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.

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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:

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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:

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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?

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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.

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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?

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“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?

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

The Catchy Nonsense of “Two Negatives Make a Positive”

My 6th- and 7th-grade students are pretty effective at calculating with negative numbers. They all know, for example, that 5 – (-2) = 7. Ask them why, and you’ll hear this:

“Because two negatives make a positive!”

Then, if you listen carefully, you will hear something else: the low rumble of my teeth grinding together with tectonic force.

“Two negatives make a positive” is one of those math slogans that drives me crazy, because it is so pithy, so memorable, so easy to apply… while also being so vague and non-mathematical that I’m amazed students find it useful at all.

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Other Ways to Carve Up the Math Curriculum

If the Food Network has taught me one thing, it’s that how you plate a meal matters almost as much as what you’re serving.

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So here are some ideas of other ways to slice, dice, and rearrange the mathematics currently taught in high schools. (And hey, maybe we’ll want to switch out an ingredient here or there, too.)

I’ll lay out four proposals.

First up…

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This is an approach with a simple goal: Make Math Useful. Continue reading