Ok, this is a pretty big title. To be honest, I’m less interested in contributing to the larger-scale discourse on active learning vs direct instruction. I’m more interested in trying to make my teaching a bit more cohesive, fitting into the themes I’m trying to build throughout a short semester with students. Two important ones that I think about a lot are:

The way I use class time, then, is really impacted by both of these. If I think mathematics is about precise communication, then I want students to practice this kind of activity. If I think mathematics can be done by everyone, then I want to give my students the opportunities to do mathematics. The only time in their schedule that I have control over is the time they spend in my classroom, so I’ve tried to set up that space to allow students to do both of these things!

Consistency, Finally

Prior to 2018, I was lecturing for much of the time in my class sessions, but in 2018 I started being a lot more intentional about having students contribute to class sessions more. It started with some activities to break up the lecture portions of class and quickly moved to small group discussions, exploration activities, and generally much more student-driven learning. In the last few years, I’ve been mainly summarizing discussions, adding some notation or historical context, and generally making sure we’re heading towards our learning outcomes for the course.

Maybe that’s lecturing, maybe it’s not. But what I know for certain is that I still have some topics that I fall back into a lecture-oriented class session for. Topics that I’m maybe not so enthusiastic about or ones that feel out of place. Stuff that I keep brushing off for some future-Peter to figure out.

And this summer is the summer! I’ve wound down some other projects I was working on and I’m working on getting all of these class sessions to match my other ones: there will be some exploration, some discussion prompts, and less time with me standing in front of silent students who write down my words.

How Do You Use Your Time?

How are you and your students spending the small amount of time that you have together? I don’t mean to try to force everyone to spend their class time exactly like I do: I don’t think scripting your class sessionNo More Lectures to match some preset format is useful. Instead, I hope that you and I both can continue to think about how we use our time with students. This framing is helpful to me: when I used to think about how I presented content, I was getting hung up on which examples to show or how to word definitions or how to order the results. When I think about how I want to spend time with students, the answer is easy!

I want to model precise communication and have them practice precise communication. I want them to go through the process of thinking carefully about mathematical objects and ideas with each other, even (especially?) the parts where we get stuck thinking about them.

I want to spend time doing mathematics with them.