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# Anything Boys Can Do...

Biology may play only a minor role in the math gender gap

Image: Illustration by Thomas Fuchs

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When then Harvard University president Lawrence Summers suggested in 2005 that innate differences between men and women may account for the lack of women in top science and engineering positions (and subsequently resigned), he was referring to the greater male variability hypothesis. Women, it holds, are on average as mathematically competent as men, but there is a greater innate spread in math ability among men. In other words, a higher proportion of men stumble mathematically, but an equally high proportion excel because of something in the way male brains develop. This supposedly explained why boys tend to dominate math competitions and why men far outnumber women in elite university math departments. Since then, scientists have put the variability hypothesis to the test, and it comes up short.

In the most ambitious study so far, mathematics professor Jonathan Kane of the University of Wisconsin–Whitewater and oncology professor Janet Mertz of the University of Wisconsin–Madison analyzed data on math performance from 52 countries, including scores from elite competitions such as the International Mathematical Olympiad. In particular, they examined variance—roughly, how spread out scores are. Two patterns emerged, they report in a paper in the January issue of the Notices of the American Mathematical Society. The first is that males’ and females’ variance is essentially equal in some countries. The other is that the ratio of males’ to females’ variance differs greatly from one country to another. These ranged from 0.91 to 1.52 (where a ratio of 1 means the two sexes’ variance is equal, and a number greater than 1 means males’ scores were more spread out than women’s).

The finding that males’ variance exceeds females’ in some countries but is less than females’ in others and that both range “all over the place suggests it can’t be biologically innate, unless you want to say that human genetics is different in different countries,” Mertz argues. “The vast majority of the differences between male and female performance must reflect social and cultural factors.”

Such as? One clue comes from the finding that a widely used measure of a nation’s gender equality, called the Global Gender Gap Index, correlates with the ratio of boys versus girls scoring in the top 5 percent on an international math competition called PISA. In some countries, such as the Czech Republic, the boys’ and girls’ distribution of math scores were nearly identical. Another clue that gender differences in math performance are not innate comes from the shrinking gender gap. In the U.S., the ratio of boys to girls scoring above 700 on the math SAT fell from 13:1 in the 1970s to 3:1 in the 1990s.

Psychology professor Stephen Ceci of Cornell University calls the new analysis “a very important argument” in the debate over the sources of sex differences in math careers. But, he adds, the findings do not mean that biology plays no role. Just because diet affects human height, for instance, does not mean “that nature is unimportant.” Now that the greater male variability hypothesis has fallen short, nature is not looking as important as scientists once thought.

This article was originally published with the title Anything Boys Can Do.

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1. 1. amalcr 06:28 PM 12/25/11

Your article doesn't make sense! In one part of your article you state that the variance in all countries is O.91(females)to 1.52 (males) and then in another part of your article you state that the ratio of boys to girls scoring above 700 on the math SAT is NOW 3:1. By your own words boys have a greater proficienty in math by 50 to 300%. How could you make the conclusion that greater male variablility has fallen short? What is short is your ability to get by your own biases and realize that males DO outscore and outperform girls in math. Go somewhere else to blow your horn. Stupidity and bias doesn't belong in Scientific American.

2. 2. JamesDavis in reply to amalcr 08:42 AM 12/26/11

"amalcr": you did notice who wrote the article didn't you? The article itself proves the point, but now, you and I are going to be called bigoted woman haters or nitpicking. In every class I have taken to get three degrees; from first grade to the last grade of graduate school, girls have always performed lower in math and science than boys...in every class, and that is a fact. And wouldn't it been easier to do this experiment by checking the math scores of boys and girls from first grade to graduate level, or are they afraid of what that would show? We do have computers, that was designed by a male, that can quickly crunch numbers, and the computers can crunch numbers from all over the world.

3. 3. JamesDavis 08:54 AM 12/26/11

Before someone does call me a woman hater and upset my wife, I should also say that girls outperform boys in social fields and communications. In these fields, boys are just as bad at or worse than girls are in math and science. We all have our skills and our place in the world, that is why we are a very successful species. For those with the attitude, "whatever you can do, I can do better", (could) cause the rapid decline of our species.

4. 4. c.o.corroboration 09:15 AM 12/26/11

Then why is that post of yours on here amalcr? Try again with some poise and pertinence please.

Genreally typing I would like to say that biological factors would seem to have effect (on mathematical performance and any other behavioural endeavor, aside (usually) from base violent intimidation). The causality of the effect is quite possibly more dependant on cognitive cogency of parents, religion/culture (i.e. current cognitive cogency of parents:o),diet, and other non-inherent constituents.
What up neuroplasticity?

5. 5. martharose 10:37 AM 12/26/11

amalcr, you seem to have misread the part of the article you quote (or perhaps you haven't quite grasped the concept of ratios).

The article doesn't cite the variance for men and the variance for women, as you seem to think it does. The figures quoted (0.91 to 1.52) are the range of ratios for female:male variance in all countries. That means that in at least one country (scoring 0.91) females had a higher variance than males, whereas in others (e.g. the country scoring 1.52) males had higher variance than females.

Please also note that SAT scores mainly reflect variance within the one country where SATs are currently taken - the United States. As such, they can't tell us much about global trends or innate biological differences that ought be independent of culture. (I'd also add that since you can study for the SATs and see your score improve, it is very unlikely to be a good measure of 'innate' biological ability anyway).

It's interesting to note that the next commenter, who wishes us to know he has three degrees, was so eager to agree with you that he forgot to check your working. Perhaps such intellectual laziness amongst graduate students when it comes to their male colleagues might be part of the explanation for fewer women currently making it to the top.

(Also, Mr. Davis: perhaps you have forgotten that the first computer program (and, indeed, the entire concept of algorithmic computations performed by computers) was devised by the great female mathematician Ada Lovelace.)

6. 6. Vidhyacharan HR 10:41 AM 12/26/11

In a limited mathematical environment, the girls have shown significant improvement especially solving "known problem". When it comes to solve difficult problems pertaining to probability or calculus, there is a lag. As the complexity increased ability to solve declined. This could relate to inability in realizing a complex logic. Girls are more nature oriented.

7. 7. InquiringConstructivist 12:13 PM 12/26/11

To me, a true sign of bias is a troll who always argues on the side of social conservatism, no matter what the scientific data, across all sorts of fields, from climate change to gender differences in STEM achievement.

8. 8. Lisssssa 12:36 PM 12/26/11

Wow. The comments on this article are amazing. I especially love how the first commenter couldn't understand ratios and still thought men were superior to women. Sigh. People seem to have issues understanding that just because they generally observe something (i.e. the 30 men they know well seem to be better at math than most of the 30 women they know well) doesn't mean that there is some genetic, innate, biological/evolutionary reason for that observation. Almost everything in science and psychology have shown to have about a max of a 50-50 split between biology/genetics and environment. Brains have been shown to be plastic. Your brain changes and grows with your environment and with learning. Men aren't necessarily "wired" to be better at math than women. Men don't have some special "math gene" that makes them superior. Just like white people aren't innately superior in math to black people, despite discrepancies in math scores on standardized tests.

I'm sure people will comment on this that I'm some crazy defensive woman, but for the most part, I rarely pay attention to gender. I work with mostly guys. I went to college with mostly guys. It doesn't bother me and I rarely think about gender when it comes to academics or careers. However, I take particular offense to this because I am a woman and I love math and science. And I'm good at it. I went to one of the best colleges for math and science in the world. I took lots of math and science classes. I did better than some men in my class. I did worse than some women in my class. Some of my best (girl) friends are getting their PhDs in engineering. In fact, I'm working on my PhD right now. I don't think I'm superior to men, or other women. I'm just doing what I love, and what I'm good at. It is these sorts of comments, and this sort of sexist thinking, that makes women think they can't achieve in math and science. Which, most likely, partially explains this gap between men and women in math & science.

9. 9. Lisssssa 12:39 PM 12/26/11

JamesDavis, I think it's equally offensive to say that men are worse than women in social fields and communication. I know plenty of men who are fantastic businessmen, and who could give a speech and capture an entire audience in just a few minutes. I know fantastic researchers and professors in social science. Please stop gender stereotyping and telling both men and women what they are "naturally bad at", because frankly, it's not true.

10. 10. zehlyi 01:07 PM 12/26/11

It's problematic to take the number of girls at the top of their math classes as evidence for a biological difference anyway -- girls are told from a young age that they shouldn't like or be good at the STEM fields, and stereotype threat, getting funnelled into easier math/science courses, etc can be factors.

As someone in computer science, another field that women aren't supposed to be good at, I find it hard to believe that there is some biological difference as the primary cause of the gender imbalance, when the social aspects are so obvious. Even in college I was told not to take introduction to computer science because I would hate it and would end up failing the class, and that I should take a humanities class instead. I liked it so much I switched majors to CS, but I believed all the men in my classes were much better and considered switching back, until they told us our rank in the classes and I found out I was at the top. I ran into other women in the same situation once I started TAing intro classes. How many other women end up dropping before they realize they're doing well?

I know that I'm just one person, but I doubt my experience is completely atypical.

11. 11. julia smith 03:05 PM 12/26/11

I find that there is a problem in that "gender ideology" has so much corrupted the debate on gender differences that any new study "confirming" their dogmas is suspect. By the way, Summers' "resignation" is a good example of what's going on.

12. 12. elriana 03:39 PM 12/26/11

My third grade teacher refused to recommend me for the Talented and Gifted math program at our school because "Girls just don't do well in math." At that time I had the highest math scores in my class and had received a perfect score on the placement exam. She told my mother this, knowing that my mother is an electrical engineer.
My fourth grade teacher eventually got me into the program. She was the only teacher at my elementary school who gave boys and girls the same list of potential careers when asking "what do you want to be when you grow up?" Until fourth grade, my teachers told me I could be a nurse, a teacher or a veterinarian, while the boys with the same math and science score were being told they could be engineers, doctors and astronomers.
You cannot compare abilities without giving children the same opportunities. If girls are told they cannot do math, what chance do they have to discover that they can? If they are not allowed into the advanced placement classes, how are they supposed to score well in calculus? I persevered because I had my mother as a role model. She did not push me into math and science, but she did tell me I should take the classes I wanted, despite what other people thought.
I was the valedictorian of my high school class, went to a top tier college and now have a PhD in Geophysics. And despite that, my third grade teacher still has never recommended a girl for the accelerated math program. I do not know if there is a gender disparity in innate analytical ability, but there is no way anyone can prove or disprove it in a society where males and females with the same demonstrated skills are treated so differently.

13. 13. julia smith 04:25 PM 12/26/11

The title says it all: anything that boys can do.. [women can do better].

14. 14. way2ec 04:57 PM 12/26/11

I hope to further complicate the simplistic "innate" male/female dichotomy that is at the core of this study. Sexual orientation and gender identity studies reveal a complete range in whatever "innate" differences exist between male and female brains, showing once again that plasticity begins at the moment of conception. Why not "crunch" the numbers further to see if "masculine" gay males math abilities are different from "feminine" gay males, same for lesbians, and of course as Kinsey's studies revealed, bisexuality forms the bulk of the bell curve between a 1 and a 6. On the other hand, trying to study "innate math ability" implies that math ability itself is something totally different from say "communication skills". Finally, as martharose points out, using SAT scores is hardly an objective starting point, or any other math test devised by men(?) and completely influenced by the language(s) and culture(s) used to both teach, test, and report the implied "innate" math abilities used to obtain the high scores. Might as well study the influence of the "mother tongue" vs. the "father tongue" on the development of her sons' and daughters' "innate" math abilities. Never the less, let the studies continue as they do more to reveal our biases, filters, and stereotypes than reveal innate anythings. This is like trying to study racism when science reveals that the concept of race is bogus, a social construct, that there is more variability within any "race" than between any "races". Lets count how many times the dog chases its own tail.

15. 15. IC in reply to way2ec 05:15 PM 12/26/11

I believe that terms such as "progress" or "advanced" have been thoroughly discredited and should be dispensed with.
Who knows how many budding Newtons or Einsteins among the aboriginal set have had their spirits crushed by the overflight of an airplane.
The pure lucky happenstance that resulted in European primacy in tools and weapons might also benefit those cultures left by the wayside in Borneo and Brazil, were it not for the fact that Europeans have to be cocky and use their tools excessively and too well.

16. 16. Science Outsider 07:07 PM 12/26/11

I'm surprised that many researchers are totally uninterested in the second part of the argument of the original research, which argued that, because of the same variability, men would also make up a disproportionate number of those with below average math proficiency. Why hasn't that facet of the argument provoked as much reaction from researchers like Sharon Begley? The responses and the responses to those responses seem to show more passionate gender-bias of both women and men, respectively, than did the original research.

17. 17. Bops in reply to martharose 07:45 PM 12/26/11

From Wikipedia below.

"Her mother's obsession with rooting out any of the insanity of which she accused Lord Byron was one of the reasons that Lovelace was taught mathematics from an early age. Lovelace was privately schooled in mathematics and science by William Frend, William King and Mary Somerville.[11] One of her later tutors was the noted mathematician and logician Augustus De Morgan. From 1832, when she was seventeen, her remarkable mathematical abilities began to emerge,[9] and her interest in mathematics dominated her life even after her marriage. In a letter to Lovelace's mother, De Morgan suggested that Lovelace's skill in mathematics could lead her to become "an original mathematical investigator, perhaps of first-rate eminence".[12]

18. 18. Bops in reply to Lisssssa 08:01 PM 12/26/11

Sorry, you are so wrong! I'm a female and live with a gifted, born that way, math guy. Males have a NATURAL ability. Most people can learn almost anything. It's a way of thinking that's different. I think his son has almost the same abilities, not sure yet he's still young.

19. 19. Bops in reply to Lisssssa 08:06 PM 12/26/11

People have different skills.
Too Bad... you have a problem with that.

20. 20. Bops in reply to elriana 08:11 PM 12/26/11

21. 21. snowhill 09:55 PM 12/26/11

I recall that my five brothers were good at math in school and were provided with advanced coursework at an early age (elementary school) whereas I was initially good at math and forced to tutor other students, without being allowed or encouraged to pursue more challenging coursework in math- it was easy for the teachers to just have me work as a tutor, and seemed to fit their image of me (the first girl in my family) as a "natural teacher." (I am in fact now a teacher, but an art teacher.) My parents were similarly supportive of my brothers' advancement, and rather non-supportive of my interest in wanting to advance in math. I grew bored and frustrated at not being challenged, and ended up disliking math. (My father was somewhat of a math genius.)

The son and daughter of one of my brothers both earned perfect scores on their math SATs, and another brother's son and daughter in high school both excel at math and science. I'm sure there is a cultural/familial component, as well as a genetic one.

This is just one anecdotal situation, but perhaps is a common theme in some families and cultures.

22. 22. Padgie 11:27 PM 12/26/11

A soon as anything with a statistical base gets mentioned we get a flurry of "well I know someone who". There may well be some underlying mind skill biases that are gender based, I only have a problem with people who try to use this to make a point.

23. 23. jtoomim 01:55 AM 12/27/11

Okay, that article had in it one of the silliest statements I've seen in a while:

'The finding that males’ variance exceeds females’ in some countries but is less than females’ in others and that both range “all over the place suggests it can’t be biologically innate, unless you want to say that human genetics is different in different countries,” Mertz argues. “The vast majority of the differences between male and female performance must reflect social and cultural factors.”'

OF COURSE human genetics is different in different countries. The reason that most people in China have epicanthal folds (read: Asian eyes) and most in England do not is genetic. If male/female variance ratios vary between countries, that could just as easily be due genetics as due to social or cultural factors.

The original research article can be found here, if anyone cares:

http://www.ams.org/notices/201201/rtx120100010p.pdf

It's worth mentioning that this study found male/female variance ratios among countries to be approximately normally distributed with a mean of around 1.12. If I'm reading their graph right, only 3 countries out of 52 had variance ratios less than 1 (i.e., females more variable). That isn't very strongly supportive of the authors' conclusions. I also see no per-country sample size data (can you find any?), so it very well could be that they just had a bunch of sampling error with some countries. Would be really nice to see a forest plot of those data. (Bad statistics in a mathematics journal? Fo' shame!)

I'm all for more women in science, and I'm all for spending money on programs which help women into science, but I find it pretty ironic when people base their arguments therefor on ... bad science.

Clearly, there are social and cultural factors which make fewer women enter STEM, and they should be countered. Whether or not there are any biological factors as well is pretty much irrelevant, especially when the proposed mechanism would only describe differences at the extremes, like with Fields Medals.

24. 24. julia smith in reply to IC 04:18 AM 12/27/11

IC: I said "The title says it all: anything that boys can do.. [women can do better].", and you reply: "Well, maybe women can do some things better! We cannot allow men to entertain the idea that they may be better suited for some tasks. This can only lead to the oppression of women, minorities, whales and result in Global Warming." This lack of logic and equanimity reflects well the discourse of gender feminism. BTW, did you notice that you claim that women are better at some things but you attack men for believing that they are better at some things?

25. 25. JamesDavis 08:22 AM 12/27/11

Read all the comments without taking a break by commenting on someone's comment that rubbed you the wrong way and you may realize that everyone is coming back to the first three comments and the logic or illogic (your preference) they contain and the bias illogic the article itself contain. None of the comments are saying that girls cannot do math or with practice cannot become proficient in it, and no one is saying that boys cannot become proficient in communications or social skills...they have and they do all the time. I think that both sexes can do anything that they want to do if they have a great enough desire to do it and the strength and determination to stay with it, but that does not mean that girls love math and science and boys love communications and the social sciences; we do not. I have an incredible ability to determine what children are going to do before they do it, but I don't like working with children because of their young age they have too many behavioral problems. I like telling stories, so that is what I do for a living. We all do what we are good at, no matter what anyone says to us.

26. 26. bigbopper 11:46 AM 12/27/11

Given that we still know next to nothing about the neurobiology and neurodevelopmental factors involved in doing math, it's clearly way too early to draw any definitive conclusions about relative gender ability in math. But it's interesting to see well-done studies which suggest that if there is a gender difference, it's less based on biology than previously thought.

Someday we'll know what makes the brain of a Newton, or Gauss, or Poincare, or Einstein, or Feynman different than the brains of you and I, and then we'll be able to tell whether these differences are related in any way to gender. In the meantime, it's best not to be too dogmatic one way or the other.

27. 27. David N'Gog 12:02 PM 12/27/11

Some points.

1) You can't really tell if SAT scores- and class scores, or any test really determines natural ability.

There is currently no clear consensus or strong experiment that shows how much genetics as opposed to environment is affecting the scores.

2) We know men typically and historically have scored better at certain subjects than women- but we don't know why. That was the point behind this study- but it doesn't sound like it has determined anything conclusive. It does score one goal for the "environment" over genetics hypothesis.

There could very well be a genetic advantage to men- or it could be entirely social. It is quite possibly something in the middle.

One could feasibly conceive it is both. IF society favoured men with better engineering type skills- then the ability could become linked with genes that are activated with men. Or if me WERE naturally better at math and engineering- generations of society could push men to take those subjects.

3) You know a man or a woman (or multiple) who are good at certain tasks doesn't mean anything. You have to be careful just assuming your own experiences are typical.

A man living within the arctic circle could not correctly assume that all the earth is covered in permafrost.

4) I think emotions are touching too much on this subject- science should never be about "us against them". Take a stance from a distance. It would not be sexist to say men are on average taller than women. Differences exist- the point is discover why- not to deny them.

5) There is 0 evidence that all people have "identical" abilities. Evolution would just be random genetic drift if different genes did not provide certain advantages- and yes, we're all different.

A species like cockroaches would not be able to remain almost unchanged for hundreds of millions of years if evolution were just genetic drift. Furthermore, to say humans defy these same "rules" of evolution seems very naive.

Certainly environment has an affect on ability- but to deny something as obvious and accepted as evolution with no evidence behind your argument doesn't really belong here.

28. 28. c.o.corroboration 12:43 PM 12/27/11

James Davis, your last comment was kinda creepy. The last sentance is delusional, as well as your apparent perception of the actuality of desire.

May we excercize safety and incisive investigative measures in examining the dynamics of mingling beings and our genetic variance.

29. 29. whatmeworry 04:57 PM 12/27/11

Yes! I knew it! I'm now officially as good at math as boys, and stronger in social fields and communications and nurturing and empathy and the list goes on and on! That makes me a better homo sapiens!

It's so cool that boys aren't allowed to be better than girls at anything at all ... there are always reasons/excuses/explanations for the perceived but never actual differences! Whereas I'm naturally more gifted in communications, boys can't be naturally more gifted in anything!!! Yeeeaahhhh we girls ROCK!

30. 30. InquiringConstructivist 01:37 PM 12/28/11

Due to some bug or other, many comments are attributed to my name, but only the first did I actually write. I believe someone made comments and then their account was removed, and the script for comments interprets their unique id down to mine, or there is a collision of supposedly unique identifiers, which rarely happens but can if the id generator is not randomized or seeded properly.
I either disagree with or don't even understand comment 15, and it's odd that "julia smith" attributes a reply as to herself that actually appears to be to "way2ec." I think there is some weird stuff going on with the way these comments are being handled, so be careful replying to them.

31. 31. DrKrishnaKumariChalla 12:07 AM 12/29/11

Earlier when the cultural conditions here in India made girls and women sit at homes, they fared very poorly in maths and Engineering subjects. Now when the times have changed and the girls are coming out and getting educated and competing with men in all the fields, interestingly they are proving to be as good as their male counterparts and in some cases better than men! Although there aren't any scientific studies on the subject to prove this beyond any doubt here, it is our observation and newspaper reports that are increasingly stressing this point.

32. 32. Carburn 10:16 PM 12/30/11

Any study of controversial topic needs to have controls for ALL the variables acting to influence performance. I do not think this can currently be tested because you cannot control for culture and differences in power. We do not have a gender neutral society to compare against.

That being said, we already know that people will generally adjust their behavior to fit with established social hierarchies. There has also been research done in the areas of communications and psychology that indicate females perform differently depending on the gender makeup of the group she is in. If you want to test for biological differences, you have to be able to control for culture, and that has not be sufficiently accomplished. You also need to look at socialization, educational history, economic background, education of the primary caretaker, early play and developmental aspects (you don't learn to solve problems with dolls). That doesn’t even begin to cover it. Girls are socially rewarded for displaying stereotypical female traits and are often discouraged from going against what is expected of them. Classroom dynamics may also be at work.

I think the findings discussed in the article are important but there is just way more involved here.

33. 33. Mr. Natural in reply to jtoomim 12:49 AM 1/1/12

"OF COURSE human genetics is different in different countries."

Genetic variation makes up about one-tenth of a percent of each person's DNA. Any two people from anywhere on Earth are more similar to each other than two chimps from the same troop.

One theory for our remarkable genetic similarity is the theory that a catastrophic volcanic eruption 75,000 years ago reduced human population to 1,000-10,000 breeding pairs, creating a genetic bottleneck.

34. 34. suzannez in reply to amalcr 12:32 PM 1/3/12

I'm blushing on your behalf. Uhum:

"The other is that the ratio of males’ to females’ variance differs greatly from one country to another. These ranged from 0.91 to 1.52 (where a ratio of 1 means the two sexes’ variance is equal, and a number greater than 1 means males’ scores were more spread out than women’s)."

HOW can a person be utterly, stubbornly convinced that females are genetically inferior to men at math, when they can't even understand the basic concepts presented above? I've only taken a little bit of college statistics, which I hated, and I had no trouble following.

35. 35. Mr. Natural in reply to amalcr 08:55 PM 1/3/12

Amalcr, the author of the article is not denying that males outscore and outperform girls in math. What she wrote is that, "the ratio of boys to girls scoring above 700 on the math SAT fell from 13:1 in the 1970s to 3:1 in the 1990s."

She is making the argument that such a radical change over a relatively short period of time is evidence that male superiority in math is not innate, but rather social and cultural.

Now let's take a minute and see if we can think of any major cultural movement that has occurred in the United States during that 20 year period which might account for the closing of the math gap between the sexes.

Any light bulbs going on?

36. 36. gunnarenglund 09:26 AM 1/17/12

The observed variance-ratios are reported to be 0.91 up to 1.52 and the fact that some of them are below 1 (greater variability for woman than men) are taken as evidence that the difference can not be biological in origin. What is totally ignored is the uncertainty of these estimates. It could well be that if confidence intervals were calculated they are all compatible with a value above 1. In addition, estimates of variances are extremely variable in themselves.

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