The stereotyping of women is not as much an issue, I think, as the stereotype of a scientist that is presented to students. In science classes during elementary school and high school, students learn all about great discoveries--the vast majority of them, made by male scientists. Female scientists do not get as much credit as their male counterparts. When we start teaching our students about breakthroughs made by women in the field of science, more girls will want to grow up to be scientists.
The world of science has many possibilities, but those opportunities are not as available to women. Mostly there is no basis for this stereotype, but women still face this opinion. We live in a world that claims to be equal, but there are so many ways that we fall short, especially in the sciences.
Stereotyping tends to be a huge problem for a lot of women, regardless of the field. It seems to me that people are more apt to hire white men, or to hire women or minorities in order to boost their diversity. It really is a shame, especially when in this day and age, science really should be open minded to anyone entering the field.
The same for men, not quitting is the biggest obstacle. Science is hard, perhaps being discriminated against is hard to? However it doesn't matter if you're discriminated against as long as you don't quit. There are no obstacles to becoming a scientist, the option to be a scientist is free and available to anyone. Science is hard, it's difficult, and it's math intensive but if you don't quit then it doesn't matter.
I feel that stereotyping is not what keeps women away from science, it is simply that many of them are not interested in the subject to begin with. Heck, even most males are not interested in scientific subjects. It takes a certain type of person to want to go into science to begin with. If women are interested in science, they will go into science.