Escape From the Textbook Conference

Today was the conference. This morning I got on BART, and worked on a math problem the whole way in to SF. (I'll post about that tomorrow.) This post comes from the notes I took at the conference, and will be a bit choppy.

We were welcomed by Henri Picciotto. (Check out some of his cool stuff!) And then Jo Boaler, author of What's Math Got To Do With It?, spoke.

Jo Boaler's Talk
She points out 3 characteristics of good classrooms:

• They are mixed ability
• The students work on problem-solving
• The students work in groups

She and her graduate students worked with 6th and 7th grade students in a summer school program as part of their research. They developed an Exploratory Algebra course for the students that met for 5 weeks. The students came in ready to hate it (90% were 'made' to come by parents, teachers, or school), and left loving it. Boaler et al had 4 principles for their teaching. They wanted to:

• Engage the students as active and capable learners,
• Teach mathematical practices,
• Develop a collaborative mathematical community, and
• Help the students develop their own voices.

The students did much better in their fall math classes than students who had taken a regular summer school math class. (However, all gains were lost by the winter.) The two things that were most important to the kids were collaboration and agency (getting to choose how to proceed in a problem).

One student said: "After finding a pattern, you can stretch it in many ways, instead of just staring at it."

At first, when asked "How many squares (of any size) on a chessboard?", the students were willing to play around with the problem, but they were not willing to look systematically, or to record their thinking. The teachers encouraged them to try a smaller case, but the kids felt like that would be cheating. (!)

She showed some video clips of these classes, and asked us to discuss our reactions. That gave me just enough interaction to keep me focused. (Usually an hour-plus talk would be too long for me, and I'd be off thinking about something else. I actually managed to listen and think about it the whole time.)


Paul Zeitz, Puppies, and Kittens
We had a short break, and then came Paul Zeitz's talk. (Paul Zeitz is the author of The Art and Craft of Problem Solving.) Except that it was a math play session instead of a talk. Before we started playing, he said he thought math class should be more like:

• Field Biology
• Shop
• Sports 

Regarding the analogy with sports, he said, "I want to de-emphasize competition, but not to throw it out." He says math class should always be/involve:

• Hands-On
• Interactive
• Discovery
• Comradeship

"What you need to learn is how to investigate."

He gave us some handouts with good math games, and asked us to think about this kittens and puppies game.

The two players come in turns to the pet store, and each time have to buy at least one pet. The rules are that they can buy:

• As many puppies as they want, or
• As many kittens as they want, or
• An equal number of puppies and kittens.

The pet store starts out with 10 puppies and 7 kittens. The last person who can make a legal move wins. He played the game out once with us, and then had us play against our neighbor a few times. Then he showed us that if he could get the numbers down to 1 puppy and two kittens (or vice versa), the other player had no good move. (Buying one of the kittens leaves it equal, so he can take both the animals that are left. Buying both kittens leaves only the puppy, which he buys. Buying the puppy allows him to buy both kittens.) He asked for a participant who wouldn't mind losing, and very nonchalantly beat her. Paul called the 1 kitten, 2 puppies and 1 puppy, 2 kittens situations oases. We played against our neighbor, looking for other oases.

Then Paul showed us a way to graph the oases, which helps you find more of them. The patten is very interesting. (I won't wreck your fun by telling more.)

After Paul's session was lunch, where we got to chat with other teachers. The folks there were over 80% high school teachers, I'd guess. It was a lively crowd, and I had fun chatting with two people I'd just met and a colleague I get to see at every one of these conferences. After lunch we went to one of about 6 workshops. I went to Avery's and had a blast.

I liked that he focused on the idea of getting students to pose their own questions. After some discussion, he handed out unifix cubes, and asked us to make a patten that:

• Could be repeated indefinitely
• Can be counted

One person in our group hooked a unifix cube onto each face of a central cube. Our first stage was the central cube; our second stage was the object with 7 cubes total.  We talked about what our next stage would be and had (at least) two different notions of how to proceed. One person made the 6 'arms' 2 cubes long for the next stage; two others of us saw it as - put cubes on every exposed face of this object. That seemed to me to be a fractal (but maybe I'm wrong). I spent some time figuring out how many cubes would be used for each stage.

I loved each of the 3 sessions, and the energy of the teachers there. I hope there will be another conference like this in the fall.