unlearning helplessness

Posted on July 11, 2013

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It’s Thursday-Friday. YOu *might* have thunk things would be quiet around here… but we did have to kick ’em out at closing time, and no, we didn’t have margaritas.
There are ways to attend so that you can do it on your own, and there are ways to attend paying fierce attention to what moves you can make so that I’ll do more of it for you, probably because you’re afraid/sure you’ll never be able to learn it anyway. It’s really hard to do both at the same time, and the more you do of the second, the more you prove yourself right.
Still, this student has been thinking about meaning… she’s got one of my favorite math teachers, who really works the concepts and selects homework carefully so that they don’t get boomerangs tossed at their heads. WORD PROBLEM (heaven forfend)… How much fence do we need for a 1/6 by 1/3 mile rectangular space (with sketch in book). Hey, she knew to add them… was it a half a mile? I pointed at the picture, drawing down the distance next to the numbers shehad chosen. Would that get all the way around?
No… but hey, she said, couldn’t she multiply by two? Which would be 3/6 times two, which would be 6/6, which would be one?
No, she hadn’t realized that she could have just multiplied the reduced one-half by two… or that two halves would have just made a one.. but … she was thinking about *meaning*. Not “which numbers do I stick into the formula?”
And then she was confronted with 4 minus 1 and 5/8.
She was confounded.
But, she told me she … it was just a guess… it would take 3/8 to get up to 2, and then there would be two more… so was 2 and 3/8 it? (Also note that yes, she is trying stuff before I get there.)
I chided her sternly (well, sort of 🙂 )… no… that was *not* a guess. *That* was logical, mathematical thinking, her answer was right for all the right answers, and this was awesome.
I also reminded myself that it was going to take more than me just telling her that it was not guessing; that building confidence was going to take overtly pointing out the good “guessing” from the bad “guessing,” ’cause that happens, too.
Holy cow, after all… these are FRACTIONS. The F WORD.

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Posted in: high five, math, w00t!