On Wed, Oct 22, 2014 at 11:00 AM, Henry Baker <hbaker1@pipeline.com> wrote:
FYI -- I suspect that many on this list would agree with these conclusions w.r.t. math education.
...and a lot would disagree, too. Giving students accurate feedback on their work is important. But I've had violent and abusive teachers, and never learned anything from them. If I went to a class today, and the teacher called me an idiot and threw things, I wouldn't be back for class 2. The difference isn't that young people benefit from this sort of treatment; it's that they aren't allowed to walk away. The thing I disagree with most strongly is the praise for rote learning. I would have learned so much more mathematics if I wasn't required to spend hundreds (thousands?) of hours in rote repetition of things I already knew perfectly well how to do. And not just at the multiplication table level! What possible benefit was their, in an honors-level linear algebra class at a good university, of wasting my time making me do Graham-Shmidt orthogonalization of 4x4 matrices by hand? I saw the results of the emphasis on rote learning when I taught calculus at Harvard. These are supposed to be the best and the brightest, and all they understood of mathematics was being taught to execute rote procedures. Teach them the chain rule and the product rule and have them differentiate things, and they were happy. Try to explain the definition of a limit, and they were baffled. And not just because statements with multiple quantifiers are difficult to understand. They didn't understand *why* it could be useful, or part of what they would do in a mathematics class, to obtain this sort of conceptual understanding; what was the rote procedure this definition would help them execute? And if there wasn't one, then what was the point of learning it? The ability to perform a rote procedure is much easier to test than conceptual understanding. And big surprise, studies show that students drilled at performing a rote procedure do better, as long as you define better as "performs better on a test of ability to perform exactly the rote procedures drilled". Yes, if your goal is to do well on spelling bees, a test of rote memorization, you do better if you waste your time on rote memorization. So what? What use is the ability to do well on a spelling bee? And anyone who uses "success at West Point" as a measure of anything good has radically different values than I do. West Point and the military put a strong value on instant and unquestioning obedience to authority; any education which produces success in an environment like that is a bad education in my book. Andy