

Math Quiz: Why do men predominate? - meterplech
http://spectrum.ieee.org/at-work/education/math-quiz-why-do-men-predominate

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apsec112
"Hyde and Mertz found there are more girls in the top tier in countries such
as Iceland, Thailand, and the United Kingdom–and even in certain U.S.
populations, such as Asian-Americans."

I don't buy this at all, if you mean "top tier" in the sense of people who are
at the Olympiad/math professor level. Look at the numbers- there have been ten
Fields/Abel/Wolf Prize winners from the UK, all of whom have been male. The
odds of this happening given "more girls in the top tier" are less than
1:1000.

"Furthermore, they noted that a small math gender gap correlated with a higher
rank on the World Economic Forum’s 2007 measures of gender equality, in which
the United States ranked 31st, between Estonia and Kazakhstan. A similar
correlation was found for the number of girls on International Mathematical
Olympiad teams."

Yes, but _what was the correlation_? 0.02? 0.2? 0.9? The article doesn't tell
you, conveniently for them.

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idlewords
Did you even understand the article? The argument is not that there are more
women Fields medalists from the UK; rather, it's that supposed 'innate'
differences in mathematical aptitude between young men and women turn out to
be not so innate at all.

To get Fields medal, it's not enough to be a brainiac. You need someone to
step up and give you a good mathematical education in your formative years,
take your questions seriously when you're a more advanced student, and so on.

See the biographies of Sophie Germain or Rosamund Franklin if you want
examples of how being the 'wrong' gender can hold back a first rate mind.

~~~
apsec112
"Did you even understand the article? The argument is not that there are more
women Fields medalists from the UK; rather, it's that supposed 'innate'
differences in mathematical aptitude between young men and women turn out to
be not so innate at all."

The claim was, specifically, that "in (presumably less sexist) countries, the
difference between male and female mathematical ability goes away, so sexism
must be the cause of these differences". She named the United Kingdom as an
example of a country which is supposed to be less sexist. Yet, we do not see a
single Fields, Wolf, or Abel medalist. If math in the UK _is_ sexist, then why
attribute the better female performance in the UK to lack of sexism, rather
than luck or genetic differences or climate variation or some other random
factor? If it's _not_ sexist, where are the female Fields medalists and IMO
team members?

"To get Fields medal, it's not enough to be a brainiac. You need someone to
step up and give you a good mathematical education in your formative years,
take your questions seriously when you're a more advanced student, and so on."

Then why don't British IMO teams (<http://www.imo-register.org.uk/>) have a
larger proportion of women?

"See the biographies of Sophie Germain or Rosamund Franklin if you want
examples of how being the 'wrong' gender can hold back a first rate mind."

(I presume you mean Rosalind Franklin?) You mean, fifty years ago, when it was
perfectly legal standard practice to openly discriminate against women (and
blacks, and Jews... ) in employment? No surprises there. But the article is
talking about today.

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pgbovine
"Then there’s the cultural perception of math achievers–the nerds who are
heckled in one society are exalted in another. Irina Mitrea, a math professor
at Worcester Polytechnic Institute, in Massachusetts, who finished high school
in Romania, says she never felt discouraged there ..."

in my experience (with a sample size of ~10), the only women i've interacted
with who were super excited about (and good at) pure math and theoretical CS
(Ph.D. students) grew up in eastern europe or india, and when i asked them
about their experiences growing up as females who loved math, they said that
it felt completely normal in their home society and that they were shocked
that there was this stigma against girls being able to do math in the US ...
[again, this is only my tiny biased sample size, just my 2 cents!]

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amichail
It must be easy to publish research like this in a journal.

How could a reviewer -- even an anonymous one -- object? Doing so would put
his/her career at risk.

Maybe it's best not to do research like this at all.

~~~
lionhearted
I don't know why you were voted down. Yes, speaking out against the
conclusions of the article has harmed people's careers. Even mild speculating
that maybe there's inborn cognitive differences between men and women can
derail a science career.

It's crazy that people can't investigate the topic thoroughly - arguing "all
culture no biology" demands a really high burden of proof. Arguing "some
culture some biology" shouldn't be academic suicide, which it currently is.

~~~
amichail
But maybe for the good of society, this sort of research should be banned.

~~~
lionhearted
This could work. In the interests of truth, perhaps it'd work best if we did
it very explicitly and publicly: "All research on potential mental differences
between men and women are hereby banned for the good of society." Then we
could start brainstorming what other research to ban for the good of society.

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gambling8nt
The original paper by Hyde and Mertz can be found at
<http://tctvideo.madison.com/uw/gender.pdf> . In it, the authors reference
data from the Program for International Student Assessment as their primary
evidence in attempting to discredit the Greater Male Variability Hypothesis
(apart from their discussion of differing degrees of female membership on IMO
teams). Careful examination of the 2006 PISA data, however, indicates a
positive correlation between variance ratio and mean performance amongst OECD
countries with above average performance (selected to control for availability
of educational resources, and overall social stigma against mathematics). This
suggests that countries which have taken action to reduce Variance Ratio in
order to equalize educational outcomes have also reduced overall mean
outcomes.

In other words, countries which have successfully suppressed greater male
variance (if it is inherent) or have through cultural engineering increased
apparent female variance, have done so at the cost of reducing mean outcome.

It is worth noting, however, that this result was achieved by looking at
countries that were assumed to already have adequate educational resources,
and have already achieved above average mean outcomes--presumably through some
sort of cultural emphasis on the value of mathematics. Both of these effects
appear greater than that of suppression of male variability.

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scotty79
Interesting. Men have more variance in aptitude but there is same amount of
boys and girls in math olympics (in countries with gender equality).

That might mean that people able to achieve olympic level of math skill are
actually abundant enough so small random pick from all available people with
such potential does not show differences.

~~~
DaniFong
Once more,

It's been shown that for a few cultures on a small norming sample on
particular tests (IQ, SAT) that standard deviation on math related scores is
greater than that for women. The bulk of the standard deviation is accounts
for by people testing around the mean, because most of the scores are _around_
the mean.

Knowledge of the standard deviation does not, as our financial markets
recently showed, correlate so well with extreme outliers, as those with
Olympic level abilities are likely to have. And the sorts of thinking demanded
by those taking an IQ test or the SAT are not so similar to those required by
Olympiad level problem solving (correlated and similar though they are). And
the sort of thinking required of Olympiad level problems is not so similar to
that required for success in research mathematics (helpful and correlated
though they are), as shown by the large numbers of people who attain great
honors in such competitions and do not end up really producing much original
work. _And_ it's been shown and is frankly straightforward to see how cultural
influences can effect both interest and resources available for bright young
minds of any background or gender.

We just don't know enough about one's aptitude and its interaction with the
environment to make such blanket statements. Men have more variance in
aptitude! It's like a difference of a standard deviation of 14.5 points for
women and 15.5 points for men. Keep in mind also that a core component of most
IQ tests and the SAT is time pressure. In the SAT it's raw time pressure, and
in psychologist administered IQ tests you have several factor: one being an
explicit time weighting, two being the the fact that the speed of one's
response can give you a much higher score, three being that your answers are
subjectively weighted by the psychologist (which could already introduce
bias), and if you seem unsure you'll be docked points, and if you seem sure
but speak vaguely you can often turn a yes into a no, and four whether or not
they move forward in sections depends on how quickly you're answering. It's
been shown by Benbow et. al. that, at least in America, girl's confidence with
mathematics is astonishingly uncorrelated with their performance (unlike with
boys, who, if they're good, tend to think they're even better.) It is
completely reasonable that if you're more unsure about your own abilities you
might hesitate for just a bit longer, sound a little less confident, hazard
fewer guesses. This will, by itself, reduce variance in one's score. You'd
need to account for only a 6% difference to explain the variance in score.

(Also, from what I know, too, the selection processes of countries like
Romania, Bulgaria, Russia, Ukraine, Hungary, China, and the USA are anything
but a random pick. They can be quite grueling, actually.)

~~~
scotty79
Thank you. I should have realized that differences in standard deviations can
tell almost nothing about differences in number of far outliers.

> (Also, from what I know, too, the selection processes of countries like
> Romania, Bulgaria, Russia, Ukraine, Hungary, China, and the USA are anything
> but a random pick. They can be quite grueling, actually.)

I didn't mean that getting into Olympic is random pick from general
population. But since not every person that is able to achieve Olympic level
is in the Olympics (some smart students might not care, some not so smart
teachers might not care) it is kind of random pick of all who could
theoretically pass the grueling trials.

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Daniel_Newby
"In a 1990 study, Hyde had found that high school boys solved complex problems
on standardized tests better than girls. But 19 years later, test scores of 7
million students across 10 states show that the gap is close to zero."

That's because many of the tests were redesigned in the 1990s to eliminate
their correlation with _g_ , the general intelligence factor. This was
explicitly done to eliminate the gaps between sexes and races.

~~~
DaniFong
What? Cite, please.

Girls have been closing the gap in the study of mathematically precocious
youth, and the international science Olympiads, too. The SAT and the IMO et.
al. have been re-engineered? News to me.

How the heck do you make a math test with the _g_ correlation eliminated,
anyway? That seems pretty hard.

~~~
Daniel_Newby
American MENSA has cut-off dates for various U.S. standardized tests:
[http://www.mensafoundation.org/Content/AML/NavigationMenu/Jo...](http://www.mensafoundation.org/Content/AML/NavigationMenu/Join/SubmitTestScores/QualifyingTestScores/QualifyingScores.htm)

I'm not entirely sure if the _g_ -loading changes were made in the math
portion, or just the verbal. As to how to decorrelate math, I suspect it canbe
done by simply reducing the number of chained dependencies. For example, have
one question involving sin(x) and another involving x^2, instead of one
question involving sin(x^2).

~~~
DaniFong
I don't understand how reducing chained dependencies will eliminate _g_
loading.

If you eliminated _g_ loading of a mathematical test, you'd need to be able to
take a developmentally challenged person, and expect, statistically, for them
to get the same score as a fields medalist. I just don't see how you're going
to swing that.

RE: The Mensa site. They claim that the GRE and the SAT and the ACT no longer
correlate with IQ. Or _g_. That's just wrong. The old SAT correlates
positively with the new SAT. The old SAT correlates positively with _g_. You'd
have to have an extremely unusual statistical correlation between the old SAT
and some other variables to yield 0 correlation with _g._

They could be concerned that it's less well correlated. Or that preparatory
courses from Kaplan, et. al. were killing the correlation.

But in all seriousness, who's keeping count. There are pretty severe
conceptual problems with _g_ anyway. I mean, all it is is the principal factor
in a kind of multivariate linear regression analysis of a bunch of scores on
tests, which are arbitrarily selected and claimed to represent 'intelligence.'
You can't expect that linear statistical relationships mapping a few scores
from a few tests chosen ad hoc really capture the breadth and diversity and
range of human intelligence. It's crazy! If we look for _some_ linear
relationship, we'll find it. But it can't possibly tell the whole story.

~~~
Daniel_Newby
To the best of my limited knowledge, general intelligence is produced by
finding associations between ideas held in working memory. The machines that
carry it out in the brain are unreliable and have capacity limits, so the
fewer ideas and associations needed to solve a problem, the more likely
success is.

For a math test, reducing _g_ loading means having simple problems that rely
on previously-learned information, rather than multi-step problems and
problems that require invention. This is trivial to arrange.

Obviously this will not make a dull person able to pass the test, but we're
talking about college prep tests, where the competition is among the people on
the top part of the _g_ bell curve.

The MENSA issue is one of grossly insufficient correlation, since the
organization is based on intelligence, not educational history.

 _g_ is the psychometric measure most highly correlated with practical
outcomes like annual income and mortality risk. I suspect the second most
correlated measure is attentional control (focus versus ADD), which is the
fuel for the brain's _g_ engine. (Time preference likely has more practical
importance than either, but we don't yet know how to measure it.)

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drhowarddrfine
This again? Who the hell knows? Who the hell cares? Why do women predominate
sewing circles? If women wanted to have math careers they would. Move on to
something important. Geez.

