For the last two summers, I’ve spent a week doing the Focus on Math workshops that are run out of BU. They’ve been pretty fun, and the instructors did a largely great job putting together series of questions about their topics.
I definitely changed the way that I run my class last year after going through one of the workshops. Now, most days, I start with some sort of ‘do now’ question, we review it together, I hand out a list of questions, they spend the bulk of the class working on them, and then we review together.
It has gone pretty well. But something was missing. They still got nervous when I asked questions that required them to dig down a couple of levels – they couldn’t figure out where to start if the beginning place wasn’t obvious. When I was student teaching, I would tell my students “Don’t freak out!” “Try anything!” But that wasn’t extremely helpful. I think it does a nice thing for the vibe of the room, but it still leaves kids wondering what sorts of things to try. What exactly is ‘anything’?
The ‘anything’ seems obvious to me, but that’s because I’ve spent so many years doing math. I do remember when I first started taking high level courses in college and my professors would ask us to prove things in our homework. I had absolutely no idea how to do that. I don’t think anybody ever gave me any tips, and I floundered around not really understanding what I was doing but somehow getting by okay, until I had floundered long enough to get a bit of intuition about what to do.
So now I know lots of cool things to try when I don’t know what’s going on, but the floundering bit took a long time and was rather disheartening. For a while I’ve been thinking, “how can I get the kids to try the same kinds of things that I try?” So I was pumped when I saw Bryan Meyer’s list of “Habits of a Mathematician” and the accompanying portfolio project. I discovered them less than a week before school so really I just stole them nearly word for word.
Anyway they’re going pretty well. I’m relatively pleased. I introduced the habits early on and every Friday, I’ve had my students look through their notebooks and choose something to put into it. I also make sure to use the habits themselves as every day vocabulary when I discuss how to solve the problems that we work on. The students have been responding pretty well. They don’t seem to think that they’re lame, which is what I half-expected. I think there are parts that I plan to change in order to make it more meaningful, but I’d like to see them all through the year before I do so.
One other change that I’ve made is to frequently start class with puzzles. My students have really gotten into them. And most surely we talk about them in terms of the habits. The enthusiasm and getting used to using the habits has definitely spilled into the regular curriculum. I think my students have been more interested than before, which is exciting.
Doing these puzzles has definitely taken up class time, but I think it has also made the rate at which they pick up new material slightly quicker. Maybe I’m making that up, of course. I do seem to be moving at the same pace as the other teachers. The difficulty now is to keep it up. Ideally I won’t need to use cute puzzles anymore, but, rather, have intriguing curricular bits. Who knows if that will do it.