Alison Booth and Patrick Nolen ran some experiments in which they offered teenage boys and girls the choice of whether to compete or not against each other in some simple tasks - solving maze puzzles (it‘s always solving maze puzzles!). And they found that girls from single-sex schools were much more likely to want to compete against boys or other girls than were girls from mixed schools.
Girls from single sex schools, then, behave more like boys, insofar as they are more competitive.
The difference between girls from single-sex schools and coed ones is bigger than the difference between single-sex schooled girls and boys.
This matters. It has been suggested (pdf) that one contributor to the gender pay gap is women’s reluctance to compete in tournaments against men. Now, if this reluctance is a wholly free* choice, there’s no problem. But if - as Booth and Nolen suggest - it is the result of socialization, then this element of the pay gap is indeed symptomatic of women’s oppression, not in the workplace but in education.
Theirs, though, is not the only evidence on this point. This paper shows that women from a matriarchal community - the Khasi in India - do choose to compete more than men.
So, perhaps at least one element of what we regard as femininity - a submissive reluctance to compete - is socially constructed. Laboratory experiments then, in one respect, corroborate Simone de Beauvoir’s claim: “One is not born but becomes a woman"
* Of course, you can argue about the meaning of “free.” Silly vulgar libertarians will allege that the absence of state restraint is sufficient. But most of us would surely think that if a group of people were indoctrinated to choose subjugation, their subsequent subjugation would not be “free.”