math that makes sense vs. math assignments…

Posted on January 22, 2015

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So the man is telling me that what he’s doing has to be right, because … well, he was following what that other problem looked like. They’re solving quadratics with factoring, and he’s copying dutifully and plugging in the different numbers in roughly the same place, hoping it comes out right, hoping he passes the course, and lamenting that gosh, things just don’t stick in his head, no matter how much he studies.

Well, I duly inform him that if he were to try to attend to meaning, instead of trying to imitate problems without understanding, things would have a *much* better chance of sticking (sensing, however, that part of him is hearing “YOU ARE DOING IT ALL WRONG!!! YOU ARE A FAILURE!!!” )  … and pointing out that two factors that multiply to -10 (the problem he was trying to imitate and bungling) … could be *anythign* — 10 x -1, 2 x -5, 20 x -1/2, on to infinity… but that if they multiplied to 0… it was special, because… one of the factors **had** to be zero.

A tell-tale moment came when confronted with 2x – 5 = 0.   He declared that no, this couldn’t actually make sense because **no number times two equaled five.**  Hidden placard reading: “See??? Math we have to do has nothing to do with math that makes sense!!”

I asked, ‘what about 2 and a half?’

(and here’s that nasty affective thing.   The hale and hearty reasonably confident learner would have had the light bulb go on and sought out ways to apply this new insight to other problem situations.  Yes, this made sense to him, and I don’t venture to read minds, but wonder if he realized its truth and then went to “gosh, what a hopeless idiot I am for not understanding that.”)

Yes, he got that.

He even got the idea that there were two answers for these things because they’re quadratics and you can have the ++ or the — combination to get your answer…

we’ll see.

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