Today we finished discussing an activity we created last week. We were to take a paper fold and use it to teach mathematics. The most challenging aspect of this task was to design a problem that would actually teach a mathematical concept. I, and it seemed like many of the others, have traditionally used problem solving activities as a means to test our students' knowledge about a particular topic.
Several times in our discussions we were asked "What new math are they learning as a result of this problem"? This struck me as an important aspect to teaching mathematics that I have overlooked. One portion of what we do as teachers at PCMI is to learn more mathematics. In these lessons I find it much more interesting to explore things that I don't necessarily know the formula for. I think that, with some training, our students will be the same. They will be much more interested in learning the math when the problems they are solving are teaching them this math.
I will let you know when I have it figured out.
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