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Solving Our Math Problem
If we ever decide we need a mathematician laureate for the United States, Steven Strogatz may get the first call. On Radiolab, on a blog at The New York Times, and in books like The Joy of x, Strogatz has been asked again and again to bring human interest and importance to a subject that's abstract and, often, very complicated.
Strogatz knows that math is America's worst subject, and tied to anxious memories in many people's minds. At Cornell, he teaches math for non-math majors — an exercise in pushing buttons, he says. ("Joy" is the operative word.) He wrote about it in a 2014 article, "Writing About Math For The Traumatized and the Perplexed."
This interview has been edited for clarity.
If you're illiterate, it’s an incapacitating thing — but at least our education system tends to notice. Whereas it seems like a lot of people go through 12 years of math education, and yet they’re missing the deep comprehension of some of math's more complex themes.
That’s right. You can get by by being a good citizen. That is, if you follow the rules, if you do what you're told, if you do your homework, memorize the right formulas, and get a feeling for when to invoke those formulas, you can probably get an “A,” you know? And I think a lot of people do. My wife certainly admits to that.
It’s a funny thing. Mathematicians are always harping about the beauty of math or the importance of math. That’s a conceit that comes much later. I think for many students — they like that math comes out right. There's no need for further insight beyond that.
But if you take that point of view about math — and also if the teachers don't ask really provocative questions that require a struggle and genuine thought — then it's kind of like, 'We can pretend that I'm teaching you math, and you can pretend that you're learning it, and by all measures everything will be fine' — except when you get tested on genuine math. Then you discover you really didn't understand anything.
When you walk into your math class for liberal arts students, how do you start it off? How do you hook them or bring them along?
Well, it’s an unusual class, because it’s not taught in that way that we think of a normal college course. It’s not a lecture at all; in fact, I never lecture. I try to make it very clear on the first day that everything's going to be different.
There's a lot of making fun of the concept of a “safe space.” But this is a safe space, and I'm not embarrassed about that: “safe” in the sense that it's safe to take real intellectual chances. You can look stupid, and that's good because you're brave for taking a chance, for making a guess. The truth is you can't really learn math without that. That’s the way professional mathematicians work with each other. When we're working on some problem that hasn't been solved before, we have to trust each other enough to say some stupid things.
We had a teacher tell us that she wants students to have a fight. If they start to debate, you’ve got some real math cooking in the classroom.
Maybe I should just enunciate one little principle, a good one for us to talk about. If I had to boil down what works in the classroom, what doesn't work is this: If you tell a student the answer to a question that they would never think of asking, that's trouble. That's not going to work.
So many of the things that we do in math education — and maybe more generally in education — are giving students answers to questions that they would never think of asking. By definition, that's what it is to be boring. If you're sitting at a bar and someone’s telling you stuff that you're not interested in and you would never think of asking about — what is more boring than that? That seems to be the model of our educational system: 'Here’s the formula for the cosine of the double angle.' 'Well, I don't care about that.'
So what's the solution? The solution is to make them care. I think the secret to why students hate math is that it's meaningless to so many of them. And the reason I loved math is that it always was meaningful to me — and often because it was me asking the questions.
'I'm a kid, doing puzzles because I feel like it': That is so natural. And yet somehow we beat it out of them in school. Rather than giving people puzzles to solve, we’re giving them the answers. It's like, 'Here's how you do this puzzle. Now, you do a similar puzzle.' Well, that's boring. Just give me the damn puzzle.
We've heard many people's stories of math class, and they're surprisingly emotional. It's the first time people feel inadequate or think, “I don't get this.” I wonder if you've had any success getting students to talk about their experiences, and what you hear.
That's a big part of the course: to keep a portfolio, or write down your random thoughts in your notebook. Those could include sketches, emotional things, like “I'm really irritated and stumped.” What are you stuck on, what’s the part that's confusing?
And I have them as their first assignment do what I call a “mathematical autobiography,” from the time they were little kids to the present. That can include good and bad things: teachers that inspired you, teachers that either depressed you or insulted you, parts of math that you liked, parts that you didn't like. Whatever they want. So they do write that way, and those journals are really interesting.
When I read my students' essays, most of them start with, “I liked math until…” and then something happens. They usually do like math at the start. Nobody complains about arithmetic. The first hard thing is fractions and decimals and percentages. So division is complicated — all things related to division. For some people there is a clear bifurcation between algebra and geometry — and it's not really predictable.
But everybody has this experience when they “hit the wall.” That’s where you'll find out will they ever take math again or not — or is that the end of it for them?
How do you make math, which is so abstract, meaningful?
It varies so much. For some people, it starts to come alive when they hear how it can relate to auto mechanics or airplanes or space flight or electricity. Some people want to hear biology. They're interested in human behavior. I, as an applied mathematician, am very sympathetic to people who want to see how math connects to the real world — but that's not it for everyone. For some people, it's a game.
Your goal is to get the student to teach himself or herself. You can guide them but ultimately they're the ones who have to create the mental structures. That is the key. If math is a book and I'm handing you the book, if you don't have book cases — you don't have any place to put the book. It’s going to drop to the floor. If I try to learn some new bit of math it's not hard because I have all my bookcases built. I can just put that book on the shelf somewhere. But for someone who's learning algebra or calculus or whatever for the first time, they don't even have the bookcases. That's the hard work of learning.
America ranks 31st among 35 industrialized nations in math score on the international PISA exam. Why do you think that is?
Why are we 31st on PISA? There's nothing wrong with our brains in America. I honestly think [it's] because we have a profoundly anti-intellectual culture, for the most part. I know I'm not supposed to say that, but I don't think we have a great tradition of being thoughtful and taking education seriously. We do respect business. We respect making money. We respect inventiveness and entrepreneurship. Obviously, it's a ridiculous generalization — but since I'm airing out and ventilating here, can I tell you what I really think? We are not an intellectual culture.
Some cultures respect intellectualism. Some cultures also respect hard work. The parents in Japan and Singapore don't want to hear that you're not a math person. They will tell their kids, 'You can do it like I did, and you're going to study until you get it.' So they use what I consider a sort of inhumane philosophy — but it works.
For me, you start with joy. Joy is, to me, a means to get the student to do the end, which is to be active. If you're joyful, you're going to try.