By Benjamin Braun, Editor-in-Chief, University of Kentucky.

This post is inspired by an article by Karen Marrongelle and Chris Rasmussen [1], in which they discuss the false dichotomy between all lecture and all student discovery as the two exclusive teaching strategies available for mathematics teachers.  I’ve noticed that many discussions among postsecondary mathematics teachers lead to a debate of the merits of these two classroom teaching strategies, with the result that interesting teaching practices are left undiscussed.  Below I describe three key teaching practices that I’ve learned about and used over the past several years that fit between and beyond these extremes.  I’ve observed that when I use these practices, students are generally more engaged in the course, e.g. attending office hours, asking questions in class, forming study groups, etc.  Though they appear simple, using these practices successfully has required perseverance and effort on my part, and a willingness to regularly revise their implementation. Continue reading →