Math Proficiency: The Difference Between Individual and Systemic Success

Miles Kimball and Noah Smith recently wrote a post, “There’s one key difference between kids who excel at math and those who don’t“, that zipped around the intertoobz. I want to like it. In fact, this is the part I really like (boldface mine):

“I’m just not a math person.”

We hear it all the time. And we’ve had enough. Because we believe that the idea of “math people” is the most self-destructive idea in America today. The truth is, you probably are a math person, and by thinking otherwise, you are possibly hamstringing your own career. Worse, you may be helping to perpetuate a pernicious myth that is harming underprivileged children—the myth of inborn genetic math ability….

For high school math, inborn talent is just much less important than hard work, preparation, and self-confidence.

How do we know this? First of all, both of us have taught math for many years—as professors, teaching assistants, and private tutors. Again and again, we have seen the following pattern repeat itself:

1. Different kids with different levels of preparation come into a math class. Some of these kids have parents who have drilled them on math from a young age, while others never had that kind of parental input.

2. On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it—maybe 80 or 85%, a solid B.

3. The unprepared kids, not realizing that the top scorers were well-prepared, assume that genetic ability was what determined the performance differences. Deciding that they “just aren’t math people,” they don’t try hard in future classes, and fall further behind.

4. The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are “math people,” and work hard in the future, cementing their advantage.

Thus, people’s belief that math ability can’t change becomes a self-fulfilling prophecy.

The idea that math ability is mostly genetic is one dark facet of a larger fallacy that intelligence is mostly genetic.

I agree! I’ll admit I’m inclined to like this explanation, given my feelings about the overestimation of the heritability of IQ (An aside: I think they give far too much credence to the PISA evaluations, but there’s a lot of that going around). And I would love it if accomplished students garnered more respect. But I think their recommendations don’t necessarily follow:

Nisbett describes how the educational systems of East Asian countries focus more on hard work than on inborn talent:

1. “Children in Japan go to school about 240 days a year, whereas children in the United States go to school about 180 days a year.”
2. “Japanese high school students of the 1980s studied 3 ½ hours a day, and that number is likely to be, if anything, higher today.”
3. “[The inhabitants of Japan and Korea] do not need to read this book to find out that intelligence and intellectual accomplishment are highly malleable. Confucius set that matter straight twenty-five hundred years ago.”
4. “When they do badly at something, [Japanese, Koreans, etc.] respond by working harder at it.”
5. “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.”

We certainly don’t want America’s education system to copy everything Japan does (and we remain agnostic regarding the wisdom of Confucius). But it seems to us that an emphasis on hard work is a hallmark not just of modern East Asia, but of America’s past as well.

It’s the longer school day that bothers me. First, the hypothesis that longer school days has already been tested, albeit indirectly: most U.S. states have essentially the same amount of classroom hours (.xlsx), yet there can be massive discrepancies in educational outcomes. Massachusetts, which always scores high, has relatively low classroom hours, while Alabama, which is routinely abysmal, has the second most classroom hours. Within the U.S. context, it’s not clear at all that hours/year has anything to do with success. Maybe I’m selling my fellow residents of the Commonwealth (God save it!) short, but I’m not entirely certain that Massachusetts is more ‘Confucian’ than Alabama either; I’m pretty sure our kids can be just as lazy as Alabama’s. Are states that fall between these extremes ‘kinda Confucian?’

A useful strategy for psychologically defeated students doesn’t mean that it should be a cornerstone policy for all students. A key problem with the U.S. education system is that K-6 math is taught broadly but not deeply–students repeatedly cover the same topics year after year without ever mastering the basics (and these repeated failures could discourage poor performers). It’s worth noting that the Japanese math curriculum doesn’t repeat the same topics year after year. Instead, programs like the JUMP curriculum, which break mathematics down into ‘microsteps’, have been shown to be incredibly successful in increasing confidence in basic mathematical skills and, importantly, outcomes. The other intriguing method is to ‘flip’ education–exercises are done in class, while students watch videos (or read) at home. On the limited scale that flipped classrooms have been tried, the method seems to work (if nothing else, children shouldn’t be working through problems in the evening when they’re tired, but during the day when they’re more awake. Instead of watching TV in the evening, they can ‘watch’ lectures). Massachusetts’ performance did increase after the education reforms of the mid-1990s, and that was, in large part, a curricular reformation.

Kimball and Smith’s solution is appealing: work harder (ya bastids!). But the corollaries from this approach don’t seem to apply in the U.S. Are high performing states harder workers than low performing states? Let’s figure out how to teach students better–that is, focus on pedagogy and curriculum because that’s where the evidence points.

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2 Responses to Math Proficiency: The Difference Between Individual and Systemic Success

  1. Noah Smith says:

    Note that we reference both TIMSS and PISA data.

  2. Ed says:

    Interesting … Math skill gets much pro forma attention as valuable, BUT doing long division of stock or home prices by CPI — to show their real price histories — is nearly never seen, because they look like the first two charts here
    and heads in the dark make better customers!
    “What is intellectual honesty’s cash flow?”

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