"Well, gender is not a social construct. It's a biological, psychological _and_ a social construct."
I disagree about the biological part - (see my reply to Nix above, along with a definition for gender) and the psychological can be explained as learned behaviour too.
Regarding the 'very real gender differences in gender-related behavior that start before the age of 3', I would want to look very carefully indeed at these studies if they are trying to demonstrate that the behaviour arises from a biologically-determined origin.
As I mentioned in my previous post in response to giraffedata (which is very long, so I am not surprised if you have not read it ;-) cognitive neuroscientist Cordelia Fine has analysed quite a few studies involving young children and found them to be flawed, and unfortunately the lack of challenge over these flaws by the scientific community, combined with an uncritical and naive uptake of the studies by pop science magazines and forums taking their claims at face value, has led to researchers getting away with claims that range from highly questionable to downright daft .
I would be very interested if you could point me to the research that you are referring to that backs up what you are saying, but from what I have seen already I am not confident that it will be capable of swaying my opinion.
Behaviour is so utterly transformed in adults compared to anything that might be hinted at from an early age that it is silly to try and crudely extrapolate an elaborate social concept like gendered behaviour in adults from a few primitive behavioural traits apparently displayed in very young children (particularly when the design of tests trying to demonstrate these traits is fraught with conceptual and structural problems ). By the time children are even 10 years old they have necessarily been subject to such an immense amount of inescapable cultural conditioning and social learning that it is simply inappropriate to put down their behaviour to having a biological origin anymore - if this ever _had been_ the case, it would have long since been overwritten during the upbringing of the child.
"ex-USSR countries often have high percentages of women in hard science. And that's not just a fluke, but a result of deliberate policy of attracting women to scientific and engineering disciplines.
For all its faults, the USSR had been extremely egalitarian.
Russia is my home country and I'm a mathematician by education. About a half of my classmates in university were women. And they were definitely as good as men in all classes."
Which just goes to demonstrate what I am saying, right? The power of social and cultural determinants rather than biological ones, combined with the (explicitly human and deliberately-designed) factor of education. ;-)
 This goes for studies that try and 'prove' a biological determinant for specific socially-derived human behaviours or socially-determined concepts (e.g. 'morality') in general, not just for studies that examine gender.
 Like, for example, getting children of both sexes to play with various toys and then deducing from the choice of toys that they are being chosen by the children on a sex-derived basis. So (to give a couple of examples from studies quoted by Fine) researchers think they can seriously suggest that when a girl chooses to dress up as a witch, and a boy chooses to dress up as an alien, this is a choice they make according to a biologically-predetermined basis.
This of course is nonsense: children are not born knowing what a witch and alien are, they learn the meaning of these (fantasy cultural) inventions as they grow - along with, necessarily, their gender associations at the same time.
Or, for the second example, researchers define a pan as a 'girl' toy. Why on earth should that be the case when children are not born into the world knowing how to cook? You might as well identify it as a 'boy' toy because it looks like a helmet.
What is inevitably happening here is that researchers are projecting their _own_ idea of what constitutes a 'male' or 'female' toy onto the toys, and this is undermining the entire objective basis of their experiment (a flaw which they completely ignore when reporting the results of their studies).
And this is at the heart of the problem of trying to prove sex-determined behaviour exists in young children.
Also, as Fine successfully argues and demonstrates in her chosen studies - you may well find gender associations made by children younger than 3 - because children start to absorb these associations before the age of 3.
The very definition of gendered behaviour is a social one, gender associations are acquired via social interaction and observation, so it is hard to see how 'associated dress, roles, stereotypes, etc.' can be 'proved' to be determined on a genetic, neurological or biological basis.