[A parent letter from November, 2012 at Emerson Elementary.]
A few notes from our recent and upcoming Math Circles:
1. In an effort to figure out how to teach girls better, I have hired a gender consultant, someone with an M.A. in Women and Gender Studies, to observe and critique my teaching, and to discuss with me some of the academic literature on gender and math. Sarah has visited class once so far, but she’s been great at spotting some of my teaching errors and challenging assumptions I have about working with girls. I would welcome more people to talk with about these issues. If any of you have a formal background in gender or simply an interest from having observed yourself and your children, please tell me and let’s talk. This is a moment when I am unusually teachable.
One of the things that Sarah noticed last week was that three of the girls had independently written above their scratch work a sentence stating that the problem we were working on was hard. (It was, in fact it was impossible.) Reflecting on the fact that this dovetails with some of the literature on girl’s self-perception, I decided to begin class yesterday differently than I usually do. I started with three short anecdotes about my confronting, and sometimes failing to solve, problems in my own life that were hard. I then asked the children to reflect on when they’ve had problems that were really hard — in school or otherwise — and how they approached them. They became quiet and earnest. I told them that my teaching is not really about math; Math Circle could just as well be titled, “This is a Hard Problem. What are You Going to Do About It?” That’s as far as we got yesterday, but I’ll follow up in future lessons.
2. Yesterday we finished our penultimate lesson on parity (the mathematics of odd and even numbers). They’ve worked on five short problems that are each about parity , but which have had such varied settings that the children haven’t realized that the problems are all related. Next lesson will be a summation, or as I told them at the end yesterday, “Next lesson, all will be revealed — or not.”
Sometimes in class we treat math as an inductive subject — the students try to find examples that satisfy a certain condition; when they can’t, they conclude, “It’s impossible.” This is fine as a heuristic, but in the end math needs to be deductive, depending upon proofs, and not only inductive, depending upon examples. The next lesson, I expect that they will do their first proof, and to make it more dramatic, we won’t fiddle with examples beforehand, I will invite them to dream up their parity proof out of pure thought. [Note: I did try this the following week, but it flopped miserably. That was probably my fault; most failures seem to happen when I get excited and rush the curriculum.]
3. Next problem due up:
How much time would Santa Claus have to visit each family in America that he visits? How many reindeer would he need to pull his sleigh?
This is a Fermi Problem, a back-of-the envelope calculation that uses a little bit of math and a lot of cleverness to estimate something in the real world. The classic Fermi Problem is, “How many piano tuners are there in Manhattan?” but that’s more of adult-interest. I made up the Santa Claus problem several years ago and it has been well received. At first I worried about its Christian reference, but everyone seems to get into the spirit of it. It should take three hours or so to muck through the problem.