The problem here is mean vs variance. The biggest performers in math and science are going to be at least a few standard deviations away from the mean.
Identical mean and slightly higher variance in men would significantly contribute to the ratios we see today.
Either way, the goal shouldn't be to make everyone feel good about innate abilities. The goal should be to find the reason why one person is innately better than someone else in a particular skill. Step 1: understanding. Step 2: enhancement. Step 3: repeat.
Similar to the recent JL post: forget the gap, focus on the product. It matters most.
Sure, variance is another question (and one not addressed either way by linked article), but there were some folks in the other thread arguing that maybe men are evolutionarily predisposed to be better at math than women. If that were true, you would expect to see differences in the mean and not just the variance.
The conversation is usually about the higher end. Higher variance would also lead to a greater number of math underachievers. I'm pretty sure the numbers play this out, but I think lower bounds on achievement tend to be heavily skewed by 'nurture'. Also, this assumes a symmetric curve. This highlights the gross over simplifications even a more advanced model suffers from. We're modeling brains here, after all, with one or two numbers.
But you are technically incorrect. You can see more of a certain group in the high end if there is higher variance with equal mean.
Everything you said here is true but I'm not sure what it has to do with what I said.
You are focusing on the highest end of the curve, presumably because that's where things like advancements in math (and the status it brings) lie.
I'm saying that even if you leave aside the entire discussion about a possible gender gap at the ends of the spectrum, there were other people who were suggesting that the gender gap in mathematical ability might be just like the gender gap in physical strength. This study seems to indicate that this isn't the case, therefore it's a valuable part of the discussion.
If you want ammunition against those claims, you should go back to math, not these studies: all claims show the gap to be small and the mean to be very close.
Most importantly he variance between groups is smaller than between individuals. This means that you have no way of knowing when you meet someone whether they are good at math because of their sex. That's the most important lesson for most people: don't be biased, because you're probably wrong.
The same argument applies to the race/IQ discussion. Variance between groups is smaller than between individuals.
So even if the claims of innate superiority are correct, you should treat individuals with respect.
good. Now they can start studying some computer science. Being in a class with 95% guys, is depressing. Some more balanced demographic, makes it more fun.
Why is it even worth discussing? Or even worth discovering? Why do we always break ourselves down (by age, gender, education, whatever) into groups and bump them into each other?
Breaking things into groups allows for contrast, and to discover patterns. Instead of a program which might allow a small proportion of students to better at maths (with better teaching perhaps), this could lead to an improvement in the mathematical ability of 50% of the population. That has huge economic and societal implications.
The worst thing about breaking things into groups is members of groups other than the target seem to be simply blind to the importance of it.
It doesn't work. It's enormously difficult to construct a solid study with one properly isolated variable that's the subject in question. Even much, much, much easier tasks as exploring effects of smoking have been done over and over again, only to be declared invalid by yet another variable not accounted for. Statistics is hard to get right, this is why there are so many jokes about it. And trying to come up with a "proof" of anything by separating everybody into just two groups is idiotic.
Yes, it makes one feel good about oneself, and can score you some votes if you're a politician, but it's a waste of time - it doesn't prove anything and only reminds blacks and women that they're "in a group", i.e. must be different by some criteria. This is what I call "recursive racism/sexism".
It is not OK to say "first black president is a great achievement of America". The real achievement would have happened if nobody even noticed the color of his skin, you never heard of CNN anchormen talking about Bush's eye color, haven't you?
That's why the study broke it into two groups and then compared across many different countries (also groups). When what you are studying is the difference in cultures then it seems its impossible to isolate a variable like its a simple drug you're introducing.
Exactly. Why is it important whether boys or girls or Chinese or gay people are better at maths? Why are scarce research funds going into this?
Questions I would be more interesting in: how can elementary maths be made more interesting? And how can we save children who aren't interested in maths from having it forced upon them?
I would rather find the answer to the question, "How can we make it more interesting for them."
Regardless of whether or not mathematics interests you, it's a vital skill like reading. I don't really like "reading"* per se, but I still need to do it anyway.
If a skill is truly vital then I will _want_ to learn it, sooner or later, whatever my present interests are.
So there's no need for 'needs' to overrule 'wants'. (And in particular no need for thousands of people to be paid to deem what children's needs supposedly are.)
For example, if I'm interested in a sport then eventually I'll want to learn elementary arithmetic to keep track of scores and the league tables.
If my favourite thing is fantasy computer games I'll eventually want to read the names of other characters, etc.
The new knowledge in both cases will enhance my love of the activity and I will not regard it as a sacrifice to learn it.
Identity politics. Follow the money. If you can get a person in authority to declare, "We are all equal, given 'fair' conditions," then you have an opportunity to make the following argument:
1. Men and women are equal, when society treats women fairly.
2. Men and women make different incomes.
3. Therefore, society is not treating women fairly.
4. Corrective action is needed.
This is a standard move in identity politics, and you will see it whenever two groups are different. Different people = different outcomes. But the vast bulk of people, including scientists, have been trained from birth to say, "All men [sic] are created equal".
Once you decide that society isn't treating a group fairly, it is time to correct that. How? Affirmative action, set-asides, diversity training, repairations, etc.
Then you have an opportunity to make the following argument:
1. Men and women are equal, when society treats women fairly.
2. Men and women make different incomes.
3. Therefore, society is not treating women fairly.
But the thing is - you can't. Our approach to statistical drug studies is more careful and mathematically sound than studies about our own identities.
There isn't enough evidence in #1 and #2 to jump to #3, and normally outside of sensitive politics absurd like that simply goes ignored, kinda like child speak.
Lemme offer you similarly absurd statement:
Men and women are equal, yet men don't live as long as women do. Therefore, men's quality of life is lower and they are discriminated against.
That's not the point. In politics, if you can trick people into believe rubbish X causes trash Y which leads to bullshit Z and make money off it, then that's what you do. Generally, it's best to have a semi-reasonable argument. In the case above, the flaw is in the statement "Men and women are equal", which is obviously not the case. (Nothing is equal to anything, except in pure mathematics.)
Really, saying "men and women are equal" is a moral statement, with built-in failure, like the commands in the sermon on the mount. This leads to built-in transgression. Which leads to guilt. Which leads to submission. And so on.
There is a moral statement to be made about sexual equality, but it is not the same statement that is made about income or intelligence. Various political groups find it useful to conflate the following types of equality:
1. Equality under the law/Equal rights as humans -- the law should treat men and women equally. "It is wrong to punish men more severely for crimes than women."
2. "Societal" equality -- the attitudes and viewpoints of mainstream society should consider men and women to be equal. "It is wrong to believe that women should have children."
3. Statistical equality -- men and women must be statistically identical for a politically useful class of statistics (e.g., intelligence). "Anyone who speculates that women are not as smart as/have different variance/etc is a sexist."
4. Equality of outcome -- men and women should achieve the same outcomes, for a politically useful class of endeavors. "Professors in every field should be 50% male, 50% female."
#1 and #2 are moral questions, #3 is a scientific one. #4 is a consequence of #1,#2 and #3. The moral statements are hardly rubbish, they are perfectly legitimate moral claims (I even agree with #1). The bullshit is trying to claim that 1 == 2 == 3 == 4.
That is mere statistical manipulation. Here in the UK, we have a "Minister for Women", Harriet Harman. She compares the hourly rate paid to full-time male workers to the hourly rate compared to part-time female workers in her statistics to conclude that women are worse off, which in turn she uses to justify advocating quotas etc. The Guardian's politics are very similar.
My only real problem with this is that I do not really care about what is achieved in children's mathematics classes. Surely, the better test of true ability in this field would be to look at researchers and research accomplishments.
Of course it is subjective, it is is me that does not care about children's mathematics. I make no claim for the wider world. That's why I said "My only problem" and not "the problem".
Its not entirely arbitrary though. I care about research mathematics as to do well at it(or to do it at all) requires very strong mathematical abilities. To do well in classroom mathematics is as much, and probably more, to do with being a good student.
So it seems to me that by looking at children's mathematics rather than research mathematics your results are going to be confounded by the issue that your measuring mathematics ability via a proxy(schoolroom mathematics) rather than the real thing(research mathematics). Your results might still be correct, but I find it hard to know if that is the case.
I suppose, if your just interested in day to day average numeracy skills then looking at children is fine, except even then I would prefer the study was performed on adults rather than regularly drilled students. That way you will find out who is more capable of retaining numeracy skills and who has the higher natural levels of numeracy, rather than just finding out which students revise the hardest and listen to the teacher most attentively.
It'd be interesting to see how these disparities change (or not) with age and through into university study. I've always heard that girls mature faster, which may mean that differences in ability by sex that appear in childhood are different in adulthood.
Completely aside from that, it does show how broad societal trends can affect maths learning for females.
Identical mean and slightly higher variance in men would significantly contribute to the ratios we see today.
Either way, the goal shouldn't be to make everyone feel good about innate abilities. The goal should be to find the reason why one person is innately better than someone else in a particular skill. Step 1: understanding. Step 2: enhancement. Step 3: repeat.
Similar to the recent JL post: forget the gap, focus on the product. It matters most.