I am in Irvine, CA right now for two really cool reasons.

1) To visit a long-time Math Forum Problem of the Week (PoW) user, Doug Compton. If you follow the AlgPoW and read the solutions and commentary regularly, you see Rancho San Joaquin Middle School quite regularly. That’s because Doug has his nearly 70 algebra students submit to the PoW each week. They focus on writing detailed explanations of their problem-solving and why their answers make sense. They also reflect each week on where they got stuck and how they got unstuck, if needed, or what they thought of the problem’s relative difficulty. Reading their thinking is one of the highlights of my week; picking just one or two to highlight is one of the hardest parts!

Visiting their classroom was fun! The kids treated me like a celebrity and had lots of questions about my job, how I pick the solutions to highlight, and who writes the PoWs (and why we make them so hard). I’m still wondering why Kenneth wanted the next one to be about ice cubes, but I can see some definitely possibilities there… I could tell from my brief visit that the students focus a lot on explanation and justification. Even putting the answers to warm-up problems on the board was an opportunity for Doug to reinforce that without work shown, the designated “checker” wouldn’t be able to determine why his answer might disagree with the answer on the board and justify which solution he thought was right. With that kind of practice, I could begin to see how these students learned to be such great explainers.

2) Attending the Association of Math Teacher Educators conference here in Irvine. Three highlights for me so far:

- Hearing Marilyn Burns’ latest thoughts on informal assessment and the components of mathematical reasoning and problem-solving. I found that her three components (conceptual understanding, number sense, and procedural fluency) mapped really nicely onto the Math Forum’s unit-structure framework of Concept-Method-Procedure. When she described number sense, she was describing the mental math that students use to solve problems based on solid conceptual understanding and flexibility working with numbers, which sounds like just the kinds of methods we are trying to elicit. Seems like there must be some validity to that structure if Marilyn Burns thought of it too…
- The idea of “curriculum vision” that was discussed by Corey Drake from Iowa State University. She noticed that when teachers could articulate the big mathematical ideas in a lesson, where the lesson was going, and how the tasks got you there, then they made adaptations “in the curriculum envelope” rather than abandoning the curriculum, lowering the cognitive demand of the task, or teaching incorrect math. She had some suggestions for professional development tasks that focused teachers on developing that curriculum vision and refining it.
- Accidentally walking into the wrong session and discovering it was a session all about virtually pairing pre-service teachers and elementary/middle school students. They were excited to learn about the Math Forum’s Online Mentoring Program. This was nice because the reason I cam to AMTE was to look for more teachers of pre-service teacher who want to be partners in the OMP.

Phew… As lovely as 75-degree, sunny days are, I’ll be glad to be home in Philadelphia soon.

Max