Active Learning in Proof-Based Mathematics Courses: Pedagogical Approaches and Observations

Writing-intensive and proof-based mathematics courses have a variety of unique course outcomes and challenges. As such, active learning in these courses may differ from what we traditionally expect to see in an “active” first-year calculus course: an interactive in-class activity can be replaced with an out-of-class reading and homework problem in a proof-based course. We argue that the latter is no less “active” and claim that reading and writing mathematics form the foundation of how students learn by doing in writing-intensive mathematics courses. In this commentary, we discuss our pedagogical approaches to supporting students’ learning in introductory mathematical writing courses and how we promote active engagement. We outline potential benefits and challenges of these teaching methods and assessment strategies and conclude with some questions for reflection.