Impact and Prevalence of Diagrammatic Supports in Mathematics Classrooms

Mathematical problem solving typically involves manipulating visual symbols (e.g., equations), and prior research suggests that those symbols serve as diagrammatic representations (e.g., Landy and Goldstone 2010). The present work examines the ways that instructional design of student engagement with these diagrammatic representations may impact student learning. We report on two studies. The first describes systematic cross-cultural differences in the ways that teachers use mathematical representations as diagrammatic supports during middle school mathematics lessons, finding that teachers in two higher achieving regions, Hong Kong, and Japan, more frequently provided multiple layers of support for engaging with these diagrams (e.g. making them visible for a longer period, using linking gestures, and drawing on familiarity in those representations), than teachers in the U.S., a lower achieving region. In Study 2, we experimentally manipulated the amount of diagrammatic support for visually presented problems in a video-based fifth-grade lesson on proportional reasoning to determine whether these multiple layers of support impact learning. Results suggest that learning was optimized when supports were used in combination. Taken together, these studies suggest that providing visual, temporal, and familiarity cues as supports for learning from a diagrammatic representation is likely to improve mathematics learning, but that administering these supports non-systematically is likely to be overall less effective.