I wanted to jot down some thoughts inspired by being at PCMI (Park City Mathematics Institute) this summer. Ideally, I would have been keeping a journal, and I’m sure I will fail to mention a lot of juicy tidbits that came out of our sessions and discussions. But here I go anyway…
- I liked Cal Armstrong’s comment on our last day about shooting for slow, nay “glacial” progress. It’s very tempting to try to change everything right away, and I know the kind of chaos and exhaustion that can lead to.
- Nonetheless, I want to make myself change, and constantly experiment. That’s the one word I wrote down on a card at the end of our sessions to remind myself of what I want to do this year.
- I learned that how I use the blackboard is not something I have ever thought through carefully. (That’s one of the many, many aspects of my teaching that come from the fact that I started at the college level, where thinking about pedagogy is nonexistent.) We were presented with a description of how a typical Japanese teacher uses the board, and while I was not convinced I need to switch to that style, it did make me think that here is yet another aspect of my practice that I need to evaluate. Given all the rest of my plans, that probably won’t happen in a serious way this year—see “glacial change” above.
- Both this year and last year emphasized for me the work I still need to do on specific strategies and moves to foster good student discussions. I was pleased to hear strategies from my fellow teachers in the program about explicitly addressing classroom norms with the kids, and working with them very openly to develop a safe, but productive and challenging, space for discussion and learning.
- It was great to work on deceptively simple, but ultimately rich, problems. Example (from John Mahoney): a restaurant charges $14.99 for a six-ounce steak and $19.99 for a nine-ounce steak. How much should it charge for a 20-ounce steak? (I may have change the numbers a bit.) The key was to let the discussion flow without channelling it into a single method for the “correct” solution. I love open-ended problems, but my tendency is to make them more general than this example, and sometimes a bit overwhelming in their open-endedness. It’s good to see the openness in even a seemingly simple problem.
That’s only a small sample of what came up during the three weeks, but that’s where I’ll stop for now.