Visual-Spatial Thinking in Geometry and the Visual Arts

The goal of this study was to investigate potential connections between the kind of visual-spatial thinking required in drawing and that required in geometric reasoning. We compared growth in geometric reasoning in students engaged in intensive study of either the visual arts or theater. The study was longitudinal, with 3 testing points: the beginning of 9th grade, end of 9th grade, and end of 10th grade. We tested students' performance in geometric reasoning and on a new measure of artistic envisioning which calls on visual-spatial thinking, as well as on standard spatial reasoning measures. We hypothesized that (a) students engaged in intensive study of visual arts should improve more in geometric reasoning than students engaged in equally intensive study of theater; (b) students engaged in intensive study of visual arts should improve more in artistic envisioning than students engaged in equally intensive study of theater; and (c) growth in artistic envisioning should predict growth in geometric reasoning. Results supported the first hypothesis. A secondary analysis revealed that students whose drawings of a simple still life were extremely spatially disorganized performed significantly worse on the geometric reasoning assessment than students whose drawings were at least adequate spatial representations of the scene. We suggest that the overlap demonstrated between visual-spatial thinking in geometry and art could have educational implications for the teaching of geometry: development of visual-spatial thinking through the visual arts could support geometry learning for students who are not succeeding in mathematics classes.