I used to drive my teachers crazy because I would 'skip' or 'combine' steps. Or sometimes come up with more elegant solutions than the one they wanted or whatever. Of course, they drove me crazy because they'd get upset at my doing, say, a whole bunch of associative stuff as one step. I think I really did end up staring at one at one point and saying something like, 'If you can't follow this or don't understand that the associative property means that any string of things connected by plus signs can be rearranged any way you want, perhaps you should be doing something else.' It may not have been the most politic, but it did get across that I knew what I was doing and they were being stupidly pedantic. I don't mind pedantic, but I strongly object to the stupid.
Of course, the other important point sometimes is that math != arithmetic. And many people who are /good/ at higher math really aren't at arithmetic, particularly if they're dyslexic or dyscalculic or even have a bad enough case of dysgraphia. The worse case is when people who /would/ be good at higher math get so discouraged by arithmetic and the over reliance on speed and memorization that they never discover that geometry or calculus or group theory is something that they can just do.
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Date: 2010-06-15 10:43 pm (UTC)Of course, the other important point sometimes is that math != arithmetic. And many people who are /good/ at higher math really aren't at arithmetic, particularly if they're dyslexic or dyscalculic or even have a bad enough case of dysgraphia. The worse case is when people who /would/ be good at higher math get so discouraged by arithmetic and the over reliance on speed and memorization that they never discover that geometry or calculus or group theory is something that they can just do.