- Email: [email protected]
Coordination of perspective by sixth graders and teacher trainees
CONTEMPORARY
EDUCATIONAL
Coordination
13, 358-370 (1988)
PSYCHOLOGY
of Perspective by Sixth Graders and Teacher Trainees AND JOSEPH T. KELLY
GWENDOLYN N.KELLY University
of Idaho
AND WALLACE S.JOHNSON College of Southern Idaho
Sixth grade students were compared by sex for their performance on two perspective coordination tasks. Responses were compared with understanding of the principle that still water remains invariantly horizontal. Forty-eight randomly selected sixth grade students (24 girls and 24 boys) and 12 college women were individually shown a standardized three-dimensional scene. While seated in a single position, subjects completed two tasks: (1) selecting from a set of 12 pictures (displayed together) the one which could be seen from each of eight positions marked on the displayed scene and (2) choosing the positions from which could be seen eight of the 12 pictures (shown one at a time). Four of the 12 pictures were mirror images which were impossible views. Males outperformed females on both of the coordination-of-perspective tasks. For both males and females, choosing the place was more difficult than choosing the picture. Strong relationships were found between understanding of horizontality and performance on the perspective tasks. Selection of mirror images (impossible views) indicated more understanding of perspective than other, less systematic errors. Finally, female teacher trainees performed only marginally better than sixth grade students, suggesting possible remediation needs. 0 1988 Academic Press, Inc.
In all elementary and secondary school subject areas, textbooks make extensive use of pictures. In current mathematics and geography texts, for example, elementary children encounter numerous pictures and diagrams which are included to clarify or help them visualize a concept. Frequently they are asked to imagine what pictures would look like from another perspective. Thus, it becomes important for educators to understand children’s ability to interpret three-dimensional space and its twodimensional representation. Piaget and Inhelder investigated development of children’s ability to coordinate perspective (Piaget & Inhelder, 1956). In that research children were shown an arrangement of three mountains of varying sizes and were given three separate but complementary tasks designed to assess Requests for reprints should be sent to Joseph T. Kelly, College of Education, University of Idaho, Moscow, ID 83843. 3.58 0361-476X/88 $3.00 Copyright 0 1988 by Academic Press, Inc. All rights of reproduction in any form reserved.
COORDINATION
OF PERSPECTIVE
359
their understanding. For the first task children were given duplicate mountains and were asked to construct the scene as it would look from a given perspective. In the second task children received a set of pictures and were instructed to choose the one most like the view seen from a given position. For the third task children were asked to select one of the pictures and then to determine the position a viewer must occupy to see it. Piaget and Inhelder proposed three main stages of development toward an understanding of the coordination of perspectives (1956, pp. 212-213). At stage I the problem is meaningless to the child. In stage IIA children egocentrically think observes at all positions selected see the same as the view they see. Stage IIB encompasses those subjects who demonstrate some attempts at discrimination of perspectives but whose responses lapse into egocentric constructions. At state IIIA children perceive that object relationships vary with changes in observer position but fail to apply that insight consistently. When mastery of simple perspective is complete, stage IIIB is achieved. Piaget believed this occurs by about age 9 or 10. Using similar methods others have continued this line of research. Laurendeau and Pinard (1970) generally confirmed the stages postulated by Piaget and Inhelder. Flavell, Omanson, and Latham (1978); Salatas and Flavell (1976); and Fishbein, Lewis, and Keiffer (1972) generally found that accuracy in perspective-coordinating tasks increased with age and they generally described development in terms of the acquisition of rules which govern the child’s responses. The perspective coordination experiment reported here was designed to investigate four questions. (1) Is there a sex difference in performance on a coordination-of-perspective task? (2) Are the two perspective task modes (choosing the correct view places when shown pictures and choosing the correct pictures when shown view places) of equal difficulty? (3) What is the relationship between performance on the perspective task and understanding of horizontality/verticality? (4) How does the performance of teacher trainees compare to that of sixth graders? We felt that answers to these questions would offer insights for improving educational practice in the areas requiring spatial thinking. First, is there a sex difference in performance on a coordinationof-perspectives task? Piaget and Inhelder, whose investigations show little interest in sex differences, reported none. Eliot and Dayton (1976) and Fishbein, Lewis, and Keiffer (1972), using children 10 years old or younger, reported no sex differences in performance on a perspectivecoordinating task. Laurendeau and Pinard (1970), however, reported significant sex differences appearing for the first time by age 12. Kurdek and Rodgon (1975) studied perceptual, cognitive, and affective perspective-taking in kindergarten through sixth-grade children and con-
360
KELLY,
KELLY,
AND
JOHNSON
eluded that “males were significantly better perceptual . . . perspective takers than females” (p. 647). Our previous research on understanding of horizontality (Kelly & Kelly, 1977, 1978) and verticality (Johnson, Kelly, & Kelly, 1980) identified significant sex differences. Those results, and similar findings by other researchers, led us to postulate sex differences in responding to perspective-coordinating tasks. The second question in our study derived from Laurendeau and Pinard’s research. They concluded that it was more difftcult for subjects to identify the correct picture (from a set of pictures) for a given position than it was to identify the place the subject would have to be to see a given picture (Laurendeau & Pinard, 1970). Piaget and Inhelder regarded these two modes of responding as equivalent (1956, p. 212). We sought to study further whether the two task modes were of equal difficulty. The third question concerned the relationship between performance on the perspective task and understanding of horizontality. The following studies of the child’s ability to coordinate objects influenced our thinking on this question. Eiser (1977) studied children of 8 and 11 and asserted that coordination of perspective follows an orderly development. She concluded that children first develop awareness of what is seen by another observer, then of its aspect, and finally of relationships among objects. Cox (1978) confirmed that sequence. Coie, Costanzo, and Farnill (1973); Nigl and Fishbein (1974); and Cox (1978) all investigated development of the child’s ability to orient objects as they would appear from another viewpoint. Tasks similar to the one used by Piaget and Inhelder were employed in these studies which generally found that before-behind errors were mastered first and then right-left errors. Cox found IO-year-olds were still making numerous right-left errors. Flavell, Omanson, and Latham (1978) concluded that views of other observers were identified through various calculations or rules. That is, the children calculate the appearance of a display from the viewpoint of another position, or develop rules which govern the general relationships among differing viewpoints. For example, the same position always yields the same picture, while different positions must yield different pictures. They found support for a developmental progression toward the use of rules. Gzesh and Surber (1985) also concluded that as children grow older they increasingly adopt the use of rules and computation. In the absence of any hypothesized rule, a computation is the only means available for them to solve the problem. We were led to postulate a relationship between coordinating perspectives and understanding horizontality by the following logic. In order to develop a rule establishing the appearance of objects from another point of view, a subject must consciously or unconsciously organize the objects
COORDINATION
OF PERSPECTIVE
361
one to another along two dimensions or axes. Before-behind relationships, as ordinarily viewed from a partly elevated perspective, must logically be oriented along a vertical axis and right-left relationships along a horizontal axis. Because of this logical orientation and since the studies cited above found that right-left errors were mastered last, our third question focused on the possible relationship between coordination of perspective and understanding of horizontality and verticality. The fourth question derived from our earlier finding that many adults do not demonstrate full understanding of the invariant horizontality of still water (Kelly & Kelly, 1977, 1978). We hoped that a comparison of the perspective-taking performance of sixth graders and teacher trainees might yield useful insight for improvement of educational practice. To carry out our experiment a sample of 48 sixth grade students was selected. Although Piaget and Inhelder hypothesized that the final stage of development was reached by about 9 or 10, recent studies support age 12 as more typical. Cox (1978) found children of 10 still making numerous right-left errors. Nigl and Fishbein (1974) observed that the greatest increases in performance occurred between 9 and 11 and suggested that a developmental shift occurred during that age range. Laurendeau and Pinard (1970) observed that less than one fourth of their subjects age 12 solved all three problems in their experimental task. Kurdek and Rodgon (1975) studied kindergarten through sixth grade children and concluded that “perceptual perspective taking is a relatively late acquisition, since perfect performance was not achieved even by the sixth graders; in contrast, fifth and sixth graders achieved near perfect scores in the cognitive perspective-taking task” (p. 647). Thus, it appears probable that age 12 is when mastery begins and our selection of a sixth grade population was based on that assumption. Our methods and apparatus were designed in light of prior studies of the influence on subject performance of specific aspects of perspective coordination tasks. Eliot and Dayton (1976) studied fifth grade and college students for the effects of the shape of the base on which the objects were placed, the pattern or arrangement of objects, and the number and shape of the objects used. They found that accuracy in performance was independent of stimulus features. Cox (1977b) tested children 6 to 10 for the effects of the ways they were asked to communicate their answers. She found no significant difference in performance between selecting responses from three-dimensional models and selecting responses from two-dimensional photographs. Studying children seven and nine, Cox (1977a) found no significant differences between tasks requiring selfprojection and tasks employing a doll as an intermediary to represent another person’s view.
362
KELLY,
KELLY,
AND JOHNSON
METHOD Subjects and design. Forty-eight sixth grade students, 24 boys and 24 girls, participated in this study. They were randomly selected from 198 sixth grade students enrolled in 11 classrooms in two neighboring university towns, balancing the sample number from each room. A lab class of 12 elementary teacher candidates was also included in the experiment. The class consisted of females in their third or fourth year of undergraduate work toward a degree in elementary education. Materials. Apparatus for the perspective task included a house, a round castle tower, and a tree (arranged in a standard pattern), and 12 pictures representing the array from eight actual viewpoints plus mirror images (impossible views) of four of those views. The three objects and eight pictures were published by the Nuffteld Mathematics Project (1972) and the four mirror images were produced photographically for this study from the published pictures. The red brick house was 8 x 8 cm square and 10 cm tall, the brown stone castle tower was 10 cm in diameter and 13 cm tall, and the tree was 7 cm in diameter and 9 cm in height. These three objects were arrayed in a right-triangular pattern on a light green base measuring 26 x 26 cm placed on a large table top. As viewed by the subjects, the house was in the right foreground, the tree in the left foreground, and the castle in the left background directly behind the tree (Fig. 1). The viewpoints represented by the pictures were from eight positions, located perpen-
FIG. 1. For choosing the place, apparatus was arrayed as diagrammed. Each subject remained seated at position A while the 12 pictures were presented one at a time in reverse order from that in choosing the picture (Fig. 2). That is, the sequence began with 12 and finished with 1.
COORDINATION
OF PERSPECTIVE
363
dicularly from the center of each of the four sides of the base and diagonally from each of the four comers. These viewpoints were located 70 cm out from the base along the table surface and elevated to the eye level of a seated subject. Four of the eight pictures were photographically reversed to form mirror images, or impossible views. To ensure uniformity of stimulus features both real views and mirror images shown to subjects were photographs of the published pictures. The eight positions were located at the outer tips of eight thin sticks 70 cm long and 1 x 1 cm in cross section. The sticks were laid flat on a large table along with the green base so that they radiated outward like spokes from the base (Fig. 1). These sticks represented lines-of-sight. The tips carried small vertical letters, A through H, clearly visible to the subject. Apparatus for the horizontality task included a bottle half full of blue colored water and scoring sheets with outlines of the bottle printed in random order at 12 tilts representing the hourly clock positions. For the verticality task, the apparatus consisted of a pendulum hanging from a steeple and scoring sheets with outlines of the steeple printed in random order at 12 tilts representing the hourly clock positions. Apparatus and procedures for the horizontality and verticality tasks are described in more detail in our earlier articles (Kelly & Kelly, 1977, 1978; Johnson, Kelly, & Kelly, 1980). Mirror reversals of four of the pictures were included to provide a measure of the subjects’ stability of understanding that perspective changes alter the relative nature of right-left relationships. It was assumed that students would be disoriented by having a choice between two pictures (one impossible) containing the same objects but in different positions and that students who possess fragile rules and/or incomplete understanding of the right-left relationship would make their selection by chance, thus, often choosing the incorrect picture. Inclusion of the mirror reversals was intended to assess each subject’s ability to use consistently a set of rules governing left-right orientation in perspective taking. Procedure. All subjects were tested for coordination of perspective and for understanding the concepts of horizontality and verticality. Each subject performed two separate perspective-choosing tasks. One task required subjects to select the correct view position, among eight possibilities, when shown 12 pictures (including four mirror reversals) one at a time. In the other task they were asked to choose the correct picture, from among the 12 displayed together on a board, when shown the eight positions one at a time. To assess understanding of horizontality all subjects drew water lines as they should appear on 12 outlines of a bottle printed on a scoring sheet in the hourly clock positions. To assess understanding of verticality all subjects drew pendulums as they should appear on 12 outlines of a steeple printed on a scoring sheet in the hourly clock positions. Understanding of horizontality and verticality was assessed in classroom group sessions. Understanding of perspective was measured in individual sessions. Immediately upon arrival for individual testing each subject was seated facing the model. Each part of the equipment was pointed out and named and the activity was explained. The experiment was divided into two tasks, choosing the place and choosing the picture. In choosing the place the subject was shown 12 pictures (the eight perspectives and four mirror images), one at a time, and asked where, among the eight positions marked on the table, one would have to sit to see that view. The order of picture presentation had been predetermined randomly and was the same for all subjects. Subjects remained seated during the experiment and indicated their choices by naming the letter representing that view position. When choosing the picture the eight sticks were removed from the table and the subject was shown all 12 pictures displayed together on a large board in the same random order as for the other task (Fig. 2). The experimenter placed one stick on the table at a time, in one of the eight view positions, and asked the subject to choose the picture representing the view which would be seen from that position. The order of this presentation had been established randomly and was the same for each subject. The two tasks, choosing the place
364
KELLY, #l
RC
#5 D
KELLY,
AND JOHNSON
#2
#3
#4
H
B
RB
#6
#7
#8
F
RF
E
#12 #lO %ll A RD G C FIG. 2. For choosing the picture, the 12 photographs were numbered and displayed together on a board as shown. Each subject remained seated at position A while the eight viewpoints were presented one at a time. The letter indicates the view position as labeled in Fig. 1. “R” indicates a right-left reversal of that view. #9
and choosing the picture, were assigned to subjects in a counterbalanced order to cancel potential learning effects. Scoring was performed as follows. For the perspective tasks one point was given for each correct response. The total score for the test was the sum of correct responses. Response latencies (elapsed times) were also recorded, in seconds, for all picture and place test choices. Directionally correct responses (choice of a mirror image of the correct picture) were also tallied, for separate analysis. For the horizontality and verticality tests one point was given for each correct response. The total score for each of these tests was the sum of correct responses.
RESULTS Total scores on both picture and place tests for all sixth grade students were analyzed with a 2 x 2 x 2 (Sex x School x Task) analysis of variance with repeated measures on the third factor. Also, for sixth grade students, response latencies for all test choices were analyzed separately for each task mode (picture and place). For the picture mode, a 2 x 2 x 8 (Sex x School x Response) analysis of variance was used and, for the place mode, the design was 2 x 2 x 12 (Sex x School x Response), both with repeated measures on the third factor. A 2 x 2 (School x Task) analysis of variance, with repeated measures on the second factor and total test scores as dependent variables, was applied to data for all female subjects (sixth grade and university teacher trainees). Response latencies were also analyzed for them. Correlations (Pearson R) and a multiple regression analysis were computed to determine relations between performance on both the horizontality and the verticality tests and performance on both the place and picture tasks. In addition, correlations and a multiple regression analysis were computed to compare errors which were directionally correct (scored as a proportion of all errors) with the total score of each of the place and picture tasks. The analysis of variance of sixth grade scores for choosing the place and for choosing the picture produced no significant interactions (for this
COORDINATION
365
OF PERSPECTIVE
analysis the number correct was divided by the number of choices, 12 on one task and 8 on the other). The main effects of sex F(1,44) = 5.75, p < .021; school F(1,44) = 4.21, p < .046; and task F(1,44) = 18.50, p < JO05 were significant. The means indicated that males performed better than females on both tasks. Performance on the choosing-the-picture task was better for both males and females. An analysis of all female responses indicated a significant effect for school F(2,33) = 8.12, p < .0005. Means indicated the college age women (one of the school groups) performed best. Tukey-B multiple comparison tests indicated significant performance differences between college females and only one of the two female sixth grade groups on both tasks. When compared to six grade males the college women did significantly better than only one group and only on one task. There were no signiticant interactions. The analysis of variance of response latencies for the place task revealed that the main effect of response was significant, F( 11,34) = 11.45, p < .0005. No interactions were significant. Parallel analysis of females’ scores produced a significant main effect for response, F(11,23) = 6.53, p < .0005. There were no significant interactions. The analysis of variance of response latencies for the picture task produced no significant interactions. The main effect of response was significant F(7,38) = 3.81, p < .003. Parallel analysis of females’ scores produced a significant main effect for response, F(7,27) = 2.61, p < .034 and school, F(2,33) = 3.75, p < .034, for the school effect means favored the female college students. In order to determine which response latencies differed, Tukey-B procedures were used. These analyses yielded the following significant differences (all p < .05). For all sixth graders the mean times taken (latency) TABLE 1 NUMBER CORRECT DIVIDED BY NUMBER POSSIBLE
Task mode Select picture Subjects Male School School Female School School School
Select place
x
cr
x
rr
1 2
.75 30
.20 .19
.5’6 .65
.18 .08
1 2 3 (college)
.56 .68 .80
.21 .18 .16
.49 ho .74
.18 .22 .17
366
KELLY,
KELLY,
AND JOHNSON
to choose the place were greater for pictures 11 and 12 than for 8 and 10; 5 was greater than 8, 10, and 1; and 7,6, 2, and 3 were greater than 8, 10, 1, and 9. For all females, response latencies on the place task differed as follows. Latencies for pictures 12, 6, and 4 were greater than for 8 and 10. Latencies for numbers 2, 7, 11, 5, and 3 were greater than for 8, 10, and 9. For all sixth graders the mean response latency to choose pictures was greater for place H than for place E. For the female college students (to select pictures) the latency was greater for place H than for place A. No other latencies differed significantly for this task. To identify any relationship between understanding of horizontality/ verticality and performance on the perspective tasks, correlations were calculated and regression analyses completed. The Pearson R correlation between place task scores and verticality scores was .063 (oblique angles only) and for horizontality was .324 (oblique angles only). For the picture task scores the correlations were .049 for verticality and .493 for horizontality. Calculations of ? indicated that .3% of the variance in performance on the place task and .2% on the picture task were predictable from performance on the verticality test. Performance on the horizontality task accounted for 10% of the variability in responses on the place task and 24% on the picture task. The equation for the prediction of place task scores (from the horizontality test) was Y’ = 6.105 + .238X and was Y’ = 4.43 + .262X for the picture task. To identify any relationship between the percentage of directionally TABLE 2 ERRORS FOR CHOOSING THE PLACE Picture Group Sixth grade males (24) Total errorsC Reversals Egocentric choice Sixth grade females (24) Total errorsC Reversals Egocentric choice College females (12) Total errorsC Reversals Egocentric choice
12
11”
lob
96
gb
7”
6
5
4”
3
2
1”
Total
2 0
24 21 0
1
1
1
18 12
5 -
5 -
22 18
6 -
5 -
24 23
114 74 6
2 1
24 20 2
13 5
5 1
21 10 1
9 2
8 4
22 19 3
133 61 26
1 0
7 6 0
2
1 0
8 5 0
3 0
0 0
9 8 0
37 21 1
;TO1200020 2 y
4 0
2 1
21 12 4
0 0
0 0
0 0
6 2 1
0
L1Photographic reversals and thus impossible views. Also called directionally correct choices. b Pictures of views visible from positions defined as egocentric choices: (10) where the subject was seated, (9) to the subject’s immediate right, and (8) to the subject’s immediate left. c Errors other than reversals and egocentric choices were unclassified.
COORDINATION
367
OF PERSPECTIVE
TABLE 3 ERRORS FOR CHOOSING THE PICTURE
Place Group Sixth grade males (24) Total errors’ Reversals” Egocentric choicesb Sixth grade females (24) Total errorsc Reversals” Egocentric choicesb College females (12) Total errorsc Reversals” Egocentric choicesb
A
B
C
D
E
F
G
H
Total
0 0
11 53 1
6
5
1
4
2
11 5 8-4-2 3
1
1
3
43 20 13
1
15 7 0
9 5 2
15 10 0
7 6
9 5 3
8 4
8 4
72 27 20
7 2 4-0-0 1
0
0
1
0
0
1
19 8 3
1 0 0
7 40 0
2 1
d No reversal for positions A, E, G, and H. Also called directionally correct choices. b Three places were defined as egocentric choices: (A) where the subject was seated, (G) to the subject’s immediate right, and (E) to the subject’s immediate left. c Errors other than reversals and egocentric choices were unclassified.
correct choices and scores on the picture and place tasks, correlations and regression analyses were employed. The Pearson R correlation between the percentage of directionally correct choices and scores on the place task was .612 and for picture scores it was .402. The 2 indicated that 37% of the variance on the place task and 16% on the picture task were predictable from the percentage of directionally correct choices. The equation for the prediction of place task scores (from directionally correct choices) was Y’ = 4.47 + .042X and for the picture task was Y’ = 4.57 + .015x DISCUSSION In regard to the first question addressed in this study, sex differences, favoring males, were statistically significant both for choosing the picture and for choosing the place. As for the second question, correct response scores indicate that for both sexes the task of choosing the place was more difficult. We believe that this difficulty was based on the method of presentation in which subjects were asked to consider separately each of the 12 pictures, including the four mirror images, and to select the position from which one would see the perspective shown in each. Since subjects were not told that four of the pictures were of impossible views, only those whose understanding was most well established could be expected to assert positively that a given mirror image could not be seen
368
KELLY,
KELLY,
AND
JOHNSON
from any of the eight positions or was not even a possible view. It should be noted that Piaget and Inhelder similarly employed impossible views to refine their evaluation of perspective development (1956, pp. 240-241). In the other task, choosing the picture, subjects were shown a view position and asked to select the correct picture from the 12 displayed together. Subjects were not specifically directed to consider the reversals which were mixed in with the others and could be passed over. Thus, the procedure employed in choosing the place required a higher level of confidence than in choosing the picture. In planning this study we carefully considered whether subjects should be informed that the pictures included impossible views. We knew that without this information some subjects might choose reversals in spite of inner doubts. On the other hand, we did not want conditions that would ease the choices, thus weakening the testing of their understanding. Observations of subject behavior clearly showed that many were puzzled by the impossible views but apparently did not fully understand what was wrong. We believe failure to deal correctly with the reversals can most plausibly be interpreted as insufficient understanding of perspective. Those subjects who really understood perspective could have identified impossible views as such and 10 of our subjects did. Although Piaget and Inhelder viewed the two modes, choosing the place and choosing the picture, as equivalent, Laurendeau and Pinard (1970) concluded that choosing the picture was more difficult. We initially found that choosing the place was more difficult, both for the entire sample and for each sex considered separately. However, when the effects of the forced choice reversals were removed, a count of correct responses for males showed totals of 149 for choosing the picture and 166 for choosing the place. Total correct responses for females were 120 and 147, respectively. Considered in that manner, our findings paralleled those of Laurendeau and Pinard. A breakdown of errors made in choosing the picture shows that the majority of errors, 50% or greater for all but one position, involved selection of mirror images and/or egocentric view points. This was true for both male and female subjects although females made significantly more errors. When choosing the picture 75% of the girls made at least one reversal error compared to 54% of the boys. The largest numbers of errors made by both sexes in choosing the picture were for the positions which were the most remote from where they were seated (further supported by analysis of response latencies). That result was expected as those positions required the maximum coordination of perspective. The mirror images, or reversals, used in this study require further consideration. Males more often chose these positions which, though incorrect, would have been correct were it not for the mirror image factor. We
COORDINATION
OF PERSPECTIVE
369
have called those choices directionally correct, concluding that they were less random than other choices and therefore implied more understanding. Analysis of the four positions for which mirror images were presented indicated that for choosing the place, selection of those reversals (directionally correct errors) was the major source of error for the top half of the total sample (those making the fewest errors on the total test). Reversal errors were not as strongly evident for the bottom half (those making the most errors on the total test). For males 93% of all errors on the four mirror images were directionally correct errors for the top half of the sample as opposed to 78% for the bottom half. For the females the error percentages were 88% for the upper half of the sample and 60% for the lower half. These proportions lit our assumption that mirror image errors imply more understanding than random choices. In addition, the ? calculations indicated that 37% of the variance on the place task and 16% on the picture task were predictable from the percentage of mirror image choices. Our third research question was aimed at a possible connection between understanding of horizontality and coordination of perspective. As we explained in our introduction, right-left relationships must logically be oriented along a horizontal axis, which implies that understanding of horizontality may contribute to coordination of perspective. Based on this assumption, we had expected to find a relationship between scores on perspective tasks and scores on the horizontality test. As reported earlier, performance on the horizontality task accounted for 10% of the variance in responses on the place task and 24% on the picture task. Therefore, we continue to suspect that coordination of perspective may be more dependent on understanding of horizontality than implied by Piaget and Inhelder (1956). We also remain convinced that this line of reasoning may be fruitful for further investigation. Our fourth question aimed to compare the performance of the college females (teacher trainees) with that of sixth grade students. Since sex differences had been evident (Question One), we compared the college women’s performance separately with that of male and female sixth grade students. Although mean scores were higher for the college group in all instances, statistical significance was attained for the differences in only one of the two comparisons with the younger females (on both tasks) and for only one group of the younger males (on only one task). Since we had expected a clear superiority for the teacher trainees, their only marginally better performance was disappointing and difticult to interpret. We suspect that their relatively modest performance may derive from traditional female socialization, generally regarded as insufficiently focused on development of spatial concepts. Whatever the cause,
370
KELLY,
KELLY,
AND JOHNSON
these findings, if generalizable, suggest that female elementary teacher candidates may need more spatial development activities if they are to gain understanding suffkiently beyond that of the students they will be teaching. REFERENCES COIE, J., COSTANZO,P., & FARNILL, D. (1973). Specific transitions in the development of spatial perspective-taking ability. Developmental Psychology, 9, 167-177. Cox, M. (1977a). Perspective ability: The other observer in the task. Perceptual and Motor Skills, 44, 76.
Cox, M. (1977b). Perspective ability: Mode of presentation of another’s view. Perceptual and Motor Skills, 44, 214. Cox, M. (1978). Order of the acquisition of perspective-taking skills. Developmental Psychology, 14, 421422. EISER, C. (1977). Strategies children use to co-ordinate perspective as a function of task demand. British Journal of Educational Psychology, 47, 327-329. ELIOT, J., & DAYTON, C. (1976). Factors affecting accuracy of perception on a task requiring the ability to identify viewpoints. The Journal ofGenetic Psychology, 12&201-214. FISHBEIN, H., LEWIS, S., & KEIFFER, K. (1972). Children’s understanding of spatial relations: Coordination of perspectives. Developmental Psychology, 7, 21-33. FLAVELL, J., EVERETT,B., CROFT,K., & FLAVELL, E. (1981). Young children’s knowledge about visual perception: Further evidence for the level l-level 2 distinction. Developmental Psychology, 17, 99-103. FLAVELL, J., OMANSON,R., & LATHAM, C. (1978). Solving spatial perspective-taking problems by rule versus computation: A developmental study. Developmental Psychology, 14, 462-473.
GZESH, S., & SURBER,C. (1985). Visual perspective-taking skills in children. Child Development, 56, 1204-1213. JOHNSON,W., KELLY, G., & KELLY, J. (1980). Perception of verticality by boys and girls in grade 6. Perceptual and Motor Skills, 51, 355-358. KELLY, J., & KELLY, G. (1977). Perception of horizontality by male and female college students. Perceptual and Motor Skills, 44, 724-726. KELLY, J., & KELLY, G. (1978). Science activity centers: Basic concepts of the physical world. Science and Children, 16, 25-26. KURDEK, L., & RODGON,M. (1975). Perceptual, cognitive, and affective perspective taking in kindergarten through sixth-grade children. Developmental Psychology, 11, 643-650. LAURENDEAU, M., & PINARD, A. (1970). The development of the concept of space in the child. New York: International University Press. NIGL, A., & FISHBEIN, H. (1974). Perception and conception in coordination of perspectives. Developmental Psychology, 10, 858-866. NUFFIELD MATHEMATICSPROJECT(1972). Checking up ZZ. New York: Wiley. PIAGET, J., L INHELDER, B. (1956). The child’s conception ofspace. London: Routledge & Kegan Paul. SALATAS, H., & FLAVELL, J. (1976). Perspective taking: The development of two components of knowledge. Child Development, 47, 103-109.
EDUCATIONAL
Coordination
13, 358-370 (1988)
PSYCHOLOGY
of Perspective by Sixth Graders and Teacher Trainees AND JOSEPH T. KELLY
GWENDOLYN N.KELLY University
of Idaho
AND WALLACE S.JOHNSON College of Southern Idaho
Sixth grade students were compared by sex for their performance on two perspective coordination tasks. Responses were compared with understanding of the principle that still water remains invariantly horizontal. Forty-eight randomly selected sixth grade students (24 girls and 24 boys) and 12 college women were individually shown a standardized three-dimensional scene. While seated in a single position, subjects completed two tasks: (1) selecting from a set of 12 pictures (displayed together) the one which could be seen from each of eight positions marked on the displayed scene and (2) choosing the positions from which could be seen eight of the 12 pictures (shown one at a time). Four of the 12 pictures were mirror images which were impossible views. Males outperformed females on both of the coordination-of-perspective tasks. For both males and females, choosing the place was more difficult than choosing the picture. Strong relationships were found between understanding of horizontality and performance on the perspective tasks. Selection of mirror images (impossible views) indicated more understanding of perspective than other, less systematic errors. Finally, female teacher trainees performed only marginally better than sixth grade students, suggesting possible remediation needs. 0 1988 Academic Press, Inc.
In all elementary and secondary school subject areas, textbooks make extensive use of pictures. In current mathematics and geography texts, for example, elementary children encounter numerous pictures and diagrams which are included to clarify or help them visualize a concept. Frequently they are asked to imagine what pictures would look like from another perspective. Thus, it becomes important for educators to understand children’s ability to interpret three-dimensional space and its twodimensional representation. Piaget and Inhelder investigated development of children’s ability to coordinate perspective (Piaget & Inhelder, 1956). In that research children were shown an arrangement of three mountains of varying sizes and were given three separate but complementary tasks designed to assess Requests for reprints should be sent to Joseph T. Kelly, College of Education, University of Idaho, Moscow, ID 83843. 3.58 0361-476X/88 $3.00 Copyright 0 1988 by Academic Press, Inc. All rights of reproduction in any form reserved.
COORDINATION
OF PERSPECTIVE
359
their understanding. For the first task children were given duplicate mountains and were asked to construct the scene as it would look from a given perspective. In the second task children received a set of pictures and were instructed to choose the one most like the view seen from a given position. For the third task children were asked to select one of the pictures and then to determine the position a viewer must occupy to see it. Piaget and Inhelder proposed three main stages of development toward an understanding of the coordination of perspectives (1956, pp. 212-213). At stage I the problem is meaningless to the child. In stage IIA children egocentrically think observes at all positions selected see the same as the view they see. Stage IIB encompasses those subjects who demonstrate some attempts at discrimination of perspectives but whose responses lapse into egocentric constructions. At state IIIA children perceive that object relationships vary with changes in observer position but fail to apply that insight consistently. When mastery of simple perspective is complete, stage IIIB is achieved. Piaget believed this occurs by about age 9 or 10. Using similar methods others have continued this line of research. Laurendeau and Pinard (1970) generally confirmed the stages postulated by Piaget and Inhelder. Flavell, Omanson, and Latham (1978); Salatas and Flavell (1976); and Fishbein, Lewis, and Keiffer (1972) generally found that accuracy in perspective-coordinating tasks increased with age and they generally described development in terms of the acquisition of rules which govern the child’s responses. The perspective coordination experiment reported here was designed to investigate four questions. (1) Is there a sex difference in performance on a coordination-of-perspective task? (2) Are the two perspective task modes (choosing the correct view places when shown pictures and choosing the correct pictures when shown view places) of equal difficulty? (3) What is the relationship between performance on the perspective task and understanding of horizontality/verticality? (4) How does the performance of teacher trainees compare to that of sixth graders? We felt that answers to these questions would offer insights for improving educational practice in the areas requiring spatial thinking. First, is there a sex difference in performance on a coordinationof-perspectives task? Piaget and Inhelder, whose investigations show little interest in sex differences, reported none. Eliot and Dayton (1976) and Fishbein, Lewis, and Keiffer (1972), using children 10 years old or younger, reported no sex differences in performance on a perspectivecoordinating task. Laurendeau and Pinard (1970), however, reported significant sex differences appearing for the first time by age 12. Kurdek and Rodgon (1975) studied perceptual, cognitive, and affective perspective-taking in kindergarten through sixth-grade children and con-
360
KELLY,
KELLY,
AND
JOHNSON
eluded that “males were significantly better perceptual . . . perspective takers than females” (p. 647). Our previous research on understanding of horizontality (Kelly & Kelly, 1977, 1978) and verticality (Johnson, Kelly, & Kelly, 1980) identified significant sex differences. Those results, and similar findings by other researchers, led us to postulate sex differences in responding to perspective-coordinating tasks. The second question in our study derived from Laurendeau and Pinard’s research. They concluded that it was more difftcult for subjects to identify the correct picture (from a set of pictures) for a given position than it was to identify the place the subject would have to be to see a given picture (Laurendeau & Pinard, 1970). Piaget and Inhelder regarded these two modes of responding as equivalent (1956, p. 212). We sought to study further whether the two task modes were of equal difficulty. The third question concerned the relationship between performance on the perspective task and understanding of horizontality. The following studies of the child’s ability to coordinate objects influenced our thinking on this question. Eiser (1977) studied children of 8 and 11 and asserted that coordination of perspective follows an orderly development. She concluded that children first develop awareness of what is seen by another observer, then of its aspect, and finally of relationships among objects. Cox (1978) confirmed that sequence. Coie, Costanzo, and Farnill (1973); Nigl and Fishbein (1974); and Cox (1978) all investigated development of the child’s ability to orient objects as they would appear from another viewpoint. Tasks similar to the one used by Piaget and Inhelder were employed in these studies which generally found that before-behind errors were mastered first and then right-left errors. Cox found IO-year-olds were still making numerous right-left errors. Flavell, Omanson, and Latham (1978) concluded that views of other observers were identified through various calculations or rules. That is, the children calculate the appearance of a display from the viewpoint of another position, or develop rules which govern the general relationships among differing viewpoints. For example, the same position always yields the same picture, while different positions must yield different pictures. They found support for a developmental progression toward the use of rules. Gzesh and Surber (1985) also concluded that as children grow older they increasingly adopt the use of rules and computation. In the absence of any hypothesized rule, a computation is the only means available for them to solve the problem. We were led to postulate a relationship between coordinating perspectives and understanding horizontality by the following logic. In order to develop a rule establishing the appearance of objects from another point of view, a subject must consciously or unconsciously organize the objects
COORDINATION
OF PERSPECTIVE
361
one to another along two dimensions or axes. Before-behind relationships, as ordinarily viewed from a partly elevated perspective, must logically be oriented along a vertical axis and right-left relationships along a horizontal axis. Because of this logical orientation and since the studies cited above found that right-left errors were mastered last, our third question focused on the possible relationship between coordination of perspective and understanding of horizontality and verticality. The fourth question derived from our earlier finding that many adults do not demonstrate full understanding of the invariant horizontality of still water (Kelly & Kelly, 1977, 1978). We hoped that a comparison of the perspective-taking performance of sixth graders and teacher trainees might yield useful insight for improvement of educational practice. To carry out our experiment a sample of 48 sixth grade students was selected. Although Piaget and Inhelder hypothesized that the final stage of development was reached by about 9 or 10, recent studies support age 12 as more typical. Cox (1978) found children of 10 still making numerous right-left errors. Nigl and Fishbein (1974) observed that the greatest increases in performance occurred between 9 and 11 and suggested that a developmental shift occurred during that age range. Laurendeau and Pinard (1970) observed that less than one fourth of their subjects age 12 solved all three problems in their experimental task. Kurdek and Rodgon (1975) studied kindergarten through sixth grade children and concluded that “perceptual perspective taking is a relatively late acquisition, since perfect performance was not achieved even by the sixth graders; in contrast, fifth and sixth graders achieved near perfect scores in the cognitive perspective-taking task” (p. 647). Thus, it appears probable that age 12 is when mastery begins and our selection of a sixth grade population was based on that assumption. Our methods and apparatus were designed in light of prior studies of the influence on subject performance of specific aspects of perspective coordination tasks. Eliot and Dayton (1976) studied fifth grade and college students for the effects of the shape of the base on which the objects were placed, the pattern or arrangement of objects, and the number and shape of the objects used. They found that accuracy in performance was independent of stimulus features. Cox (1977b) tested children 6 to 10 for the effects of the ways they were asked to communicate their answers. She found no significant difference in performance between selecting responses from three-dimensional models and selecting responses from two-dimensional photographs. Studying children seven and nine, Cox (1977a) found no significant differences between tasks requiring selfprojection and tasks employing a doll as an intermediary to represent another person’s view.
362
KELLY,
KELLY,
AND JOHNSON
METHOD Subjects and design. Forty-eight sixth grade students, 24 boys and 24 girls, participated in this study. They were randomly selected from 198 sixth grade students enrolled in 11 classrooms in two neighboring university towns, balancing the sample number from each room. A lab class of 12 elementary teacher candidates was also included in the experiment. The class consisted of females in their third or fourth year of undergraduate work toward a degree in elementary education. Materials. Apparatus for the perspective task included a house, a round castle tower, and a tree (arranged in a standard pattern), and 12 pictures representing the array from eight actual viewpoints plus mirror images (impossible views) of four of those views. The three objects and eight pictures were published by the Nuffteld Mathematics Project (1972) and the four mirror images were produced photographically for this study from the published pictures. The red brick house was 8 x 8 cm square and 10 cm tall, the brown stone castle tower was 10 cm in diameter and 13 cm tall, and the tree was 7 cm in diameter and 9 cm in height. These three objects were arrayed in a right-triangular pattern on a light green base measuring 26 x 26 cm placed on a large table top. As viewed by the subjects, the house was in the right foreground, the tree in the left foreground, and the castle in the left background directly behind the tree (Fig. 1). The viewpoints represented by the pictures were from eight positions, located perpen-
FIG. 1. For choosing the place, apparatus was arrayed as diagrammed. Each subject remained seated at position A while the 12 pictures were presented one at a time in reverse order from that in choosing the picture (Fig. 2). That is, the sequence began with 12 and finished with 1.
COORDINATION
OF PERSPECTIVE
363
dicularly from the center of each of the four sides of the base and diagonally from each of the four comers. These viewpoints were located 70 cm out from the base along the table surface and elevated to the eye level of a seated subject. Four of the eight pictures were photographically reversed to form mirror images, or impossible views. To ensure uniformity of stimulus features both real views and mirror images shown to subjects were photographs of the published pictures. The eight positions were located at the outer tips of eight thin sticks 70 cm long and 1 x 1 cm in cross section. The sticks were laid flat on a large table along with the green base so that they radiated outward like spokes from the base (Fig. 1). These sticks represented lines-of-sight. The tips carried small vertical letters, A through H, clearly visible to the subject. Apparatus for the horizontality task included a bottle half full of blue colored water and scoring sheets with outlines of the bottle printed in random order at 12 tilts representing the hourly clock positions. For the verticality task, the apparatus consisted of a pendulum hanging from a steeple and scoring sheets with outlines of the steeple printed in random order at 12 tilts representing the hourly clock positions. Apparatus and procedures for the horizontality and verticality tasks are described in more detail in our earlier articles (Kelly & Kelly, 1977, 1978; Johnson, Kelly, & Kelly, 1980). Mirror reversals of four of the pictures were included to provide a measure of the subjects’ stability of understanding that perspective changes alter the relative nature of right-left relationships. It was assumed that students would be disoriented by having a choice between two pictures (one impossible) containing the same objects but in different positions and that students who possess fragile rules and/or incomplete understanding of the right-left relationship would make their selection by chance, thus, often choosing the incorrect picture. Inclusion of the mirror reversals was intended to assess each subject’s ability to use consistently a set of rules governing left-right orientation in perspective taking. Procedure. All subjects were tested for coordination of perspective and for understanding the concepts of horizontality and verticality. Each subject performed two separate perspective-choosing tasks. One task required subjects to select the correct view position, among eight possibilities, when shown 12 pictures (including four mirror reversals) one at a time. In the other task they were asked to choose the correct picture, from among the 12 displayed together on a board, when shown the eight positions one at a time. To assess understanding of horizontality all subjects drew water lines as they should appear on 12 outlines of a bottle printed on a scoring sheet in the hourly clock positions. To assess understanding of verticality all subjects drew pendulums as they should appear on 12 outlines of a steeple printed on a scoring sheet in the hourly clock positions. Understanding of horizontality and verticality was assessed in classroom group sessions. Understanding of perspective was measured in individual sessions. Immediately upon arrival for individual testing each subject was seated facing the model. Each part of the equipment was pointed out and named and the activity was explained. The experiment was divided into two tasks, choosing the place and choosing the picture. In choosing the place the subject was shown 12 pictures (the eight perspectives and four mirror images), one at a time, and asked where, among the eight positions marked on the table, one would have to sit to see that view. The order of picture presentation had been predetermined randomly and was the same for all subjects. Subjects remained seated during the experiment and indicated their choices by naming the letter representing that view position. When choosing the picture the eight sticks were removed from the table and the subject was shown all 12 pictures displayed together on a large board in the same random order as for the other task (Fig. 2). The experimenter placed one stick on the table at a time, in one of the eight view positions, and asked the subject to choose the picture representing the view which would be seen from that position. The order of this presentation had been established randomly and was the same for each subject. The two tasks, choosing the place
364
KELLY, #l
RC
#5 D
KELLY,
AND JOHNSON
#2
#3
#4
H
B
RB
#6
#7
#8
F
RF
E
#12 #lO %ll A RD G C FIG. 2. For choosing the picture, the 12 photographs were numbered and displayed together on a board as shown. Each subject remained seated at position A while the eight viewpoints were presented one at a time. The letter indicates the view position as labeled in Fig. 1. “R” indicates a right-left reversal of that view. #9
and choosing the picture, were assigned to subjects in a counterbalanced order to cancel potential learning effects. Scoring was performed as follows. For the perspective tasks one point was given for each correct response. The total score for the test was the sum of correct responses. Response latencies (elapsed times) were also recorded, in seconds, for all picture and place test choices. Directionally correct responses (choice of a mirror image of the correct picture) were also tallied, for separate analysis. For the horizontality and verticality tests one point was given for each correct response. The total score for each of these tests was the sum of correct responses.
RESULTS Total scores on both picture and place tests for all sixth grade students were analyzed with a 2 x 2 x 2 (Sex x School x Task) analysis of variance with repeated measures on the third factor. Also, for sixth grade students, response latencies for all test choices were analyzed separately for each task mode (picture and place). For the picture mode, a 2 x 2 x 8 (Sex x School x Response) analysis of variance was used and, for the place mode, the design was 2 x 2 x 12 (Sex x School x Response), both with repeated measures on the third factor. A 2 x 2 (School x Task) analysis of variance, with repeated measures on the second factor and total test scores as dependent variables, was applied to data for all female subjects (sixth grade and university teacher trainees). Response latencies were also analyzed for them. Correlations (Pearson R) and a multiple regression analysis were computed to determine relations between performance on both the horizontality and the verticality tests and performance on both the place and picture tasks. In addition, correlations and a multiple regression analysis were computed to compare errors which were directionally correct (scored as a proportion of all errors) with the total score of each of the place and picture tasks. The analysis of variance of sixth grade scores for choosing the place and for choosing the picture produced no significant interactions (for this
COORDINATION
365
OF PERSPECTIVE
analysis the number correct was divided by the number of choices, 12 on one task and 8 on the other). The main effects of sex F(1,44) = 5.75, p < .021; school F(1,44) = 4.21, p < .046; and task F(1,44) = 18.50, p < JO05 were significant. The means indicated that males performed better than females on both tasks. Performance on the choosing-the-picture task was better for both males and females. An analysis of all female responses indicated a significant effect for school F(2,33) = 8.12, p < .0005. Means indicated the college age women (one of the school groups) performed best. Tukey-B multiple comparison tests indicated significant performance differences between college females and only one of the two female sixth grade groups on both tasks. When compared to six grade males the college women did significantly better than only one group and only on one task. There were no signiticant interactions. The analysis of variance of response latencies for the place task revealed that the main effect of response was significant, F( 11,34) = 11.45, p < .0005. No interactions were significant. Parallel analysis of females’ scores produced a significant main effect for response, F(11,23) = 6.53, p < .0005. There were no significant interactions. The analysis of variance of response latencies for the picture task produced no significant interactions. The main effect of response was significant F(7,38) = 3.81, p < .003. Parallel analysis of females’ scores produced a significant main effect for response, F(7,27) = 2.61, p < .034 and school, F(2,33) = 3.75, p < .034, for the school effect means favored the female college students. In order to determine which response latencies differed, Tukey-B procedures were used. These analyses yielded the following significant differences (all p < .05). For all sixth graders the mean times taken (latency) TABLE 1 NUMBER CORRECT DIVIDED BY NUMBER POSSIBLE
Task mode Select picture Subjects Male School School Female School School School
Select place
x
cr
x
rr
1 2
.75 30
.20 .19
.5’6 .65
.18 .08
1 2 3 (college)
.56 .68 .80
.21 .18 .16
.49 ho .74
.18 .22 .17
366
KELLY,
KELLY,
AND JOHNSON
to choose the place were greater for pictures 11 and 12 than for 8 and 10; 5 was greater than 8, 10, and 1; and 7,6, 2, and 3 were greater than 8, 10, 1, and 9. For all females, response latencies on the place task differed as follows. Latencies for pictures 12, 6, and 4 were greater than for 8 and 10. Latencies for numbers 2, 7, 11, 5, and 3 were greater than for 8, 10, and 9. For all sixth graders the mean response latency to choose pictures was greater for place H than for place E. For the female college students (to select pictures) the latency was greater for place H than for place A. No other latencies differed significantly for this task. To identify any relationship between understanding of horizontality/ verticality and performance on the perspective tasks, correlations were calculated and regression analyses completed. The Pearson R correlation between place task scores and verticality scores was .063 (oblique angles only) and for horizontality was .324 (oblique angles only). For the picture task scores the correlations were .049 for verticality and .493 for horizontality. Calculations of ? indicated that .3% of the variance in performance on the place task and .2% on the picture task were predictable from performance on the verticality test. Performance on the horizontality task accounted for 10% of the variability in responses on the place task and 24% on the picture task. The equation for the prediction of place task scores (from the horizontality test) was Y’ = 6.105 + .238X and was Y’ = 4.43 + .262X for the picture task. To identify any relationship between the percentage of directionally TABLE 2 ERRORS FOR CHOOSING THE PLACE Picture Group Sixth grade males (24) Total errorsC Reversals Egocentric choice Sixth grade females (24) Total errorsC Reversals Egocentric choice College females (12) Total errorsC Reversals Egocentric choice
12
11”
lob
96
gb
7”
6
5
4”
3
2
1”
Total
2 0
24 21 0
1
1
1
18 12
5 -
5 -
22 18
6 -
5 -
24 23
114 74 6
2 1
24 20 2
13 5
5 1
21 10 1
9 2
8 4
22 19 3
133 61 26
1 0
7 6 0
2
1 0
8 5 0
3 0
0 0
9 8 0
37 21 1
;TO1200020 2 y
4 0
2 1
21 12 4
0 0
0 0
0 0
6 2 1
0
L1Photographic reversals and thus impossible views. Also called directionally correct choices. b Pictures of views visible from positions defined as egocentric choices: (10) where the subject was seated, (9) to the subject’s immediate right, and (8) to the subject’s immediate left. c Errors other than reversals and egocentric choices were unclassified.
COORDINATION
367
OF PERSPECTIVE
TABLE 3 ERRORS FOR CHOOSING THE PICTURE
Place Group Sixth grade males (24) Total errors’ Reversals” Egocentric choicesb Sixth grade females (24) Total errorsc Reversals” Egocentric choicesb College females (12) Total errorsc Reversals” Egocentric choicesb
A
B
C
D
E
F
G
H
Total
0 0
11 53 1
6
5
1
4
2
11 5 8-4-2 3
1
1
3
43 20 13
1
15 7 0
9 5 2
15 10 0
7 6
9 5 3
8 4
8 4
72 27 20
7 2 4-0-0 1
0
0
1
0
0
1
19 8 3
1 0 0
7 40 0
2 1
d No reversal for positions A, E, G, and H. Also called directionally correct choices. b Three places were defined as egocentric choices: (A) where the subject was seated, (G) to the subject’s immediate right, and (E) to the subject’s immediate left. c Errors other than reversals and egocentric choices were unclassified.
correct choices and scores on the picture and place tasks, correlations and regression analyses were employed. The Pearson R correlation between the percentage of directionally correct choices and scores on the place task was .612 and for picture scores it was .402. The 2 indicated that 37% of the variance on the place task and 16% on the picture task were predictable from the percentage of directionally correct choices. The equation for the prediction of place task scores (from directionally correct choices) was Y’ = 4.47 + .042X and for the picture task was Y’ = 4.57 + .015x DISCUSSION In regard to the first question addressed in this study, sex differences, favoring males, were statistically significant both for choosing the picture and for choosing the place. As for the second question, correct response scores indicate that for both sexes the task of choosing the place was more difficult. We believe that this difficulty was based on the method of presentation in which subjects were asked to consider separately each of the 12 pictures, including the four mirror images, and to select the position from which one would see the perspective shown in each. Since subjects were not told that four of the pictures were of impossible views, only those whose understanding was most well established could be expected to assert positively that a given mirror image could not be seen
368
KELLY,
KELLY,
AND
JOHNSON
from any of the eight positions or was not even a possible view. It should be noted that Piaget and Inhelder similarly employed impossible views to refine their evaluation of perspective development (1956, pp. 240-241). In the other task, choosing the picture, subjects were shown a view position and asked to select the correct picture from the 12 displayed together. Subjects were not specifically directed to consider the reversals which were mixed in with the others and could be passed over. Thus, the procedure employed in choosing the place required a higher level of confidence than in choosing the picture. In planning this study we carefully considered whether subjects should be informed that the pictures included impossible views. We knew that without this information some subjects might choose reversals in spite of inner doubts. On the other hand, we did not want conditions that would ease the choices, thus weakening the testing of their understanding. Observations of subject behavior clearly showed that many were puzzled by the impossible views but apparently did not fully understand what was wrong. We believe failure to deal correctly with the reversals can most plausibly be interpreted as insufficient understanding of perspective. Those subjects who really understood perspective could have identified impossible views as such and 10 of our subjects did. Although Piaget and Inhelder viewed the two modes, choosing the place and choosing the picture, as equivalent, Laurendeau and Pinard (1970) concluded that choosing the picture was more difficult. We initially found that choosing the place was more difficult, both for the entire sample and for each sex considered separately. However, when the effects of the forced choice reversals were removed, a count of correct responses for males showed totals of 149 for choosing the picture and 166 for choosing the place. Total correct responses for females were 120 and 147, respectively. Considered in that manner, our findings paralleled those of Laurendeau and Pinard. A breakdown of errors made in choosing the picture shows that the majority of errors, 50% or greater for all but one position, involved selection of mirror images and/or egocentric view points. This was true for both male and female subjects although females made significantly more errors. When choosing the picture 75% of the girls made at least one reversal error compared to 54% of the boys. The largest numbers of errors made by both sexes in choosing the picture were for the positions which were the most remote from where they were seated (further supported by analysis of response latencies). That result was expected as those positions required the maximum coordination of perspective. The mirror images, or reversals, used in this study require further consideration. Males more often chose these positions which, though incorrect, would have been correct were it not for the mirror image factor. We
COORDINATION
OF PERSPECTIVE
369
have called those choices directionally correct, concluding that they were less random than other choices and therefore implied more understanding. Analysis of the four positions for which mirror images were presented indicated that for choosing the place, selection of those reversals (directionally correct errors) was the major source of error for the top half of the total sample (those making the fewest errors on the total test). Reversal errors were not as strongly evident for the bottom half (those making the most errors on the total test). For males 93% of all errors on the four mirror images were directionally correct errors for the top half of the sample as opposed to 78% for the bottom half. For the females the error percentages were 88% for the upper half of the sample and 60% for the lower half. These proportions lit our assumption that mirror image errors imply more understanding than random choices. In addition, the ? calculations indicated that 37% of the variance on the place task and 16% on the picture task were predictable from the percentage of mirror image choices. Our third research question was aimed at a possible connection between understanding of horizontality and coordination of perspective. As we explained in our introduction, right-left relationships must logically be oriented along a horizontal axis, which implies that understanding of horizontality may contribute to coordination of perspective. Based on this assumption, we had expected to find a relationship between scores on perspective tasks and scores on the horizontality test. As reported earlier, performance on the horizontality task accounted for 10% of the variance in responses on the place task and 24% on the picture task. Therefore, we continue to suspect that coordination of perspective may be more dependent on understanding of horizontality than implied by Piaget and Inhelder (1956). We also remain convinced that this line of reasoning may be fruitful for further investigation. Our fourth question aimed to compare the performance of the college females (teacher trainees) with that of sixth grade students. Since sex differences had been evident (Question One), we compared the college women’s performance separately with that of male and female sixth grade students. Although mean scores were higher for the college group in all instances, statistical significance was attained for the differences in only one of the two comparisons with the younger females (on both tasks) and for only one group of the younger males (on only one task). Since we had expected a clear superiority for the teacher trainees, their only marginally better performance was disappointing and difticult to interpret. We suspect that their relatively modest performance may derive from traditional female socialization, generally regarded as insufficiently focused on development of spatial concepts. Whatever the cause,
370
KELLY,
KELLY,
AND JOHNSON
these findings, if generalizable, suggest that female elementary teacher candidates may need more spatial development activities if they are to gain understanding suffkiently beyond that of the students they will be teaching. REFERENCES COIE, J., COSTANZO,P., & FARNILL, D. (1973). Specific transitions in the development of spatial perspective-taking ability. Developmental Psychology, 9, 167-177. Cox, M. (1977a). Perspective ability: The other observer in the task. Perceptual and Motor Skills, 44, 76.
Cox, M. (1977b). Perspective ability: Mode of presentation of another’s view. Perceptual and Motor Skills, 44, 214. Cox, M. (1978). Order of the acquisition of perspective-taking skills. Developmental Psychology, 14, 421422. EISER, C. (1977). Strategies children use to co-ordinate perspective as a function of task demand. British Journal of Educational Psychology, 47, 327-329. ELIOT, J., & DAYTON, C. (1976). Factors affecting accuracy of perception on a task requiring the ability to identify viewpoints. The Journal ofGenetic Psychology, 12&201-214. FISHBEIN, H., LEWIS, S., & KEIFFER, K. (1972). Children’s understanding of spatial relations: Coordination of perspectives. Developmental Psychology, 7, 21-33. FLAVELL, J., EVERETT,B., CROFT,K., & FLAVELL, E. (1981). Young children’s knowledge about visual perception: Further evidence for the level l-level 2 distinction. Developmental Psychology, 17, 99-103. FLAVELL, J., OMANSON,R., & LATHAM, C. (1978). Solving spatial perspective-taking problems by rule versus computation: A developmental study. Developmental Psychology, 14, 462-473.
GZESH, S., & SURBER,C. (1985). Visual perspective-taking skills in children. Child Development, 56, 1204-1213. JOHNSON,W., KELLY, G., & KELLY, J. (1980). Perception of verticality by boys and girls in grade 6. Perceptual and Motor Skills, 51, 355-358. KELLY, J., & KELLY, G. (1977). Perception of horizontality by male and female college students. Perceptual and Motor Skills, 44, 724-726. KELLY, J., & KELLY, G. (1978). Science activity centers: Basic concepts of the physical world. Science and Children, 16, 25-26. KURDEK, L., & RODGON,M. (1975). Perceptual, cognitive, and affective perspective taking in kindergarten through sixth-grade children. Developmental Psychology, 11, 643-650. LAURENDEAU, M., & PINARD, A. (1970). The development of the concept of space in the child. New York: International University Press. NIGL, A., & FISHBEIN, H. (1974). Perception and conception in coordination of perspectives. Developmental Psychology, 10, 858-866. NUFFIELD MATHEMATICSPROJECT(1972). Checking up ZZ. New York: Wiley. PIAGET, J., L INHELDER, B. (1956). The child’s conception ofspace. London: Routledge & Kegan Paul. SALATAS, H., & FLAVELL, J. (1976). Perspective taking: The development of two components of knowledge. Child Development, 47, 103-109.