The Reluctant Gatekeeper

From time to time, math folks can’t help wrestling with the old, pot-stirring question “Is [algebra/calculus/trigonometry/mathematics] class really necessary?”


The argument goes like this: At every step of education, students face math requirements.


What’s weird is that, once you’ve cleared the bar, you rarely use the math you learned. Continue reading


The Three Barriers to Deep Thinking in School

Almost a decade into my teaching career, I’ve learned a lot—about recurring decimals, British slang, the life cycle of fidget spinners. But one lesson I seem to relearn in new ways every day: Deep thinking is a very, very delicate flower.

It blooms only under rare and perfect conditions, when you’ve given the seedling absolutely everything it needs.

It's always creepy when your students are as tall as you.

There’s no perfect recipe. What gets my 6th– and 8th-graders’ thoughts blooming might flop with my 7th-graders. This work is wonderfully and maddeningly specific. Each seedling presents its own unique and irreducible case. The best you can do is kneel down in the soil and try to help it along.

Even so, I find a few recurring themes: three crude reasons why deep thinking fails to bloom, and the hardy but colorless perennial of “rote learning” surfaces instead.

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What To Do When the Whole Class is Failing

I like to keep an eye on the Google search terms that bring people to this blog. Some warm the cockles of my heart. Some chill the cockles of my soul. Some bewilder the cockles of my mind, forcing me to Google things like “why do people search for such strange terms” and “what exactly are cockles.”

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And the occasional search term will tap into a matter of real depth, like this one: “my students are failing my math class.”

It’s bleak. It’s discouraging. And if you’ve taught math, it’s an experience you know. Continue reading

The State of Being Stuck

Last year, I got the high school math teacher’s version of a wish on a magic lamp: a chance to ask a question of the world’s most famous mathematician.


Andrew Wiles gained his fame by solving a nearly 400-year-old problem: Fermat’s Last Theorem. The same puzzle had captivated Wiles as a child and inspired him to pursue mathematics. His solution touched off a mathematical craze in a culture where “mathematical craze” is an oxymoron. Wiles found himself the subject of books, radio programs, TV documentaries—the biggest mathematical celebrity of the last half-century.

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What Do You Do With 11-to-13-Year-Olds?

A few weeks ago, my school asked me to give a 10-minute speech to our 400 youngest students, a sort of farewell address before I return to my American homeland.

Ten minutes isn’t very long, but it is roughly 297 times their average attention span, and I didn’t want to bore them. So I asked my class of 12-year-olds: What should I talk about?

Here’s how the conversation went:


Then they sort of yelled indiscriminately for a while, which I suppose was my own fault for riling them up. You might as well feed them sugar right before bedtime.

Seeking greater pliability and innocence, I asked my class of 11-year-olds. This is how that went:


Then they spent the afternoon giggling, for which, once again, I can only blame myself.

After this, I realized what I wanted to talk to them about: them. After all, it’s not just me who finds that this age-group ping-pongs between “charmingly ungovernable” and “utterly feral.” Everybody seems to share that feeling.

The world isn’t quite sure what to do with 11-to-13-year-olds.


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The Professor with a Billion Students


This September in Germany, between talks at the Heidelberg Laureate Forum, I managed to catch a few minutes with Cornell professor John Hopcroft.

He’s a guy with bigger things on his mind.

“I’m at a stage in my life,” he says, “where I’d like to do something which makes the world better for a large number of people.”

Skimming Hopcroft’s C.V., you start to wonder: Um… hasn’t he done that already?


Born to a janitor and a bookkeeper, he grew up to become a foundational figure in computer science. Exhibit A: His textbooks on automata, algorithms, and discrete math have been adopted across the world. (His most recent one—on data science—is free online.) Exhibit B: He has a distinguished research record, highlighted in 1986 with a Turing Award— the closest thing to a Nobel for computer science. And finally, Exhibit C: During a decorated teaching career, he was twice named Cornell’s “most inspiring” professor.

With all this, you’ve got to figure he’s done at least a little good for a few people, right?

Well, Hopcroft has a larger number in mind: 1.3 billion.


Hopcroft has become an advisor to Li Keqiang, the Premier of China. He describes this as “the opportunity of a lifetime”: to transform Chinese education for the better.

“They have one quarter of the world’s talent,” Hopcroft says, “but their university educational system is really very poor.”

What makes Hopcroft—working-class Seattle-ite turned Ivy League professor—think he can leave his mark on a country as vast, distant, and internally diverse as China? Isn’t this like a swimmer trying to steer an aircraft carrier?


“A couple of things are going in my favor,” he says. First, he is apolitical. “I don’t have any special agenda to push in China,” Hopcroft explains. “I’m pushing education.”

The second is subtler, and carries echoes of Hopcroft’s engineering background.

“I understand the scale of the problem,” Hopcroft says.

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It’s Obvious Why Students Cheat; We Just Can’t Agree on the Reason

If you love cringes – and hey, who doesn’t? – then walk into a school and try to start a conversation about cheating.

Depending on the school, I suspect you’ll find a superficial consensus (cheating is terrible! and, thankfully, our students do it very rarely!) masking deep rifts. Is the problem with cheating that it undercuts your own learning? That it steals glory from classmates in the zero-sum competition for grades? That it betrays the teacher’s trust? Are all acts of cheating equally terrible, and if not, what does that mean for “zero tolerance” policies?

We all know cheating is bad. But we seem unable to talk honestly about why.

So, I offer up these dialogue-starting cartoons, a few badly drawn meditations on the most basic question: Why do students cheat?


Is cheating a crime of character, or of opportunity? Continue reading