I recently made the comment that “music is heard geometry” in my conversation with Andrew Kern about the Great Dance on the “Ask Andrew” podcast. A friend asked if I could unpack that phrase and hopefully bring some understanding to that idea.
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Allow me to tell you The Fable of the Fearsome √2, a proud irrational number with an unsettlingly sinister story behind it.
Feel free to share this story with the little children whom you tuck in. Please note that this is, like any respectable fairytale, the stuff of legend. Furthermore, as is a storyteller’s prerogative, I’ve taken a few minor liberties—mostly with respect to vocabulary—in retelling the legend.
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In my last article, “Can Mathematics be Parables?” I considered the fantastical realm of “imaginary” numbers. Now, wander with me across a terrain of numbers even more dazzlingly head-spinning . . . and even more hazardous, perhaps, to encounter.
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“Why do we have to know this?" This question is the bane of every math teacher's existence. It gets asked in math class more frequently than in any other subject area (Latin teachers, please form a queue if you wish to lodge a complaint against that claim). But many math teachers don't know how to the answer it.
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There are three kinds of people in this word, it has been said. Those that think math is a waste of time beyond learning to count, add, subtract, multiply, and divide and thus is primarily useful for consumerism. Those that think that math is amazing because it is extremely useful for the construction of bridges, building, airplanes, cars, and more. These are the engineers. And, finally, those that think math is beautiful for its own sake. Each group is smaller than the previous.
A person's approach to teaching math will differ based on which group he is in.
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From December 2008, so lacking in the mellowness of my late years:
Speak all you like about the economic and political ideals of the contemporary school, the education they provide is an education for slaves. Consider this scenario:
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As an undergraduate, I studied mathematics, with the single ambition of teaching it to high school students who, except for getting into college, would also have no other use for it. The major was not easy. I remember one night when, instead of watching the Super Bowl, I spent the evening trying to maximize the area of an industrial building. But schlepping a six-pound Calculus book makes you look smarter and improves muscle tone, which was good, because, as it turns out, I never actually taught mathematics to high school students. At least it wasn't a total waste.
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As a physics teacher, I get to play with toys as part of my job. Physics labs give me the chance to dig out classic favorites such as Slinkys and Hot Wheels cars and put them to educational use. Occasionally I get catalogs from laboratory equipment manufacturers full of strange and sterile contraptions, but I find that students learn better when they personally connect the lessons to familiar things, and the more nostalgic the better. And so, where I am able, I make the childhood playground my laboratory.
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I have been told that fear of math is irrational. Perhaps this is so, but it seems very rational to acknowledge one’s algebraic limitations or to express a tested dislike of geometry.
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I used to think that classical Christian education was all about rigor and challenge–a time-tested method by which to best develop intelligent, logical minds.
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