RUME 26
2024
Omaha, Nebraska
What Makes a Proof a Proof?: It’s Your Job to Decide
Page: 694
This study investigates students' conceptions of what makes a particular written mathematical communication a proof. To that end, we implemented one-on-one task-based interviews involving mathematical communications. These communications were presented as trios, and we called each communication a job. We intentionally designed some of these jobs to sit in the vague space between proof and calculation. Our study investigated the reasons why participants believed certain jobs were proofs, allowing us to develop a model of students' conceptions of proofiness. This model revealed differences among students in terms of which attributes they thought contributed to or detracted from proofiness, as well as those they thought were and were not relevant to whether a job is a proof. These differences and how they relate to normative conceptions of proofiness point to aspects of proof that may require further attention in these students' introduction to proof courses.