and motoric aspects, taps both symbolic and perceptual-motoric resources. The fourth major finding involved the relationship among grade level, performance in the maze learning task, and performance in the verbal description task. Age-related differences in task performance were found only for the number of trials to criterion in the learning task and the number of intersections described correctly in the verbal description task. When speed of learning was covaried in analyses of performance measures, the only analysis affected was that involving performance on the verbal description task; covarying trials to criterion eliminated the grade level effect for the number of intersections described accurately. This finding permits cautious speculation that verbal mediation facilitates the rate of maze learning. It seems reasonable to posit, for example, that rehearsal of appropriate cues and associated movements would contribute to rapid learning, and improvement in this rehearsal per se over the age span 3-9 years has been well documented (e.g., Ornstein & Naus, 1978). No doubt, verbal mediation is of central importance in providing a description of a route, and perhaps it plays a useful role in constructing a model of a spatial layout. Consistent with this line of data-
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based speculation, however, verbal mediation may be peripheral to the ability to execute or reverse a route after it is learned. While it is true that one or more age-related cognitive advancements not yet considered could be responsible for the improvement in both the rate of maze learning and accuracy of verbal description, it is also true that the factors that would influence these two tasks to a much greater extent than the others is rather limited. At the very least, the speculation that verbal rehearsal is a source of common variance provides a testable hypothesis for future experiments. To date, relatively little attention has been directed to how processes that are basically verbal and processes that are basically spatial interact as children and adults construct representations (spatial products) of their experience in large-scale environments. Future studies focusing on the application of mnemonic skills in the service of spatial cognition and on the development of linguistic conventions for describing such experience will very likely provide valuable insight into this interaction of processes in everyday cognition. Theoretical
Considerations
Although many of the experimental procedures used in the study of the development of spatial cognition can be traced to Piagetian origins, most of the research in this area has been methodologically driven rather than theoretically motivated (Allen, 1985; Liben, 1982; Newcombe, 1985). The present study arguably represents something of a middle ground in this regard, concentrating on the concept of spatial product rather than on the methodological issue of how to best measure a state of knowledge. With regard to spatial products as spatial representations, Liben (1982, 1988) is one of the few investigators to interpret available evidence consistently in terms of an explicit theoretical approach. Employing a Piagetianbased approach, she has focused on the role of conceptual growth in distinguishing between “doing,” which implies activity in the surrounding environment, and “knowing,” which implies an internal cognitive state (Liben, 1988). This distinction brings to bear on the issue of different expression of spatial knowledge the well-established themes of developmental transitions from concrete to abstract, simple to complex, and action to thought. The results of the present study can support a distinction between “doing” (a relatively simple, concrete series of actions, such as executing a route) and “knowing” (a relatively complex, abstract product of thought, such as a route description). Even after all subjects could navigate the maze flawlessly, the older children described the route more accurately. However, the relationship between “doing” and “knowing” must be much more complex than can be described in terms of a general developmental transition from one to the other. First, we must consider the much-discussed fact that our window on any state of knowing necessitates
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specific actions on the part of the subject (e.g., verbal description and model construction in the present study) Consequently, spatial products carry two distinct connotations of knowing: information regarding a specific environment and skills for expressing this knowledge. In addition, we must acknowledge that the acquisition of information regarding a specific environment is probably not strictly a “bottom-up” affair; the very skills used to express spatial knowledge no doubt exert an influence on acquisition. Consider, for example, a mobility instructor for blind individuals who teaches her clients to use a “map-in-the-head” metaphor to organize their movements. The verbal descriptions produced by these individuals would contain many more references to cardinal directions than would those produced by many sighted individuals learning the same environment. In the final analysis, the study of the skills involved in expressing spatial knowledge must be considered an important factor in understanding what spatial information is acquired through experience. A skill theory (Corrigan & Fischer, 1985; Fischer, 1980) approach to spatial products may have important application in this regard. Such an approach is based on the propositions that various expressions of spatial knowledge involve multiple task domains and that the skills in different domains may be developed independently of each other and be task-specific (see Corrigan & Fischer, 1985). As with Piagetian theory, the cognitive or representational capabilities of the individual are critically important, but the specific demands of the task-in-context play a considerably more important role in skill theory as compared to Piagetian theory. A skill theory approach has particular appeal because of the variety of task domains that can be involved in expressions of spatial knowledge. Contemporary research on the skills involved in map interpretation (Downs & Liben, 1987) and the comprehension of route directions (Klein, 1983) may yield useful means for assessing skill levels in these domains. The integration of such assessment techniques into future studies that control environmental experience and provide multiple means for expressing spatial knowledge would make important strides toward the goal of understanding developmental and individual differences in spatial cognition. REFERENCES Allen, G. L. (1985). Strengthening weak links in the study of the development of spatial cognition. In R. Cohen (Ed.), The development of spatial cognition (pp. 301-321). Hillsdale, NJ: Erlbaum. Anooshian, L. J., & Young, D. (1981). Developmental changes in cognitive maps of a familiar neighborhood. Child Development, 52, 341-348. Brown, A. L. (1976). The construction of temporal succession by preoperational children. In A. Pick (Ed.), Minnesota Symposiu on Child Psychology (Vol. 10). Minneapolis: Univ. of Minnesota Press. Cohen, R., Weatherford, D. L., & Byrd, D. (1980). Distance estimates of children as a function of acquisition and response activities. Journal ofExperimental Child Psychology, 30,
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Corrigan, R., & Fischer, K. (198.5). Controlling sources of variation in search tasks: A skill theory approach. In H. Wellman (Ed.), Children’s searching (pp. 287-318). Hillsdale, NJ: Erlbaum. Cousins, J. H., Siegel, A. W., & Maxwell, S. (1983). Wayfinding and cognitive mapping in large-scale environments: A test of a developmental model. Journal of Experimental Child Psychology, 35, I-20. Downs, R. M., & Liben, L. S. (1987). Children’s understanding of maps. In P. Ellen & C. Thinus-Blanc (Eds), Cognitive Processes and spatial orientation in animal and man (Vol. 2, pp. 202-219). Dordrecht: Martinus Nijhoff. Fischer, K. (1980). A theory of cognitive development: The control and construction of hierarchies of skills. Psychological Review, 87, 477-531. Gauvain, M., & Rogoff, B. (1987, April). Ways of speaking about space: The development of children’s skill at communicating spatial knowledge. Paper presented at the meeting of the Society for Research in Child Development, Baltimore. Hazen, N. L., Lockman, J. J., & Pick, H. L.. Jr. (1978). The development of children’s representations of large-scale environments. Child Development, 49, 623-636. Klein, W. (1983). Deixis and spatial orientation in route directions. In H. Pick & L. Acredolo (Eds.), Spatial orientation: Theory, research, and application (pp. 283-31 I). New York: Plenum. Levine, M., Jankovic, I., & Palij, A. (1982). Principles of spatial problem solving. Journal of Experimental
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Liben, L. S. (1982). Children’s large-scale spatial cognition: Is the measure the message? In R. Cohen (Ed.), New directions for child development: Children’s conceptions of spatial relationships. 15, 51-64. San Francisco: Jossey-Bass. Liben, L. S. (1988). Conceptual issues in the development of spatial cognition. In J. StilesDavis, M. Kritchevsky, & U. Bellugi (Eds.), Spatial cognition: Brain buses and development (pp. 167-194). Hillsdale, NJ: Erlbaum. Liben, L. S., Moore, M. L., & Golbeck, S. L. (1982). Preschoolers’ knowledge of their classroom environments: Evidence from small-scale and life-size spatial tasks. Child Development, 53, 1275-1284. Newcombe, N. (1985). Methods for the study of spatial cognition. In R. Cohen (Ed.), The development of spatial cognition (pp. 277-300). Hillsdale, NJ: Erlbaum. Ornstein, P. A., & Naus, M. J. (1978). Rehearsal processes in children’s memory. In P. Ornstein (Ed.), Memory development in children (pp. 69-99). Hillsdale, NJ: Erlbaum. Piaget, J. (1954). The construction of reality in the child. New York: Basic Books. Piaget, J. (1962). Play, dreams, and imitation in childhood. New York: Norton. Presson, C. C. (1982). The development of map-reading skills. Child Development, 53, 196-199. Scotton. C. M. (1987, August). In what ways are conversations conventionalized? Paper presented at the meeting of the International Pragmatics Association, Antwerp. Siegel, A. W. (1981). The externalization of cognitive maps by children and adults: In search of ways to ask better questions. In L. Liben, A. Patterson, & N. Newcombe (Eds.), Spatial representation and behavior across the life span (pp. 167-194). New York: Academic Press. Siegel, A. W., & Schadler, M. (1977). Young children’s cognitive maps of their classroom. Child
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Wapner, S., Kaplan, B., & Ciottone, R. (1981). Self-world relationships in critical environmental transitions: Childhood and beyond. In L. Liben, A. Patterson, & N. Newcombe (Eds.), Spatial representation and behavior across the life span (pp. 251-282). New York: Academic Press. RECEIVED:
April
18,
1988;
REVISED:
October 25, 1988.