Thoughts on Math
I volunteered at the San Francisco Math Circle today, and helped a few kids and one very persistent grown up solve the "tiling torment" which involved figuring out if it's possible to tile a n by n board wtih 2 by 1 (and later 3 by 1) tiles. It was fun and exhausting. Afterwards, I talked a little bit with the math teacher who organized all this (who is quite a notable organizer of math things in the south bay). I told him that one of the kids started working on the puzzle I was helping out with, and then got bored and left, saying "I don't like to explain, I only like to do things."
Josh (the math teacher) said that it's a shame that math in schools is so heavily biased towards "getting to calculus" and thus math involves more rote computation and less thinking. This is a problem because people who would like math in it's higher-level incarnation that involves proofs and such end up deciding, in high school, that they don't like math, and people who think they like math and are good at it get rather disillusioned upon taking real analysis with proofs when they get to college. I'm not sure what he exactly meant by disillusioned, but maybe he meant that people give up on math, or else they feel really bad about themselves and decide that they are stupid. Yes, yes, that last part happened to me.
But I don't think he meant that rote calculation is necessarily a bad thing in itself. I think it's very important to be able to know multipliation tables and to be proficient with rote calculations. Just because something is rote and straightforward doesn't mean it's non-trivial. It's the difference between knowing the alphabet and being good at reading. Knowing basic multiplication, knowing certain trig identities, and knowing the indefinite integral of various basic functions is very important to me because it means that when I try to learn physics or some more advanced math, I know why the details that involve these rotes steps are true.
Ignoring for the moment that maybe non-technical people have different needs than I do. Assuming that the point of a math class is to get people to learn a body of knowledge, I think that doing rote calculations is a good thing. I think that familiarity with a subject matter is very important, and I don't think I got enough of that in my education
Of course, that's important to me because I spend a lot of my time doing things that involve a lot math. The question, though, is what is the most important math that people in high-school need to learn? What should be considered basic requirements, and what should be considred "extra" that technically-oriented people learn in college? Are integrals more important than group theory? More important than probability theory? Or maybe some other math that I don't even know? Maybe learning to recognize symmetry is a more valuable skill for people to have than knowing how to integrate things.
I want to continue writing about this later, but this post has been sitting opened for over a week now, and so I will post it and hopefully put up something more coherent and
Josh (the math teacher) said that it's a shame that math in schools is so heavily biased towards "getting to calculus" and thus math involves more rote computation and less thinking. This is a problem because people who would like math in it's higher-level incarnation that involves proofs and such end up deciding, in high school, that they don't like math, and people who think they like math and are good at it get rather disillusioned upon taking real analysis with proofs when they get to college. I'm not sure what he exactly meant by disillusioned, but maybe he meant that people give up on math, or else they feel really bad about themselves and decide that they are stupid. Yes, yes, that last part happened to me.
But I don't think he meant that rote calculation is necessarily a bad thing in itself. I think it's very important to be able to know multipliation tables and to be proficient with rote calculations. Just because something is rote and straightforward doesn't mean it's non-trivial. It's the difference between knowing the alphabet and being good at reading. Knowing basic multiplication, knowing certain trig identities, and knowing the indefinite integral of various basic functions is very important to me because it means that when I try to learn physics or some more advanced math, I know why the details that involve these rotes steps are true.
Ignoring for the moment that maybe non-technical people have different needs than I do. Assuming that the point of a math class is to get people to learn a body of knowledge, I think that doing rote calculations is a good thing. I think that familiarity with a subject matter is very important, and I don't think I got enough of that in my education
Of course, that's important to me because I spend a lot of my time doing things that involve a lot math. The question, though, is what is the most important math that people in high-school need to learn? What should be considered basic requirements, and what should be considred "extra" that technically-oriented people learn in college? Are integrals more important than group theory? More important than probability theory? Or maybe some other math that I don't even know? Maybe learning to recognize symmetry is a more valuable skill for people to have than knowing how to integrate things.
I want to continue writing about this later, but this post has been sitting opened for over a week now, and so I will post it and hopefully put up something more coherent and