On Existence Proofs, Mathematical Norms, and Professional Obligations

Proof is a central pillar of mathematical practice, and so teaching proof to undergraduate students is an important responsibility for undergraduate mathematics instructors. Our study contributes to research on one facet of this goal by examining instructors’ responses to student-generated existence proofs. Existing literature on the topic suggests that students might include unnecessary statements or utilize an unnecessary proof structure when writing existence proofs, even if a single confirming example would be sufficient. Instructors in our study \(\:n=86\) ) ranked five students’ existence proofs containing an unnecessary aspect; using the language of norms and professional obligations, we analyzed these rankings and the instructors’ corresponding justifications. We found that mathematics instructors are willing to accept proofs with an unnecessary aspect from students when doing so allowed the instructors to fulfill a professional obligation to an individual student, to mathematics as a discipline, or to their classroom as a space for collaborative and student-centered mathematics.