In a comment on this post at Majikthise, commenter Nancy mentioned this great paper by Elizabeth Spelke on sex differences in mathematics, of which I was not previously aware. Some of you may have heard of Dr. Spelke because she recently debated Stephen Pinker. You may not be aware, though, that much of her recent work has been on the development of the different cognitive mechanisms underlying our mathematical abilities. Her work, along with that of Fei Xu, Karen Wynn, and Susan Carey, has shaped the debate in the literature on infant numerical cognition over the last several years. In other words, unlike Stephen Pinker (do you know what Pinker actually studies? I recommend this paper to get an idea) and some of the others who have commented on sex differences in mathematical ability, she knows what she's talking about. She's an expert on the cognitive capacities that underlie mathematical ability, and she's also an expert on the literature (and the author of much of it) within which evidence for sex differences, and innate sex differences in particular, would be found.
The paper, which I highly recommend you read if you've been at all swayed by the arguments hinted at by Summers, and later made by Pinker and many others, about the potential role of innate sex differences in cognitive abilities in creating the gender disparity in math and science departments, discusses the cognitive abilities that underlie mathematical cognition, and shows that in development, few, if any sex differences in math-related ability have been observed. In fact, where they have been observed they actually favor female children. She discusses research demonstrating that rather than differences in ability, differences in problem-solving strategies actually underlie the observed gender differences in math performance. Along the way, she debunks the oft-cited study showing that male infants prefer objects, while female objects prefer people; she points out that there is absolutely no evidence for the innateness of sex differences underlying the observed differences in math test scores (and argues that innateness is irrelevant to the actual debate over gender disparities among faculties in certain fields); she discusses the inadequacy of the SAT-M, the test on which most of the sex differences have been observed; and she discusses the actual performance of men and women at the top end of the curve. The last two allow her to debunk the oft-cited claim that men outperform women at the top end of the curve (and in the process, debunk the 12:1 ratio that is also frequently cited). In the end she concludes, correctly I think, that there is no evidence for sex differences in math-related cognitive abilities that can account for the gender disparity in math and science departments, while there is a wealth of evidence for gender equality in both primary and secondary mathematical abilities.
The paper has yet to be published, or even submitted, which means that it has yet to be peer reviewed. This may give some people pause, but as someone who knows the literature that she discusses fairly well, I can assure you that her factual claims are all true. You can evaluate the arguments she develops from these facts for yourself.
After you read that one, you might also want to read this very good book chapter by Spelke and one of my favorite cognitive scientists, Marc Hauser, on the evolution of mathematical ability. It would make a great addition to my list of writings on evolutionary psychology (as opposed to Evolutionary Psychology), as it explicitly avoids the primary sin discussed in the paper to which Lindsay linked in her post.
9 comments:
I saw the Pinker debate, and Spelke's performance didn't impress me.
She emphasized the role that social conditioning plays in explaining alleged sex differences. But I don't think she ever adequately addressed, and I would be happy to know, why any difference in social conditioning exists in the first place? Suppose that men do outperform women in math *just* because society conditions them to do so. The question remains: why would such a bizarre stereotype emerge for no apparent reason? Why would society say "women can become doctors and lawyers, but women can't become physicists?"
Another telling part of the Pinker debate (about which an audience member questioned her):
Spelke thinks that performance in undergrad is the best estimate of mathematical abilities. This is so, on her view, despite the fact that everything undergrads learn is "spoon fed" to them, and involves no innovation.
A final point, Pinker really demolishes Spelke's argument that a lack of objectivity encourages discrimination. Surely math is more objective than sociology.
Reading the most recent Spelke paper, it becomes apparent that we don't really have an answer to the question "why are most mathematicians male?" I see Spelke's main accomplishment in playing a very strong devil's advocate to the "conventional" view that supplies easy answers to this question. She points out huge holes in the logic. I read her speculation about social causes as more of a counterweight to a prevailing view than an convincing argument; if you apply her own standard of critical thought to her speculation, you wind up with nothing about the original question (why are most mathematicians male). However, that is not to say that we know nothing about the topic of gender differences and mathematical ability; we know a lot.
why would such a bizarre stereotype emerge for no apparent reason? Why would society say "women can become doctors and lawyers, but women can't become physicists?"
This is a good question, except for the "bizarre." While it is something that should be explained in a comprehensive theory, we don't go around wondering today: "Why would society say that black people are born to be slaves? You're telling me that it was *just* social conditioning! Surely there had to be some truth to that fact!" People can have all sorts of self-serving beliefs.
why would such a bizarre stereotype emerge for no apparent reason? Why would society say "women can become doctors and lawyers, but women can't become physicists?"
Honestly, you may as well ask, "why would the bizarre stereotype of women as being inferior to men emerge for no apparent reason?" Throughout Western history, and probably in most if not all other human civilizations/societies as well, women have been viewed as inferior to men in almost every substantial way. What we have seen in modern times is the steady chipping away at sexist stereotypes. You might forget that women became doctors and lawyers in substantial numbers only in the last 50 years!
Kip, Dr. Myers' comment is dead on. I think you, and to some extent Pinker, fail to understand many of Spelke's points. Math is quite objective, however, as Spelke shows quite convincingly using empirical evidence (you know, that stuff Pinker never really worries about), men and women, while they have the same cognitive abilities (read the paper) use different cognitive strategies. As a result, men perform better on some types of math problems, and women perform better on other types of math problems. Men perform consistently better on tests like the SAT-M (and the GRE-Q), in part because the questions favor them. If we look at advanced level math performance in college (both undergrad and grad), women get better grades. Why is it that a test designed to predict college grades (the SAT-M) consistently predicts that men will do better than women, but the opposite occurs? Because the test sucks, that's why. It's far from objective, and there are barriers to objectivity all the way up to tenure committees, and even higher, as Summers' remarks indicate, as the popularity of Pinker's idle speculation makes even clearer, and as the refusal to accept any amount evidence against the stereotype makes completely transparent.
Here's the highlight of that debate:
SPELKE: "In science, the judgments are subjective, every step of the way. Who's really talented? Who deserves bigger lab space? Who should get the next fellowship? Who should get promoted to tenure? These decisions are not based on clear and objective criteria. These are the cases where you see discrimination persisting..."
PINKER: "But that makes the wrong prediction: the harder the science, the greater the participation of women! We find exactly the opposite: it's the most subjective fields within academia — the social sciences, the humanities, the helping professions — that have the greatest representation of women. This follows exactly from the choices that women express in what gives them satisfaction in life. But it goes in the opposite direction to the prediction you made about the role of objective criteria in bringing about gender equity. Surely it's physics, and not, say, sociology, that has the more objective criteria for success."
Unable to come up with a reply, Spelke changed the subject.
Here's what I'd written previously documenting differences in accomplishment:
Apparently, the Patriarchy had conceded to power-share with women in such trivial outposts as law and business, but it desperately clung to that central bastion of male control of society: the college mathematics department.
All 23 tenured mathematicians at Harvard are indeed men. Yet, can you name one? Do you know even two living mathematicians? Those who feel the necessity of pursuing mathematics are an odd breed. A mathematician has almost zero chance for celebrity, yet his primary reward, if he discovers something important enough to have it named after him, is fame. It's a strange kind of renown, however, one that the vast majority of humanity will never notice. Among the handful who comprehend, however, his fame will be as undying as Achilles's.
The more meritocratic the field, the more feminists accuse it of discriminating against women. In mathematics, new proofs either quickly fail or are accepted forever. In contrast, women flourish most in notoriously faddish, cliquish domains like the humanities. In Harvard's English department, 20 out of 51 professors are women, and at less exclusive colleges, they often comprise a majority...
The first scientific challenge to academia's traditional assumption that men were smarter than women came in 1912 when pioneering IQ test researcher Cyril Burt announced they scored equally -- on average. Yet, as Summers noted, men are more variable, so they are more numerous among the extremely intelligent, such as Harvard professors and Nobel Prize winners (40 of whom have taught at Harvard).
The Nobel Prize lists show a striking pattern: the fuzzier the field, the better women do. Twelve women have won the most political and least intellectually rigorous Nobel Prize, Peace (13 percent of all individual winners), and ten have been Literature laureates (ten percent). In Physiology & Medicine, there have been seven female laureates (four percent). In Chemistry, three (two percent), and in Physics, the most abstract of the Nobels, just two (one percent).
What about mathematics, that most unworldly of subjects? The Fields Medal for mathematicians under age 40 is the equivalent of the Nobel. No women number among its 44 recipients.
But, surely, the trendline must be turning upwards as discrimination lessens?
That's true in Physiology & Medicine, where women won only once before 1977, but six times (nine percent) since. Yet, by aggregating Physics and Chemistry, we can see the opposite pattern: five women ranked among their first 160 laureates, but over the last 40 years, not a single woman features among the latest 160 winners.
Overall, in the bad old days from 1901 through 1964, women won 2.5 percent of the hard science Nobels. Since then, they've declined to 2.3 percent.
http://www.isteve.com/2005_Education_of_Larry_Summers.htm
The empirical point is that the more falsifiable the contents of a field of study are, in the Popperian sense, the more male dominated it is. Women do best in softer fields where logical or empirical falsification plays less of a role in determining prestige.
why are most mathematicians male?
If you really want to piss off a female mathematician, ask this question.
First of all, I am not convinced that this is true. My graduate class in math was 50% women. The top grad student in my class was a woman (not me).
If the question is why there aren't more female math professors, consider the following:
1. Women might want to take time off to have babies. Could this hurt their chances at tenure?
2. There is quite a bit of sexism from professors due to studies such as this. Why would a woman want to continue on in such an environment when Google is hiring.
3. Female grad students frequently marry male grad students. I know of several (at least 3) cases where the woman half of the couple required the school that she was hired at to take her husband as well. Yes, that means the woman was the more desired (read better) mathematician.
Why aren't their any studies questioning why there aren't more black mathematicians or why there are so many Indian mathematicians? Why is it Ok to be prejudiced in one way and not another?
Axiomatically deciding that men are better at math then women is just as bad as assuming that African Americans are stupid. Neither are true but both are the subjects of books. Unfortunately for women, theories such as in "The Bell Curve" have been debunked but "Sex Differences in Math" is a scientific paper.
Its too bad these social scientists wouldn't know a great mathematician if they were bit on the butt by one.
I had the pleasure of meeting Spelke in person a few times. Aside from being smart and eloquent (at a talk of hers I attended), she's super nice. Anyway, here's a Nature Neuroscience editorial that is already published which summarizes the cognitive science and sociology studies on gender and science. I know you may need a subscription to view it, but I don't want to violate copyright.
The reference is:
Nat Neurosci. 2005 Mar;8(3):253.
The link on the Nature Neuroscience website is here
One point Spelke brought up to me in person is that Asian females score better on average than white males do on the SAT-M. But you don't see that reflected in math professorships. This is just one point, obviously, but people who believe too strongly in standardized tests *or* in the awarding of professorships as good measures of ability should consider these things.
Secondly, if you go over Summers's transcript on the orginal speech, he brings up the disparity in a field of surgery. (Maybe neurosurgery; I forgot.) There the proportion of white males is underrepresented, and there is a higher proportion of first and second generation immigrants. Interestingly, Summers doesn't offer any explanation involving innate abilities. The only suggestion he has to explain the disparity is entirely "social."
Why does he look at that problem differently than that of gender and science?
I wonder.
um, Chris, thanks for the links to good reading and all, but the Spelke draft that you linked via Nancy is a draft and on it says "This paper has not yet been peer reviewed. Please do not copy or cite without author's permission." Just so you know; I don't know if Spelke wants it linked all over the Internet.
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