Attention to Detail: Norms for Proof Evaluation in a Summer Mathematics Program

In this study, we explore the norms by which students and undergraduate mentors in a summer mathematics program evaluate proofs of theorems in number theory. By utilizing cognitive interviews during which students and mentors evaluate number theory proofs written by a hypothetical student, we find that for students as well as mentors, “rigor” is a dimension of mathematical acceptability of proofs distinct from, though related to, proof validity. Additionally, we find that both students and mentors frequently adhere to strict unwritten norms that govern how they believe proofs should be constructed and presented, and that these norms may be more rigid than the intended proof-writing norms of the mathematicians who teach in the summer program. This study suggests some potential challenges associated with the growing practice of asking undergraduate student graders to evaluate proofs written by students in introduction-toproof courses.