What It Feels Like to Have Wonderful Readers

The response to my last post has been totally overwhelming. Whether you found it via Slate, Facebook, Twitter, Reddit, skywriting, or messenger owl, I’m grateful that so many of you discovered something resonant in my little story.

Most of all, it’s been wonderful reading your stories. Far and away the most common response – and my favorite type to read – has been: “Ah yes, I remember the time that happened to me…” Your tales of academic struggle run from elementary school to research postdocs, from mathematics to English Lit. Most encouraging are the stories from professionals (even professors!) who now make a living on their quantitative skills, after facing the same doubts as the rest of us. Continue reading

What It Feels Like to Be Bad at Math

4 - Pulling out hairAs a math teacher, it’s easy to get frustrated with struggling students. They miss class. They procrastinate. When you take away their calculators, they moan like children who’ve lost their teddy bears. (Admittedly, a trauma.)

Even worse is what they don’t do. Ask questions. Take notes. Correct failing quizzes, even when promised that corrections will raise their scores. Don’t they care that they’re failing? Are they trying not to pass?

There are plenty of ways to diagnose such behavior. Chalk it up to sloth, disinterest, out-of-school distractions – surely those all play a role. But if you ask me, there’s a more powerful and underlying cause.

Math makes people feel stupid. It hurts to feel stupid.

It’s hard to realize this unless you’ve experienced it firsthand. Luckily, I have (although it didn’t feel so lucky at the time). So here is my tale of mathematical failure. See if it sounds familiar. Continue reading

The Anxieties of Hermit Crabs

With the Trigonometry class struggling, I attempt a pep talk. As usual, the students swiftly grasp my metaphor – and then hijack it.

Me: You’ve seen hermit crabs, right? They move from shell to shell throughout their lives. And it’s scary for them to leave their warm, safe shells behind. It makes them feel anxious and vulnerable, because their pink little crab bellies are exposed.

Student #1: Poor crabs!

Me: But they keep on moving. And do you know why?

Student #2: Because life is pain! Continue reading

Stupid Graphs!

Dear Students Who Think Graphing is Stupid,

Right on! Graphs are stupid. Cosmically stupid. Deliberately stupid. In fact – and I hate to pull this rhetorical trick on you, but you leave me with no choice – that’s kind of the point.

A graph is not an end product. It’s more like a map – a simplified picture of something big and complex, a schematic diagram that shows important features and omits distracting details.

Take the function f(x) = x2. This relationship includes a dizzying number of input-output pairs, more than you could ever hope to list. Even with every atom in the cosmos at your disposal, you could never create a “complete” graph of it: to fill in the details, you’d need particles smaller than quarks, and to reach the extremities, you’d have to extend far past the most distant galaxies.

So when you graph f(x) = x2, you’re not depicting the whole function. You’re drawing a simplified version, a pocket-sized map. “Function for Dummies,” you might call it, or “Idiot’s Guide to This Function.” Continue reading

Fistfuls of Sand (or, Why It Pays to Be a Stubborn Teacher)


Teaching is full of compromises. This is a story about one small compromise that I refused to make, a stubborn act that paid off, though I didn’t expect it to. The setting is a Calculus classroom, but I hope the story will resonate with anyone who spies something dubious in the rigid and widespread assumption that learning can be endlessly itemized, carefully quantized, and instantaneously measured. This story has a moral, which I’ll tell you up front: Some lessons don’t sink in right away.

***

By my third year of teaching, I expected my classes to go all right. Not great, mind you: I might stumble over a definition, or botch the phrasing of a question, or optimistically allocate 5 minutes for an example that takes 15. Many days, I still made a minor idiot of myself. But I had put the fiascos of my first year behind me: no more droning 20-minute lectures, no more kids nodding off in the front row, no more pleading for their attention or castigating them for losing focus, as if my sloppy lessons were their fault.

Best of all – perhaps my only real strength as a teacher – I knew the terrain of their minds, how much mathematical territory we could cover in a day together.

So I was perfectly confident when I allotted one day for the Intermediate Value Theorem. The IVT captures a perfectly obvious idea: If at one time you’re 4 feet tall, and later on you’re 6 feet tall, then at some point in between you must be 5 feet tall. In other words: if you reach two different values (e.g., 4 and 6), you must also reach any “intermediate value” between them (e.g., 5, or 4.2, or 5.97).

Of course, the theorem frames this in the rather technical language of the mathematician: Continue reading