The Role of Visual Representations in College Students’ Understanding of Mathematical Notation

摘要

Developing understanding of fractions involves connections between non-symbolic visual representations and symbolic representations. Initially, teachers introduce fraction concepts with visual representations before moving to symbolic representations. Once the focus is shifted to symbolic representations, the connections between visual representations and symbolic notation are considered to be less useful, and students are rarely asked to connect symbolic notation back to visual representations. In two experiments, we ask whether visual representations affect understanding of symbolic notation for adults who understand symbolic notation. In a conceptual fraction comparison task (e.g., Which is larger, 5a or 8a?), participants were given comparisons paired with accurate, helpful visual representations, misleading visual representations, or no visual representations. The results show that even college students perform significantly better when accurate visuals are provided over misleading or no visuals. Further, eye-tracking data suggest that these visual representations may affect performance even when only briefly looked at. Implications for theories of fraction understanding and education are discussed.