Monday, November 13, 2006

What do we know about mathematics curricula?

Thinking about where mathematics education is, what science education can learn from them, and how science differs from math, has been intriguing to me lately. I rely on certain core ideas in reasoning about new problems in science: energy, momentum, certain conservation laws, symmetries-- and it seems to me that there are some key "content" ideas that can help anchor your science thinking. I wonder if this is different from mathematics.

Schoenfeld, describing a mathematics course in problem solving that is not tied to a particular "content" topic but rather to problem solving heuristics, quotes a conversation with the department chair. He's trying to get credit towards the major for students who take the course, and argues that students in this class can outperform senior math majors on difficult math problems. The department chair replies: "I'm sure you're right, but we still can't give credit toward the major. You're not teaching them content-- you're just teaching them to think."

Schoenfeld goes on to say (p. 4):

The moral of this story and the reason that I tell it is that it demonstrates clearly that what counts as mathematical content depends on one's point of view. From Professor Y (the dept. chair)'s perspective, teh mathematical content of a course is teh sum total of the topics covered...

I would characterize the mathematics a person understands by describing what that person can do mathematically, rather than by an inventory of what a person "knows."... Note that this performance standard is the one that Professor Y lives by in his professional life, and the one that he uses to judge his colleagues.

This course he describes feels similar to a science course I've co-taught, where the students brought in questions and then reasoned through them. Topics included "will a human blow up in space (or freeze)" and "why is the sky blue." But in these courses I didn't just provide guidance on heuristics or scientific thinking, but also added a lot of content-- about how things lose heat, how prisms work, etc. And while some students might be well-prepared to reason scientifically at the end of the course, I doubt they could go toe-to-toe with a student with more content knowledge.

from Schoenfeld, A.H. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13(1), 55 - 80.

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