Sorry posting has been light. We’re getting ready for the move, and I’m just not up to being creative in the evenings.
I like to check in with the American Federation of Teachers’ blog (”Let’s Get It Right“) every so often, just to get a sense for what’s on the minds of folks who represent the teacher’s union.
I was intrigued by the post headlined “Are Mathematicians Smarter Than Math Teachers?” Here’s the first paragraph:
Maybe. But math teachers know things that are (1) useful for teaching math and (2) difficult for non-teaching mathematicians to grasp, according to Deborah Loewenberg Ball, a University of Michigan researcher who spoke recently to a gathering of AFT leaders and staff.
The specific example cited has to do with discerning how students make particular kinds of errors when solving math problems.
Ball reports that math teachers were much better than mathematicians at identifying where students went wrong–an important fact to know to help put students back on track.
Fine, but as I point out in my comment to the post (still under moderation), that does not imply that non-teaching mathematicians couldn’t “grasp” this knowledge. I looked through the paper by Ball cited in the post, but I don’t think it addressed this specific point.
In any case, the same would apply with any other sphere of mathematical application. Let’s say I was a mathematician who focused on how to analyze models of weather prediction. As I went along, I’d get better and better at recognizing patterns in the models or perhaps finding glitches in the model. A mathematician who was plying his trade on Wall Street (to analyze the best times for trades, for example) couldn’t walk up to the code I was working on and immediately find the errors. But that’s simply because he’s been applying his math skills in another application area. Given enough experience, he might be just as good as I am at analyzing weather models.
Are there bodies of knowledge required for specific mathematical sub-disciplines? I think the answer is yes, whether you’re talking about math education, stock analysis, or weather models. But that still doesn’t get to the question of where that body of knowledge can or should be acquired.