Since we're on a new page, here's a summary for anyone interested:

Is there a difference in math performance?
Well, the title of the thread says no, and if you read the first few pages of the thread, you'll see people triumphantly celebrating the belief that there is no difference in performance.

Unfortunately, many scientific studies show otherwise. The difference is not in the average performance, but in the variance (the difference between the highest and lowest achievers). Here are three such studies:

1. The Hyde study
2. The PISA study
3. The Hedges study

Each of these, and others, showed a greater difference in variance among males than among females. Essentially, the data looks something like this:



This is an established scientific fact, shown with multiple studies. It's no longer up for debate. If you came in here thinking there was no difference between male and female math performance, you're just flat wrong.

What's causing this?
Two hypotheses have been proposed. Here's how science works: a hypothesis enables predictions about a system. If attributes of the system are not explained by, or do not fit the hypothesis, then the hypothesis must be modified or discarded. Let's see which hypothesis best fits the observed data.

Environment
Hypothesis 1: This is caused by environmental factors - basically cultural pressure and outright discrimination. This is a very appealing hypothesis because discrimination is wrong, so if you support this hypothesis you get to feel like you are righting a great injustice.

What does this hypothesis predict? Chiefly that as culture changes, the observed effect must change. In particular, a culture with less unjust pressure and discrimination should show a lower difference, and a culture with no injustice at all should show zero difference.

Does the data support this? No, not for variance. The PISA study, posted above, did find a decreasing difference in average ability, correlated to some measure of social justice. So we know that the PISA study works. But it did not show a decreasing difference in variance.

What else does this hypothesis predict? Constant pressure, in either direction, should cause constant movement. Imagine two children. One is encouraged to study music, the other is discouraged. We would expect the distance between these children, in terms of musical ability, to increase over time.

Does the data support this? No. While the Hyde study did show an increasing difference over a few grades, the effect hit a peak in the 8th grade and became chaotic each year after.

And there's another, more worrying problem: If boys are being encouraged, and/or girls discouraged, then we would expect that process to move the average, and not the variance. In fact, it's difficult to imagine any possible way to intentionally affect variance. Indeed, in experiments in which children are actively and intentionally privileged or discriminated against, such as Jane Elliott's famous experiment she observed that all of the brown-eyed children did worse and all of the blue-eyed children improved. That is to say, she saw a change in average, but not variance.

This hypothesis cannot explain the observed data. It must be rejected.

Evolution
Hypothesis 2: This is a normal part of our species, a result of the unique hominid evolutionary path, and an adaptation that helped our ancestors survive.

What does this hypothesis predict? For starters, the reason there is greater variance among males is because of a male mammal's lower inherent worth to the group. Imagine a group of almost any kind of mammal. If you kill off half of the males, the group will recover in a generation or two. The remaining males can easily pick up the slack. But if you kill off half the females, the group will not recover for many generations. What this means is that the process of evolution can safely cause greater variability among males - when evolution hits on a beneficial adaptation, great! But when it doesn't, there's no great loss if a male or two dies. Evolution rolls the dice much more liberally with males of our species. What this hypothesis predicts, therefore, is that we should see greater variance in other areas - not just in math performance.

Does the data support this? Yes. The PISA study is a good example. They found greater variance in geometry, reading skill, etc. In fact, this effect is seen even outside of academic performance. More males become rich in our society, but more males also become criminals. In almost any trait you care to consider, you'll find this effect.

What else does this hypothesis predict? This hypothesis is essentially extending sexual dimorphism to the brain. As anyone can see, males and females are different externally. The hypothesis predicts that there should be differences in the brain as well, and that the observed difference in math performance is one consequence of that.

Does the data support this? Yes. There are many studies that show that male and female brains are organized differently, storing information in different places and in different ways. This can actually be observed in action in functional MRI scanners.

So what does this mean for me, personally?
As an individual, already alive, it means absolutely nothing (except where society stereotypes you). The dice of your genetic heritage were thrown before you were born. For example, as a male, this scientific fact does not mean that I should be able to outperform and particular female on a math test. It turns out that girls perform better on reading tests. But that (also a scientific fact) doesn't mean that I'm going lose to a female on a reading comprehension test. My dice have already been rolled, and so have hers. I may well be a naturally better reader than her.

Should I feel bad because my gender has lower average reading scores? Certainly not. I am not my gender. I am not a bell curve. I am an individual. I have certain gifts and certain shortcomings that are seemingly random. Unless I'm very immature, and anchoring my ego and self-worth to my "gender team" this scientific fact is nothing more than an interesting attribute of my species.

Isn't this sexist?
No. Sexism is applying something that may actually be true of a population, to an individual. It is true that women perform better on reading tests. That isn't sexist. But if you disregard all the resumes of males and keep all the resumes of women, telling yourself "well, these guys can't read" that certainly is sexist. Because some of those males are definitely better readers than some of the females. You're hurting yourself if you fail to consider each person as an individual.

Sexism is something we should guard against, but our fear of it shouldn't blind us to facts. I would rather face the terrible truth about Santa Claus than take comfort in the fantasy. I would rather face the truth that men and women have different brains and different average abilities than to live in the fantasy that we're all the same.

So men are better?
Ridiculous. Anyone who would suggest that, or claim that I'm suggesting that is projecting some insecurity that they have about themselves. The better performance in reading tests among women doesn't translate to "women are better" either. This is just a really childish, ignorant way of thinking.

What's next?
Ken G will go through this post, select a sentence here or there, and post responses like, "so you're saying that Santa Claus has something to do with evolution." I ask that everyone keep in mind that I've gone out and researched this and presented a sound case, backed by solid science. If you look back through this long thread, you'll find that Ken G has posted nothing but his opinion, and even admitted twice that instead of supporting facts, he has only "common sense." But his comon sense is colored by a view of the world that is at odds with the data we have before us.

And if anyone came here expecting to see a summary of a thread about innate gender differences in math aptitude, they are just plain wrong-- instead what they get above is a summary about an issue that the thread is not about, to wit: that some performance differences persist, quite likely due to residual environmental factors. The differences have lessened to a degree that the average is not shifted, but environmental influences may well persist at the upper and lower ends of the distributions. What these environmental effects might possible be require about one ounce of common sense to imagine. But due to some mystery agenda, that obvious explanation will be rejected by tofu, for basically no good reason other than it would agree with political correctness and disagree with a completely invented evolutionary story.

Which is precisely what the data does show, in regard to the average performance. But this does not deter the "innate difference" camp, they simply retreat to making great hay out of the variance, their second line of defense-- having had their claims about the average refuted.
What it also did not show is a culture where there are no differences, where boys and girls are treated equally in regard to mathematical aptitude and performance. As I said above, even an "equal" culture can discourage in a hundred subtle but effective ways a "brainy" girl or an "athletically gifted" boy from pursuing mathematics. That would explain the variance differences. But does our present "equal" society really include those subtle discouragements? Are you kidding me? The role models alone make it perfectly clear that it does. It must take considerable effort to ignore such a pervasively obvious fact of our culture.

Yes, I'm quite certain that is exactly what you will find. Apparently, it does not occur to you that the influences we are talking about might also hit a peak in the 8th grade, when children are most susceptible to societal cues about their intellectual growth patterns. At later ages, those patterns might already be established, such that further divergence does not occur and experiences random variations. This is all perfectly plain, nothing you are saying in any way casts doubt on an environmental interpretation of these variances.
Which is precisely what happens in the cultures that uniformly encourage boys and discourage girls! You admitted that yourself, it is one of the most clearly apparent signals in the data. No, it's not difficult at all-- I did so several posts ago, and repeated again here. When it is considered improper for girls to be "too brainy", and when it is considered acceptable for athletically gifted boys to be not brainy at all, we have a very obvious environmental influence lending to precisely the variance effect that is reported (and even that is a pretty small effect, so we are not looking for blatant environmental factors here, but rather quite subtle ones).

Obviously. You seem to fail to recognize how readily that makes my point-- when considering large populations, environment is vastly more important in producing performance differences than innate aptitude differences between the groups, for the simple reason that environment affects them all, while innate differences are statistically mixed. I pointed that out long ago in the thread. I showed how the hypothesis explains the data just fine.
I found this pretty lacking when it was first raised in the thread, for these reasons:
1) It requires that a different environment can influence people to stress the importance of different skills. Well, once you assert that pretty obvious fact, you then have to ignore that very same truth in regard to modern culture!
2) When you find environments that equalize to a large degree, the average performance differences go away. Poof! That's a pretty telling fact, but the innate camp is nothing if not persistent-- they turn to the issue of variance. Let's look at that more closely:

The basic problem with evolutionary arguments, as is by now quite well known, is that you can use them to argue absolutely anything. Anything at all, it's no problem. But for someone to make a legitimate case that evolution "rolls the dice" more liberally with males, they really should actually look at the process governing evolution: genes. Let's say, for the purposes of argument, that there is indeed something about the y chromosome that turns on greater variation in the action of all the other genes, since evolution can take more risks with males and thereby let males carry the greater share of testing genetic variations for survival benefits. What happens when a male does find a survival benefit? Well, for evolution to work, he must pass that benefit on-- to both male and female offspring. The offspring then exhibit the variance in the male population (and female, but we are considering the hypothetical situation being described) of the previous generation.

So the claim that the variance is carried by the males in no way establishes that the likelihood of advanced intelligence is not passed equally to both genders. This is the whole point-- evolution does not bestow survival advantages associated with analytic reasoning skills onto only one gender, for that would obviously lack benefit for the other gender. That is why fully developed men and women are so amazingly equal in their innate mental aptitudes, regardless of where they send the blood in their brains-- until environmental factors come into play.

Let's look at the whole point here. The claim by the "genetic variance" camp is that the next Einstein is more likely to be male, because the y chromosome is more likely to take "risks" with the mental patterns, and thereby generate the next Einstein along with a few dunces. This somehow should explain why most of the math professors in our country are male (don't ask me how this camp tries to explain why in some countries math professors are equally distributed in gender, and in others they are essentially entirely male-- I guess there's greater genetic variance in some countries than others!). But that is clearly a specious argument, because why would the daughters of yesterday's math professors not be among the math professors of today? It's just obviously the wrong explanation. Let's contrast that with a far more reasonable explanation-- the daughters of yesterday's math professors were not encouraged by their environment, in most of today's cultures, to become the math professors of today.
Replacing my arguments with your own imagined cartoons certainly does nothing to make your case. I am perfectly happy to stand by the arguments I actually gave, then and now. One of which holds just as plainly now as ever-- none of the data you researched is capable of disentangling environmental factors from genetic ones-- none of it. All one needs to assert that fact is simple logic. What I have done is supply that logic, accompanied by a basic and unrequited demand to see actual evidence of claims that are made-- instead I am given nothing but environmentally uncontrolled data and a make believe speculation of how evolution might have happened with no effort to conform to the realities of biological procreation.

The study posted by tofu in the other thread (pdf) lends yet more support to the contention that gender differences in math performance are sufficiently explained by social factors.

Skimming through the tables, I notice right away that gender differences in math scores are significantly correlated with indicators of such variables as:

- women emancipation;
- female economic activity rate;
- women political empowerment.

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

That's the second study that I cited in the post two posts above this one.

You're right in that it shows no difference in average performance. It does show the difference in variance.

Both issues are resolved. There is no difference in average performance. There is a difference in variance.

Hope no-one has said this already (if so, sorry)

If the studies of both the skills that you're all arguing about (maths and reading) are true, then it still makes sense, for society as a whole, for men to be maths professors, and ladies to be language professors.

Just thought I'd point that out.

And on a lighter note

Computers will beat us all. Men and women ought to stick together.

The study is not about variance, and I don't see how differences in variance would be relevant, anyway.

When folks claim that "boys have simply evolved to be better at math than girls", they're comparing and arguing with average performances, not variances.

__________________
"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

One must beware of the chicken-and-egg problem-- opportunity leads to performance which explains opportunity. To pick a very exaggerated example, if you look at the southern part of the US in the year 1850, you will find a large black population, but very few of them would score well on reading exams. By the exact logic of this thread, I could use that to assert that it is quite natural that there were also no black language professors in the colleges of the region, and we should simply embrace that conclusion.

Is everything perfectly reasonable in that situation? Of course not, because the role of the environment in establishing those conditions has not been established. If one makes no effort to examine that role, one would simply conclude, as often occured in this thread, that differences in the evolutionary environment must be producing genetic differences in reading ability, which explain the poor reading performance and the absence of black language professors in 1850.

Oh no you don't Ken. You're not dragging me into a nature vs. nurture debate that easily. You're one of the smarter posters on here; you know very well I was talking about comparative advantage.

Let's use your recent example. Assume that black people are slightly better than white people at language ability. Assume also that black people are much better than white people at sports. Note that blacks have an absolute advantage in both languages and sport, but they have a relative advantage in sport.

Under these conditions, the situation where all blacks are professional sportsmen, and all whites are language professors, results in maximum benefit for the group as a whole.

The nation would win more Olympic Golds, and more Nobel Prizes in Literature, than under any other combination.

Note also that both groups, by trading, can become better off than they would be under any other combination:
Whites would enjoy the highest possible quality of competitive sports, and Blacks would enjoy the highest possible quality of literature.

And that is what I meant by men being maths professors, and women being language professors.

Phew! That's as much as I'm saying. Not a big fan of controversial topics. This is just simple trade theory if anyone wants to look it up.

But this all follows from an unsubstantiated assumption. The thread isn't about how we should structure our society if certain innate differences are in place (which is what you are talking about, but that's a whole thread of its own, and a political one at that, because there are many issues beyond maximizing total utility). The question on the table is, what innate differences have been established, as distinct from environmental influences that we ourselves are responsible for? My answer to that is quite direct: none, in the areas of adult reading and math skill. Then all one has to do is note the potential harm in confusing our own handiwork for innate differences (a common outcome that is called "prejudice").

Societal norms seem to force one into categories that are "somewhat" counter to their own wants and needs. Case in point: take a blind man who does not know anything of visual stereotypes but his/her own assertions or desires. This person can shape their destiny if enough knowledge is garnished about the world around them w/o perturbing their own environment adversely...Most newborns are equally capable to attain levels of excellence as adults---- we are, all, rough diamonds...but some of us must expend more energy to get to our rightful potentials than others.

__________________
"The candle flame gutters. Its little pool of light trembles. Darkness gathers. The demons begin to stir."
---Carl Sagan

I agree that there are societal norms, and that these may shape our behavior, and I agree that we're "diamonds in the rough" in the sense that we have tremendous control over our own destiny, but there are gender differences too, even among children too young to have been influenced by culture (this study, for example). Clearly, our brains tend to be very different.

Also, I love this quote from the abstract: "girls are more object oriented." I knew it! C++ is oppressing me!

Although the statistics tend to give a strong support for major wiring differences of neurons and ultimately neuro-chemistry between the sexes---must we embrace it at face-value--- w/o "seeing" brain-imaging results for a large population? The studies are very well done. I am not so much attacking the study--as I am questioning whether we should throw out any data that does not conform to the statistics? Does this not, in some, instances require those who would rather conform to a norm of society that is imposed by a scientific study? "People" for better or worse usually choose a path of least resistance...I believe that if one is given a choice of "better-outcome" as opposed to "poor-outcome" in their daily affairs--he/she will choose the latter. And this may not always conform to the statistical mean---the "outliers" of a statistical study--for better or worse are usually thrown out----and it is those outliers that may lead to a next discovery or breakthrough.

__________________
"The candle flame gutters. Its little pool of light trembles. Darkness gathers. The demons begin to stir."
---Carl Sagan