I find it rather horrifying that a decade into the new millennium still finds thirteen year old girls who never even considered the possibility of excelling in math or science solely because of their gender.
Seems kinda backwards to me, and I've been out of school for 10 years.
I guess a lot comes down to individual family and cultural background. Education tends to be valued more by those who already have a fair share of it, and those people are more likely to look beyond stereotypes as well.
What I'm wondering is - by 13, shouldn't it be reasonably clear whether someone has a predisposition for math and analytical thinking or not? The jury would still be out on chemistry and biology and stuff at this point, of course (can't knock it until you've tried it).
All I can say from my years at university is that there were depressingly few girls in physics and electrical engineering. Those who made it past the first few semesters tended to be among the best though. Supposedly it's less severe in other European countries.
"Non-technical" sciences (chemistry, biology, medicine, economics) looked
entirely different. From what I remember, it wasn't too bad in maths either.