Thirteen Ways of Looking at a Parabola

with sincere apologies to Wallace Stevens,
and to all poets, everywhere

I.

All my life
I had known only lines
so when my teacher
drew a parabola
I said,
“Huh?”

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II.

I took all the numbers,
and squared them.
The big ones grew.
The little ones shrank.
The negative ones
became positive.
Opposites agreed.
It was kinda cool.

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III.

I watched an object falling,
tracing its arc,
the ink of time leaving curves
on the paper of space—
a perfect parabola.
(Except for air resistance.)
(NO ONE LIKES YOU, AIR RESISTANCE.)

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Why Do We Pay Pure Mathematicians?

Or, the Many Uses of Uselessness

One of the joys of being married to a pure mathematician—other than finding coffee-stained notebooks full of integrals lying around the flat—is hearing her try to explain her job to other people.

“Are there…uh… a lot of computers involved?”

“Do you write equations? I mean, you know, long ones?”

“Do you work with really big numbers?”

No, sometimes, and no. She rarely uses a computer, traffics more with inequalities than equations, and—like most researchers in her subfield—considers any number larger than 5 to be monstrously big.

Still, she doesn’t begrudge the questions. Pure math research is a weird job, and hard to explain. (The irreplaceable Jordy Greenblatt wrote a great piece poking fun at the many misconceptions.)

So, here’s this teacher’s feeble attempt to explain the profession, on behalf of all the pure mathematicians out there.

Q: So, what is pure math?

A: Picture mathematics as a big yin-yang symbol. But instead of light vs. dark, or fire vs. water, it’s “pure” vs. “applied.”

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The Math Learner’s Checklist

Bored with math lately?

Have you been doing math, but not sure you’re really learning it?

Fret and fume no longer! Below, you will find a definitive (read: not definitive) checklist. Simply think back to your latest mathematical experience, and check a box for each question to which you can answer yes. (Boxes not provided.)

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  1. Did you recognize a strange pattern, or the beginnings of a pattern, or the lack of a pattern, and say to yourself, “Wait… what?!20150218082622_00002
  1. Did you find your jaw hanging open wider than a Warner Brothers cartoon?20150218082622_00003
  1. Did you feel a primal, animal thirst to understand whether (and why!) a certain pattern held true?20150218082622_00005
  1. Did you say aloud, “What in Gauss’s name is going on?20150218082622_00004

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The Church of the Right Answer

I had a surreal moment this year. I’d almost finished a lesson when one boy, usually a hyperkinetic little bundle of enthusiasm, raised his hand.

“So, like, I don’t really understand anything you’re saying,” he informed me, “But I can still get the right answer.”

He smiled, waiting.

“Which part is giving you trouble?” I asked.

“Oh, you were talking about this extra stuff,” he said, “like the ideas behind it and everything. I don’t… you know… do that.”

I blinked. He blinked. We stood in silence.

“So is that okay?” he concluded. “I mean, as long as I can get the right answer?”

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Here it was, out in the open: the subtext of practically every class I’ve ever taught. I’ve grown accustomed to yanking my side of the rope in an unspoken tug-of-war. The teacher emphasizes conceptual understanding. The students conspire to find shortcuts around it. So it always goes.

But I’d never heard a student break the fourth wall quite like this. It was as if Peter Jackson popped up on camera saying, “I know you want a good story, but what about a bloated trilogy full of mind-numbing battle scenes instead? You’ll still buy a ticket, right?”

“Is that okay?” my student repeated. “I mean, I can get the right answer!”

He had a point. What else is there?

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There’s a powerful ideology at work here, one my student has perhaps internalized without realizing: the unshakeable belief that math is all about right answers, and nothing more.

The Church of the Right Answer. Continue reading

Fearing the Unknown

Or, How to Avoid Thinking in Math Class, Part 5
(See Also Parts 1, 2, 3, and 4)

Sometimes I fantasize about making scarecrows of myself.

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They’d wear jackets, ties, and expressions of thoughtful patience. I’d scatter them around my classroom—maybe even one every desk (if scarecrow manufacturers happen to give bulk discounts). And they’d work wonders for my students, because a lot of the time, the students don’t actually need me.

They just think they do. Continue reading

The “Word Problem” Problem

Or, How to Avoid Thinking in Math Class, Part 4
(See Also Parts 1, 2, and 3)

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This speaks more to my naiveté as a first-year teacher than anything else, but I was shocked to find how fervently my students despised the things they called “word problems.”

“I hate these! What is this, an English lesson?”

“Can’t we do regular math?”

“Why are there words in math class?”

Their chorus: I’m okay with math, except word problems.

They treated “word problems” as some exotic and poisonous breed. These had nothing to do with the main thrust of mathematics, which was apparently to chug through computations and arrive at clean numerical solutions.

I was mystified—which is to say, clueless. Why all this word-problem hatred? Continue reading

Are You a Dish-Washing Robot?

or, How to Avoid Thinking in Math Class #3
(See Also Parts 1, 2, and 4)

On Friday I realized—yet again—that my too-clever-for-their-own-good students were finding ways to answer questions without understanding the ideas.

Rather than reckon with the concept of slope, they were memorizing a complex rule:

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That’s all true, so far as it goes, but it’s as opaque and sinister as the tax code.

“Math is supposed to make sense!” I told them, and in my flailing to explain why, I found myself reaching for my favorite rhetorical tool: the overly-detailed analogy.

So, to see what math class is like for memorization-driven students, imagine that you’re a household robot.

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