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TL;DR

This paper critically examines active learning in mathematics education, emphasizing the importance of thoughtful teaching practices over blanket slogans, and reflects on effective ways to facilitate student understanding in undergraduate mathematics courses.

Contribution

It offers a nuanced perspective on active learning, advocating for deliberate teaching strategies rather than blindly following popular trends.

Findings

Active learning requires careful implementation for effectiveness.

Blanket slogans may oversimplify complex teaching practices.

Reflective teaching enhances student understanding in mathematics.

Abstract

"Math is not a spectator sport." "Lecturing is educational malpractice." Slogans like these rally some mathematicians to teach classes that feature "active learning", where lecturing is eschewed for student participation. Yet as much as I believe that students must do math to learn math, I also find blanket statements to be more about bandwagons than considered reflection on teaching. In this column, published in the Fall 2021 AWM Newsletter, I urge us to think through the math we offer students and how we set up students to learn. Although I draw primarily from my experiences teaching proofs in abstract algebra and real analysis, the scenarios extend to other topics in first year undergraduate education and beyond.