Practice Math Like a Baby

I’ve always felt conflicted about repetitive practice.

On the one hand, I see how vital practice is. Musicians repeat the same piece again and again. Soccer players run drills. Chefs hone their chopping motion. Shouldn’t math students do the same: rehearse the skills that matter?

But sometimes, I backtrack. “This is just going to bore them,” I fret, scanning a textbook exercise. “I’m emphasizing the rote aspects of math at the expense of the creative ones. They’re going to forget this skill anyway, and be left only with the insidious impression that math is a jackhammer subject of tooth-grinding repetition.”


(Then I assign the exercise anyway, because class starts in five minutes and— despite my repeated petitions—the administration has denied me access to a time turner.)

These two trains of thought suffer daily collisions in my mind: repetition is dull, but repetition is necessary. This inner conflict takes for granted the idea that repetitive practice is a separate endeavor, a distinct stage of the learning process. First, you learn the concept. Second, you practice it. In this view, practice is like cleaning up after a picnic: absolutely essential, but not much fun.

But this summer, a very wise teacher showed me a path forward, a way to reconciliation.

I’m referring, of course, to a two-year-old named Leo.


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Why I’ve Stopped Doing Interviews for Yale

Last year, I conducted alumni interviews for Yale applicants. It’s an easy gig. You take a smart, ambitious 17-year-old out for hot chocolate, ask them about their life, and then report back to the university, “Yup, this is another great kid.”

I recently got an email asking me to re-enlist. Was I ready for another admissions season?

I checked “No,” mostly because “Aw, hell no” wasn’t an option.

Why my reluctance? No grudge, no beef, no axe to grind. It’s just that the whole admissions process is so spectacularly crazy that participating in it— even in the peripheral role of “alumni interviewer”—feels like having spiders crawling out of my eyeballs.

In the last 15 to 20 years, Yale’s applicant pool has gone from “hypercompetitive” to “a Darwinian dystopia so cutthroat you’d feel guilty even simulating it on a computer, just in case the simulations had emotions.”

I don’t fault the admissions office. For every bed in the freshman dorms, twenty kids are lining up, at least five of whom are flawless high-school rock stars. From that murderer’s row, they face the impossible task of picking just one to admit. There’s no right answer.

But two things freak me out about this process.

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A Technique is Just a Trick That Went Viral


In February, I was throwing together a geometry test for my 12-year-olds. I wanted a standard angle-chasing problem, but – and here’s the trick – I’m lazy. So I grabbed a Google image result, checked that I could do it in my head, and pasted it into the document.


But when I started writing up an answer key, I ran into a wall. Wait… how did I solve this last time? I trotted out all the standard techniques. They weren’t enough. A rung of the logical ladder seemed to have vanished overnight, and now I was stuck, grasping at air.

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One-Word Math Classes

You know what’s often missing from math class? Yes, candy bars, but even more important than that: coherence.


Math class shouldn’t be a mishmash pile of facts, thrown together haphazardly, like an academic version of The White Album. It should be a perfectly interlocking tower of truths, climbing upwards with singular purpose—an academic Sgt. Pepper or Abbey Road.

A good class isn’t a greatest hits record. It’s a concept album.

In that spirit, I’ve been taking each topic in the secondary math curriculum—algebra, geometry, calculus, etc.—and trying to boil it down to its one-word essence. Here are the rules of the game:

  1. You must choose a single word to complete the sentence, “[Branch of math] is the mathematics of _____.”

For example, you might say, “Topology is the mathematics of dinosaurs,” or “Category theory is the mathematics of abstraction,” or “Combinatorics is the mathematics of sadness.” (To be clear, only one of those is remotely accurate; you have my sympathy, combinatorists.)

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America Will Run Out Of Good Questions By 2050

Or, Math Class is Too Full of Spoilers

In grad school, my wife took a class that assigned no homework. The topic was an advanced, hyper-specific area of research—the only plausible problems to give for homework had literally never been solved. Any answer to such a question would have constituted novel research, advancing the field and meriting a publication in a professional journal. The professor assigned no homework for the simple reason that there was no practical homework to assign.

This tickled me. I’d never thought of good questions like a fossil fuel. A nonrenewable resource. Built up over eons and consumed in minutes.


But the thought kept popping back up: Good questions are a resource. And in this new light, something started to make sense, an uncomfortable little fact that had nagged at me since my first year teaching. Continue reading

A Math Teacher’s Guide to Explaining Technology to Your Parents

This is my second century. I was 13 when it began—young enough to be almost fluent, but old enough that my technological skills retain a quaint 20th-century accent. (For example, I still use email.)


My parents’ generation, on the other hand, didn’t encounter the 21st century until they were full-grown adults. They’d settled into their habits when this digital tide began rising around them: Facebook, Twitter, viral videos, actual computer viruses, Android, Snapchat, gifs, Reddit…


And so was born that tragicomedy of 21st-century life: young people trying to explain technology to their parents. It’s frustrating both for the kids (“Why are you so incompetent?!”) and for the parents (“Why do I need this stupid device anyway?!”).

“This is so easy. Why can’t you do it?” vs. “This is so hard. What’s the point?” Now, why does that sound so familiar…?

Oh, that’s right! Because I’m a math teacher. Continue reading