I'm going to sound crazy, but I think you have a shitty teacher.

I have had that idea, but I don't think she is. I think she may just have a teaching style so radically different from what I'm used to that I don''t understand it at all. I THINK (and this is just a conjecture) that she teaches math like other teachers teach art; I think she is trying to get us to just FUCK WITH IT and throw things at the wall to see if they stick. This just happens to be at odds with all my former experiences with math teachers, who just want you to follow the rules and get it right.

Unfortunately, one of the things I love about math, after years of art, is that I can just follow the rules and get it right.

So I suspect that I have some learning to do, with this chick.

I totally hear you, but I suspect that if this teacher truly sees math as art, she has the right of it, and is a rare and special snowflake in that. Are you familiar with Lockhart's Lament? (http://www.maa.org/devlin/devlin_03_08.html)

IIRC, the gist of it is that teaching math as "just following the rules" is as silly as it would be to do the same with art, except that with math it's the norm. As a mathematician, Lockhart sees math as the purest form of art (because it is as abstract as humanly possible, meaning everything is potentially possible.) But it's been a few years since I read it, so I'm probably remembering it kinda wrong.

That was a very interesting essay, and he makes a number of good points. What he, unfortunately, fails to recognize is that what he finds interesting and fun is pretty much exactly what I find boring and dry. He makes the very typical mistake of assuming that all people enjoy learning in the same ways he enjoys learning (false consensus) and, sadly, proceeds to spend some time more or less bashing scientists for their scientific curiosity, as if science and art are opposites. They are not opposite, and the artistic mind, which asks "can I create?" is often the same as the scientific mind, which asks "what can I do with this creation?"

The rivalry between mathematicians and scientists seems to be old and possibly permanent. Mathematicians seem to view scientists as hopelessly pragmatic; a mathematician says "Squeeeee! I made a pretty thing with numbers!" and a scientist looks and says "Squeeeee! Look what I can DO with it!"

The "Art vs. Science" categories he seems to want to divide things into are simply invalid. I've been an artist for roughly my entire life, and a career artist for nearly ten years. I started training in the art I'm most skilled at about 21 years ago. In order to get as good as I am, I had to learn a phenomenal amount of chemistry and physics, but I learned them primarily not in words, but visually and through touch. Where I agree with him is that while children need to learn the "boring" facts and formulas, the best way for them to learn that is through play. It's through play that you can "see" the math in your head... well, that might be false consensus again. It's through play that I can see it in mine. Knowing the science allows you to express it as art.

Take his example of the triangle; he is glum that it is reduced to just a formula. Honestly, on their own, neither the nifty visualization nor the formula do much for me. It's not until the two are combined that they become exciting - when I can visualize WHY the area is 1/2 base times height, because that unlocks things I can actually do with it. Lockhart, like many mathematicians I have met, seems to be under the impression that if only people understood why math is fun for mathematicians, everyone would find math fun. I like math. I find it fun. But I find it fun mostly, if not entirely, because it helps me interpret the world around me.

I am sure that Lockhart is right about the way we teach math, and the way we SHOULD teach math. I'm sure we would have more mathematicians if we taught it better. But for many of us, doing math games and puzzles and explorations all day is almost exactly as fun as being plunked into a room full of musical instruments for eight hours, which is to say, not fun at all.