Visual Arithmetic, Computational Graphics, and the Spatial Metaphor

Abstract

People who interact with graphs to perform arithmetic tasks typically employ quantitative features. However, they may employ the spatial metaphor under two alternative conditions: if they have been trained to apply visual arithmetic methods to traditional line and bar graphs, or if they interact with specially constructed and special-purpose computational graphics. Two experiments explored a visual arithmetic method used to train subjects to determine a mean by locating the spatial midpoint of a set of indicators (bars in a bar graph or points in a line graph). In Experiment 1 visual arithmetic subjects determined the mean of five indicators as quickly as they did the mean of two indicators; control subjects performed slower with five indicators. Both groups took more time to add the values of five indicators than to add two indicators. In Experiment 2, unlike control subjects, visual arithmetic subjects' response times in mean trials were unaffected by changes in the y-axis scale. However, both groups were affected by the y-axis scale on addition trials. Neither group was influenced by changes in the distance between indicators. The discussion addresses the transfer of visual arithmetic training to tasks that differ from the one used during training, uses for visual arithmetic and computational graphics, and the role of parallel processing and task restructuring in visual arithmetic.