Thursday, September 18, 2014

Beauty in Mathematics

I, of course, find plenty of beauty in mathematics, but I'm not sure that seeking it out is the right way to teach mathematics.  Since the beauty is not in a linear, sequential, one-step-build-on-the-last process, trying to teach it that way would make math into an unrelated hodgepodge that nobody but the naturally gifted would be able to see past.  Great, people would understand fractals, but would they understand fractions?  If you wanted "the masses" to know one or the other, wouldn't you choose the latter?

My view is not universally accepted:
Math has a bad rap, writes math professor Manil Suri in a recent New York Times op-ed, and would be better geared to students as a playful and stimulating subject of ideas. Unfortunately, that’s not at all what our culture currently embraces...

Cornell Math Professor and New York Times columnist Steven Strogatz, author of The Joy of x, said much of middle and high school math curriculum (which covers not basic arithmetic, but higher math) doesn’t appeal to students’ hearts, instead offering answers to questions that kids would never ask — which he calls “the definition of boredom.”

“When people want to learn about music, they’ve reacted to it, they love it and naturally want to learn more about it. They have their own questions,” Strogatz said. When introducing higher math to a group of curious young students, he suggests first “showing them math’s greatest hits” and allowing them to become fascinated; students then naturally come up with their own questions. Suri was on the right track, Strogatz said, when he suggested students learn something like the origin of numbers — because the first step is falling in love with the mathematical ideas behind the formulas and procedures.

Strogatz acknowledges that grasping the concepts of higher math can pave the way to many wonderful careers — many in the popular and highly needed STEM fields. But rationalizing to students that math improves reasoning skills or that “you’ll need it in the real world” are two strategies doomed to fail, he said, because they not-so-subtly suggest that math isn’t worth learning for its own sake, but parallels something more akin to “mental push-ups.”
K-12 math isn't the place for "following your bliss", but that's just my opinion. I think mental push-ups are a good idea for any number of reasons.
Grabbing students’ hearts, however, is only the first step to falling in love with math. High school math teacher Dan Meyer realized his algebra classes needed a makeover, the subject of an inspiring TED talk in which Meyer takes a larger look at how math is taught. “We have defined math rather narrowly in the U.S. to mean memorizing procedures and performing them accurately and quickly,” he said. “Those are certainly important parts of mathematics, but they aren’t the only parts, or even the most important parts. We need to define math to include skills like prediction, argumentation, and systematic thinking. These are important skills to have whether you go into a STEM field or not.”
Meyer has done interesting work in his classes, but I disagree with his diagnosis.  Math, if taught poorly, is about "memorizing procedures and performing them accurately and quickly".  I deny that that's how I teach math, and I resent any implication that I should change how I teach because some do teach poorly.

But again, that's just me.

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