Why Can't Johnny Take a Derivative?



John Hood at The Corner cites a recent Brookings report in support of the familiar conclusion that American students are far more confident in their math abilities than students in other countries who do better on average. Indeed, across countries, there seems to be an inverse correlation between average confidence in math ability and average scores. One read on that data is that focusing on boosting student self-esteem has created a nation of Lake Woebegone classrooms, full of mostly mediocre kids convinced they're all above average. But that seems like a hasty inference for a couple reasons.

First, as Brookings notes, though confidence and achievement are inversely correlated between countries, they're positively related within each country. This is not, pace Brookings, a paradox, because when you think about it, there's no reason at all to expect confidence to track achievement across countries. To paraphrase Robert Nozick, very few of us sit around thinking: "Hey, I've got two opposable thumbs and I've mastered a natural language—I'm pretty good for a primate!" When we want to know how successful we are at something, we compare ourselves to our own social groups, not to all other Americans, and certainly not to all human beings. So even in the absence of any kind of unusual national egotism, you'd expect average national confidence to track, not average national score, but the distribution of scores.

Imagine two countries. One has a familiar bell curve distribution of math scores, with a steep drop-off from the median around which most students are clustered. Most kids are going to look around and conclude they're about average. The second has a double-peaked or bimodal distribution, with lots of kids clustered at the bottom, a dip toward the median, and another big cluster a bit above average. You'll see something like half the kids in that country concluding they're better than average. Note that I haven't said anything about the average scores between countries here; the average in the first country could be much higher, and nothing changes. The effect could be magnified if you've got, say, clusters of crappy schools in which nobody's very good at math, but someone's got to be valedictorian—at least, for certain ways of breaking the math-talent distribution out into discrete schools.

One additional factor is that some of the lowest levels of math confidence come out of high-scoring Asian countries where, at the risk of overgeneralizing, there tend to be norms against seeming boastful. The low reported levels of confidence there might very well just be a sign of higher rigor and more stringent expectations in schools there. But it might also reflect the desire of kids who are good at math (even by local standards) and know it to avoid seeming arrogant.

The Lake Woebegone explanation is actually plausible enough on face: Kids who're made to think they're very good at something, unless they have a special passion for the subject, probably won't feel much pressure to improve. But it'd be interesting to see someone check the alternative hypothesis by looking at a breakdown of the score distributions within each country.

NEXT: The Vitiated Center

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  1. This could also be chalked up to the traditional axiom that as a person’s skills improve he is able to see areas where his skills are deficient. In other words, a person who does not know enough to identify his flaws will think that he has none.

  2. Isn’t that what I said in the last graf?

  3. Wow… didn’t know that self-esteem was such a focus in the Islamic world. Explains a lot, though.

  4. I think there was a similar studies across ethnic groups within the US. Asian kids had the lowest self-esteem scores and the highest academic scores. Blacks had the highest self-esteem and lowest academic, and the relationship was almost exactly inverse among the other groups as well.

  5. I think there was a similar studies

    I are great at number agreement!

  6. Isn’t that what I said in the last graf?

    I didn’t think you said quite the same thing. Kwix’s point isn’t about people who are made to feel good about themselves; its about the ability to self assess.

    Kwix is right; there is plenty of evidence that people who are skilled at a certain task tend to be more self-critical when performing that task; more aware of their own mistakes.

    This makes sense — the better one is at spotting errors before (or as) they occur, the fewer errors they commit. Those unaware of their errors assume they’re doing well, because they don’t recognize where they’re going wrong.

  7. As supporting evidence for Kwix and independent worm, an old joke from rhf…

  8. This from an AP article via Yahoo …

    “If I’m a math student and I don’t perceive myself as confident, you think I’m going to major in it? The answer is no,” said Francis “Skip” Fennell, president of the National Council of Teachers of Mathematics and another member of the federal math panel.”

    Skip is a fucking idiot. Are math teachers trying to teach math or create math majors? Self esteem is shit without skills. I majored in math, as presumably Skip did (or maybe not, he’s only teaching it). All of my undergraduate colleagues were apprehensive and self-critical. That’s just competition. If you aren’t nervous you are probably too thick to know you should be.

  9. So the whole self-esteem movement in schools is almost a guarantor of producing stupid graduates. Astute teachers have been saying this for years and have been getting the hell out of the profession. That leaves us with a school system full of teachers and administrators with the utmost in confidence that their inability to teach has nothing to do with the shitty performance of their students.

  10. FWIW, if Iowa were treated as a separate country, it would top all others countries in ‘school performance’ (’tis really student, not school, performance).

    I majored in math,
    Me too. (physics and EE until my last undergraduate semester, when I changed majors to math because I’d skipped most of the labs for the other majors).

    If you aren’t nervous you are probably too thick to know you should be.
    I wasn’t nervous because it was all pretty damned easy; you can be self-critical without being nervous or unconfident.

  11. yeah, we libertarians never have issues with authority figures!

    also, check out this research paper:
    Unskilled and unaware

  12. OK, I reject the authority of html coding and therefore lack awareness of my lack of html skills

    try this link instead:
    Unskilled and unaware

  13. “I wasn’t nervous because it was all pretty damned easy … ”

    Thats a weird thing to say. All of my major related classes were fairly difficult. I’m no slouch either; this summer I was awarded my PhD in Physical Chemistry, theory and computation. Maybe my undergraduate professors were unusually rigorous. I did seem to be better prepared than most of my graduate colleagues. None of it was easy though.

  14. pretty much the only way to avoid anxiety is to be perfect, and i dont know anyone who is….except me

  15. Biologist,
    Thank you! That is the paper I was looking for earlier today.

  16. Didn’t the noted libertarian John Stossel use this same argument in comparing foreign kids with American kids in his piece on schools last month?

    Maybe Juan and John should have a talk. Juan’s makes more sense.

  17. Sorry Julian I was talking to my friend Juan 2 minutes ago. I meant Julian not Juan.

  18. I’m 110% sure that something is wrong with this study….

  19. Having lived in Japan, I am not surprised it is at the bottom of this list. Saying anything good about yourself (or your family or close friends or coworkers to anyone not personally close to you) is tabboo there. Japanese routinely deny being even average at anything, even when the damned well are highly skilled.

    Conversely, I didn’t know that the Middle East was full of braggarts…

  20. I think self-esteem (I would rather call it self-confidence or even arrogance) is one of the most important and useful American character traits. I worked at a large US company with many young engineers and geologist brought over from other countries, primarily Asians. These guys were sharp but didn?t know how make a decision or have conviction about what they knew. I found the same thing in grad school. Taking risks, stepping out of your comfort zone, and giving things a try is how money is made and things get done.

    In the American culture talking modestly is positive, acting modestly is being a loser. We like Rudy and Rocky because they never let anyone tell them they were not good enough.

    That said we need to drop the fake self-esteem crap that some teachers love. If a kid sucks at something, someone should tell him. He should just decide for himself if he believe it or if he really even gives a shit what someone else thinks.

  21. Julian why do you always put these nerdy titles on your posts

  22. biologist: Thanks for the link.

  23. Two facts:

    1) I suck at math.
    2) I’m acutely, painfully, aware of this fact.

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