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DOCUMENT RESUME IR 017 667 ED 391 514 Delicio, Gail C. AUTHOR The Power of the Center Revisited. TITLE PUB DATE [95) 15p.; In: Eyes on the Future: Converging Images, NOTE Ideas, and Instruction. Selected Readings from the Annual Conference of the International Visual Literacy Association (27th, Chicago, IL, October 18-22, 1995); see IR 017 629. Research/Technical (143) Reports PUB TYPE Speeches/Conference Papers (150) MF01/PC01 Plus Postage. EDRS PRICE *Behavior Theories; *Children; *Cognitive DESCRIPTORS Measurement; Elementary Education; Elementary School Students; *Perceptual Development; *Visual Perception Arnheim (Rudolf); Cartesian Coordinates; Centering; IDENTIFIERS *Childrens Drawings ABSTRACT Rudolf Arnheim, former Harvard Professor of the Psychology of Art, developed a theory that the perception of the structure of things in the world is based on simultaneous use of two the cosmic system of concentricity and (2) the primary systems: (1) parochial system of the Cartesian grid. The Cartesin grid imposes order, while the concentric system provides a midpoint or balancing center for everything that is seen. This paper provides experimental evidence in support of Arnheim's theory by demonstrating that a drawing's balancing center is measurable and that the measurement can be reliable and valid when compared with human judgment. The measure is then applied to test the hypothesis that the child's placement of a halancing center changes predictably with age. Thirty drawings, each representing one of 13 hypothesized balancing center locations, were collected from students in grades K-6; location of the balancing center was determined by computer and teacher judgments using (x,y) coordinates on a grid. Computer generated estimates of balancing point position on the vertical and horizontal axis of picture space displayed a very strong relationship to subjective teacher judgments of balancing centers. A set of 140 drawings from students in grades K-6 was also examined to determine whether the balancing centers changed predictably with age. Results suggest that children in grades K-6 show a strong bias for balancing centers situated near the geometric center of picture space. Five figures depict study results. An appendix shows the 30 drawings used in the balpncing center analyses. (Contains 14 references.) (AEF) *********************************************************************** Reproductions supplied by EDRS are the bk;t that can be made from the original document. *********************************************************************** U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement EDUCATIONAL ItSOURCES INFORMATION "PERMISSION TO REPRODUCE THIS CENTER (ERIC) MATERIAL HAS BEEN GRANTED BY O This document has been reproduced as received from the person or organization originating it Alice D. Walker O Minor changes have been made to improve reproduction quality. Points of view or opinions stated in this document do not necessarily represent TO THE EDUCATIONAL RESOURCES official OERI position or policy INFORMATION CENTER (ERIC)" The Power of the Center Revisited Gail C. Delicio C1) shapes, like those in free-form drawings, Introduction are nc in the geometric middle, and occur Rudolf Arnheim, former Harvard in a place where compositional pushes and Pmfessor of the Psychology of Art, searched pulls are perceived as counterbalanced. The for and truly believed that he found a key to "balancing center" is the point at which spatial organization in the arts. His premise visual forces converge to hold a composi- is that our perception of the structure of tion in equilibrium. things in the world is based on two primary A balancing center generally is not systems, (a) the cosmic system of concen- made explicitly visible, but rather is graphi- tricity, and (b) the parochial system of the cally emphasized by the artist and intuited Cartesian grid. Elements of the cosmic by the observer. Although the location of system organize themselves around a this point is determined primarily by the central point, and include snow crystals, structural characteristics of the picture, most hurricanes, ring-molecules, planetary studies that investigate it deal with the motion and other wondrous things in the recording of eye movements over, around, array of symmetrical objects and events that and toward it (e.g., Nodine & Locher, 1988; comprise most of the natural world. The Van Sommers, 1984; Vurpillot, 1976). In parochial system, with everything "in a state 1974, Amheim himself recognized the meth- of arrested downward motion", adjusts for odological weaknesses inherent in modeling the constraints of gravity, and is organized visual perception, and observed that "no around conveniently rigid horizontal and known method of rational calculation can vertical surfaces based on the Cartesian grid replace the eye's intuitive sense of balance" (1982, p. 10). The Cartesian grid imposes Today however, advances in computer (p. 19) order in our lives, while the concentric . technology have enabled researchers to system provides a midpoint or balancing analyze pictorial structure and test various center for everything we see. The simulta- models of visual perception (see Delicio, 1989). neous use of both systems is necessary to perceptually organize and visually under- Development And The Balancing Center stand every object within our view. A child's first experience with drawing starts with the act of looking. In the preverbal The Balancing Center child, it is difficult to determine whether the We take it for granted that the "center" balancing center of a drawing can be iden- of a regular shape like a circle, square, or tified as the place where he begins to scan it, triangle is always in the geometric middle or the point at which he decides to rest. of it, that it defines a structural constant, and Ghent (1961) hypothesized that the balancing that its location can be derived through center marks the point of departure for The centers of irregular measurement. 325 0 871 rcrT rpny rir.pol Method visual exploratiun, and that the location of Purpose this point changes predictably with age. This paper will first provide experi- She demonstrated that the very young child mental evidence in support of Arnheim's tends to visually explore a picture in a theory by demonstrating that a drawing's vertical direction, from top to bottom. balancing center is indeed measurable, and Presumably, this bias toward the vertical that the measurement can reliable and valid occurs because it is coincident with the when compared with human judgment. longitudinal axis of the body, and with the Second, it will apply the measure to test the It is earth's gravitational attraction to it. hypothesis that the child's placement of a almost as if the child's body itself serves as balancing center changes predictably with age. the frame of reference for the structure of Since visual ex- representational space. Deriving a Measure of The Balancing ploration begins at the top of the picture, Center objects situated in the upper half of picture In order to measure the location of a space are given privileged status, and are drawing's balancing center as Arnheim described it, the picture must first be en- perceived as more likely candidates for the balancing center. coded within a Cartesian grid, or converted Further evidence supports the to a digitized image. According to Marr notion that, by age six, when a child first (1982) and other representationalists (Gregory, experiences reading, a left-right scanning 1981; Sutherland,1973; Zimmerman,1987), invariant key patterns like the balancing strategy is adopted, and the upper left center are embedded in pictures, and they portion of the visual field is given priority can be decoded by analyzing the surface In her research in visual-motor tasks. geometry of the picture. This principle can concerning visual fixations on balancing be easily demonstrated using a composition points, Vurpillot (1976) determined that which has been transferred to ordinary graph children aged three to five years consis- paper (see Klee, 1953), or, for a more tently preferred to inspect the left center sophisticated interpretation, a bitmapped of a stimulus. Older children maintained picture. In both of these examples, assuming their preference for the geometric center, a high contrast drawing is used, each (x,y) but viewed the left and right portions of the element in the pictorial array can be coded stimulus as equally important. with either a 1 (figural space) or 0 (ground If preference for the departure point space). The processes involved in perceiving of perceptual exploration changes with age, the drawing of a black shape on a white it seems reasonable to assume that its physical background would require the "summation" placement within the child's drawing also of the retina's response to the individual Van Sommers (1984) showed changes. picture elements, taken together as a whole that, in sketching and dot-making tasks, a (Cornsweet, 1970). Hubel & Wiesel (1962) position near 11 o'clock is the preferred emphasize that an exact point-for-point starting point for adults, regardless of relationship between the drawing and the handedness. In random line drawing, right- receptive field map does not exist, but rather handed children aged three to six consciously a correspondence between the picture avoided the upper left region in favor of the surface and encoded information in the lower right of center, while left-handed Nevertheless, the bitmap can be retina. children showed the reverse pattern. In dot- viewed as a mathematically convenient way cluster tracing, right-handed children aged of reproducing the geometric organization of the drawing as well as a model of how the three to four preferred to start at lower right, drawing is believed to be projected in early but by age six, showed a tendency to start at visual pathways. the preferred adult positionupper left. 326 Figure I HYPOTHESIZED BALANCING CENTER LOCATIONS TC TR 11, CLT CRT C MR ML CRB CLB BC BR BL (h) BC, bottom-center (a) TL, top-left (i) BR, bottom-right (b) TC, top-center (j) CLT, center-left-top (c) TR, top-right (k) CRT, center-right-top (d) ML, middle-left (1) CLB, center-left-bottom (e) C, center (j) CRB, center-right-bottom (f) MR, middle-right (g) BL, bottom-left set of 30 black and white high contrast Procedure orightal ink drawings for which computer Computing the Balancing Centers estimates of balancing center location were Six hundred fifty-two 6" X 6" high already obtained. Each of the 30 drawings contrast ink drawings on white card stock was backed on white paper, and covered were collected from students in grades A water with a sheet of clear acetate. Kindergarten through grade six. Thirty soluble marker was provided for marking drawings labeled AA to Z (Appendix ) were on the acetate. selected from the pool of 652 on the basis of In order to establish a frame of ref- their representativeness of hypothesized erence, the entire collection of 30 drawings balancing center locations spanning the was presented to each individual art teacher The 13 possible balancing entire page. at the outset. The teachers were then asked center locations under consideration are to "locate and mark the center of balance on found in Figure 1. each single drawing". Teachers were A file was generated containing encouraged to interpret the meaning of computer-generated (x,y) coordinates "center of balance" in any way they deemed corresponding to black pixel locations for appropriate, drawing upon past experience each picture. Each picture contained one or training. balancing center which was computed by For each of the ten marks (across 30 estimating the mean of all black pixels in drawings), the distance along the horizontal terms of their distances along the X-axis, (x) axis and the distance on the vertical (y) and the mean of all black pixels in terms of axis was digitized and measured. For each their distances along the Y-axis. The of the thirty drawings, the mean of all judg- balancing center was plotted as a function ments of balancing center distances along of the intersection of these means. the x-axis and along the y-axis were Deriving Human Judgments Of Balanc- computed. This set of means was used to ing Center Location represent the set of perceived balancing The purpose of the following proce- center locations each of the 30 drawings . dure was to establish a set of perceived ReliabilityandValidityofHumanJudgments balancing center locations for each of 30 A reliability estimate of the ten drawings. Ten Kindergarten through twelfth teacher judgments on balancing center grade art teachers volunteered to participate location was obtained by intercorrelating in this phase of the study. the (x,y) coord nate values in 30 pictures for Stimulus materials consisted of the 327 the computer estimates and teacher judg- every possible pair of the teachers. The ments of balancing center locations for the average intraclass correlation coefficient 30 drawings is found in Figure 2. The calculated for the 10 X 10 matrix for x-axis overall pattern of subjectively judged coor- values was 0.647. For y-axis values, the dinates is strikingly similar to the plot of obtained intraclass correlation coefficient computer estimates. The Euclidian dis- Overall, teachers were in was 0.753. tances between teacher-judged and com- moderately high agreement on the vertical puter-generated balancing centers is pre- dimension of balancing center locations, sented in Figure 3. The greatest difference and and in moderate agreement on the hori- between computer and human judgment zontal. occurs for Picture EE (30 mm), while the Teacher judgment means for the 30 greatest similarity occurs for Picture G (1 balancing centers were correlated with cor- mm). These differences are interpretable responding computer estimates to produce within a 152.40 mm X 152.40 mm picture a strong agreement on the horizontal axis space (equivalent to 6" X 6", the original (r=.843), and a very strong agreement on drawing size). the vertical axis (r=.912). A plot showing Figure 2 COMPUTER-ESTIMATED AND TEACHER-JUDGED BALANCLNG CENTER LOCATIONS FOR 140 DRAWINGS 1 X-ESTIMATE Clear = Teacher Judgments Shaded = Computer Estimates 328 Figure 3 EUCLIDIAN DISTANCES BETWEEN TEACHER-JUDGED AND COMPUTER- GENERATED ESTIMATES OF BALANCING CENTERS FOR 30 PICTURES Distance Picture Distance Picture (mm) (mm) Code Code 9 AA 5 3 7 A 2 BB 8 9 11 CC 11 12 5 15 6 DD 15 4 12 16 EE 30 8 16 20 FF 14 8 18 X 16 GG 16 9 0 15 HH 9 Cluster Analysis of Balancing point neous with respect to grade level, with the exception of clusters three and four (no Location The purpose of this analysis was to representation by Kindergartners), cluster four (no representation by first graders), and determine whether the balancing centers in the set of 140 randomly selected drawings cluster six, (no representation by fifth grad- from children in grades Kindergarten ers). The breakdown of the cluster member- through Six, changed predictably with age, ship by grade is presented in Figure 5. or whether they varied randomly. Input data for this analysis were composed of the sets of computer estimates of balancing center position on the (x,y) axes for the 140 pictures. The procedure involved computing the (x,y) coordinates for six cluster centers, and classifying pictures so that members of the same cluster were similar with respect to balancing point location. Clusters are interpretable within a picture space scaled, in pixels, from -100 to +100 on both axes, with the origin at the center. The graphic interpretation of the six cluster centers reveals that most of the balancing points in the 140 drawings tend to be situated near the geometric center of the picture space (See Figure 4). Forty-three per cent of the drawings in the largest cluster, slightly to the lower left of center, are primarily from children in Kindergarten and first grade. Clusters appear to be heteroge- 329 Figure 4 FINAL CLUSTER CENTERS FOR 140 DRAWINGS I I 1 - _ 4 1 - _ a 6 2 a 5 3. - - 1 Position on X Figure 5 CLUSTER MEMBERSHIP BY GRADE Cluster Membership 3 4 5 6 2 1 Grade 0 0 K 13 5 1 1 0 2 4 2 11 1 1 4 4 4 4 2 3 1 6 4 2 2 3 5 1 4 4 5 2 3 5 1 0 2 2 5 3 5 8 9 4 2 6 3 1 1 A Grade X Cluster Membership ANOVA was performed to determine whether clusters differed significantly with respect to grade level. The results indicate that grade level makes no significant contribution to ex- plaining the variability in cluster member- 4 ship (F=2.03, 6,133; p=.07). 1 330 Interpretation played a preference for balancing centers trar the geometric center of the drawing. The outcomes of this study can be inter- The position to the lower left of center was preted as follows: dominated by drawings made by the yoLng- 1. Computer generated estimates of esi artists (aged six to seven). In Vurpilot's balancing point position on the vertical and experiment, which used line drawings of horizontal axis of picture space displayed a houses as stimuli, exactly the same location very strong relationship to subjective teacher judgments. was cited by three-, four- and five-year-olds 2. The majority of drawings ana- as the preferred fixation point in visual lyzed in this study were organized around scanning. balancing centers situated near the geomet- Van Sommers found that in sketch- ric center of picture space. ing and dot-making tasks, the lower right 3. Six (x,y) coordinate positions, all was the preferred starting position for draw- situated near the geometric center of picture ings produced by right handed children aged space, emerged as possible classification three to six. In the present study, however, criteria for balancing centers in the 140 only thirteen per cent of the pictures dis- drawings analyzed. played balancing centers in the cluster to the 4. Using the obtained classification lower right of center. Pictures from all age criteria, children's preferences for balanc- groups were represented in this cluster, with ing center location were not explained by the greatest number (6) from third grade, differences in chronological age for groups and the least (1) from Kindergarten and spanning Kindergarten to Sixth Grade. from fourth grade: Only ten percent of the Arnheim predicted that intuitive in- pictures showed balancing centers in a po- trospection alone would be sufficient for sition to the upper left of center. Pictures the detection of the balancing center (1982, from all grades, with the exception of Kin- This hypothesis was shown to be p. 6). dergarten and first grade, were represented correct in the high degree of agreement in this cluster. between teacher judged, and computer-gen- These results contradict Ghent's pre- erated, balancing centers for 30 drawings. diction that, due to the influence of visual A cluster analysis was performed reading behaviors, the primary location of on computer estimates for 140 drawings to determine whether a developmental trend choice for children six and older would be occurred in the selection of balancing cen- the upper left region. It is interesting, how- ter locations. Six cluster centers emerged, ever, that pictures from the youngest artists representing the mean of means (of posi- are not represented in this group. tions on the x- and y-axis) of all cases The data obtained in this study associated with the coordinate address of suggests that children in Kindergarten The locations preferred by the cluster. through the sixth grade show a strong bias children in Kindergarten and first grade for balancing pictures around a balancing were slightly to the lower left of center, and center situated close to the geometric center slightly to the upper left of center, respec- of picture space. The area of picture space tively. Under the assumption that the bal- that captured balancing centers in all draw- ancing center represents the starting point ings was bordered, on average, by about of visual-motor exploration on the page, three centimeters of blank space, in all di- these results concur somewhat with those of rections. Preferences for balancing center Vurpillot (1972). They are in contradiction location were not explained by differences to Ghent's experimental results on in chronological age. Counter to the expec- children's scanning behavior, and to Van tations of Ghent and Van Sommers, neither Sommer's work with drawing production the upper half of the picture nor the 11:00 tasks. position eme .ged as privileged areas in the As predicted by Vurpillot, children drawings in this analysis. composition in all age groups of the present study dis- 331 v i s e s y l a n A r e t n e C E L g B n A i c L n x I A a i d V l a n A B e Y p n P p I O A d C e T s S U E s B g n i w a r D y t r i h T A N N R I B A M A A A L B A L I A V A Y P O C T S E 3