She Wants Us to Study for Math

Our teacher’s gone utterly crazy.
No one can fathom her wrath.
She wants us to do the impossible:
She wants us to study for math.

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How can you study for something
where talent is so black-and-white?
You get it, or don’t.
You’ll pass, or you won’t.
It’s pointless to put up a fight.

Her mind must have leaked out, like water,
and slipped down the drain of the bath.
I might as well “read up on breathing”
as study for something like math.

Math’s an implacable tyrant,
a game that I never can win.
And even if I stood a prayer of success,
how would I even begin?

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My teacher, the madwoman, told me:
First, list the things that you know.
Her mind’s gone to rot.
Still, I’ll give it a shot,
though I’m sure that there’s nothing to—

oh!

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The Math Major Who Never Reads Math

In college, I was one of those compulsive read-everything kids. I even felt pangs of guilt when I skipped optional reading. But there was one gaping hole in this policy of mine, large enough to squeeze a whole degree through.

I never did the reading for math. You know, my major.

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I’m not proud of it, but I know I’m not alone. As students from primary school to PhD have discovered, mathematical writing is a different beast. It’s not just a matter of jargon, equations, or obscure Greek letters. It’s something more basic about the way mathematical texts are structured and paced.

The trick is this: In mathematics, you say things precisely once.

(And no, I’m not going to repeat that.)

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The Secret to All Areas

(Except Area 51, which I Am Not Authorized to Divulge)

or, The World Through Rectangular Glasses

Now that I’m teaching middle school, I find myself wrestling with the sheer number of area formulas that my students need to know (or at least be passingly familiar with). Rectangles, triangles, parallelograms, trapezia…

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The logic is this: A handful of geometric figures keep recurring throughout our world. Once you know how to spot them, they’re everywhere, like the Wilhelm Scream. It’s useful to determine the sizes of these shapes effortlessly, via formulas.

That’s all true, so far as it goes. But reducing geometry to formulas alone can lead to tragic misunderstandings, like when a student asked a friend of mine: “Is there a simple way to remember the difference between volume and surface area?” That’s like asking for a simple way to remember the difference between oceans and deserts: You can only confuse them if you have deep misconceptions about each.

So when I teach these formulas, I try to remind myself of an elegant truth: when it comes to area, everything is rectangles.

And yes, I mean everything.

So let’s begin. With rectangles, finding area is a simple matter of multiplication. In each rectangle, you’ve got a little array of squares:

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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