Perceptual and Motor Skills, 1979. 48, 223-227. @ Perceptual and Motor Skills 1979



SUSAN G. NUMMEDAL California State University. Long Beach

Summary.-50 boys and 50 girls, from Grades K through 4, were presented with 180" perspective-taking tasks that varied arrays in terms of the number of front-back and left-right orientation reversals and left-right position reversals. Results confirmed existing evidence that left-right orientation reversals are more difficult than front-back orientation reversals in arrays of one object. However, with arrays of two objects, left-right orientation reversals appear easier than front-back orientation reversals, apparently because of the relationship between the objects.

The ability of a child to understand how objects in space appear to another person (spatial perspective taking) has been assessed by a variety of tasks, beginning with Piaget's classic "three mountains" problem (Piaget & Inhelder, 1956). In this task, the child views a model of three mountains and is asked to identify, usually by selecting a picture, the view of the mountains seen by a person facing the model from a different position. Subsequent s ~ d i e shave used variations of the three-mountain model (Laurendeau & Pinard, 1970; Borke, 1975 ) or quite different stimuli such as colored b l d s (Flavell, Botkin, Fry, Wright, & Jarvis, 1968), toys (Masangay, et al., 1974), and miniature scenes (Fishbein, Lewis. & Keiffer, 1972). Young children have difficulty in taking the perspective of another person, a fact which Piaget attributes to the child's egocentrism, that is, the tendency to assume that others see what he sees. Results generally have shown that while perspective-taking ability increases with age, the particuh stimuli used greatly affect performance. With sufficiently simple tasks, such as a sheet with a different picture on each side, children as young as three years of age can identify what another person sees (Flavell, et al., 1968). However, with complex tasks, such as the three mountains or other three-dimensional arrays, accurate perspective taking does not occur until age 9 or 10 (Piaget & Inhelder, 1956). At least two components are involved in the task (possibly more; see Flavell, 1974) : the child must realize that another person sees things differently; and he must figure out exactly how objects appear from another perspective. The present study deals with the latter component, i.e., the way children figure out how objects appear to another person. When a person moves around a group of 3-dimensional objects, a number of changes in their appearance take place; the objects may change in shape, become hidden or reappear, or change their relative position. In attempting to



take another person's perspective, a child may be able to recognize some of these changes but make errors by failing to infer or coordinate others. Coie, Costanzo, and Farnill (1973) identified four types of errors (interposition, aspect, distance, and left-right reversal) made by children in attempting to select pictures of objects as they appear to others. However, a problem with this and similar studies is that the errors cannot- be examined independently, since several errors may occur in any one task. Coie, et al. (1975) dealt with this problem by weighting children's responses in terms of the predominant error. Their results support the position of Piaget and others (Cox, 1978) that the understanding of left-right reversals is the most difficult for children and the last to be mastered. The purpose of the present study was to isolate certain components of a perspective-taking task and study the levels of difficulty for each component both separately and in combination. T o do this one must limit and control the number and types of changes in appearance which must be considered in the task. In the present study, this was done, first, by using either completely symmetrical stimuli or stimuli wich left-right symmetry. Second, it was decided to examine the child's understanding of the appearance of objects seen from opposite him ( 180") and not consider views seen from the left or right ( 9 0 ' ) or intermediate angles. Finally, to avoid confounding, only certain types of changes in perspective were examined. Problems of interposition and distance, which appear to be the easiest to master (Coie, et nl., 1973), were not included. The focus of the study was the more difficult front-back and left-right reversals. A distinction was needed between two types of left-right reversals: (1) leftright orientation reversals ( a single figure which faces right to the subject appears to face left when viewed from opposite) and ( 2 ) left-right position reversals (two figures side by side reverse their relative position when viewed from opposite). These two types of reversals, together with front-back orientation reversals ( a figure seen face forward by the subject shows a back when viewed from opposite), comprised the three types of problems presented to children, either alone or in controlled combinations, in this study. Based on work of Piaget and Inhelder (1956) and others (Coie, et al., 1973), it was predicted that left-right reversals would be more difficult than front-back reversals and that task difficulty would increase as number of reversals increased.

METHOD Snbjects There were 100 children in the study, 10 boys and 10 girls each, from Grades K through 4 of a private middle-class school wich a racially-mixed population. Materials Two types of stimuli were used: (1) three completely symmetrical toys,



2 to 5 in. high, which appear the same from all four sides ( a round table, a symmetrical tree, and a house wich fonr identical sides) ; and ( 2 ) three human figures with distinct faces and thus obvious front-back differences, but with left-right symmetry (a man and a woman, standing, about 4 in. high, and a seated baby). These six stimuli were used singly or in pairs to create 21 arrays. Each array represented a problem in which the child had to identify the view seen from opposite. The arrays were grouped into seven tasks wich three sub-tasks each. The tasks varied systematically in terms of type and number of reversals that the child would have to make in identifying the view from opposite. The sub-tasks for each task were identical in terms of type and number of reversals, but varied in the specific stimuli used. The tasks were ordered in terms of number of reversals (see Table 1).


1 2


4 5 6 7



Reversals A B

Example of Stimulus Array Man, front view Lady, side view

Tree beside table B,C Lady (side view) facing table A.C Man (front view) beside table B.B.C Man and lady (side views) back to back A,B.C Man (side view) facing lady (back view) front-back orientation; B = left-right orientation; C = left-right position. C

For each array, four black-and-white line drawings ( o n 3- by 5-in. cards) were drawn to show four different perspectives: the subject's view of the array, the view from opposite. and two alternative views. The alternative views included some impossible views, in which one reversal was made and another was not.

Procedure All children were seen individually in a small room in the school. The child was seated at a table with the experimenter opposite him. For each task, the experimenter laid out the four drawings for that array in a rack that held them upright and then set the stimuli in position on top of a small box, just below the subject's eye level. Before beginning the scored trials, each child was given three training casks, in which he was asked to select the picture that showed his own view, then the picture that showed the experimenter's view; he was then required to walk around the table to check and if necessary to correct his selection to be sure that he understood what was required. For each scored task, the child was asked: "Which is the picture that shows what I see when I look at the (man)?" The child was given the seven tasks in fixed





order. Children were scored for passing a task if they selected the correct drawing for at least two of the three sub-tasks.

RESULTSAND DISCUSSION The percentage of children within each grade level and in the total sample passing each task is presented in Table 2. For each task, performance was related to grade level; that is, the proportion of children passing increased from Grades K to 4. I n addition, within each grade level and for the total sample, Task 1 was the easiest and Task 7 the most difficult. The difficulty level of the intervening tasks was not related to the number of reversals alone. Performance on tasks with one reversal (1, 2, and 3) supported clearly the existing evidence that a left-right reversal is more difficult than a front-back reversal; the percentage of children passing the front-back problem (Task 1) was consistently greater than that passing the two left-right reversal problems ( 2 and 3 ) . In addition, the left-right position reversal (Task 3) was consistently easier than the left-right orientation reversal (Task 2 ) . This pattern of difficulty for the three tasks held within each gsade level in the sample, although the actual percentages varied somewhat. Performance on Tasks 4 and 5, involving two reversals each, showed quite different results. TABLE 2


K 1

2 3 4 Total




Tasks 4




70 90 95 95 95 89

10 10 35 GO 70 37

15 20 40 75 85 47

10 15 40 70 75 42

15 10 20 45 60 30

10 10 35 70 75 40

5 10 25 35 40 23

Both tasks used similar stimuli and involved a left-right position reversal; the only difference was that Task 4 had a left-right orientation reversal whereas Task 5 had a front-back orientation reversal. If front-back reversals are easier, Task 5 should have been easier than 4. In fact, the opposite was the case. For Grades 1-4, Task 4 was passed by a greater percentage of subjects than 5. The kindergarten subjects did not follow this pattern, although it should be noted that two subjects passed Task 4 and three passed Task 5. A McNemar test of the relationship for the total sample between passing Tasks 4 and 5 was significant (x2= 5.50, @ < .02). A similar relationship was found for tasks involving three reversals ( 6 and 7 ) . Two of the three reversals were identical for these tasks. The tasks differed only in that Task G had a left-right orientation reversal, whereas Task 7



had a front-back orientation reversal. Again, Task 7 was far more difficult than Task 6. This pattern held at each grade level with the exception of Grade 1, in which equal proportions of subjects passed. A McNemar test of the relationship between passing Tasks G and 7 was significant (x2 = 13.47, p < .01). Thus, as with the relationship between Tasks 4 and 5, when reversals occur in combination, tasks with the left-right orientation reversal appear to be mastered prior to tasks with the front-back reversal. In summary, for spatial perspective-taking tasks involving a single reversal (Tasks 1, 2, and 3 ) , this study supports findings of other research that a frontback reversal is easier for a child to master than a left-right reversal. However, when two or more reversals are involved, the relative difficulty levels are changed. When a front-back reversal is combined with a left-right reversal in a perspective-taking task (Task 5 ) , the problem appears more difficult for children than a problem involving two left-right reversals (Task 4 ) . From inspection of the tasks in such cases, it appears that a new factor is introduced, namely, the relationship between the elements. For example, in Task 4, the lady is "facing" the table. In spite of the reversals that must be made, the relationship of "facing" defines the position of the lady relative to the table and remains constant. In contrast, in Task 5, the man is "beside" the table, a more vague relationship which determines position much less stringently. Thus, left-right orientation reversals pose a difficult problem when presented alone; but when elements are combined, problems involving left-right orientation reversals appear easier than those involving front-back orientation reversals, possibly because of the relationship between the elements. REFERENCES

BORKE,H. Piaget's mountains revisited: changes in the egocentric landscape. Develop-

mental Psychology, 1975, 11, 240-243. & FARNHILL,D. Spatial perspective taking ability. Deve~opmentalPsychology. 1973. 9, 167-177. Cox, M. V. Order of acquisition of perspective-taking skills. Developmental Psychology, 1978, 14, 421-422. FISHBHIN, H. D., LEWIS,S., & KEIFPER.K. Children's understanding of spacial relations. Developmentd Psychology, 1972, 7, 21-33. FLAVELL, J. H. The development of inferences about others. In T . Mischel (Ed.), Understanding other persons. Totowa, N . J . : Rowan & Littlefield, 1974. Pp. 66116. FLAVELL, J. H.. BOTKIN, P. T., FRY,C. L.. WRIGHT. J. W.. & JARVIS, P. E. The development of vole-taking and communication skills irz children. N e w York: Wiley. 1968. LAURENDEAU, M., & PINARD.A. Development of the concept o f space in the child. N e w York: International Universities Press. 1970. MASANGAY, Z., MCCLUSKEY, K.. MCINNRE,C., SIMS-KNIGHT.J.. VAUGHN,B., ~ l FLAVELL. J. The early development of inferences about the visual percepts of others. Child Development, 1974. 45. 357-366. PIAGET.J., & INHELDER. B. The child's conceptiorz of space. London: Rourledge ~ l Kegan Paul, 1956.

Cora, 1. D., COSTANZO, P. R.,

Accepted December 27, 1978.



Effects of left-right orientation and position reversals on spatial perspective taking in young children.

Perceptual and Motor Skills, 1979. 48, 223-227. @ Perceptual and Motor Skills 1979 EFFECTS OF LEFT-RIGHT ORIENTATION AND POSITION REVERSALS O N SPATI...
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