It's a kind of "done-to-death" topic in classes going through education and getting the teacher's license swt...
From the realm of education research and education today, the answer is simply "we don't have an unified response to that question." The problem comes from 2 fronts: the nature vs nurture debate remains, and the student body itself is a variable.
The easier part is the student body part... Let's *assume* that teachers teach in the same manner for any gender. However a typical public school is composed of a student body of mixed, various genders. Even if the adults have policy in place and welcome students to take courses that are generally unusual to the gender's stereotypical norm, a student probably want to stick with his/her/whatever's friends and just follow the crowd, and it's the crowd playing the gender input instead.
For example, Engineering is stereotypically not something that a lot of females enter. You may have a female student in high school who is interested to enter faculty of engineering for college. However, none of her friends are taking classes that lead to that in high school staying with 'typical female classes' (whatever they may be), and so she may also be influenced by peers and miss the requirements to enter engineering.
Outside of direct academic influence, a student may have trouble fitting in for whatever reasons that may relate to his/her/whatever gender/sex, creating social issues that are out of the norm or it may cause negative affects on his/her/whatever's mental health. Indirectly, the school social environment affects the academic as well then.
I'm just really briefly summing things up with 2 random examples but hopefully you can understand what I'm trying to say... and all of this is already assuming that the adults aren't also acting as a factor on this entire issue.
As for the nature vs nurture in education context... do genes dictate "natural talent" and especially "limits" on learning? Or, does it work in the other way of "all children can learn anything, equally well" and if a child is having problem in a particular subject, it's all because of improper nurture or the fatal downward spiral of failures?
You got so-called experts on both side of the issue, and so my honest answer from my academic background: we have no idea.
@Yellow: "Now, if we discriminate between the two and cater to avoiding weaknesses and exploiting strengths they just happen to consistently have, we get a better overall education and more equally consistent averages!"
Bold statement that isn't necessarily wrong nor is it proven statistically/psychologically to be correct or incorrect... but this is a traditional question over the past century in education research called "streaming/tracking vs detracking." It usually swings back and forth in terms of what the gov't/majority likes. Currently for North America, we're swinging full force towards detracking.
Britain is the pioneer and flagship of tracking, favoring statements that you said. California is the opposite end of that spectrum. If you're interested in more about it, even wikipedia does a decent introduction to the topic which I think that you may like to have a glance at.