After all my talk about Algebra 2, it has worked out that this year I’m teaching precalculus instead. So I’m trying a hybrid of my favorite models: IBL, based on the Moore method; the Math Circle; and, following Lockhart, the art class at my school.

I have 80 minutes a day. I put up definitions and problems, which are often theorems to prove. Students work on the ones that interest them, or if none appeal, they can try to tackle one of the classic puzzles I have in a binder in the corner. We start each day with presentations. (Once a student has presented a solution that meets with class approval, they can submit it for publication in the class journal.) Then I might talk for a few minutes on problem-solving strategies, or values like persistence, or just give them the next few problems. Then work time for 30 minutes or so. I wander around to help or encourage. Students at a dead end can recharge with a Rubik’s cube or soma blocks. We end with a short reflection on where people are and how they’re feeling.

So, Friday – day 2. Everyone’s working. A few are still a little freaked out, but everyone is working productively on one problem or another. The first presentations were all over the map, but they were an occasion to talk about taking time to get good at presenting, which opened up a conversation about what makes a presentation good. Still, twenty percent of the students are ready to draft their first articles. And it’s only day 2! A student calls me over. I see he is working on Problem 1. He looks up at me and says, “I had a breakthrough.”

I know just how he feels.