I've experienced something similar from the other point of view. I was one of the 15 guys in class and sat next to the only girl in the class. I remember the teacher giving us exercises and I would type up the code in few minutes, while she would struggle for half hour. She kept telling me how much smarter I was and how she didn't get it, and I would help her through it.
What she never realized was that I've already implemented a 90% similar code twice in the last month in my spare time. Or that after she got off the school to hang out with her friends, I went to the library to do some reading, or write the next module of the awesome game I was developing.
What I'm trying to say is that in my experience the smarter ones is a lazy way of saying "the ones that had more interest and spent much more time on it already than you did". And of course, the argument isn't unique to girls and applies just as well to other guy friends. But in the end, in my experience it has always traced back to raw interest in the topic. So I've always said that girls are not different in any mystical raw Mathematical intelligence way, it's just that for some reason they tend to have less interest in these topics, on average. And why is that? Upbringing and early biases is my best guess - The mother who pulls away the rocket ship from a girls hands and puts in a Barbie is at fault. (But realistically, it is probably only one of the factors.) Worst of all, there is a positive feedback loop involved where if someone thinks they are not good at something, they will only become less and less interested.
I think you're largely correct, but you're probably underestimating how much societal pressure goes into making things this way. Parents taking away the rocket ship is just the tip of the iceberg. Not only are young girls pushed away from science and other subjects that are considered masculine, but they're also socialized to have a "broad range" of interests and not to obsess over any one thing, which is the exact trait that enabled me and many other programmers I know to get ahead in programming. I underestimated it too until I read Unlocking the Clubhouse (http://mitpress.mit.edu/catalog/item/default.asp?tid=8515...) a few months ago.
For problems this large and systemic, significant corrective action and positive reinforcement are required.
I was friends with one highschooler who constantly showed off his math knowledge. He much preferred to leave people (many of whom were poor) with the impression that he was superhuman, rather than proactively explaining that his father was a mathematician, his mother taught him at his Montessori grade school, and his family was very well-off...
I think a significant problem is the self-aggrandizing way males are socialized. Often to intimidate. This interacts badly with how females are pressured to defer and feel inferior.
I had a somewhat similar experience. I took a CS class in high school and, having had something like a four-year head start, did pick the material up somewhat faster than other people.
The biggest difference I noted didn't have anything to do with what the other students did in their spare time. Rather, the major difference was that some students would immediately ask for help as soon as they ran into any sort of trouble where others would spend some time trying to overcome the problem themselves.
The latter approach is far more important than anything you do in the subject itself--it teaches you the skills you need to solve problems yourself. Forcing yourself to sift through documentation, try different approaches and just sit there staring at the screen and thinking prepares you for similar problems in the future where just asking for help only teaches you how to solve your immediate issue (at best).
This post is gender-agnostic because it applied to both boys and girls in my class. I'm sure there are plenty of gender-specific issues as well, but this was the single most important factor I saw in how well other students did.
What she never realized was that I've already implemented a 90% similar code twice in the last month in my spare time. Or that after she got off the school to hang out with her friends, I went to the library to do some reading, or write the next module of the awesome game I was developing.
What I'm trying to say is that in my experience the smarter ones is a lazy way of saying "the ones that had more interest and spent much more time on it already than you did". And of course, the argument isn't unique to girls and applies just as well to other guy friends. But in the end, in my experience it has always traced back to raw interest in the topic. So I've always said that girls are not different in any mystical raw Mathematical intelligence way, it's just that for some reason they tend to have less interest in these topics, on average. And why is that? Upbringing and early biases is my best guess - The mother who pulls away the rocket ship from a girls hands and puts in a Barbie is at fault. (But realistically, it is probably only one of the factors.) Worst of all, there is a positive feedback loop involved where if someone thinks they are not good at something, they will only become less and less interested.