Recently I heard a local girl's high school basketball coach (who's had outstanding success) interviewed on a local PBS radio station. When asked about the differences between coaching girls and boys he indicated that the girls had to be taught that they could focus on themselves, rather than the team in some of their play. He indicated that boys had to be taught to pass the ball and not shoot it each time. Girls he said had to be taught that they could shoot the ball and not pass it all the time.
In understanding why he was so successful it was clear that he allowed his teams collectively to help make some decisions and really worked using their desires to cooperate.
When my step-son plays on his soccer team the coach has to work to build teamwork. When older girls' teams are practicing nearby their teamwork and general camaraderie are always very evident.
Socialization is certainly part of this, but biology also plays a role. Watching young children I've seen very little boys playing very different from similar girls. TV, other kids as well as parents affect behavior, but it's more than that.
I wonder how, if at all, it may be different in subcultures (and other cultures in general) where cooperation is valued much more than our individualistic culture.