High Leverage Teaching Practices for the Proof-Based Undergraduate Mathematics Classroom

Kristen Lew
Assistant professor
Texas State University

Need: Professional organizations have called for undergraduate mathematics courses to become less lecture-focused. However, transitioning to more active approaches is pedagogically challenging.Guiding Question: In the Orchestrating Discussions Around Proof (ODAP) project, we used a design-based research approach to test and refine instructional practices that may support rich student engagement in proof. Outcomes: We found that many teaching practices from the K-12 setting could be adapted to the proof-based classroom, although implementation often relied on navigating between formal and informal mathematics and making sense of abstract referent objects. Products from ODAP include three abstract algebra lesson guides and a set of structured instructional practices that may help facilitate more active learning. Broader Impacts: Ultimately, we hope such practices may support more positive classroom experiences for mathematics majors and future high school teachers who take proof courses.


Kathleen Melhuish, Texas State University, San Marcos, TX; Paul Christian Dawkins, Texas State University, San Marcos, TX