Math Class Isn’t That Tough
| July 25th, 2008
So, people, do you remember Larry Summers? Poor, poor Larry Summers, who was attacked mercilessly by those humorless feminists, just because he said women weren’t as good as men at math? He’s been held up by the gender essentialist set as a martyr to the cause of political correctness, convicted in what professional concern-troll William Saletan called a “pseudo-feminist show trial” for daring to give voice to the truth: that women are simply inferior to men when it comes to math. Though they do, I’m told, excel at baking.
This was all very horrible for poor Larry, except for the fact that he was absolutely, categorically wrong. As most of the feminist meanies already knew, women aren’t inferior to men in ability to learn math, science, or anything else. And now we have the data to prove it:
Sixteen years after Barbie dolls declared, “Math class is tough!” girls are proving that when it comes to math they are just as tough as boys.
In the largest study of its kind, girls measured up to boys in every grade, from second through 11th. The research was released Thursday in the journal Science.
Parents and teachers persist in thinking boys are simply better at math, said Janet Hyde, the University of Wisconsin-Madison researcher who led the study. And girls who grow up believing it wind up avoiding harder math classes.
[...]
Women are now earning 48 percent of undergraduate college degrees in math; they still lag far behind in physics and engineering.
But in primary and secondary school, girls have caught up, with researchers attributing that advance to increasing numbers of girls taking advanced math classes such as calculus.
So it turns out that the reason there aren’t as many women in the hard sciences isn’t that they’re just too emotional and giggly to do math; no, it turns out that sexism, both internalized and external, has been keeping women out of the hard sciences. And why wouldn’t it? When you spend your life hearing that you’re not able to do something because of who you are, even if you want to believe otherwise, there’s going to be part of you that believes it. That’s true whether you’re a woman who wanted to be an engineer but went into teaching instead, or a man who wanted to be a nurse, but went into business instead. Far from being attacked unfairly, Summers didn’t get the kicking around he deserved; the president of Harvard should be sensitive to the fact that women are subtly and unsubtly discouraged from pursuing careers in math and science, and he should have worked to ensure that he was not part of that discouragement. It is to his everlasting shame that instead of actively trying to tear down those barriers, he helped to shore them up. And it is to the credit of the women and men who have chosen not to believe that lie, the girls who have pushed into math despite being told they won’t do well, that women are achieving equality despite that sexist claptrap.
July 25th, 2008 at 6:49 am
This is what always kills me about the thinking the men are naturally better at some things and women are naturally better at others. I mean even if we could suspend disbelief and say that it is true (and not just the self fulfilling prophesy it actually is), that STILL wouldn’t justify the discrimination people receive when they try to do something not attributed to their gender.
This comment was written by Ali.So even if boys were on average inately better than math than girls, the girls (like myself) you do excel at math and want to go on to become engineers (and men who want to become nurses) shouldn’t have all hell thrown at them trying to keep them out of those fields.
Luckily for me I thrived on proving wrong all the people who told me I couldn’t do certain thigs because I’m female.
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July 25th, 2008 at 8:09 am
Summers’ logic is faulty, dangerous, and comes as no surprise: Because women are not making it, they must be dumb.
According to him (in his famous speech which eventually got him canned), women are not represented equally amongst the most elite in math and science because they are probably not smart enough. If they were, they would reach the highest levels, because the Halls of Math and Science are pure meritocracies, and thus hardly any discrimination occurs.
Even more than the slight on women’s intelligence is the glaring and preposterous refusal to acknowledge that discrimination is the LARGEST factor which prevents women from realizing their potential in those fields, and indeed in most others.
Clueless idiot.
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July 25th, 2008 at 8:15 am
[...] post started out as little more than a comment on Jeff Fecke’s post on Alas, to which I am prohibited from responding. But then it grew and grew, like Topsy. Fecke: So it [...]
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July 25th, 2008 at 8:30 am
Summers didn’t get heckled because he said something “anti-feminist”, he got heckled because he said something stupid and contrary to the data in front of a bunch of academics. Can’t get much dumber than that. Well, yes, you can: you can draw attention to how stupid you were by continuing to whine about it for months afterwards.
Since we’re on the subject, a recent article in the Economist (not the original source, obviously, but a respectable newspaper with usually good science writers) suggests that the math gender gap largely disappears and may even reverse as gender prejudice disappears. However, the language gender gap remains. If taken literally, it might suggest that while girls aren’t innately worse at math, boys are innately worse at languge. However, I suspect that confounding factors are still at work.
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July 25th, 2008 at 10:02 am
I think these studies aren’t responsive to Larry Summers. His argument was not that “boys are better at girls in math.” His argument assumed that there wasn’t a “math gap” at all, and that men and women are, on average, identical in math skills.
Larry Summers’ argument was that the normal distribution around that identical average was different.
So, if the “average” is a grade of all students is 75 (a “C”), and the five girls score 73, 74, 75, 76, and 77, while the five boys score 65, 70, 75, 80, and 85, both genders have an average score of 75 (there is no “gender gap”). But if you need a score of “80″ to make it into the advanced math class, only the two boys get in, while the one boy with a 65 gets sent to remedial math.
No, as I understand it, the “normal distribution” argument is not correct either, but it is a different argument from the “boys, on average, are better than girls” argument.
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July 25th, 2008 at 11:38 am
I thought that most of the studies proved that there was a difference, but not in skill but in preference - men are willing to put up with a lot more solitude, and so are more able to pursue interests that involve little to no human communication… it seems quite likely that intensely studying number-crunching could apply here just as well.
Either way, it’s a half-remembered snippet so not really useful to the discussion.
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July 25th, 2008 at 11:55 am
I just deleted a well-intended comment by a non-feminist.
The main thing he wanted to do was put in a link to a transcript of Summer’s speech, so that people could read it for themselves. That does seem reasonable to me; with all due respect, Jeff, I do think your summary of Summers’ argument wasn’t totally accurate.
Edited to append: In addition, here are some links (from an old post of mine) to criticism of Summers’ speech:
Four Points on Summers’ Transcript, by Colin Danby.
Response to Laurence Summers’ Remarks on Women in Science (pdf file), by WISELI
Raise Your Hand If You’re a Woman In Science, by Virginia Valian
Sex and Science, by Sean at Preposterous Universe.
Statement of the American Sociological Association
Summers Lovin’, by Kieran at Crooked Timber.
Genetics is Only a Red Herring, by Matthew Yglesias.
Open Mouth, Insert Dick, Larry by Bitch Ph.D.
Sexist Calvinism, by PZ Myers at Pharyngula
The following links are not direct responses to Summers, but nonetheless add useful information:
Sex Differences in Intrinsic Aptitude For Mathematics and Science: A Critical Review (pdf link), by Elizabeth Spelke
Debate between Elizabeth Spelke and Stephen Pinker
The Cost of Being a Woman In Science, by PZ Myers at Pharyngula
Is the Science and Engineering Workforce Drawn from the Far Upper Tail of the Math Ability Distribution? (pdf link), by Catherine Weinberger
The discussion in this thread at Pharyngula is interesting, as well.
This comment was written by Ampersand.Report this comment to the moderators
July 25th, 2008 at 12:09 pm
Sorry, Brandon, but I just read Summers’ speech (I’ll admit to having only seen excerpts before) and he’s even more of an idiot than I thought. Anyone speaking to an academic audience should know to cite their sources (which he did only rarely and extremely incompletely), NOT use anecdotes as definitive proof of anything other than that a certain thing can happen, and not use examples that contradict your hypothesis.
For example, his statement, “It does appear that on many, many different human attributes-height, weight, propensity for criminality, overall IQ, mathematical ability, scientific ability-there is relatively clear evidence that whatever the difference in means-which can be debated-there is a difference in the standard deviation, and variability of a male and a female population.” Um, no. There are clear gender differences between mean weight and height, but both have broad statndard deviations. I’ve never heard of any difference in overall IQ and, apart from some differences in mental retardation due to X-linked conditions, little evidence for differences in the standard deviation. The math gap was always hypothesized as a difference in mean performance. I’ll admit that he didn’t have access then to all the data we have now, such as the article referenced in the post, but he really didn’t give any data, not even flawed data from older studies, to back his hypothesis.
I think what he was trying to argue was the old, “Ok, so women are, on average as smart as men. But men are more likely to be geniuses therefore they are more valuable. After all, it’s worse to loose one Marie Curie, er, Rosalin Franklin, er, Albert and Mileva Einstein, er, Niels Bohr (whew) than 100 mediocre scientists, right? Except that the evidence isn’t really there for the genius hypothesis either. Fewer women are known for their science historically, but somehow one might suspect that that has something to do with prejudice too. Especially when one considers the fates of Mileva Einstein and Rosalin Franklin.
This statement at the end of the speech made my irony meter explode:”But I think we all need to be thinking very hard about how to do better on these issues and that they are too important to sentimentalize rather than to think about in as rigorous and careful ways as we can.” If so, we couldn’t have done better than to get rid of Summers as president of Harvard because it’s pretty clear that he’s incapable of thinking about these issues rigorously and without sentiment.
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July 25th, 2008 at 4:41 pm
In all that linkage from Ampersand, I was sad not to see a related article that particularly resonated with me, my hard science friends of both genders, and the quite bright women who did well in science (like myself) who did not go on to get degrees in the sciences.
Women in Science, Philip Greenspun. “This article explores this fourth possible explanation for the dearth of women in science: They found better jobs.”
I have to agree with the overall gist of the opinion piece, although I think the author is a little too dismissing of non-economic reasons to stay out of the sciences. But heck, the people that I know who are in PhD programs are people who:
-said “I am doing this!” at age 12, and stuck to the course for love, despite better job opportunities with nicer salaries and working situations, or
-were swallowed by academia and had little experience outside of it, had little idea about what else to do after undergrad, and had no idea how much the PhD process sucks and how unlikely that ivory tower job is after so much “training” and so little pay. And these folks are noticing that their friends who left the ivory tower bubble are working fewer hours for better pay, have an actual home life [i.e. not in the lab for months at a time with 14 hour shifts], and better job security. And yes, this is in the sciences. It’s not just the liberal arts programs that have issues.
I know I’m worth more than the US$25,000 stipend and crappy work conditions that my male and female friends are currently receiving for sticking with the sciences. They are worth more than that, too. And they aren’t even paying off their undergraduate debt yet, if they accrued any.
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July 26th, 2008 at 2:37 pm
I find it hard to believe that anyone would think women are inferior at math and science when women in Asia and Africa are represented in those fields in high numbers. Its not like American and European women are inherently stupider than women in other countries
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July 28th, 2008 at 7:59 am
[...] reaction in the left blogosphere to the recent study of math performance in US schools is interesting. The post at Alas seems fairly [...]
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July 28th, 2008 at 8:42 am
Actually, please note that the study discussed above actually CONFIRMS the “greater variance” theory, and is being cited by some for that proposition (link below is titled “Summers Vindicated.”
http://www.marginalrevolution.com/marginalrevolution/2008/07/summers-vindica.html
Please note that this post is problematic to the extent that you are praising an article for the part that you agree with (no difference in mean), but are also implicitly supporting the “greater variance” point that is the basis of Summers’ speech, and is also found by this study.
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July 28th, 2008 at 12:58 pm
@Molly
Actually research from a variety of sources that show that in countries where women have the most freedom to choose their careers, the gender divide is the most pronounced.
According to Susan Pinker, the United States, Norway, Switzerland, Canada, and the United Kingdom, which offer women the most financial stability and legal protections in job choice, have the greatest gender split in careers. In countries with less economic opportunity, like the Philippines, Thailand, and Russia, she writes, the number of women in physics is as high as 30 to 35 percent, versus 5 percent in Canada, Japan, and Germany.
I also wonder how much effect curriculum changes over the last 20 years has had on higher test results being now be achieved by girls.
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July 28th, 2008 at 3:19 pm
Like others noted, I thought Larry Summers argued that men and women had, on average, the same aptitude for science, but the distribution was different, with men congregating more to the extremes.
Apparently, this study lends credence to Summers argument:
“But the study also found that boys’ scores were more variable than those of girls. More boys scored extremely well — or extremely poorly — than girls, who were more likely to earn scores closer to the average for all students.”
http://online.wsj.com/article/SB121691806472381521.html
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July 28th, 2008 at 3:40 pm
As caterpillar’s marginal revolution link says, the results of the study can be interpreted as consistent with what Larry Summer said: That girls and boys have the same average achievement, but boys have higher variance, leading to an over-abundance of males at the higher (and lower) ends of the achievement spectrum.
It seems that only the wall street journal reported on the “boys higher variance” part of the study with this headline: “Boys’ Math Scores Hit Highs and Lows”
Here is Andrew Gelman of Columbia talking about the variance part of the study as well, and the contrasting parts that were emphasized by the WSJ vs the NYT (and virtually all other newspapers).
This comment was written by scottynx.http://www.stat.columbia.edu/~cook/movabletype/archives/2008/07/nyt_vs_wsj_on_g.html
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July 28th, 2008 at 6:00 pm
Something is amiss here. The news release from the University of Wisconsin-Madison states:
Some news articles seem to be implying that there will be more boy math geniuses than girls (and more dunces, for that matter) while the original news release implies that this isn’t true.
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July 28th, 2008 at 6:03 pm
Oh, I forgot to mention that the study was conducted by researchers from the University of Wisconsin-Madison and the University of California-Berkley.
So, it’s their news release.
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July 28th, 2008 at 6:18 pm
Oh shoot, I forgot to supply a link to that news release:
UW-Madison news release:
http://www.news.wisc.edu/releases/14632
There is a similar news release at UC-Berkley, with a similar quote:
This comment was written by timberwraith.http://www.universityofcalifornia.edu/news/article/18281
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July 28th, 2008 at 11:07 pm
Summers Vindicated; Feminists Spinning
From Jeff Fecke, the new guy at Alas, a bit of feminist triumphalism regarding a study finding no significant difference in math performance between boys and girls:
So, people, do you remember Larry Summers? Poor, poor Larry Summers, who was attacked mer
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July 28th, 2008 at 11:37 pm
timberwraith
As I understand it, the difference is that white boys’ scores still vary more than white girls’ scores do, but that doesn’t hold true for other races. Which refutes the idea that the variance is due to genetics and suggests that his has more to do with culture.
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July 29th, 2008 at 5:07 am
Mickle says:
Yup, I’ve read that too. Although, I’m sure there are people who are willing to frame this in terms of biological differences between different races and ethnicities. I don’t support that explanation and I think it’s a dangerous road to travel down. That’s one of the potential shortcomings of focusing on biological explanations of gender differences: that kind of thinking is only a few steps away from generalizing the notion to race and ethnicity. Luckily, there’s a strong social prohibition against linking race, ethnicity and biological explanations of differing academic performance.
There’s another study that shows a correlation between indicators of gender equality and the gap between male and female math scores. That correlation also appears for the number of highest performing girls, thus suggesting that at least some of the variability in test scores for girls (that is, how flat the bell cure is) exists as an artifact of culture.
What I’ve read in a number of different places, is that the gap between girls and boys scores have been closing as the years pass. There’s a trend that indicates that culture does indeed have a measurable effect on the math performance of boys and girls. I’d love to see people try to argue that human beings’ biology has changed over the decades. :)
Besides that, both of the news releases indicate that women earn 48% of mathematics bachelor degrees. So, in spite of the supposed greater number of boy math geniuses, men and women seem to be neck and neck in the actual study of mathematics.
I find it hard to accept that differences at the extreme end of the distribution (we’re talking about the highest or lowest 1%) necessarily translates into who strives to become a part of which field of study. Again, the 48% figure that I just mentioned calls into question the notion that the number of people on the far extreme of the distribution (the number of dunces and geniuses) necessarily translates into who is drawn to which field.
I certainly wasn’t a math genius, but I did get a degree in engineering. I can assure you that I wasn’t surrounded by geniuses. When I went to college, folks who sought out that kind of degree were often looking for a skill set they could turn into $$$. Some people were extremely intelligent, some were run of the mill. It ran the gamut.
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July 29th, 2008 at 7:30 am
I certainly wasn’t a math genius, but I did get a degree in engineering. I can assure you that I wasn’t surrounded by geniuses.
Yeah. I think someone should take a look at the assumption that “PhD in Engineering” is a largely overlapping group with “people on the extreme end of the distribution of math ability.”
The correlation is probably about as close as “people duped into becoming terrorists.” If I recall correctly, many of the more famous terrorists in the recent decade had engineering degrees (and were men!).
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July 30th, 2008 at 7:26 am
Whew, so many things to say.
* Even if there were more male math geniuses than female, what does that prove? Until you compare a group of random males and females who had identical education, identical support, have identical self-image, and identical five bazillion other conditions that contribute to the final test score, that statistic is meaningless.
* I have a reason to be skeptical that this study showed gender variance because I have seen so many other studies which people claimed show gender variance, but upon peer inspection show that there is none at all. The Benbow and Stanley studies are the ones that constantly get publicity, and constantly get touted as “proof” of inherent differences. This, despite that it didn’t pass peer review, as the peers found that
1) The males in the study had taken more math classes than the females.
2) Benbow and Stanley’s own data show that girls outperformed boys in the classroom (which they fixed by ignoring that and only using the SAT scores as evidence) .
3) Benbow and Stanley’s own data showed that the high-performing boys received more parental encouragement than the high-performing girls.
4) Most laughably, the statistics only show variance at the bottom of the curve! This was explained by the fact that more males had physical injury which slowed them down when they wrote the test - which is just another example of the bazillions of conditions that contribute to the final test score.
* How desperately invested in gender difference do you have to be to make the leaps of faith here? If you see some statistics about test scores and you manage to ignore the millions of conditions that go into a test score, jumping straight to the conclusion that you have proof of inherent differences, then there is no doubt of your tremendous bias.
* Timberwraith, THANK YOU for saying that. The idea that you have to be a genius in order to go into maths or physics or engineering is a huge part of the problem. Perpetuating that myth ensures that only those who identify themselves as geniuses go into those fields. That invariably means that the fields will be dominated by members of privileged classes. As someone with an engineering degree, I have a secret to tell you that so many other engineers don’t want you to know. It’s not that hard. It’s something that just about anybody can do with the right academic background, practice and self-confidence.
Jeez, if I’m going to be this mouthy, I should make my own blog. Not that the internet needs another.
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July 30th, 2008 at 9:48 am
That’s one of the potential shortcomings of focusing on biological explanations of gender differences: that kind of thinking is only a few steps away from generalizing the notion to race and ethnicity. Luckily, there’s a strong social prohibition against linking race, ethnicity and biological explanations of differing academic performance.
One doesn’t have to focus on biological explanations of gender differences but it would be inappropriate to ignore or dismiss lines of inquiry based on a distaste for the results or possible implications. Gender equality is a social goal based on the equality of the human person and notions of common humanity rather than on actual physical/biological/genetic equality; it is a qualitative equality, not a quantitative one.
If science (biological, medical and social) is going to be useful and informative, it is important that we ask honest questions and attempt to parse the validity of the data and methodologies used without bias as much as we can; that goes for left/right, conservative/progress biases equally. If there is a biological role for gender (or racial) differences in academic performance, there is no use ignoring them because uneducated buffoons would use such information to discriminate further. Education is really essential toward this end; emphasizing that data on mean performances does not translate into data on probabilities of individual performance.
Ignoring possible biological influences on gender (or racial) differences in academic performance and focusing solely on cultural sources could lead to a failure to promote inequality. In the Science article, a possible explanation for fewer women in STEM careers was hypothesized to be differences in abilities in complex problem-solving. “Earlier studies [had] indicated that, although girls equaled or surpassed boys in basic computation and understanding of mathematical concepts, boys exceeded girls in complex problem-solving beginning in the high school years, d = + 0.29.” These skills are essential for success in STEM careers. For complex (and in some ways troubling) reasons, the authors were unable to successfully examine strategic and extended thinking cognitive demands to any accuracy. But now let’s hypothesize that this is an accurate assessment of the data, that there is a gender-gap in item complexity that contributes to a gender gap in STEM careers.
Simply addressing the cultural inequalities surrounding this gap may not result in gender equality in those careers, if educators ignore gender differences in the problem-solving capabilities and styles of learning. One can imagine that changes in curricula that address this gender variance might better prepare girls (or racial minorities) for STEM careers, and focusing solely on cultural or socioeconomic factors could end up failing or ill-preparing all students for those careers (the authors suggest that the lack of data on extended and strategic thinking implies that American students may not be getting proper education at these levels).
Furthermore, I don’t think it is antithetical to the desire for social justice as reflected in equal opportunities for men and women to say that females might be poorer at complex problem-solving than males (if it is indeed true). The challenge we have as a society is to not dismiss the data because some dolts say that since girls are poorer at complex problem-solving, ergo girls iz dumb. The challenge is to say that we cannot and should not place a value judgment on complex-problem solving capabilities vis-a-vis other uses of brain-power or intellect. And that is a taller order, in my opinion.
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July 30th, 2008 at 5:35 pm
Michael, you may have a point if the data supported it. But when peer-reviewed study repeatedly show no gender difference, and those that do show gender difference are shown to employ obvious bias and general bad science, why is it worth discussing? What is the point of such a “what if?” except to derail the discussion?
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July 31st, 2008 at 12:52 pm
funnybunny,
I want to make sure we are talking about the same thing. All data suggests that boys and girls perform equally on virtually all tests. This is all good science and has no obvious bias. What I am talking about is specifically where there is a gender gap, which is in Levels 3&4 complex problem-solving. When the last reliable meta-analysis was done in 1990 (J. S. Hyde, E. Fennema, S. Lamon, Psychol. Bull. 107, 139 (1990)), girls were less likely to take advanced math and science courses and so the very reasonable explanation at the time was that course choice was responsible for the gender gap (even back then, which examined data from the 70s and 80s, there was no significant gender gap on average, but a large one in complex problem-solving). Well now, boys and girls take the same level courses, one of the points of this article. This is an excellent opportunity to test that hypothesis, which is what good science does. Now that the variable responsible for the demonstrated performance gap has changed, does that gap still exist? This isn’t a discussion-derailing what-if; this is exactly the kind of good science that should be done. The only way to not ask that question is if you preferred the chosen hypothesis for other reasons.
Now, because there are no good state assessments for those levels of problem-solving, the authors of this Science article were unable to answer that question. So it’s incorrect in this instance to say that the data do not support the hypothesis that innate gender differences can be responsible for performance differences; it’s that the data don’t exist. Which is an even greater problem, frankly, to the future of math and science careers in this country.
So I believe my point stands. If we allow valid social science statistics that point toward equality to be evidence of equality, we can’t reasonably reject valid social science statistics that point toward inequality as not evidence of inequality. Understanding why certain trends exist is tantamount to our success in manipulating the outcomes. The issue is far from settled and not because some asshole right-wing fringe group is trying to keep women down. We do not treat people equally because they actually are equal. What needs to be eliminated is value assessments and ranking based on our differences.
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August 3rd, 2008 at 7:01 pm
I thought I’d add a link to a table of statistics from the National Science Foundation (Bachelor’s degrees, by sex and field: 1996–2005):
http://www.nsf.gov/statistics/wmpd/pdf/tabc-4.pdf
As a women who earned a degree in Computer Science more than 25 years ago it concerns me that the percentage of women who got CS degrees has actually gone down between 1996 and 2005. I think it’s now a lower percentage than when I got my degree. Very sad.
And I don’t see how this downward trend could ever be explained away by any supposedly innate tendencies in male vs female abilities. There’s something else going on here but I have no idea what it is. What is making fewer and fewer women choose computer science? Educational choices are not made in a vacuum.
And even if there were any innate differences discovered, I completely agree with the earlier comments that we should treat people as individuals, and let folks choose careers according to their individual abilities and desires not silly preconceived notions based on gender, class, or other categories.
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August 6th, 2008 at 10:14 pm
[...] good blog entry at Alas! on evidence that girls do as well as boys in math performance. (See my old post on this topic [...]
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August 20th, 2008 at 10:22 am
Here is a suggestion to further fostering an environment for girls to learn and practice math skills without the gender bias linking that often discourages girls furthering math studies.
http://ramogames.com/blog/math-games-girls/
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November 8th, 2008 at 11:43 am
[...] the blogosphere, echoing James Baldwin: When you spend your life hearing that you’re not able to do something [...]
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