Doing math with mathematicians to support pedagogical reasoning about inquiry-oriented instruction

摘要

Given the prevalence of research in undergraduate mathematics education focused on student reasoning and the development of instructional innovations that leverage student reasoning, it is important to understand the ways undergraduate mathematics instructors make sense of these innovations. We characterize pedagogical reasoning about inquiry-oriented instruction relative to vertices of the instructional triangle (content, students, and instructor). Through this lens, we analyze conversations of twenty-five mathematicians who elected to attend a workshop on inquiry-oriented instruction at a large national mathematics conference. Identifying differences in talk between two breakout groups, we argue that deeper mathematical engagement in task sequences designed for students supported deeper engagement in students' mathematical reasoning and engendered reasoning about instruction that was more frequently accompanied by rationale based in mathematics or students' reasoning about mathematics. Importantly, deeper mathematical engagement was observed when the discussion facilitator prompted participants to engage through a mathematical lens rather than an instructional lens.