I’m going with number 2 on this one (possibly a result of doing 4 either ‘actively’ or ‘passively’).
I have a very high error rate when doing basic math and am also quite slow (maybe even before accounting for fixing errors). People who’s ability to understand math tops out at basic calculus can still beat me on algebra tests. This effect is increased by the fact that due to mathematica and such, I have no reason to store things like the algorithm for doing polynomial long division. It takes more time and errors to rederive it on the spot.
At the higher levels of math there were people in my classes who were significantly better at it than I, and at the time it seemed like they were just better than me at math in every way. Another classmate and I (who seem to be relative peers at ‘math’) would consistently be better at “big picture” stuff, forming analogies to other problems, and just “seeing” (often actually using the visual cortex) the answer where they would just crank through math and come out with the same answer 3 pages of neat handwriting later.
As of writing this, the alternative (self serving) hypothesis has come up that maybe those that I saw as really good as math weren’t innately better than me (except for having lower error rate and possibly faster) at math, but had just put more effort into it and committed more tricks to memory. This is consistent with the fact that these were the kids that were very studious, though I don’t know how much of the variance that explains.
I’m going with number 2 on this one (possibly a result of doing 4 either ‘actively’ or ‘passively’).
I have a very high error rate when doing basic math and am also quite slow (maybe even before accounting for fixing errors). People who’s ability to understand math tops out at basic calculus can still beat me on algebra tests. This effect is increased by the fact that due to mathematica and such, I have no reason to store things like the algorithm for doing polynomial long division. It takes more time and errors to rederive it on the spot.
At the higher levels of math there were people in my classes who were significantly better at it than I, and at the time it seemed like they were just better than me at math in every way. Another classmate and I (who seem to be relative peers at ‘math’) would consistently be better at “big picture” stuff, forming analogies to other problems, and just “seeing” (often actually using the visual cortex) the answer where they would just crank through math and come out with the same answer 3 pages of neat handwriting later.
As of writing this, the alternative (self serving) hypothesis has come up that maybe those that I saw as really good as math weren’t innately better than me (except for having lower error rate and possibly faster) at math, but had just put more effort into it and committed more tricks to memory. This is consistent with the fact that these were the kids that were very studious, though I don’t know how much of the variance that explains.