Diagrams support spontaneous transfer across whole number and fraction concepts

In mathematics, learners often spontaneously draw on prior knowledge when learning new ideas. In this study, we examined whether the specific diagrams used to represent more familiar (i.e., whole number division) and less familiar ideas (i.e., fraction division) shape successful transfer. Undergraduates (N = 177) were randomly assigned to demonstrate fraction division in a 3 (Diagram: Number Line, Circle, None) × 3 (“Warm-up” Example: Whole Number Division, Fraction Addition, None) between-subjects design. We hypothesized that transfer from whole number division would be greatest in the number line condition. When using number lines and warming up with whole number division, students generated more accurate conceptual models of fraction division. However, both number lines and circles supported transfer from whole number concepts to fraction concepts, whereas having no diagrams did not. Diagrams may play a critical role in helping learners make use of their vast prior knowledge.