One of the things I’m working on is finding the proper role for a notebook/journal in a math class. I don’t want to force my students into some rigid style of taking notes, and though I’m somewhat intrigued by the whole INB concept, I don’t think I’m ready to take them on this year.
Instead, what I want is for my students to keep a sort of math journal of interesting problems we’re working on. This might include writing down work we do in class, so that we can refer back to it, and it will definitely include any homework students do, but I’m hoping that it will include some of their own mathematical investigations. The most important thing is that by looking back at their notebook, they should be able to pick up where they left off on a problem. To get students started, we bought each of them a graph paper composition notebook and had them punched by Kinkos so that they would fit in a 3 ring binder.
But in order for this to work, I need to be doing the same thing myself, so I got myself a fancy Moleskine notebook, and am now using it to record thoughts about interesting math problems I encounter, including the one I’m most interested in now—find the minimum square that can enclose a 3-4-5 right triangle, a problem I got from James Tanton. I showed this notebook to my students yesterday, and today, a student came up to me to ask me about the question I was working on again, saying that he wanted to work on it too.