Random things I learned at PCMI this year

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.

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2 Responses to Random things I learned at PCMI this year

  1. samjshah says:

    Holla! Welcome to blogging! I still am having trouble crafting my PCMI post – argh! I learned too much, and it loses things when I write it down.

    Excited to have you in my reader.

  2. brainopennow says:

    Hooray for more PCMI bloggers! I’m a neophyte myself, but I think that the online community of “math teachers who care” (or something like that) is what I was looking for in all those bland NCTM articles and over-wordy teacher books. That is, people willing to share their thoughts, theories, and queries along with a “here’s a link to the activity I used.”

    About the blackboard stuff, I don’t recall actually seeing written plans of how teachers would use their blackboards. Maybe that’s part of the point — not that there is a prescriptive best way to arrange your board, but just that a little thought in that direction can improve a lesson.


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