Posted on November 4, 2011


Here are today’s first 600-odd words. I hadn’t thought about math as being a way to build and enhance learning…. oops, better go down and put this *in*

It grieved her sorely, she thought… this guy really, really doesn’t like figuring out the area and perimeter of half a circle. Too taxing on the working memory? Probably not. More likely, he’s been trained to Find the Formula and Plug It In. This problem is supposed to “make” them think about the problem, but there he is, making a flashcard for the formula for figuring out the circumference of a semicircle. He says, “so many formulas!” and the math teachers just don’t understand that yes, for him, there *are* so many forumlae.
Yes, the first clue had been that he’d happily figured out Pir^2 for the area. Almost the entire class had confidently stated that the area of the triangle she’d drawn on the board was “lenght times height,” even when she’d drawn the grid so they oculd see the “squares” that were supposed to be represented by the “square units.”
When she had outlined the full rectangle behind it and asked the area of that rectangle, they had confidently called out 24… same as the triangle… and confirmed that yes, they were the same. Hey, that’s the formula. Yes, this was going to be one of the games she designed. They’d get to drag squares over and count those things a few times, and spend some “structured discovery time” realizing exactly *why* 6 x 4 is what provided the quick and easy answer to the question, just as her “Mathematical Analysis” teacher in high school had had them wrestle problems the hard way before learning the shortcuts to finding derivatives.
Here’s where she knew questions got begged. She was hard-wired to translate every experience into language. For an awful lot of students, though, success with visuals and manipulatives didn’t translate to success with the symbols. Even if they were successful with the symbols, it was a separate experience. Those years teaching the bright dyslexic kiddos had given her a special appreciation for the people who needed even more than the usual efforts. The language theorists would maintain that in using language our knowledge became deeper, so it would seem a much better idea to put in that effort rather than be happy with the “I’m just a visual thinker!” route, especially since so many of the touted “brilliant dyslexics” seemed to have done just that. Words might not have been Einstein’s native language, but he had known how to navigate that country pretty well.
For that matter, for the not-so-brilliant folks, how much intensive connection between the concrete and the abstract and the language to describe it did they get? Wouldn’t math be an absolutely dazzling and wonderful venue for making the connections and getting those neurons firing? Doubling is abstract… but it’s always doubling, and it’s a little easier to define and predict than, say, “hope” or “altruism,” but if a person had learned to wrestle with something that didn’t look *exactly* the same each time but behaved in similar ways, the world might be easier to understand.
Amen, sister! Math WILL save the world! She imagined that world where math was taught rigorously – no, it might not be *fun* all the time – and people actually mastered more than a procedure. She imagined the other lessons – that cognitive dissonance led to enlightened resolution, or from a simpler perspective, that sometimes problems that seemed impossible were worth wrestling with – and sometimes a light went on and it seemed obvious and simple, and not because you were a stinking moron not to have known it all along, but because that was The Way Learning Happens Sometimes, and that if the suffering was torturous, instead of avoiding it entirely, find out which strategies make it less so.

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