Unfortunately the article does not mention the standard deviation of the distribution of mathematical ability after controlling for other factors. As mentioned here: http://www.lagriffedulion.f2s.com/math.htm, Larry Summers got in a lot of trouble at Harvard for making this assertion:
"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. And that is true with respect to attributes that are and are not plausibly, culturally determined."
Is that assertion backed up by evidence? And, if true, is making this distinction useful in informing public policy and shaping our culture? In a fight between naturalistic and moral fallacies, which wins?
The article doesn't say a darn thing about methodology. For all we know, they could have done anything from comparing means to measuring the overlap of various confidence intervals to arcane statistical methods that predict the accuracy of classification based on the data.
Darn paywalls around scientific journals. I really wish more would go the route of http://www.plos.org/
I, too, was under the impression that this was pretty well accepted, at least as far as mathematical skills relating to the ability to handle spatial models.
Rephrasing your quotation, if you draw out the curves so that ability is on the X axis, and number of individuals having that ability is on the Y axis, then the curve for females will be taller and narrower than that for men.
That means that if you've got in mind a brilliant geometer, that person is more likely male than female. On the other hand, if you've got in mind an extremely bad geometer, that person is also more likely male than female.
Discussion of this that I've read have hypothesized that we've evolved this way because humans back a zillion years tended to have the males go out hunting while women took care of babies and domestic chores; and tracking and stalking prey demanded more of a person's spatial skills.
I think it's generally accepted that if you take a sampling of average men and average women, they will both perform at similar levels in regards to mathematics.
However, I believe the differences between men and women in mathematical thinking, should they exist, will only be apparent when it comes to dealing with the levels of math that deal with abstractions upon abstractions and so on.
In my personal experience, I've noticed that 90%+ of (American) women are just not interested in formal systems, be it predicate logic, computer science, pure mathematics, etc. I'm inclined to believe women are just wired to prefer more practical disciplines, but I think a compelling argument can be made for either view. I suspect the answer probably lies somewhere in between.
I think it's quite possible there are imbalances in the tails of distributions, but it still means that the middle could plausibly be more balanced. I'd personally not worry that much about gender balance among Fields Medal winners, and more about gender balance among engineering graduates from the local Big State U. The men there are probably above average in math ability, but few are world-class mathematicians; most are probably in something like the 70th-90th percentiles for math ability, a region which doesn't seem (from what data is available) to have large inherent gender imbalances.
I agree with the grandparent post, because I think it's misleading to lump all of mathematics together. I'm very bad at mental calculations and basic arithmetic, and I couldn't memorize integration formulas if my life depended on it, so I've never had very high grades in math, at least until I hit university. Yet I have a relatively easy time picking up the theory behind SAT solvers, Fourier transforms, or solving complex integrals.
I think some people are better at concrete things like geometry or arithmetic, some people are better at logic, some people are good with operators and algebra... but one does not imply the others, and engineers may have an above-average capability for abstraction or logic that does not translate to much higher results in a high-school level exam.
The study here is said to have studied people "from grade school to college and beyond", so I suspect the "math ability" they tested really has little to do with the math ability required for science and engineering.
It is enough to read a brief review in Science to see that the headlines don't follow from the paper at all. The review explains the main reason of the results: they have detected no signal because the tests were too simple. They didn't really test "g" or the ability to think mathematically but rather attainment.
I study maths and if you asked me what 30/4 was, I'd respond, "it is 30/4, obviously".
Math is not about calculating. I rarely perform calculations on numbers greater than 20, and I do not even remember when was the last time I performed a long division. What is this "2 digit math" you are talking about?
I'm sorry, I should have typed "thirty divided by four," which is what I actually said, instead of 30/4, but I was lazy. And yes, math is absolutely not about calculating. I was supporting the previous poster's point that they suck at calculating, and that math and calculating are very different things. I hate math. I am completely comfortable with calculating. WTF with the downvotes.
At Columbia there are numerous women in the mathematics department. They do not seem to be doing any worse than their male peers at handling complex work. I'm inclined to say that women probably aren't interested in formal systems in exactly the same way as men, but that lack of interest doesn't somehow mean they can't handle it or find their own way to it.
In my personal experience, I've noticed that 90%+ of (American) women are just not interested in formal systems, be it predicate logic, computer science, pure mathematics, etc. I'm inclined to believe women are just wired to prefer more practical disciplines
I'm inclined to believe women aren't naturally drawn to fields that favor autistic personality characteristics.
Autism rates are 3 times more likely in males than females, which I see as an extreme symptom of a more general trait. This is what I chalk up the math and science gender gap to, though I have absolutely no scientific data to back that up.
Has anyone ever seen an articles with a Professor's of Women's Studies or holder of a doctorate in Women's Health arguing that rates of autism in men and women should be the same and claiming that they're only different because of a misogynist agenda?
>The idea that both genders have equal math abilities is widely accepted among social scientists
Really? Seriously? Sounds like "social scientists" prefer spin to statistics.
>If, before a test, you imply that the women should expect to do a little worse than the men, that hurts performance. It's a self-fulfilling prophecy.
This sounds like a specific form of a general psychological result that would hold true for men too. If so then this article is beyond disingenuous it is a flat lie. That aside in order for the result to have a bearing on real world test scores it would require someone to be telling women just before their maths test that they're going to fail. Who's doing that, it would be pretty easy to spot in a school and certainly in my country a teacher doing that would lose their jobs.
>These changes will encourage women to pursue occupations that require lots of math.
Why? Why would measuring maths ability change the preferred career of anyone?
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>If, before a test, you imply that the women should expect to do a little worse than the men, that hurts performance. It's a self-fulfilling prophecy.
This sounds like a specific form of a general psychological result that would hold true for men too. If so then this article is beyond disingenuous it is a flat lie. That aside in order for the result to have a bearing on real world test scores it would require someone to be telling women just before their maths test that they're going to fail. Who's doing that, it would be pretty easy to spot in a school and certainly in my country a teacher doing that would lose their jobs.
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It does hold true for men -- specifically, men of African-American and Hispanic descent, when reminded that minorities generally do worse on math exams before the exam is given.
The proposition that nobody is telling women they're going to do worse on math tests, however, is simplistic. It isn't that some mean old guy is telling them they suck (although one of my female physics professors mentioned, out of the classroom, that she had been thrown out of a physics class at Georgia Tech in the early 1970's for "taking a man's spot" -- you're right that this sort of thing is much less common these days, at least in the West). It's that the whole culture is suffused with the attitude that women's mathematical abilities are suspect -- witness threads like these, which appear over and over on the interwebs, discussing whether or not women are as capable as men at math.
Measuring maths ability scientifically and publishing the results, rather than relying on folk-science and anecdote, could help encourage women to trust their own desires and abilities mathematically -- even when faced with a predominantly male culture and continual doubt being cast on their abilities to function at the highest levels.
I know this to be true because I am now a lone female coder in a group of (really great, smart, delightful) guys, loving my work on a complex, challenging system. And I remember that I dropped out of the very first coding class I took after a few weeks because I was completely intimidated by the swaggering guy classmates who threw around terms I wasn't yet familiar with -- I felt out of place and was full of self-doubt. It was only after maturing and understanding the social dynamics that I retook the class and ended up with one of the top 5 grades, out of several hundred students. Yet, at first, I had been certain I was incapable -- not because any guys were mean to me (not one was anything but helpful), but because I doubted myself, and felt alone and weird.
And surely this isn't gender-specific, and surely many geeky coders can relate, and have probably had similar experiences in different areas of life. This isn't a woman-man thing only -- it's a specific expression of a general human tendency to reflect cultural attitudes about their lives in the images they create of themselves.
>It does hold true for men -- specifically, men of African-American and Hispanic descent, when reminded that minorities generally do worse on math exams before the exam is given.
I think I've read a general result along the lines of "you have characteristic X, people with that characteristic perform worse" and that this skews the result. You're poor, you're female, you're disabled, but I couldn't really be bothered digging around for the papers.
Simplistic? Yes, but as I recalled the research was for the situation where they were told quite shortly before the test about their expected sub-par performance so I was relating it to the research.
>Yet, at first, I had been certain I was incapable -- not because any guys were mean to me (not one was anything but helpful), but because I doubted myself, and felt alone and weird.
Overcoming self-doubt and social issues is part of being in a particular field though - if jargon rich fields put you (ie "one") off then there are many fields you would struggle in. If you need someone to believe in you before you can do well in a maths test then IMO you're not going to do well when you've only got yourself to rely on to get something done.
>Measuring maths ability scientifically and publishing the results, rather than relying on folk-science and anecdote, could help encourage women to trust their own desires and abilities mathematically
Go on. What do you mean by maths ability - it's a pretty diverse subject after all. I've seen people do excellently via rote learning whilst for me it was my strength because I could pretty much start with a few "axioms" and work on from there when memory failed - clearly very different abilities that appeared (at undergrad level) to be closely equivalent.
I wish the article said what kind of math they tested for. There's a world of difference between being good at multiplication and being good at proving P≠NP.
God, really, I hope this turns out to be right. If our brains are fundamentally different, we (men and women) are doomed to never really understand each other, which I find totally depressing.
Like a wise person once said: Interest is aptitude
All of the nature/nurture constructs built around males to interest them in the autistic endeavors like math, physics, computer science are very different for females. It's not that woman can't do math, rather it's that they choose not to.
I like that researchers are drifting away from attempts at neurological gender difference explanations, and towards a gestalt of social conditioning.
I personally do not feel that there is a correlation between sex and maths skills. Its the stereotypes that result in girls not actively pursuing maths related courses. If provided the right education and motivation, anyone can be good at any subject. In India, for example, where the students have no choice but to learn predefined syllabus, girls do pretty well in Maths.
I personally do not feel that there is a correlation
I'm sorry that I'm about to sound rude, but...
For this kind of question it really doesn't matter what any of us feel. Our values, morals, aesthetics, etc. simply have no bearing on the truth of the matter. And none of us has sufficient data points (rigorous, untainted, and unprejudiced) to form a model that has any validity. We really only have two choices: (1) say "I don't care", and ignore the debate; or (2) read the study, then criticize methodological flaws if any, else deal with the results.
There is a third choice: "I care, but please bring a better case-study". As stated above, the gist of my argument is that all are born equal, it is the society and the stereotypes that shape them.
That's not a third choice. If you can show that the methodology of the study fails to account for this, then you've got a case, which I accounted for. But when it simply doesn't match your "feeling", well, I'm sorry, but that just doesn't matter.
By the way, I did not disagree with the results of the study. I agreed to it by stating my personal feeling instead of going by the article, since the article didn't mention the study in detail.
> Its the stereotypes that result in girls not actively pursuing maths related courses.
have you ever thought what is the root of these stereotypes? Historical oppression by males? Historically, males have had no problem "delegating" chores to women. Why producing tedious mathematical proofs wasn't considered a chore (what it in many cases is) and wasn't "delegated" to women?
> where the students have no choice but to learn predefined syllabus, girls do pretty well in Maths.
exactly. But when it is time for a real, not predefined, stuff and you have little to no guidance ...
There is a reason 2 sexes exist. Males or females are no better than each other. The Nature have no problem bringing together 2 sexes in 1 body at the pure biological level.
It is the behavioral and mental differences of the sexes that make the 2-sex species much stronger than otherwise.
Well, historically women were discouraged from doing anything intellectual. I read a biography of Ada Lovelace and she regularly corresponded with a medical doctor who in his letters advised her to not to so much math. It was believed that thinking too much would weaken the body. Good thing she didn't listen!
In adulthood, she also corresponded with her childhood math tutor. He wrote to her that his daughter was precocious at math, and he feared it would do her damage, so he actively discouraged his daughter... so much so that his wife complained to him that the daughter was now quite intellectually deficient.
Ada Lovelace only got where she was because she was raised by her mother who hated her poet father Lord Byron with such intensity that she considered it the ultimate revenge to completely prevent Ada from reading any literature, and spend all her time doing math. But most girls, like her tutor's daughter, were subject to the opposite treatment. It's not surprising that most women didn't do very much math.
>There is a reason 2 sexes exist... It is the behavioral and mental differences of the sexes that make the 2-sex species much stronger than otherwise.
Wow, that is the most bullshit explanation for sexual reproduction I have ever seen. The actual reason for the existence of sexual reproduction is still very much under research, but one plausible explanation is that it increases genetic diversity a la http://en.wikipedia.org/wiki/Red_Queens_Hypothesis
It certainly has absolutely nothing to do with making the species stronger. Natural selection does not work on a species level, only on the level of an individual organism or gene. If a species is not "strong" it goes extinct.
>she considered it the ultimate revenge to completely prevent Ada from reading any literature, and spend all her time doing math.
yep, her mother demonstrated a level of rationality no man can even dream to achieve.
>Wow, that is the most bullshit explanation for sexual reproduction I have ever seen.
you missed just a small detail - i didn't try to explain sexual reproduction. I was talking about existence of 2 sexes, which overlaps with sexual reproduction, yet is not the same thing.
> It certainly has absolutely nothing to do with making the species stronger. Natural selection does not work on a species level, only on the level of an individual organism or gene. If a species is not "strong" it goes extinct.
thank you. That clearly settles our discussion why women haven't been successful in areas where analysis of facts and synthesis of theories explaining the facts is the main mode of operation.
No, I did not. The existence of two sexes is only because of sexual reproduction. If organisms did not have sexual reproduction, and only reproduced asexually, there would not be two sexes. If something like two sexes arose in a species (i.e. one that is good at math and one that was good at cooking), it would speciate, because each "sex" would just keep changing individually; evolution is a chaotic process. Sexes only exist where there is sexual reproduction. The question of why two sexes exist is absolutely about why sexual reproduction exists; two sexes exist BECAUSE sexual reproduction exists, and sexual reproduction exists BECAUSE it confers some evolutionary advantage.
In fact, your confusion about this connection actually illustrates why you argument is wrong. IF it were possible for a species to evolve to be "strong" AND division of skills produced produced "strength" THEN you would expect to see asexual species with "sexes." But you don't.
>thank you. That clearly settles our discussion why women haven't been successful
You made a completely fallacious argument as some sort of absurd appeal to the naturalistic as evidence of your claim. Showing that the claim is blatantly false repudiates that claim, so it's relevant to our discussion. I'm honestly flabbergasted that you would say something like "I'm right because it's natural" when you clearly have a extremely poor understanding of nature.
>her mother demonstrated a level of rationality no man can even dream to achieve
Apparently your version of rational discourse is to respond to a claim that repudiates your claim (women were, in fact, actively discouraged from doing math) by insulting women.
>No, I did not. The existence of two sexes is only because of sexual reproduction. If organisms did not have sexual reproduction, and only reproduced asexually, there would not be two sexes. If something like two sexes arose in a species (i.e. one that is good at math and one that was good at cooking), it would speciate, because each "sex" would just keep changing individually; evolution is a chaotic process. Sexes only exist where there is sexual reproduction. The question of why two sexes exist is absolutely about why sexual reproduction exists; two sexes exist BECAUSE sexual reproduction exists, and sexual reproduction exists BECAUSE it confers some evolutionary advantage.
your post again confirms my point. You're very good a "housekeeping" of facts, yet you miss the ability to analytically transcend beyond the mere set of facts. The sexual reproduction is the _mean_ of keeping 2 sexes from speciating, and not a _goal_ of the 2 sex existence. The 2 sex specialization inside 1 species is what confers primary evolutionary advantage.
>IF it were possible for a species to evolve to be "strong" AND division of skills produced produced "strength" THEN you would expect to see asexual species with "sexes." But you don't.
because without sexual reproduction the speciating happens. Sexual reproduction is a necessary mean for keeping of (and not a goal of development of) specialization without triggering speciating.
But of course, you're not interested. You have something invested in the idea that men and women have different skills, so you invented your silly theory that evolution made men and women specialize in different spheres because it made the species stronger. And you kept on following the trajectory of the argument until it brought us to this absurdity.
The irony is that if you actually understood biology, you could easily make an appeal to the natural without inventing this dumb theory. You could have mentioned that males in many species develop specialized traits in order to attract females; human males could have such traits. In Belig's ground squirrels, only the males outbreed, and as such are the only ones that spend extensive time outside of burrows. Consequently they have superior navigation skills to the females who never leave their burrows. A difference like this could be responsible for differences in male and female human abilities. And there are a million more such valid arguments.
But you did what most people did. You rationalized. You had an opinion, and then you invented something to support it. Sadly, you knew almost no biology.
If you did, you wouldn't have missed the basic principle of the theory of natural selection: the variants which propagate themselves the most are the ones that you see go to fixation. There is nothing that drives a species to be strong; rather, individuals that are strong reproduce themselves.
Your basic problem is that you're thinking about evolution tautologically. Evolution can't predict that if one species turned into two, then both species would die out, so therefore it must develop sexual reproduction. Whatever drove those two species to speciate would still drive them to speciate. And then they would go extinct. A lot of species go extinct. Your theory requires that sexual reproduction emerges completely independently of an evolutionary pressure- which is ridiculously improbable- and then continue to exist even though it confers no advantage. This is absurd for any number of reasons, not least of which is that an asexual organism can produce 2x the number of copies of itself as a sexual organism. (When sexual organisms reproduce, only half of their genes get passed onto their offspring; this is hugely inefficient.)
>Tell that to an evolutionary biologist and they will laugh in your face. Wait... you already did that. I'm laughing.
Evolutionary biology, compare to lets say mathematics where my roots are, has a very large part which is "interpretation" and which is very susceptible to whatever is dictated by the current authority in the science (and/or by political climate).
With regard to laughing - how about evolution biologists who thinks that evolution, a large statistical dynamic system process, has produced different bodies for males and females (or are you going to argue that as well?) efficiently reflecting specialization, and ignored for the reason of PolitCorrectness another available degree of freedom extremely important in the context of the specialization - mental abilities, brain (especially considering that for K-selection behavioral/mental characteristics may be playing comparable or even more important role than pure physical body characteristics)
> Consequently they have superior navigation skills to the females who never leave their burrows.
For many, many generations ... Are you, as evolutionary biologist, saying that female squirrels have the same abilities to develop such navigational skills? When did they develop them? While never using?
Let suppose they did develop them in some past. Thus we can suppose the abilities are just dormant now. May
be the female squirrels also have dormant penises?
>- how about evolution biologists who thinks that evolution, a large statistical dynamic system process, has produced different bodies for males and females (or are you going to argue that as well?) efficiently reflecting specialization, and ignored for the reason of PolitCorrectness another available degree of freedom extremely important in the context of the specialization
I actually have no idea what the sentence actually said, but somewhere in there I think you're implying that some evolutionary biologists for reasons of political correctness believe that male and female human brains are identical. Like I said, most humans rationalize. I have no excuse for them. But in my experience, the stereotype is the opposite, see: http://xkcd.com/775/
>For many, many generations ... Are you, as evolutionary biologist, saying that female squirrels have the same abilities to develop such navigational skills?
Um. If the burrows were passed along paternally instead of maternally, and it was the female squirrels that moved about and the male squirrels that stayed in their borrows, I would expect that, yes? I'm not really sure what your point is. Or why you're talking about squirrel penis.
>Um. If the burrows were passed along paternally instead of maternally, and it was the female squirrels that moved about and the male squirrels that stayed in their borrows,
you must be kidding. "If". If a grandmother had balls, it would be a grandfather.
In the jacana, the males are the ones that are smaller and incubate the eggs (sitting on them to keep them warm), and the females are the bigger ones that go out and procure food, but the one that's called the female is the one that laid the egg. http://en.wikipedia.org/wiki/Jacana
"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. And that is true with respect to attributes that are and are not plausibly, culturally determined."
Is that assertion backed up by evidence? And, if true, is making this distinction useful in informing public policy and shaping our culture? In a fight between naturalistic and moral fallacies, which wins?