I think that the most widespread gender-based problem lies in sparking the interest of more young women in science and technology, not so much in gender-based discrimination. I believe that the reason there is a disproportionately low number of females involved in the areas of science and engineering is the fact that girls are often underexposed to the possibility of a career in those fields. The problem is not so much that girls are being discriminated against, but rather that girls are not receiving enough encouragement from the onset.
I don't believe that sexism on FIRST teams is a huge problem. There are many, many teams where girls are welcome and encouraged to participate. Why then, are there so few females in FIRST?
The real issue is that girls are usually encouraged by society to go into the arts and humanities, rather than into science or technology. They aren't encouraged to go into science or engineering in the same way that boys are - not because society is discriminatory, but because our culture has only relatively recently accepted the idea of women pursuing scientific careers. Society isn't "used to" the idea of women in science and technology, and therefore it isn't "expected". Many girls never really consider careers in engineering because their cultural experience never planted the thought in their minds.
I once asked one of my female students at my summer RoboCamp for Girls session why she had never considered joining the school's FLL team. She told me, "I was afraid it would be ruled by the boys." I have observed that oftentimes, girls in that age group (9-14) are often more reserved and reticent than boys in the same age group. Their ideas are less likely to be heard in a noisy group of boisterous boys, and they are less comfortable sharing them. All too often, the girls have had some sort of a bad experience in school trying to work with a group of boys, and they were shut out. Boys at that age are often bossier than the girls, and can be rougher and pushier.
These social characteristics of this particular age group - when left unchecked - are often what prevents young girls from feeling comfortable embarking upon a new experience that is mostly male dominated. No one discriminates against them or discourages them purposely. Rather, the girls are uncomfortable from the onset, due to social environmental factors. This mindset is learned in their preteen years, and consequently makes many girls rule out robotics in their teen years.
However, it is possible to foster a group dynamic that allows girls to feel more comfortable working in a male dominated activity. Maintaining a team that is well structured and organized prevents members from feeling overwhelmed by chaos (why is it that chaos is often present where there are boys?

). Making clear rules about allowing everyone to share their ideas is very important. Define your behavioral expectations to the kids clearly - make sure that an atmosphere of respect is highly palpable. This allows everyone to feel comfortable working with each other, and sharing their opinions. By keeping a well-run team, you are ensuring that all of the students (including the girls) have a positive experience.
But how does society in general help more girls become interested in science and technology?
I firmly believe that all-girls programs and camps are a great way to introduce pre-teen and teen girls to robotics. I ran two RoboCamp for Girls sessions this summer, and they were a great success. For the first time ever, my school district has female members on it's two FLL teams. Previously, there were none. Because the girls didn't have to worry about being pushed around by boys, they felt comfortable embarking upon a new learning experience. They were able to acquire the knowledge and skills that made them feel less intimidated to join the FLL team. They felt (and were) of equal competence to the boys who were on the team, and they felt comfortable sharing their opinions.
The other reason why girls felt comfortable in the all-girls program is that they could stick with their friends. Girls at that age seem to be more confident about trying new things when they have a friend at their side. This is true for my robotics team also - almost all of the girls on my team have joined because a friend was already on the team.
The bottom line is this:
More girls need to be directly encouraged to become interested in science and technology. More programs targeted specifically at girls need to be put in place. Sexism is not the root of this problem, as it was in the past. Even though most sexism is gone, society still has not recovered from it's effects - namely, that girls are not expected to go into science and technology the way that boys are. By directly encouraging girls, we can hopefully initiate a gradual change in society's perceptions surrounding careers and gender.
-- Jaine