Relationship Between Students' Proof Schemes and Definitions

This research investigates relationships between undergraduate students' understanding of proof and how this understanding relates to their conceptions of mathematical definitions. Three students in an introductory proofs course were each interviewed three times in order to assess their proof schemes, understand how they think of specific mathematical concepts, and investigate how the students prove relationships between these concepts. This research used theoretical frameworks from both proof and definition literature. Findings show that students' ability or inability to adapt their concept images of the mathematical concepts enhanced and impeded their proof schemes, respectively.