R Hansen: >So the talented musical students are either not playing Beethoven, or if they are playing Beethoven, then Beethoven isn?t a parallel to calculus, or if Beethoven is a parallel to calculus then it isn?t just playing Beethoven that is a parallel to calculus, it is understanding Beethoven that is a parallel to calculus, which makes just playing Beethoven a parallel to arithmetic.
Yeah - something like that. The problem is trying to take a rough analogy too far.
R Hansen: >And some people might look at these kids and say they don?t have enough theory, which floors me, considering how good they are (at what ever it is we agree they are doing).
I listen to some of them and say they don't have enough rhythm. And so there's another imperfect analogy to explore. I mentioned that at the piano recital I just recently attended, not a single performer could play with convincing rhythm. Why is that? Because students haven't had enough time to develop rhythmic sensibilities? Of course not. Its because the teacher wants the correct notes above all else.
Kirby asks, earlier on: >Why has all the joy and imagination been sucked out of math teaching? It seems deliberate.
I think there may be a rough analogy with the above. Details left as exercise ;-)