[Numeracy 644] Re: That old thinking style thing
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Mon Dec 27 18:26:54 EST 2010
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I, too, struggle with making the connection between "this problem" and "problems like this" -- but I think that all too often we simply don't *teach* the connection; we assume it will happen. It can be hard because as Mike Wolf described, often they can solve simple "real life" applications ... but then don't see the value into turning that into equations and generalizing. However, I wonder -- I bet for a lot of them might be more willing to, if they actually saw it would solve that very practical problem of Getting Through Math Class. I think a lot of my guys, like the student in the article about "what students in developmental math know," would be interested in figuring out the reasoning.
I've also watched them solve, so often and well, practical problems that are simple applications of waht I'm trying to teach... but they're not doing it with what I'm trying to teach. They're moving the symbols around in ways that look the same, "canceling," and assorted other things that when I ask, they can't translate into math. We don't have time for them to work out their own way of organizing the ideas and sorting out the language -- but maybe we do have time to translate one situation into "triangles' and then ... have them figure out which of several problems could be solved the same way (and then do it ;)).
NOw, regarding "x - 2 = 5" being an addition problem -- yes, to solve it requires addition, but it is a problem wiht subtraction in it. Maybe it isn't worth trying to convey what's happening in that statement, but to work hard on having students understand that it conveys the parts and the whole thing is what you were starting with, and to get the whole you add. I'd still like to find a way to illustrate it. I know it's a real challenge to get my students to add when there's a minus sign and to subtract when there's a plus sign. Once they have the answer, they're still, somehow, pretty sure they subtracted to get it (because when they see the equation at the end, 7-2=5, they subtract and it's right -- especially if they didn't understand the process while they were doing it, but they did understand the checking process at the end).
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