High School Students’ Use of Diagrams in Geometry Proofs

In high school geometry, proving theorems and applying them to geometry problems is an expectation for students. An essential part of most geometry proofs is the diagram because it not only helps encapsulate the claim being proved but can also be a tool in reasoning or communicating an argument. This interview-based study investigated how high school students interpret and use diagrams during the process of proving geometric claims. Particular attention is given to the semiotic resources such as symbols, visuals, and gestures that students employ in relation to the diagrams. Study participants were nine students from grades 10 to 12 and data was collected through one-on-one task-based clinical interviews with tasks that varied with regard to diagrammatic features. The findings suggest that, in general, some visual resources such as drawing a new figure occurred regularly in particular tasks such as tasks that did not adhere to the typical diagrammatic register or that had unknown truth values. Gesturing with justifications were the most frequently used proving actions in all tasks. Moreover, in all valid proof arguments produced by students, they engaged in all three semiotic resources (symbols, visuals, and gestures).