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.

Holy cow. This sounds amazing.

I know! It

isonly day 2 ….Awesome stuff, Dan! I’m really glad to hear your approach, especially the journal. Kids love to create final products they can be proud of. You’ll find they’re hesitant to publish until it’s just right – some of them at least. I can’t wait to hear how it goes, and thank you again for your good faith!!!

Nice. I’m glad we’ve gotten in touch. I’ll definitely keep tabs on your goings-on.

How has the IBL/circle/art class been doing recently? By the way, do you get your questions mostly from a single source? I guess what I really mean to ask is this: Are there sources you recommend for creating good problems for an IBL/circle/art class?

My state standards told me precalc is basically conics, trig, vectors, and complex arithmetic. I started with lines, circles, conics. I made up my own conics problems, and have learned that I was imagining the kids would use algebraic manipulation on equations to prove things, while in fact all they’ve been trained to do is to substitute numbers into things. So I need to either scaffold what I want (which I don’t know how to do) or change what I want (which I don’t know how to do either). I have about 50 blog entries started on this topic and none finished.

For trig I plan to use the beginning of Ted Mahavier’s IBL course. For vectors and complex, I got an idea from Ellen and Bob Kaplan when I took their training this summer to head toward the question “What is i^i?” and some notes on a past course they taught. From what I’ve seen so far of my class though it will take some heavy filling in.

For the “classic puzzles” I’ve been using Gardiner and similar sources plus cool things that come up in the blogs or any other neat puzzles that don’t fit the main thrust of the course. The missile problem is in that group, and if you read about that you’ll get a sense of how it’s going.

[...] Update on my precalculus experiment: [...]

[...] How will students earn grades above 90? We aren’t likely to have a lot of goalless problems in math for now, so we can’t take the approach that my physics class does. But, this is also an honors course, where students really are setting out on the path to become sophisticated mathematical thinkers, so I think there’s room to incorporate capstones into this course, which I’ve written about previously . These capstones are very similar to the papers Dan Goldner’s students complete. [...]