Cognitive Development, 5,395-404 (1990)

Systematic Errors in Children’s Drawings

Elizabeth F. Pemberton University of Iowa

Prior literature has been unclear concerning developmental effects on the numbers and kinds of systematic errors children make when copying simple figures. The copied drawings of 89 children between the ages of 4 and 10 were examined for the extent to which they contained three types of systematic errors: simplifications, schematizations, and orientation biases. Overall, systematic errors decreased in frequency with increasing age, with some subtypes declining steadily and others persisting even until ages 8 to 10. Suggestions for why systematic drawing errors occur and possible ways for overcoming them are presented.

The errors a child makes can reveal much about the concepts governing the behavior of that child. These mistakes are often not due merely to a lack of knowledge; they can reveal a sophisticated use of a rule system. A rule is a consistently applied principle that cuts across many tasks and situations. Rules are used here to categorize the systematic errors that children make in drawing.

Several investigators have described the schematic nature of young children’s drawings at certain periods in development. Schaefer-Simmem (1948/ 1970) and Wilson and Wilson (1982) both describe several principles they consider to be inherent in children’s drawing: (a) The simplicity principle leads the child to draw an object in an undifferentiated manner with as few lines as possible, (b) the perpendicular principle directs the drawer to orient objects 90” to the baseline, often resulting in a vertical or horizontal bias (Freeman, 1983; Ibbotson & Bryant, 1976; Liben, 1981; Pemer, Kohlmann, & Wimmer, 1984), and (c) sche- matization biases guide the child toward applying the same schematic configura- tions in drawing different objects or figures. For example, the schema for a human is often carried over to children’s first drawings of four-legged animals. These principles earn the status of rules when they are applied repeatedly in a

Preparation of this article was supported in part by NICHHD grant #HD07255 to the University of Kansas. The data were collected as part of a doctoral dissertation conducted at the Pennsylvania State University under the direction of Keith Nelson.

The author gratefully acknowledges Kathleen Fuller and Corinne Lewkowicz for their help in coding the data, and David Thissen and Susan Kemper for their comments on earlier drafts of this manuscript.

Correspondence and requests for reprints should be sent to Elizabeth F. Pemberton Department of Psychology, University of Iowa, Iowa City, IA 52242.

Manuscript received August 7, 1989; manuscript accepted December 15, 1989 395

396 Elizabeth F. Pemberton

consistent, predictable manner (Goodnow & Levine, 1973). Applying these gen- eral rules in copying tasks can lead to copied products that are deviant from the original in a specific, predictable manner: simpler, more schematic, or biased in orientation.

Pew studies have systematically explored the rule-governed errors made in copying a variety of shapes, with two notable exceptions. Tada and Stiles-Davis (1989) examined the errors of 3-5-year-old children in copying simple geometric shapes. These authors examined the effects of task, context, and personal style on drawing errors. Although their data allowed for them, analyses of specific systematic errors, such as orientation biases, were not made.

A study by Graham, Berman, and Emhart (1960) investigated the “primitive organization” of copied shapes first labeled as such by Werner (1957; see also Piaget & Inhelder, 1948/ 1956). The term “primitive organization” is similar to what in this study is called a “systematic error.” Both are terms used to describe children’s reorganization of stimuli-to-be-copied in certain ways. One manner of reorganization is closure; for example, a stimulus such as an incomplete circle with a small gap is copied as a complete, whole circle. Two other methods of reorganization are to simplify the original, and to make it symmetrical (cf. Bremner, 1985, and Pigram, 1984 for studies on symmetry errors). These “prim- itivizations” follow the principles of perception laid out by early Gestalt psychol- ogists (e.g., closure, simplicity, and symmetry). One of the hypotheses of Graham et al. (1960) was that as age increases, figures should be copied in more nonprimitive (visually realistic) than primitive ways (they examined copies made by 2X-5-year-olds). This prediction was supported by Graham’s data on symme- try; it was not, however, consistently supported by the data on closure and simplification.

The current study expands on the earlier work of Graham et al. (1960) and Tada and Stiles-Davis (1989) by looking at a wider age range, and a greater variety of geometric shapes to copy. One purpose was to develop a categorization system that could account for a variety of specific errors made in response to copying assorted figures. In categorizing drawing errors in a systematic way, we hoped to infer something about the implicit rules that guide children in drawing, particularly when drawing “errors.” An example of a drawing rule that leads to errors is: “In copying a complex geometrical figure, use as few lines as necessary to represent the figure.” This rule would fit under the category of simplification. In using this rule, a young child might draw a stop sign as a diamond or square shape.

We hypothesized that most systematic or rule-governed drawing errors would decrease in frequency with increasing age. While some particular systematic errors might gradually decline with increasing age, others may remain influential throughout development from ages 4 to 10 years. The purpose of the study was not only to document and categorize drawing rules, but to help us understand more about “lawful” (rule-governed) behavior of children in general.

Drawing Errors 397

Subjects

METHOD

The copied drawings of 89 children were examined for the presence of systemat- ic errors. Because past studies (Goodnow, 1977; Pemberton, 1985; Van Som- mers, 1984) have shown that certain drawing rules are affected by handedness, only right-handed children were observed. The subjects were twenty-four 4- and 5-year-olds (M = 5;6), thirty-six 6 and 7-year-olds (M = 6; 1 l), and twenty-nine 8 to IO-year-olds (M = 9;4). Roughly equal numbers of girls and boys made up each group. The children were pupils from three different rural Pennsylvania schools.

Materials The stimuli used to measure children’s drawing errors were 12 line drawings on separate 4 X 6 in laminated cards. These stimuli (shown in Figure 1) were similar to those used in studies by Graham et al. (1960) and Tada and Stiles- Davis (1989). Several of the 12 stimulus figures used here (#l, #2, and #3) were identical to the ones used by Graham et al. and/or Tada and Stiles-Davis. The rest of the current stimuli were more complex composites of stimuli used by these authors. This was done in part to ensure the attention of the older subjects in this study. The variety of stimuli also allowed for greater generalizations about the drawing errors that young children produce.

Procedures All stimulus figures were presented in a scrambled order to each child, who was seated at a low table to the right of the experimenter. The children copied 12

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4 8 12

Figure 1. 12 figures used in the copying task.

398 Elizabeth F. Pemberton

individual line drawings presented one at a time directly above their own 4 X 6 in paper. Both the model to copy and the child’s paper to draw on were fixed vertically on the table in front of the child. The instructions were to “try to make a drawing that looks just like the one shown” using a #2 pencil.

Scoring Three independent raters, blind to the drawers’ identities, scored the drawings: Two were graduate students in psychology; the third was a graphic artist. Each drawing was placed into one of the following three categories:

1. A good drawing was an accurate copy, allowing for minor alterations due to underdeveloped motor control.

2. A sysremaric error was either simplified, schematized, or biased to a vertical or horizontal orientation. A systematic error was termed simplified if parts of the figure were omitted, or if fewer lines than necessary were used to complete the figure. A schematized drawing error was one in which it appeared that a child used a stored schema, a common and repeated manner of drawing an object, in drawing from the model figure (Amheim, 1974; Piaget & Inhelder, 1948/1956). An orienrution bias resulted when a child imposed vertical or horizontal placement rules in drawing figures or figure components which actually were oriented in some way other than vertically or horizontally.

3. A drawing that was neither good nor a systematic error was categorized by the label other. (See Figure 2 for examples of each type of drawing.)

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Figure 2. Examples of good drawings, systematic errors, and other errors.

Drawing Errors 399

The categories were scored as though they were mutually exclusive. The raters made decisions based on how to best categorize each drawing when more than one category could apply. Interrater reliability was established by having two of the three raters independently score 15% of the data. The percentage of agreement for classifying the drawings into the three major categories-good, systematic error, and other-was 87% (interrater reliability ranged from 67% for figure #12 to 100% for figures #6 and #lo, shown in Figure 1). Systematic errors were classified into three subtypes: simplifications, schematizations, and orientation biases. The interrater agreement for classifying these specific system- atic errors was 94%.

RESULTS

Children’s copies of the 12 stimuli shown in Figure 1 were analyzed using multivariate analyses of variance (Bock, 1975). Natural log transformations of the frequencies of (a) good drawings and (b) systematic errors (with .5 added) were analyzed; the log transformation generally increases the homogeneity of the variances across conditions. Separate analyses were conducted on good copies and those that were specific systematic errors. The category “other” (13% of all errors) will receive little discussion, since the topic of interest is the developmen- tal progression of particular systematic errors in drawing.

As predicted, age had a significant effect on the type of drawing made, multivariate F(4,170) = 5.20, p < .OOl. As Table 1 shows, the number of good drawings steadily increased with age (from M = 4.0 out of a possible 12 for the youngest group to M = 8.6 for the oldest group), while the number of systematic errors decreased (from M = 5.3 to M = 2.9). All but three of the 89 children studied produced at least one systematic error.

A separate multivariate analysis of variance was conducted to examine the effect of age on the specific subtypes of systematic errors made. Again, log transformations of the data were analyzed. The response variables this time were (a) simplification, (b) schematization, and (c) orientation bias.

Table 1. Mean Number of Copies (out of 12 Possible) that were Systematic Errors, Other Errors, and Good Copies

Age (years)

4 & 5 (n = 24) 6 Kc 7 (n = 36) 8-10 (n = 291

Systematic Errors

5.3 3.6 2.9

Type of Copy produced Other

Errors Good

2.8 3.9 1.5 6.9 0.5 8.6

Total

12.0 12.0 12.0

Overall M (n = 89)

3.9 1.6 6.5 12.0

400 Elizabeth F. Pemberton

As Figure 3 shows, simplification and schematization errors steadily decreased in number with increasing age, while the number of orientation-bias errors did not significantly change, indicating an interaction between age and error type, multi- variate F(6,168) = 4.37, p < .OOl. The univariate F tests on simplification, F(2,86) = 7.4, p < .OOl; and schematization, F(2,86) = 7.0, p < .Ol, were significant. The number of simplification errors produced steadily decreased from M = 1.4 for the youngest group, to M = 0.6 for the middle group, to M = 0.2 for the oldest group. Likewise, schematization errors decreased from M = 1.2 (youngest) to 0.9 (middle) to 0.6 (oldest). The number of orientation biases remained relatively high across all ages studied, with means of 2.7, 2.1, and 2.1 for the three age groups. The slight decrease in the number of orientation-bias errors with increasing age was not significant, F(2,86) = 1.6, p = .21. Most orientation-bias errors were made in response to copying Figures #1 1 and #12; orientation-bias responses were also common for Figures #6, #8, and #lo. Thus, even 8 to IO-year-olds showed a tendency to err systematically, for example, by aligning dots vertically (Figure 1 l), and by orienting figures so that they rest on a horizontal plane (figures 8 and 12).

3-

2.6 -

2-

5

g 1.6-

ii

l-

0.6-

0 ’ 1 I I 4&S 6&7 a-10

AGE IN YEARS Figure 3. Frequency of children’s orientation biases, schematizations, and simplifi- cations.

Drawing Errors 401

DISCUSSION

In summary, the number of good drawings produced increased with increasing age, while in general the number of systematic errors produced decreased. Rule- governed or systematic errors accounted for a larger percentage of total errors than the category “other” for all age groups. The developmental picture present- ed is not a simple one of children drawing better with increasing age. Of the specific systematic errors produced, simplifications and schematizations steadily decreased in frequency with increasing age, but orientation-bias errors remained relatively frequent at all ages studied.

Systematic errors imply that rules have been acquired by the child who then applies them to situations in which they are not appropriate. Similar implications have been made in the area of language. A child who erroneously produces the plural forms “foots” and “gooses” is assumed to be using an implicit rule: “Add -s to the end of all nouns to make them plural” (Bowerman, 1983; Kuczaj, 1982; Mapstone & Harris, 1985; Maratsos & Chalkley, 1980). Across both domains, systematic errors decrease with age, although this decrease may not be linear and may never reach an endpoint of zero (Bowerman, 1982; Goodnow, 1977).

The results of this study firmly support the prediction that some systematic drawing rules steadily decrease in frequency with age (e.g., the schematization rule states that “When copying a geometric or abstract shape, use your stored schema for drawing that shape.“). Forty-four percent of the 4 and 5-year-olds’ copies of the 12 figures included systematic errors as compared to 30% of the 6 and 7-year-olds’, and 24% of the 8 to IO-year-olds’. These observations suggest that younger children are more likely to overapply systematic rules in their drawings than are older children, even though lo-year-olds still overapply some drawing rules.

More specifically, this study shows a steady decrease from age 4 to 10 years in the number of both schematizations and simplifications produced. These results are in line with those of Graham et al. (1960) who found that certain “primi- tivization” errors decreased in frequency with age (in particular, from age 4 to 5 years), and those of Tada and Stiles-Davis (1989) who found that drawing errors decreased in frequency from age 3 to 5. On the other hand, orientation biases only moderately (and nonsignificantly) decreased from age 4 to 10. All of the children studied showed a strong tendency to reorient some relatively complex line drawings to a vertical or horizontal baseline. It is only by looking at a variety of geometric figures varying in complexity, and at a wide span of ages, that one can make these claims about the persistence of certain rule-governed errors. It has even been suggested that orientation-bias errors persist into adolescence or adulthood for some people (Duthie, 1985; Liben, 1981; Schaefer-Simmem, 1948/ 1970).

The current study shows that many drawing errors that children from age 4 to 10 make are systematic. The causes proposed for why a child makes errors in a

402 Elizabeth F. Pemberion

systematic way, and why some persist for so long, are tentative. Some re- searchers suggest that inherent biases lead children (and untrained adults) to produce drawing errors (Schaeffer-Simmem, 1948/ 1970; Wilson & Wilson, 1982) resulting in the types of errors described here. Others propose that the bias is due to production constraints created by such things as the angle of the page or the horizontal baseline of the drawing surface (e.g., Freeman, 1980), which would result in orientation errors, such as drawing an x-shape as a +-shape. Some investigators suggest that perceptual errors may underlie errors in produc- tion (e.g., Bremner, 1985; Gibson, 1969; Pigram, 1984), although this idea was not supported by preliminary data on perception collected in conjunction with the data reported here (cf. Pemberton, 1985). Still others suggest that errors result when certain motoric and social factors interact to influence the types of draw- ings or copies made (Van Sommers, 1984). And finally, some suggest that an individual’s strategy, determined by an interaction of context, task, and style effects, can lead to drawing errors, such as leaving out lines and simplifying the drawing (Tada & Stiles-Davis, 1989).

It is likely that the above factors-inherent tendencies, production biases (including context and task effects), perceptual, motoric, and social constraints, and individual style-all play some role in influencing children’s drawing behav- ior. It is unlikely that any one factor alone can be taken as the cause for children’s produced systematic errors. Perhaps when many of these factors work together (as they do when copying objects oriented at a 45” angle on a rectangular-shaped piece of paper, placed on a horizontal table top), certain errors occur. Orienta- tion-bias errors may persist because they are overdetermined by several internal and external factors.

Another possible influence on the drawing errors described here is the limited exposure children have to graphic models in their environment. Unlike children who are exposed from an early age to a rich linguistic environment, young drawers in our culture rarely receive opportunities to observe skilled artists modeling specific techniques or producing figures from start to finish. Instead, graphic input is more often in the form of static, completed figures. In rare, controlled instances where the process of drawing sequences has been modeled, preschool children have shown rapid gains in their ability to produce complex figures (Pemberton & Nelson, 1987; Rand, 1973).

A limited graphic “vocabulary” may lead to errors, much as a limited lexicon can lead to verbal regularization errors (Goodnow, 1977). Errors reflecting rule use in drawing may be similar to errors of regularization in language, perhaps sharing a common conceptual basis. Further experimentation across domains, along the lines of the research being conducted by Case and his colleagues (e.g., Case, Marini, McKeough, Dennis, & Goldberg, 1986), needs to be done before claims about a common developmental mechanism between domains can be supported.

Perhaps as children learn a larger repertoire of planning and drawing strat-

Drawing Errors 403

egies, their use of relatively simple rules leading to systematic errors will de- cline. It may be that children of age 8 to 10 years (or older) who are still produc- ing systematic errors lack opportunities to observe and learn from skilled artists who create varied figures. Controlled manipulations of the drawing environment of children who persist in making systematic errors are needed to explore these possibilities. Such studies deserve the attention of art educators interested in facilitating drawing development, and psychologists interested in uncovering the sources of such rule-governed errors in general.

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