Teaching practices that support revising definition drafts to adhere to mathematical norms

Definitions play an integral role in mathematics and mathematics classes. Yet, expectations for definitions and how they are intended to operate, i.e., mathematical norms for definitions, can remain hidden from students and conflict with other discursive norms, explaining differences in mathematicians’ and students’ understandings of the nature of definitions. We examined how six inquiry-oriented Introduction to Proof instructors supported their students in revising their definition drafts to adhere to mathematical norms. We identified four procedures that effectively supported students’ drafts in adhering to various mathematical norms, particularly to those that worked to increase clarity. We discuss how the instructors’ teaching practices provided different opportunities for students to engage with mathematical norms for definitions, general mathematical norms, and mathematical content.