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da Vinci's window facilitates drawings of total and partial occlusion in young children
JOURNAL
OF EXPERIMENTAL
CHILD
PSYCHOLOGY
4,
222-235 (1987)
da Vinci’s Window Facilitates Drawings of Total and Partial Occlusion in Young Children ANDREA L. RADKEY AND JAMES T. ENNS Dalhousie
University
When two or more objects are present in a scene, children 5 and 6 years of age rarely draw the scene such that one object totally or partially occludes another object. Instead they draw complete objects. The present study separated two components of drawing: perspective taking and graphic skill. Perspective taking was examined by comparing a free viewing condition with a restricted viewing condition in which a model could only be viewed through four apertures. Graphic skill was examined by comparing drawings requiring total occlusion with drawings requiring partial occlusion under both viewing conditions. Experiment 1 showed that 90% of 5- and 6-year-olds drew total occlusions under restricted viewing conditions but only 32% did so in the free viewing condition. Experiment 2 showed that drawings of partial occlusion were unaffected by viewing condition among 5-year-olds. but that restricted viewing increased the number of partial occlusions that 6-year-olds drew. Thus, failures of young children to draw occlusions have less to do with graphic skill than was previously thought. Instead, it is suggested that young children have a more general difficulty selecting one perSpeCtiVe and maintaining it over time. Q 1987 Academic Press, Inc.
Children 5 and 6 years of age rarely make drawings in which one object occludes the view of a second object. Instead, they tend to draw complete objects in the same horizontal or vertical plane. However, by the age of 12 years most children represent occlusions in their drawings along with other perspective cues such as changes in size with distance, variations of height in the plane with distance, and converging lines to represent parallel edges (Freeman, 1980; Willats, 1977; Winner, 1982). The developmental shift in the use of occlusion is generally believed to reflect age-related increases in the comprehension and production of specific graphic techniques such as “hidden-line elimination” (Freeman, 1980). The authors thank the children, parents, and teachers of the South Street, Brookside, and Central Schools of Glace Bay, Nova Scotia, for their enthusiastic participation in this study. This research was funded by a grant from the Natural Sciences and Engineering Research Council of Canada to the second author. Reprint requests may be addressed to J. T. Enns, Department of Psychology, University of British Columbia, 2136 West Mall, Vancouver, British Columbia, Canada V6T 1Y7. 222 0022~0965/87 $3.00 Copyright All rights
0 1987 by Academic Press, Inc. of reproduction in any form reserved
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In the present paper we argue that in addition to reflecting improvements in the comrehension and production of graphic techniques, developmental changes in drawings of occlusion reflect more general cognitive changes in perspective taking ability (Piaget & Inhelder, 1956). The distinction we are making between the graphic and perspective aspects of drawings of occlusion is supported by logical, empirical, and historical considerations. Consider first a logical analysis of the task of drawing a scene that contains partially occluded objects. In order to represent a scene accurately from a particular vantage point, an artist must not only be able to translate three-dimensional information onto a two-dimensional surface following pictorial conventions (graphic), but the artist must also be able to maintain a consistent vantage point for the duration of the drawing (perspective). Empirical support for this distinction comes from studies which report that children find drawings of model scenes (requiring graphic and perspective skills) to be more dimcult than drawings made from photographs of the same scenes (requiring only graphic skill) (e.g., Chen & Cook, 1984). Finally, the distinction is supported by the history of art in Western culture. Arnheim (1974) claims that central perspective was discovered only once in history and he attributes its discovery to painters and architects such as Alberti, Brunelleschi, and Piero della Francesca in the 15th century. These artists instructed their students to look at a scene through an aperture. The aperture guaranteed a consistent vantage point for a drawing that could then be made on a transparent surface interposed between the scene and the artist. One extension of this idea was Leonardo da Vinci’s camera obscura, or “window,” which became the intellectual precursor of modern photography. It is important to note that the development of central perspective did not include any fundamental changes in graphic techniques: lines were still used to represent edges; pigments were still used to evoke perceptions of color. The novelty of the discovery lay in the information that was preserved in the drawing concerning the artist’s specific vantage point or perspective. Previous studies of children’s drawings of occlusion have explored the graphic component in a number of ways. One hypothesis is that children do not comprehend that occlusion is a relevant cue to depth. Hagen (1976) argued against this idea by showing that most 3- to 7-year-old children could correctly match drawings of partially occluded objects to their corresponding three-dimensional models, even though very few of these children were able to draw partial occlusions to represent the models. A second suggestion is that children understand the meaning of occlusions in both scenes and drawings but have a graphic production deficit. They have not acquired the “hidden-line elimination” rule for drawing partially occluded objects (Freeman, 1980). This hypothesis has been challenged by studies showing that children continue to draw separate
224
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objects even when transparent objects are used so that the drawing task does not require hidden-line elimination (Light & Macintosh, 1980). A third suggestion is that children do not draw occlusions because they are more concerned with providing complete information about a scene than with representing the scene from a specific vantage point (Davis, 1985; Light & Humphreys, 1981; Light & Macintosh, 1980; Light & Nix, 1983; Light & Simmons, 1983). This view does not suggest that children have a comprehension or production deficit per se, but simply that they have a strong preference to represent information about the models’ contents rather than about their own vantage point. A fourth suggestion is that children fail to draw occlusions because the objects that children are asked to draw are not meaningful to them. In support of this hypothesis, Cox (1981) used a compelling story in conjunction with a toy model of a robber hiding behind a wall to elicit drawings of partial occlusion in a majority of 6-year-olds. However, when Light and Foot (1986) explored the generality of this finding they found that most 6-year-olds correctly drew partial occlusions in this situation even when the story was deleted and the robber was replaced with a column of blocks. Light and Foot (1986) concluded that children drew occlusions in this situation because their desire to provide complete information did not conflict with the task demand to preserve information about the vantage point. The common thread of these four accounts is an emphasis on children’s inability or unwillingness to represent graphically the three-dimensional relation of occlusion on a two-dimensional surface. The comprehension deficit view claims children do not understand the relevance of occlusion, the production deficit view says children do not have the necessary graphic skills in their repertoire, the complete information view claims that children come to the task with different goals than the experimenter, and the social relevance view suggests that the objects typically used as models are not meaningful to young children. What is absent in each of the foregoing accounts is the idea that drawing occlusions involves both graphic and perspective task components. The first purpose of the present study was to see whether variations in the difficulty of the perspective component would affect the drawing of occlusions by children. To understand how perspective and graphic components may have been confounded in previous studies, consider the study by Light and Simmons (1983) in which very few children 5 and 6 years of age drew occlusions. Children ostensibly viewed two balls on a table from our different seating positions before being seated at an “end view” where one ball totally occluded the other (with head movements children could still see portions of the farther ball). Children were then carefully instructed to draw the display so that a friend could determine the seating position from which they had drawn the picture. The main finding was that almost all children drew two separate balls. However,
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note that during the procedure the children walked around the model and viewed it from a large number of potential vantage points, including some from above the model. In the present study, a procedure similar to Light and Simmons’ (1983) was followed, but the viewpoints were restricted to four apertures corresponding to the four seating positions. The apertures blocked out all views except those given at the four seating positions and provided a consistent view over time from any given seating position. If part of children’s difhculty in drawing occlusions is the accurate selection and maintenance of a vantage point, then solving this perspective problem with a da Vinci-like window should elicit more occlusions than a free viewing condition. A second purpose of this study was to compare drawings of models containing totally occluded objects and models containing only partially occluded objects. Findings obtained for total occlusion have sometimes been assumed to generalize to partial occlusion, and vice versa (e.g., Light & Foot, 1986; Light & Simmons, 1983; but see also Davis, 1985), despite the fact that the two conditions differ in potentially important ways. In total occlusion, children are asked to delete an entire object (object elimination), whereas in partial occlusion only parts of an object are deleted (hidden-line elimination). Given that young children have difficulty analyzing an object into its component parts (e.g., Shepp & Schwartz, 1976; Smith & Kemler, 1977), partial occlusion may be the more difficult task. On the other hand, because the conflict between the bias to represent the full array and the task demand to draw from a “poor” vantage point is greater in total occlusion (one object will not even appear in the drawing), total occlusion may be the more difficult task (cf. Light & Nix, 1983; Light & Simmons, 1983). In the present study, drawings of total occlusion were examined in Experiment 1 and drawings of partial occlusion were examined in Experiment 2. EXPERIMENT
1: TOTAL OCCLUSION
The first experiment used a procedure similar to Light and Simmons’ (Experiment 1, 1983) control condition for the free viewing condition. In the restricted viewing condition a large box with four peepholes was used to cover the model. Method Subjects. Forty kindergarten and first-grade children (17 m,ale) aged 5:4-6:lO years (mean = 6:l) participated as subjects in the drawing task. The children attended public schools in Glace Bay, Nova Scotia. They were assigned to one of the two viewing conditions matched for age. Stimuli and apparatus. Figure 1 is a schematic drawing of the apparatus. The model consisted of one red and one green Styrofoam ball, each 10 cm in diameter. The balls were positioned 4 mm apart on a platform
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RADKEYANDENNS
D
A FIG. I. Overhead schematic of the apparatus, showing the positions of the green (G) and red (R) balls and the four viewing positons (A, B, C. D).
11 cm in height, which rested on a table 60 cm in height. A cardboard box 62 cm long x 41 cm wide x 33 cm high covered the model in the restricted viewing condition. Positioned centrally on each side of the box was a l-cm peephole (labeled A, B, C, and D in Fig. 1). through which subjects could inspect the model along its horizontal axis. Through the two end views (A, C) subjects could see only one ball; through the two side views (B, D) both balls could be seen side by side. A flashlight illuminated the display through an opening in the top of the box. In the free viewing condition, the cardboard box covering the model was omitted. Shadows of the occluded ball could be seen from the end views in both conditions. Subjects were provided with a square blank sheet of white paper and an assortment of felt-tipped markers that included the colors red and green. Procedure
Each subject was tested individually in a small room. Upon entering the room, subjects were asked to sit at each position (peephole) in turn from A to D. At each place they were asked to describe what could be seen and to identify the color(s) of the ball(s). All of the children correctly reported seeing “two balls” from the side views. Most children reported seeing “one ball” from the end views. The few children who responded “two balls” at an end view changed their response to “one ball” when the question was repeated with more emphasis on the word “see.” Color identification was accurate in all children. Subjects were then seated at position A and given the paper and colored pens. Instructions were to “make the best drawing of the model that you can so that someone else can figure out where you were sitting (or ‘which peephole you were looking through’) when you drew the picture.” There was no limit on
OCCLUSION
IN CHILDREN’S TABLE
CATEGORIES OF DRAWINGS VIEWING CONDITIONS
DRAWINGS
227
1 MADE UNDER THE IN EXPERIMENT 1
Two
Viewing condition Drawings
Restricted
Free
Horizontal Vertical Occlusion
2 0 19
12 I 6
Total
21
19
Note. Each subject contributed
one drawing.
viewing time in both conditions and the model remained in view throughout the drawing task. If the subject asked a question about what should be drawn, the original instructions were repeated. After completing the drawing, subjects were asked how many balls were on the table (in the box). All subjects responded with “two balls.” Results and Discussion The children’s drawings fell into three categories: horizontal (two full circles side by side), vertical (one full circle above another circle), and occlusion (one full green circle). Drawings of partial occlusion did not occur and the correctly colored pens were used by all children. Table 1 shows the number of drawings in each category in the two viewing conditions. There were reliably more occlusions in the restricted viewing condition than in the free viewing condition (90% vs 32%), x2(2) = 14.81, p < .OOl. Sex differences were not reliable in either of the viewing conditions and were not signiticant overall (p > . 10). The high percentage of occlusions in the restricted viewing condition suggests that the absence of occlusions in the free viewing condition does not reflect a comprehension or production deficiency (cf. Freeman, 1980; Hagen, 1976). It is also an important demonstration that 5- and 6-year-olds are willing, at least under some circumstances, to make view-specific drawings from a vantage point that eliminates important array information (cf. Light & Humphreys, 1981). Most importantly, this finding suggests that the failure of young children to draw occlusions does not reflect a graphic skill deficiency for total occlusion. Rather, it is consistent with the view that young children have difficulty with the perspective component of drawing occlusions. One alternative explanation that deserves consideration is that children in the restricted viewing condition did not understand that each peephole provided a glimpse of the same model. Perhaps they considered the apparatus to be a “magic box” that contained four unrelated scenes.
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RADKEY
AND
ENNS
We think this possibility is unlikely for two reasons. First, many children strained (without success) to catch a glimpse of the occluded ball when they inspected the two end views, indicating that they expected the hidden ball to be there. Second, other children asked whether they could draw the model from a side view rather than an end view, suggesting that they understood the task demand for view specificity, but were still concerned that they represent as much of the array as possible. Yet these children drew total occlusions when asked to draw from the end view. EXPERIMENT
2: PARTIAL OCCLUSION
The second experiment examined drawings made from a vantage point that showed a partially occluded object. The experiment followed the procedure of Experiment 1, with the exception that children were asked to draw the model from all four viewing positions. This change increased the amount of data gathered from a single subject and permitted an examination of intrasubject reliability. Method
Sixty-one children in kindergarten and first grade (35 male) aged 5: l-6: 11 years (mean = 6:2) participated as subjects in Experiment 2. As in Experiment 1, the children were assigned to one of two viewing conditions matched for age. The results showed that younger children made drawings that were reliably different from older children in this age range. Thus, the children in each viewing condition were divided further into two equal groups on the basis of a median age split. The younger group included children 5:1-6:3 years (mean = 5:9), and the older group included children aged 6:3-6:11 years (mean = 6:7). All children attended public school in Glace Bay, Nova Scotia, and had not participated in Experiment 1. Stimuli and apparatus. The same apparatus used in Experiment 1 was used here, with the exception that the balls were moved with respect to one another so that the nearer ball occluded approximately one-half of the farther ball when viewed from the two end positions (A and C in Fig. 1). The side views (B and D in Fig. 1) showed the two balls separated by a gap of 6 cm. Procedure. Two changes were made to the procedure used in Experiment 1. First, all children drew a picture from each of the four viewing positions, and second, the order in which the four views were seen and drawn by the subject was counterbalanced to control for possible order effects. All children correctly reported the number and colors of balls from each position. When asked whether they could see “all or only part” of each ball, almost all children responded correctly. Those who reported two Subjects.
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Horizonla’ 0 0 0 0 Vertical
Separated Occlusion
Partial
Partial
0’
Occlusion CD
FIG. 2. Examples of drawings in each of the categories in Experiment 2.
whole balls from an end view were among the children who made horizontal drawings instead of partial occlusions (see Results). Results and Discussion Figure 2 shows an example of each drawing category in Experiment 2. As in the first experiment, some children made horizontal and vertical drawings. The category labeled separated partial occlusion was necessary because there was a substantial number of drawings that seemed to have all the components of a drawing of partial occlusion, except that the partially occluded ball was separated from the occluding ball. Finally, a partial occlusion represented the correct drawing from the two end views. The two drawings made from the end views by each chlid were grouped together, as were the two drawings from the side views. In the older group, the two drawings obtained from each child for each of these views were in complete agreement. Two children in the younger group split their responses for the end views (a child in the restricted viewing condition made both a horizontal and a vertical drawing, and one in the free viewing condition made a horizontal and a separated occlusion drawing), and one younger child split his responses for the side views in the free viewing condition (a horizontal and a vertical drawing). There were no drawings of total occlusion (or single balls) and the drawings from the side views were almost perfect (with the exception of the one younger child mentioned above). Table 2 shows the number of drawings in each of the categories in the two viewing conditions. Since the identical pattern of results was
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RADKEYANDENNS TABLE
CATEGORIES
2
OF DRAWINGS MADE UNDER THE Two VIEWING CONDITIONSIN GROUPEDBY TYPE OF VIEW AND MEAN AGE (YEARS: MONTHS)
EXPERIMENT
2
Viewing condition Restricted End (A, C) Age Drawings
5:9
Free Side (B, D) Age
End (A, C) Age
611
5:9
6:l
9
4 2
32 0
32 0
4
10
0
0
5:9
Side 03, 0 Age
611
5:9
6:l
11
12
29
28
6 3
6 0
I 0
0 0
Horizontal Vertical Separated partial occlusion Partial occlusion
15
4
16
0
0
10
10
Total
32
32
32
32
30
28
0 30
0 28
Note. Each subject contributed four drawings.
obtained when occlusions were treated as one category or as two, only the analyses based on both categories of occlusion are reported. There were marginally more drawings of occlusion in the restricted viewing condition than in the free viewing condition overall (53% vs 40%), x’(3) = 7.28, p < .lO, and older children drew significantly more occlusions than younger children overall (60% vs 34%), x2(2) = 8.61, p < .05. Examined separately, the younger children did not show a reliable difference between the two viewing conditions (restricted: 25% vs free: 43%), x*(3) = 3.87, whereas the older chldren drew reliably more occlusions in the restricted than in the free viewing condition (81% vs 36%), x2(3) = 17.17, p < .OOl. A reliable sex difference was found among the older children in the restricted viewing condition. A majority of the separated partial occlusion drawings were produced by boys (80%), whereas a majority of the partial occlusions were drawn by girls (71%), x2(3) = 8.05, p < .05. All other sex differences were not reliable (p > .lO>. Thus, restricted viewing facilitated drawings of partial occlusion in this experiment just as it had increased drawings of total occlusion in Experiment 1. However, the results differed from the findings for total occlusion in several important respects. First, the 6-year-olds were able to take advantage of the perspective given by the restricted viewing condition, whereas the 5-year-olds did not benefit from this procedure. Second, the difference between restricted and free viewing on partial occlusions was not as large, even for the 6-year-olds (81% vs 36%), as it was for total occlusions among 5- and 6-year-olds combined (90% vs 32%). Third, the presence of an intermediate category of drawings (separated partial oc-
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elusions) suggests that the partial occlusion task was graphically more difficult than total occlusion. Taken together, these results suggest that 6year-olds have difficulty with perspective in drawings of partial occlusion (as they do for total occlusion), but in addition, they have difficulty representing a partial occlusion graphically. GENERAL DISCUSSION This study was motivated by the observation that drawing from a specific vantage point can be separated into two components. The first component, perspective, refers to the use of a single vantage point that is maintained for the duration of the drawing. The second component, graphic, refers to the conventions for translating three-dimensional information onto a two-dimensional surface. Although previous studies of young children’s drawings have explored graphic skill, they have failed to consider that children may have a general difficulty with perspective taking. The main finding of the present study was that 5- and 6year-old children made more drawings of total occlusion, and 6-year-olds made more drawings of partial occlusion, when perspective was selected and maintained for them with aperture viewing. This suggests that previous studies of drawings in young children, all of which have used free viewing, may have underestimated the graphic skills of children. It also suggests that studies designed primarily to study graphic skills of children can control for differences in perspective taking by using a restricted viewing procedure. The second important finding of this study was that it was more difficult for children to draw models with partial occlusions that those with total occlusions. This was shown in two ways. First, although most of the 5and 6-year-olds drew total occlusions under restricted viewing conditions, only a majority of the 6-year-olds drew partial occlusions under similar conditions. Drawings of partial occlusion by 5-year-olds did not vary for restricted and free viewing conditions. Second, there were a substantial number of children even at 6 years who had not mastered all aspects of partial occlusion (see the Separated partial occlusions in Table 2). This finding suggests that caution should be used in making inferences about partial occlusion on the basis of drawing studies designed to elicit total occlusion (cf. Light & Simmons, 1983) or even transparency (cf. Light & Macintosh, 1980). Consider the implications of these findings for the two previous studies which successfully elicited drawings of partial occlusion in 6-year-old children. Cox (1981) used a story and a model of a robber hiding behind a wall as stimulus materials, whereas Light and Foot (1986) simply used a column of blocks positioned behind a wall. The present results concur with Light and Foot’s (1986) conclusion that socially relevant materials and a compelling story are not necessary conditions to produce drawings
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RADKEYANDENNS
of occlusion, However, the present findings also suggest that none of the stimulus variables manipulated by Light and Foot (1986) are necessary conditions for eliciting drawings of occlusion in this age range. In fact, the restricted viewing condition elicited drawings of occlusion with stimulus materials that previous studies had shown to work against drawings of occlusion: the model objects did not have viewing orientations that were more preferred or canonical than others (cf. Light & Foot, 1986), several colored pens were used for the drawings instead of a single pen (cf. Light & Foot, 1986), and drawings were made from the least preferred vantage point-an end view (cf. Light & Nix, 1983). One hypothesis suggested by the present results is that the procedures of Cox (1981) and Light and Foot (1986) were successful in eliciting drawing of occlusion not because their models allowed all objects to be represented without violating view specificity, but because their models helped the children to select and maintain the correct vantage point for their drawings. We suspect that the views given by different vantage points for objects with canonical orientations are perceptually more dissimilar than the views given by different vantage points of objects without a canonical orientation. To understand this intuitively, consider that walking around a toy man and a thin wall will provide a range of views that are more dissimilar from one another than walking around two balls. In short, the two objects with canonical orientations help the viewer to select the precise vantage point from which the scene is being viewed. The main theoretical implication of the present finding is that developmental changes in children’s drawings of occlusion reflect general cognitive changes in perspective taking ability. The literature on the development of perspective taking shows that young children have a great deal of difficulty distinguishing one point of view from other points of view at a number of information-processing levels. For example, at the level of visual shape recognition, young children tend not to distinguish shapes that are rotations or reflections of one another (Rude1 & Teuber, 1963). This is also seen in beginning readers, who find letters that are similar under rotation and reflection (e.g., p, b, d, q) to be the most confusable (Davidson, 1935). Viewing perspective simply does not appear to be an important consideration for shape identification by these children. Perceptual tasks which require mental rotation and/or the prediction of scenes from imagined vantage points are also notoriously difficult for children younger than 9 years of age (Huttenlocher & Presson, 1973; Piaget & Inhelder, 1956). Because the point of view that young children tend to choose in these tasks is their own (i.e., their errors are biased in favor of a subjective vantage point), they have been called “egocentric” (Piaget & Inhelder, 1956). Finally, failures to ackowledge alternative perspectives are seen in young children’s attempts to communicate in social settings. Descriptions of objects and requests for information from
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other people tend to be personal and idiosyncratic rather than conventional (Krauss & Glucksberg, 1969). The present findings suggest that children’s drawings are affected by the same insensitivity to differences in vantage point that is observed in their visual, perceptual, and social behavior. Yet, it is important to note that children’s “failure” to draw occlusions is not the result of an egocentric bias. Their drawings (horizontals and verticals) seem to reflect the failure to draw from any one vantage point in particular. Perhaps these drawings since they are reminiscent of the mixed should be labeled “acentric,” perspective drawings that predate the emergence of central perspective in art history (Arnheim, 1974). It is worth noting that the acquisition of perspective does not appear to be an all or nothing achievement, either in previous perspective taking research or in the present study of drawing. By decreasing the complexity of the task investigators have shown that rudimentary aspects of perspective taking can be observed in very young children. For example, Bornstein, Gross, and Wolf (1978) found that even 3- and 4-month-old infants were able to discriminate some rotations and reflections of shapes (45” rotations, vertical reflections) with a habituation-dishabituation procedure. However, there were still some transformations that infants were unable to discriminate (horizontal or mirror-image reflections). Others have examined perceptual perspective taking and shown that 3- and 4-year-olds are sensitive to differences in vantage point when the task response is linguistic rather than pictorial (Ives, 1980), when the model array contains distinct and familiar objects (Borke, 1975; Rosser, 1983), and when the model array is actually rotated rather than only imagined to rotate (Borke, 1975; Rosser, 1983). In the social-linguistic realm, Shatz and Gelman (1973) reported that children as young as 4 years adjusted the complexity of their speech (vocabulary and grammar) according to the age of the listener in a naturalistic setting. In the present study there was also evidence that perspective taking ability improves gradually. This was shown by the large difference in the frequency of total versus partial occlusions among Syear-olds. It seems that the more difficult graphic aspects of partial occlusion (hiddenline elimination) served to hide the perspective competence that these children were able to demonstrate under the less complex graphic conditions of total occlusion. Although the present results clearly demonstrate an improved ability in young children to draw occlusions when views of a model are restricted to a few apertures, the results do not specify which features of the procedure were critical for this finding. Candidates include the absence of overhead views of the model, monocular views of the model, the number of different views, and the particular vantage point chosen. Future studies will need to systematically investigate these features. We are
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hopeful that restricted viewing procedures will assist our understanding of the ontogenesis of drawing, analogous to the way in which da Vinci’s window facilitated the historical development of drawing. REFERENCES Amheim, R. (1974). Art and visual perception. Berkeley, CA: Univ. of California Press. Borke, H. (1975). Piaget’s mountains revisited: Changes in egocentric landscape. Developmental Psychology, 11, 240-243. Bornstein, M. H., Gross, C. G., & Wolf, J. Z. (1978). Perceptual similarity of mirror images in infancy. Cognition, 6, 89-l 16. Chen, M. J., & Cook, M. (1984). Representational drawings of solid objects by young children. Perception, 13, 377-385. COX, M. V. (1981). One thing behind another: Problems of representation in children’s drawing. Educational Psychology, 1, 275-287. Davidson, H. P. (1935). A study of the confusing letters b, d. p, and a. Journal of Genetic Psychology,
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Davis, A. (1985). Conflict between canonicality and array-specificity in young children’s drawings. Brifish Journal of Developmental Psychology, 3, 363-372. Freeman. N. (1980). Strategies of representation in young children. Orlando/London: Academic Press. Hagen, M. (1976). Development of ability to perceive and produce pictorial depth cue of overlapping. Perceptual Motor Skills, 42, 1007-1014. Huttenlocher, J., & Presson, C. C. (1973). Mental rotation and the perspective problem. Cognitive
Psychology,
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Ives, W. (1980). Preschool children’s ability to coordinate spatial perspectives through language and pictures. Child Development, 51, 1303-1306. Krauss, R. H., & Glucksberg, S. (1969). The development of communication. Child Development,
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Light, P. H., & Foot, T. (1986). Partial occlusion in young chlidren’s drawings. Journal of Experimental
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Psychology,
41, 38-48.
Light, P. H., & Humphreys, J. (1981). Internal spatial relationships in young children’s drawings. Journal of Experimental Child Psychology, 31, 521-530. Light, P. H., & Macintosh. E. (1980). Depth relationships in young children’s drawings. Journal
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Psychology,
30, 79-87.
Light, P. H., & Nix, C. (1983). “Own view” versus “good view” in a perspective-taking task. Child Developmenf, 54, 480-483. Light, P. H., & Simmons, B. (1983). The effects of a communication task upon the representation of depth relationships in young children’s drawings. Journal of Experimental Child Psychology, 35, 81-92. Piaget, J.. & Inhelder, B. (1956). The child’s conception of space. London: Routledge & Kegan Paul. Rosser, R. A. (1983). The emergence of spatial perspective taking: An information-processing alternative to egocentrism. Child Developmenf, 54, 660-668. Rudel, R. G., & Teuber. H. L. (1963). Discrimination of direction of line in children. Journal
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Smith, L. B.. & Kemler. D. G. (1977). Developmental trends in free classification: Evidence
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for a new conceptualization of perceptual development. Journal of Experimental Child Psychology, 24, 279-298. Willats, J. (1977). How children learn to represent three-dimensional space in drawings. In G. Butterworth (Ed.), The child’s representation ofthe world. New York: Plenum. Winner, E. (1982). Invented worlds. Cambridge, MA: Harvard Univ. Press. RECEIVED:
August 27, 1986;
REVISED:
February 9, 1987.
OF EXPERIMENTAL
CHILD
PSYCHOLOGY
4,
222-235 (1987)
da Vinci’s Window Facilitates Drawings of Total and Partial Occlusion in Young Children ANDREA L. RADKEY AND JAMES T. ENNS Dalhousie
University
When two or more objects are present in a scene, children 5 and 6 years of age rarely draw the scene such that one object totally or partially occludes another object. Instead they draw complete objects. The present study separated two components of drawing: perspective taking and graphic skill. Perspective taking was examined by comparing a free viewing condition with a restricted viewing condition in which a model could only be viewed through four apertures. Graphic skill was examined by comparing drawings requiring total occlusion with drawings requiring partial occlusion under both viewing conditions. Experiment 1 showed that 90% of 5- and 6-year-olds drew total occlusions under restricted viewing conditions but only 32% did so in the free viewing condition. Experiment 2 showed that drawings of partial occlusion were unaffected by viewing condition among 5-year-olds. but that restricted viewing increased the number of partial occlusions that 6-year-olds drew. Thus, failures of young children to draw occlusions have less to do with graphic skill than was previously thought. Instead, it is suggested that young children have a more general difficulty selecting one perSpeCtiVe and maintaining it over time. Q 1987 Academic Press, Inc.
Children 5 and 6 years of age rarely make drawings in which one object occludes the view of a second object. Instead, they tend to draw complete objects in the same horizontal or vertical plane. However, by the age of 12 years most children represent occlusions in their drawings along with other perspective cues such as changes in size with distance, variations of height in the plane with distance, and converging lines to represent parallel edges (Freeman, 1980; Willats, 1977; Winner, 1982). The developmental shift in the use of occlusion is generally believed to reflect age-related increases in the comprehension and production of specific graphic techniques such as “hidden-line elimination” (Freeman, 1980). The authors thank the children, parents, and teachers of the South Street, Brookside, and Central Schools of Glace Bay, Nova Scotia, for their enthusiastic participation in this study. This research was funded by a grant from the Natural Sciences and Engineering Research Council of Canada to the second author. Reprint requests may be addressed to J. T. Enns, Department of Psychology, University of British Columbia, 2136 West Mall, Vancouver, British Columbia, Canada V6T 1Y7. 222 0022~0965/87 $3.00 Copyright All rights
0 1987 by Academic Press, Inc. of reproduction in any form reserved
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In the present paper we argue that in addition to reflecting improvements in the comrehension and production of graphic techniques, developmental changes in drawings of occlusion reflect more general cognitive changes in perspective taking ability (Piaget & Inhelder, 1956). The distinction we are making between the graphic and perspective aspects of drawings of occlusion is supported by logical, empirical, and historical considerations. Consider first a logical analysis of the task of drawing a scene that contains partially occluded objects. In order to represent a scene accurately from a particular vantage point, an artist must not only be able to translate three-dimensional information onto a two-dimensional surface following pictorial conventions (graphic), but the artist must also be able to maintain a consistent vantage point for the duration of the drawing (perspective). Empirical support for this distinction comes from studies which report that children find drawings of model scenes (requiring graphic and perspective skills) to be more dimcult than drawings made from photographs of the same scenes (requiring only graphic skill) (e.g., Chen & Cook, 1984). Finally, the distinction is supported by the history of art in Western culture. Arnheim (1974) claims that central perspective was discovered only once in history and he attributes its discovery to painters and architects such as Alberti, Brunelleschi, and Piero della Francesca in the 15th century. These artists instructed their students to look at a scene through an aperture. The aperture guaranteed a consistent vantage point for a drawing that could then be made on a transparent surface interposed between the scene and the artist. One extension of this idea was Leonardo da Vinci’s camera obscura, or “window,” which became the intellectual precursor of modern photography. It is important to note that the development of central perspective did not include any fundamental changes in graphic techniques: lines were still used to represent edges; pigments were still used to evoke perceptions of color. The novelty of the discovery lay in the information that was preserved in the drawing concerning the artist’s specific vantage point or perspective. Previous studies of children’s drawings of occlusion have explored the graphic component in a number of ways. One hypothesis is that children do not comprehend that occlusion is a relevant cue to depth. Hagen (1976) argued against this idea by showing that most 3- to 7-year-old children could correctly match drawings of partially occluded objects to their corresponding three-dimensional models, even though very few of these children were able to draw partial occlusions to represent the models. A second suggestion is that children understand the meaning of occlusions in both scenes and drawings but have a graphic production deficit. They have not acquired the “hidden-line elimination” rule for drawing partially occluded objects (Freeman, 1980). This hypothesis has been challenged by studies showing that children continue to draw separate
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objects even when transparent objects are used so that the drawing task does not require hidden-line elimination (Light & Macintosh, 1980). A third suggestion is that children do not draw occlusions because they are more concerned with providing complete information about a scene than with representing the scene from a specific vantage point (Davis, 1985; Light & Humphreys, 1981; Light & Macintosh, 1980; Light & Nix, 1983; Light & Simmons, 1983). This view does not suggest that children have a comprehension or production deficit per se, but simply that they have a strong preference to represent information about the models’ contents rather than about their own vantage point. A fourth suggestion is that children fail to draw occlusions because the objects that children are asked to draw are not meaningful to them. In support of this hypothesis, Cox (1981) used a compelling story in conjunction with a toy model of a robber hiding behind a wall to elicit drawings of partial occlusion in a majority of 6-year-olds. However, when Light and Foot (1986) explored the generality of this finding they found that most 6-year-olds correctly drew partial occlusions in this situation even when the story was deleted and the robber was replaced with a column of blocks. Light and Foot (1986) concluded that children drew occlusions in this situation because their desire to provide complete information did not conflict with the task demand to preserve information about the vantage point. The common thread of these four accounts is an emphasis on children’s inability or unwillingness to represent graphically the three-dimensional relation of occlusion on a two-dimensional surface. The comprehension deficit view claims children do not understand the relevance of occlusion, the production deficit view says children do not have the necessary graphic skills in their repertoire, the complete information view claims that children come to the task with different goals than the experimenter, and the social relevance view suggests that the objects typically used as models are not meaningful to young children. What is absent in each of the foregoing accounts is the idea that drawing occlusions involves both graphic and perspective task components. The first purpose of the present study was to see whether variations in the difficulty of the perspective component would affect the drawing of occlusions by children. To understand how perspective and graphic components may have been confounded in previous studies, consider the study by Light and Simmons (1983) in which very few children 5 and 6 years of age drew occlusions. Children ostensibly viewed two balls on a table from our different seating positions before being seated at an “end view” where one ball totally occluded the other (with head movements children could still see portions of the farther ball). Children were then carefully instructed to draw the display so that a friend could determine the seating position from which they had drawn the picture. The main finding was that almost all children drew two separate balls. However,
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note that during the procedure the children walked around the model and viewed it from a large number of potential vantage points, including some from above the model. In the present study, a procedure similar to Light and Simmons’ (1983) was followed, but the viewpoints were restricted to four apertures corresponding to the four seating positions. The apertures blocked out all views except those given at the four seating positions and provided a consistent view over time from any given seating position. If part of children’s difhculty in drawing occlusions is the accurate selection and maintenance of a vantage point, then solving this perspective problem with a da Vinci-like window should elicit more occlusions than a free viewing condition. A second purpose of this study was to compare drawings of models containing totally occluded objects and models containing only partially occluded objects. Findings obtained for total occlusion have sometimes been assumed to generalize to partial occlusion, and vice versa (e.g., Light & Foot, 1986; Light & Simmons, 1983; but see also Davis, 1985), despite the fact that the two conditions differ in potentially important ways. In total occlusion, children are asked to delete an entire object (object elimination), whereas in partial occlusion only parts of an object are deleted (hidden-line elimination). Given that young children have difficulty analyzing an object into its component parts (e.g., Shepp & Schwartz, 1976; Smith & Kemler, 1977), partial occlusion may be the more difficult task. On the other hand, because the conflict between the bias to represent the full array and the task demand to draw from a “poor” vantage point is greater in total occlusion (one object will not even appear in the drawing), total occlusion may be the more difficult task (cf. Light & Nix, 1983; Light & Simmons, 1983). In the present study, drawings of total occlusion were examined in Experiment 1 and drawings of partial occlusion were examined in Experiment 2. EXPERIMENT
1: TOTAL OCCLUSION
The first experiment used a procedure similar to Light and Simmons’ (Experiment 1, 1983) control condition for the free viewing condition. In the restricted viewing condition a large box with four peepholes was used to cover the model. Method Subjects. Forty kindergarten and first-grade children (17 m,ale) aged 5:4-6:lO years (mean = 6:l) participated as subjects in the drawing task. The children attended public schools in Glace Bay, Nova Scotia. They were assigned to one of the two viewing conditions matched for age. Stimuli and apparatus. Figure 1 is a schematic drawing of the apparatus. The model consisted of one red and one green Styrofoam ball, each 10 cm in diameter. The balls were positioned 4 mm apart on a platform
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D
A FIG. I. Overhead schematic of the apparatus, showing the positions of the green (G) and red (R) balls and the four viewing positons (A, B, C. D).
11 cm in height, which rested on a table 60 cm in height. A cardboard box 62 cm long x 41 cm wide x 33 cm high covered the model in the restricted viewing condition. Positioned centrally on each side of the box was a l-cm peephole (labeled A, B, C, and D in Fig. 1). through which subjects could inspect the model along its horizontal axis. Through the two end views (A, C) subjects could see only one ball; through the two side views (B, D) both balls could be seen side by side. A flashlight illuminated the display through an opening in the top of the box. In the free viewing condition, the cardboard box covering the model was omitted. Shadows of the occluded ball could be seen from the end views in both conditions. Subjects were provided with a square blank sheet of white paper and an assortment of felt-tipped markers that included the colors red and green. Procedure
Each subject was tested individually in a small room. Upon entering the room, subjects were asked to sit at each position (peephole) in turn from A to D. At each place they were asked to describe what could be seen and to identify the color(s) of the ball(s). All of the children correctly reported seeing “two balls” from the side views. Most children reported seeing “one ball” from the end views. The few children who responded “two balls” at an end view changed their response to “one ball” when the question was repeated with more emphasis on the word “see.” Color identification was accurate in all children. Subjects were then seated at position A and given the paper and colored pens. Instructions were to “make the best drawing of the model that you can so that someone else can figure out where you were sitting (or ‘which peephole you were looking through’) when you drew the picture.” There was no limit on
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CATEGORIES OF DRAWINGS VIEWING CONDITIONS
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227
1 MADE UNDER THE IN EXPERIMENT 1
Two
Viewing condition Drawings
Restricted
Free
Horizontal Vertical Occlusion
2 0 19
12 I 6
Total
21
19
Note. Each subject contributed
one drawing.
viewing time in both conditions and the model remained in view throughout the drawing task. If the subject asked a question about what should be drawn, the original instructions were repeated. After completing the drawing, subjects were asked how many balls were on the table (in the box). All subjects responded with “two balls.” Results and Discussion The children’s drawings fell into three categories: horizontal (two full circles side by side), vertical (one full circle above another circle), and occlusion (one full green circle). Drawings of partial occlusion did not occur and the correctly colored pens were used by all children. Table 1 shows the number of drawings in each category in the two viewing conditions. There were reliably more occlusions in the restricted viewing condition than in the free viewing condition (90% vs 32%), x2(2) = 14.81, p < .OOl. Sex differences were not reliable in either of the viewing conditions and were not signiticant overall (p > . 10). The high percentage of occlusions in the restricted viewing condition suggests that the absence of occlusions in the free viewing condition does not reflect a comprehension or production deficiency (cf. Freeman, 1980; Hagen, 1976). It is also an important demonstration that 5- and 6-year-olds are willing, at least under some circumstances, to make view-specific drawings from a vantage point that eliminates important array information (cf. Light & Humphreys, 1981). Most importantly, this finding suggests that the failure of young children to draw occlusions does not reflect a graphic skill deficiency for total occlusion. Rather, it is consistent with the view that young children have difficulty with the perspective component of drawing occlusions. One alternative explanation that deserves consideration is that children in the restricted viewing condition did not understand that each peephole provided a glimpse of the same model. Perhaps they considered the apparatus to be a “magic box” that contained four unrelated scenes.
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We think this possibility is unlikely for two reasons. First, many children strained (without success) to catch a glimpse of the occluded ball when they inspected the two end views, indicating that they expected the hidden ball to be there. Second, other children asked whether they could draw the model from a side view rather than an end view, suggesting that they understood the task demand for view specificity, but were still concerned that they represent as much of the array as possible. Yet these children drew total occlusions when asked to draw from the end view. EXPERIMENT
2: PARTIAL OCCLUSION
The second experiment examined drawings made from a vantage point that showed a partially occluded object. The experiment followed the procedure of Experiment 1, with the exception that children were asked to draw the model from all four viewing positions. This change increased the amount of data gathered from a single subject and permitted an examination of intrasubject reliability. Method
Sixty-one children in kindergarten and first grade (35 male) aged 5: l-6: 11 years (mean = 6:2) participated as subjects in Experiment 2. As in Experiment 1, the children were assigned to one of two viewing conditions matched for age. The results showed that younger children made drawings that were reliably different from older children in this age range. Thus, the children in each viewing condition were divided further into two equal groups on the basis of a median age split. The younger group included children 5:1-6:3 years (mean = 5:9), and the older group included children aged 6:3-6:11 years (mean = 6:7). All children attended public school in Glace Bay, Nova Scotia, and had not participated in Experiment 1. Stimuli and apparatus. The same apparatus used in Experiment 1 was used here, with the exception that the balls were moved with respect to one another so that the nearer ball occluded approximately one-half of the farther ball when viewed from the two end positions (A and C in Fig. 1). The side views (B and D in Fig. 1) showed the two balls separated by a gap of 6 cm. Procedure. Two changes were made to the procedure used in Experiment 1. First, all children drew a picture from each of the four viewing positions, and second, the order in which the four views were seen and drawn by the subject was counterbalanced to control for possible order effects. All children correctly reported the number and colors of balls from each position. When asked whether they could see “all or only part” of each ball, almost all children responded correctly. Those who reported two Subjects.
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Horizonla’ 0 0 0 0 Vertical
Separated Occlusion
Partial
Partial
0’
Occlusion CD
FIG. 2. Examples of drawings in each of the categories in Experiment 2.
whole balls from an end view were among the children who made horizontal drawings instead of partial occlusions (see Results). Results and Discussion Figure 2 shows an example of each drawing category in Experiment 2. As in the first experiment, some children made horizontal and vertical drawings. The category labeled separated partial occlusion was necessary because there was a substantial number of drawings that seemed to have all the components of a drawing of partial occlusion, except that the partially occluded ball was separated from the occluding ball. Finally, a partial occlusion represented the correct drawing from the two end views. The two drawings made from the end views by each chlid were grouped together, as were the two drawings from the side views. In the older group, the two drawings obtained from each child for each of these views were in complete agreement. Two children in the younger group split their responses for the end views (a child in the restricted viewing condition made both a horizontal and a vertical drawing, and one in the free viewing condition made a horizontal and a separated occlusion drawing), and one younger child split his responses for the side views in the free viewing condition (a horizontal and a vertical drawing). There were no drawings of total occlusion (or single balls) and the drawings from the side views were almost perfect (with the exception of the one younger child mentioned above). Table 2 shows the number of drawings in each of the categories in the two viewing conditions. Since the identical pattern of results was
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CATEGORIES
2
OF DRAWINGS MADE UNDER THE Two VIEWING CONDITIONSIN GROUPEDBY TYPE OF VIEW AND MEAN AGE (YEARS: MONTHS)
EXPERIMENT
2
Viewing condition Restricted End (A, C) Age Drawings
5:9
Free Side (B, D) Age
End (A, C) Age
611
5:9
6:l
9
4 2
32 0
32 0
4
10
0
0
5:9
Side 03, 0 Age
611
5:9
6:l
11
12
29
28
6 3
6 0
I 0
0 0
Horizontal Vertical Separated partial occlusion Partial occlusion
15
4
16
0
0
10
10
Total
32
32
32
32
30
28
0 30
0 28
Note. Each subject contributed four drawings.
obtained when occlusions were treated as one category or as two, only the analyses based on both categories of occlusion are reported. There were marginally more drawings of occlusion in the restricted viewing condition than in the free viewing condition overall (53% vs 40%), x’(3) = 7.28, p < .lO, and older children drew significantly more occlusions than younger children overall (60% vs 34%), x2(2) = 8.61, p < .05. Examined separately, the younger children did not show a reliable difference between the two viewing conditions (restricted: 25% vs free: 43%), x*(3) = 3.87, whereas the older chldren drew reliably more occlusions in the restricted than in the free viewing condition (81% vs 36%), x2(3) = 17.17, p < .OOl. A reliable sex difference was found among the older children in the restricted viewing condition. A majority of the separated partial occlusion drawings were produced by boys (80%), whereas a majority of the partial occlusions were drawn by girls (71%), x2(3) = 8.05, p < .05. All other sex differences were not reliable (p > .lO>. Thus, restricted viewing facilitated drawings of partial occlusion in this experiment just as it had increased drawings of total occlusion in Experiment 1. However, the results differed from the findings for total occlusion in several important respects. First, the 6-year-olds were able to take advantage of the perspective given by the restricted viewing condition, whereas the 5-year-olds did not benefit from this procedure. Second, the difference between restricted and free viewing on partial occlusions was not as large, even for the 6-year-olds (81% vs 36%), as it was for total occlusions among 5- and 6-year-olds combined (90% vs 32%). Third, the presence of an intermediate category of drawings (separated partial oc-
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elusions) suggests that the partial occlusion task was graphically more difficult than total occlusion. Taken together, these results suggest that 6year-olds have difficulty with perspective in drawings of partial occlusion (as they do for total occlusion), but in addition, they have difficulty representing a partial occlusion graphically. GENERAL DISCUSSION This study was motivated by the observation that drawing from a specific vantage point can be separated into two components. The first component, perspective, refers to the use of a single vantage point that is maintained for the duration of the drawing. The second component, graphic, refers to the conventions for translating three-dimensional information onto a two-dimensional surface. Although previous studies of young children’s drawings have explored graphic skill, they have failed to consider that children may have a general difficulty with perspective taking. The main finding of the present study was that 5- and 6year-old children made more drawings of total occlusion, and 6-year-olds made more drawings of partial occlusion, when perspective was selected and maintained for them with aperture viewing. This suggests that previous studies of drawings in young children, all of which have used free viewing, may have underestimated the graphic skills of children. It also suggests that studies designed primarily to study graphic skills of children can control for differences in perspective taking by using a restricted viewing procedure. The second important finding of this study was that it was more difficult for children to draw models with partial occlusions that those with total occlusions. This was shown in two ways. First, although most of the 5and 6-year-olds drew total occlusions under restricted viewing conditions, only a majority of the 6-year-olds drew partial occlusions under similar conditions. Drawings of partial occlusion by 5-year-olds did not vary for restricted and free viewing conditions. Second, there were a substantial number of children even at 6 years who had not mastered all aspects of partial occlusion (see the Separated partial occlusions in Table 2). This finding suggests that caution should be used in making inferences about partial occlusion on the basis of drawing studies designed to elicit total occlusion (cf. Light & Simmons, 1983) or even transparency (cf. Light & Macintosh, 1980). Consider the implications of these findings for the two previous studies which successfully elicited drawings of partial occlusion in 6-year-old children. Cox (1981) used a story and a model of a robber hiding behind a wall as stimulus materials, whereas Light and Foot (1986) simply used a column of blocks positioned behind a wall. The present results concur with Light and Foot’s (1986) conclusion that socially relevant materials and a compelling story are not necessary conditions to produce drawings
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of occlusion, However, the present findings also suggest that none of the stimulus variables manipulated by Light and Foot (1986) are necessary conditions for eliciting drawings of occlusion in this age range. In fact, the restricted viewing condition elicited drawings of occlusion with stimulus materials that previous studies had shown to work against drawings of occlusion: the model objects did not have viewing orientations that were more preferred or canonical than others (cf. Light & Foot, 1986), several colored pens were used for the drawings instead of a single pen (cf. Light & Foot, 1986), and drawings were made from the least preferred vantage point-an end view (cf. Light & Nix, 1983). One hypothesis suggested by the present results is that the procedures of Cox (1981) and Light and Foot (1986) were successful in eliciting drawing of occlusion not because their models allowed all objects to be represented without violating view specificity, but because their models helped the children to select and maintain the correct vantage point for their drawings. We suspect that the views given by different vantage points for objects with canonical orientations are perceptually more dissimilar than the views given by different vantage points of objects without a canonical orientation. To understand this intuitively, consider that walking around a toy man and a thin wall will provide a range of views that are more dissimilar from one another than walking around two balls. In short, the two objects with canonical orientations help the viewer to select the precise vantage point from which the scene is being viewed. The main theoretical implication of the present finding is that developmental changes in children’s drawings of occlusion reflect general cognitive changes in perspective taking ability. The literature on the development of perspective taking shows that young children have a great deal of difficulty distinguishing one point of view from other points of view at a number of information-processing levels. For example, at the level of visual shape recognition, young children tend not to distinguish shapes that are rotations or reflections of one another (Rude1 & Teuber, 1963). This is also seen in beginning readers, who find letters that are similar under rotation and reflection (e.g., p, b, d, q) to be the most confusable (Davidson, 1935). Viewing perspective simply does not appear to be an important consideration for shape identification by these children. Perceptual tasks which require mental rotation and/or the prediction of scenes from imagined vantage points are also notoriously difficult for children younger than 9 years of age (Huttenlocher & Presson, 1973; Piaget & Inhelder, 1956). Because the point of view that young children tend to choose in these tasks is their own (i.e., their errors are biased in favor of a subjective vantage point), they have been called “egocentric” (Piaget & Inhelder, 1956). Finally, failures to ackowledge alternative perspectives are seen in young children’s attempts to communicate in social settings. Descriptions of objects and requests for information from
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other people tend to be personal and idiosyncratic rather than conventional (Krauss & Glucksberg, 1969). The present findings suggest that children’s drawings are affected by the same insensitivity to differences in vantage point that is observed in their visual, perceptual, and social behavior. Yet, it is important to note that children’s “failure” to draw occlusions is not the result of an egocentric bias. Their drawings (horizontals and verticals) seem to reflect the failure to draw from any one vantage point in particular. Perhaps these drawings since they are reminiscent of the mixed should be labeled “acentric,” perspective drawings that predate the emergence of central perspective in art history (Arnheim, 1974). It is worth noting that the acquisition of perspective does not appear to be an all or nothing achievement, either in previous perspective taking research or in the present study of drawing. By decreasing the complexity of the task investigators have shown that rudimentary aspects of perspective taking can be observed in very young children. For example, Bornstein, Gross, and Wolf (1978) found that even 3- and 4-month-old infants were able to discriminate some rotations and reflections of shapes (45” rotations, vertical reflections) with a habituation-dishabituation procedure. However, there were still some transformations that infants were unable to discriminate (horizontal or mirror-image reflections). Others have examined perceptual perspective taking and shown that 3- and 4-year-olds are sensitive to differences in vantage point when the task response is linguistic rather than pictorial (Ives, 1980), when the model array contains distinct and familiar objects (Borke, 1975; Rosser, 1983), and when the model array is actually rotated rather than only imagined to rotate (Borke, 1975; Rosser, 1983). In the social-linguistic realm, Shatz and Gelman (1973) reported that children as young as 4 years adjusted the complexity of their speech (vocabulary and grammar) according to the age of the listener in a naturalistic setting. In the present study there was also evidence that perspective taking ability improves gradually. This was shown by the large difference in the frequency of total versus partial occlusions among Syear-olds. It seems that the more difficult graphic aspects of partial occlusion (hiddenline elimination) served to hide the perspective competence that these children were able to demonstrate under the less complex graphic conditions of total occlusion. Although the present results clearly demonstrate an improved ability in young children to draw occlusions when views of a model are restricted to a few apertures, the results do not specify which features of the procedure were critical for this finding. Candidates include the absence of overhead views of the model, monocular views of the model, the number of different views, and the particular vantage point chosen. Future studies will need to systematically investigate these features. We are
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hopeful that restricted viewing procedures will assist our understanding of the ontogenesis of drawing, analogous to the way in which da Vinci’s window facilitated the historical development of drawing. REFERENCES Amheim, R. (1974). Art and visual perception. Berkeley, CA: Univ. of California Press. Borke, H. (1975). Piaget’s mountains revisited: Changes in egocentric landscape. Developmental Psychology, 11, 240-243. Bornstein, M. H., Gross, C. G., & Wolf, J. Z. (1978). Perceptual similarity of mirror images in infancy. Cognition, 6, 89-l 16. Chen, M. J., & Cook, M. (1984). Representational drawings of solid objects by young children. Perception, 13, 377-385. COX, M. V. (1981). One thing behind another: Problems of representation in children’s drawing. Educational Psychology, 1, 275-287. Davidson, H. P. (1935). A study of the confusing letters b, d. p, and a. Journal of Genetic Psychology,
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Smith, L. B.. & Kemler. D. G. (1977). Developmental trends in free classification: Evidence
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for a new conceptualization of perceptual development. Journal of Experimental Child Psychology, 24, 279-298. Willats, J. (1977). How children learn to represent three-dimensional space in drawings. In G. Butterworth (Ed.), The child’s representation ofthe world. New York: Plenum. Winner, E. (1982). Invented worlds. Cambridge, MA: Harvard Univ. Press. RECEIVED:
August 27, 1986;
REVISED:
February 9, 1987.