Leveraging the Purpose of Proof to Develop Students' Understanding of the Generality Requirement

• In Event: 64.087 - MTCC Roundtable Session 28
  In Roundtable Session: 64.087-6 - Proof, Argument, and Debate in Mathematics Classrooms

Abstract

The generality requirement represents one of the most important, yet challenging aspects of proof for students to understand. This paper describes how one student, Lexi, developed understanding of the generality requirement while participating in an introduction-to-proof design study that aimed to facilitate understanding of the generality and purpose of proof. Through analyzing Lexi’s work on proof tasks and evaluations of provided responses across four interviews, I describe her transition from believing that examples constituted proof to believing that proofs should explain why and adhere to the generality requirement. The case of Lexi reveals the potential benefits of using the explanatory feature of proof to explain the purpose of proof as well as support the transition away from examples-based arguments.

Author

• Kimberly Conner, University of Northern Iowa