*In this section, Professor Haynes Miller shares the rationale for including practice talks in the course.*

The practice talks are an essential part of the course. These are sessions, organized by students, during which one student practices the presentation he or she will make in class. The instructor does not attend. Typically, the practice talks are fractious. The presenter gets started, and two minutes into the talk, there are all these questions! The presentation gets completely derailed. It’s healthy! They seem really strange to participants, at first, but students wind up telling me that they are really important.

There are two main reasons for including practice talks in the course. The first is that they prevent bad math talks. It’s easy to imagine that you can do a lot in your talk and then discover, 40 minutes into the talk, you’ve only done a third of what you’d planned to do. So the practice talk solves that problem. The second reason is that practice talks offer students an opportunity to spend time working together—which is one of the major purposes of the course.

Attending the practice sessions of their colleagues is optional for students because scheduling is always a problem. I reserve our classroom for three hours a week. We meet twice a week for an hour, so there’s a third hour available for students to schedule practice talks. But when there are two practice talks in a week, scheduling becomes more of a problem. Students schedule these sessions themselves. So at the end of almost every seminar, there’s a discussion about when the next practice talk is going to be. They eye each other and try to figure out, “Do I want to disrupt everybody else’s schedule so I can attend the practice session, or do I want to skip it?” But even that is useful, in my opinion, because it gets people thinking about their commitment to the course.