Noah Smith, the econ blogger, and Miles Kimball have an article up at The Atlantic right now titled “The Myth of ‘I’m Bad at Math.'” Smith and Kimball want to challenge the idea, overwhelmingly commonplace in American culture, that some people are just born with math ability. I think most of us believe that the ability to do math is somehow predetermined in a way that is somehow not true of other subjects, like history or geography. (I was recently at a presentation by a lawyer who told the audience he decided to go to law school because law was an area, unlike math, where you could succeed by working hard and applying yourself.)
Smith and Kimball present plenty of evidence that, in fact, for elementary and high school-level math, at least, preparation and hard work are basically the whole ball game. Sure, they argue, there will always be a few geniuses like Terence Tao at one end, and people with genuine learning disabilities at the other. But for most people, much of mathematics is very learnable. It just takes determination. “We already venerate sports heroes who make up for lack of talent through persistence and grit; why should our educational culture be any different?”
Well, who doesn’t like persistence and grit? But I think Smith and Kimball are missing a piece of the puzzle.
They suggest that we adopt the methods and attitudes that have made math education successful in Japan and Korea. According to Smith and Kimball, one reason east Asian countries have been successful at teaching their students math is that “Persistence in the face of failure is very much part of the Asian tradition of self-improvement. And [people in those countries] are accustomed to criticism in the service of self-improvement in situations where Westerners avoid it or resent it.”
Perhaps that is true. But recently I’ve been reading Claude M. Steele’s excellent Whistling Vivaldi: How Stereotypes Affect Us and What We Can Do About It. The book is mostly about the phenomenon of “stereotype threat” — essentially, the idea that worrying about living up to a stereotype can actually impede one’s cognitive abilities. The research of Steele and other social psychologists suggests that, among other things, stereotype threat may explain why capable, motivated minorities and women often fall away from difficult subjects like math when they get into college or, sometimes, graduate school. Smith and Kimball are exploring similar territory; they discuss experiments by Carol Dweck that suggest that just teaching poor minority students that “intelligence” is malleable rather than fixed can lead to both better effort and improved grades.
But Steele points out that minority students are already aware that “hard work” is supposed to be their remedy:
[People] ask, Dear Professor, why can’t a person just buckle down and overcome the damn stereotype? I can hear my parents’ admonitions to this effect ringing in my ears . . . . I hear you, son, stereotype threat can be pretty bad, but you should use it to motivate you; get out there and prove the stereotype, and those who hold it, wrong.
In fact, says Steele, those to whom stereotype threat applies often do exactly that. Steele describes the experiences of Philip Treisman, a mathematician who developed training workshops for black and female students after he noticed talented students struggling in his undergraduate classes. Treisman, with his students’ permission, followed them around to find out more about their study habits.
[H]e saw black students — in an effort to succeed where their abilities are negatively stereotyped — follow a strategy of intense, isolated effort . . . . They were trying hard, they were taking my father’s advice (and probably their own father’s advice), but they were trying to do it all by themselves . . . .
By contrast, Treisman observed, Asian-American students (who tended to do the best in his classes) studied in groups, and they made their study groups the center of their social life.
This practice brought powerful advantages for learning calculus. It brought many heads to the homework, so that if one person couldn’t solve a problem, someone else could, and that person could explain it. They could spend more time on the concepts involved in calculus, and less time doing the arithmetic of the homework . . . . Misunderstandings could be quickly identified and corrected, even when they came from the teaching staff . . . . Saturday night studying in the library counted as social life for a group of friends bonded, in part, over studying and doing math problems together.
Black students, Treisman found . . . were intensely independent, downright private about their work. After class, they returned to their rooms, closed the door and pushed through long hours of study — more hours than either whites or Asians . . . . With no one to talk to, the only way to tell whether they understood the concept of a problem was to check their answer in the back of the book. They spent considerable time doing this, which made them focus less on calculus concepts and more on rechecking their arithmetic against answers in the book. This tactic weakened their grasp of the concepts. Despite great effort, they often performed worse on classroom tests than whites and Asians, who they knew studied no more, or even less, than they had. In light of the racial stereotype in the air over their heads, this was a frustrating experience, which made them wonder whether they belonged there.
Happily, Treisman’s story has a happy ending. He was able to develop workshops to teach the group study method. Which worked!
Black students in his early workshops at Berkeley . . . outperformed all other groups in their first-year calculus courses. A substantial portion of all the American women who have gone on to study math at the graduate level in the United States come from Treisman’s math workshops at the University of Texas.
With all the usual caveats about the limits of what can be understood from a single study, and what can be achieved through adopting a single solution to a complex problem, I think Treisman and Steele are really onto something here. I went to a mediocre Georgia high school and found myself completely overwhelmed in freshman calc at the University of Chicago. Like Treisman’s black students, I spent hours banging my head against the wall, to no avail. I left it all on the field, but two quarters in a row I had to slink away at the end with a gentleman’s C+. In physics, where I had a couple of good friends I could study with, I did significantly better.
Steele’s retelling of Treisman’s research emphasizes two points. First, how you study is at least as important as how much effort you put in. And how you study is culturally determined; the Asian-American students may not have been consciously selecting a more effective strategy — I doubt they did any research on effective study habits — but they had an effective strategy handed to them in the bundle of expectations about school that came with being an Asian-American student, at least at Berkeley.
And second, although he doesn’t say it directly, Steele strongly implies that stereotype threat itself contributed to black students’ isolation:
Discouraged . . . [black students] didn’t talk much academic shop outside of class, sternly separating their academic and social lives. This, in turn, prevented them from knowing that other students, too, had anxieties and difficulties with their work; it allowed them to think that their problems were theirs exclusively, reflective of their own, or perhaps their group’s, inability . . . . After a poor performance, they would redouble their efforts, but in the same isolated way. Intense work would then be followed by relatively poor performance. Eventually they’d get discouraged, deciding that calculus . . . wasn’t for them.
All of this is very, very interesting in terms of differences in academic performance between racial groups. But the point is broader. Sheer effort is often not enough to make the difference in a difficult subject like math. The support of a study group — not to mention other school “skills,” like auditing the course once before taking it, or seeking out free tutoring — can multiply the effects of a student’s efforts. But more crucially, working with a group enables the student to see, in a very concrete way, that others are also struggling, also have questions, also make mistakes. This reduces the influence of the “I’m bad at math” demon that would otherwise run circles in one’s brain late at night in a quiet dorm room. Everyone is bad at math; working together enables you to see that in a way that heroic-but-isolated effort simply does not.
That IS interesting, but I do think that there IS such a thing as “I’m bad at math.” It’s just not what people think it is.
I suck at math. That is, I suck at arithmetic. I’ve always been scorekeeper when we play cards, as my parents started that habit, in the hopes practice makes perfect. It didn’t help. As the practice carried over into adulthood, the joke is, “We never have any idea who really won or lost, we just know when we can end the game.”
I loved algebra and geometry and calculus and did very well at them in school (as long as I could use a calculator for the arithmetic–otherwise I’d inevitably lose points for a stupid mistake).
I managed to never confuse my issues with arithmetic with a problem with math in general, and I think that’s where some people get tripped up. They have problems with arithmetic and get it into their heads they’re bad at math, and so they never even try when they get to higher maths, thinking it’s beyond them.
The problem is that a lot of math classes in school seem to focus on the result, rather than the process.
One of the advantages of study groups is that when you have to try and explain a concept, you learn it better yourself. I don’t think the importance of that can be overstated.