But I think that on the whole (talking about massive generalisations and not studies of individuals), those preferences are innate.
jeez. I hope whatever you teach it isn't science. The evidence shows the vast majority is taught. There may or may not be a tiny minority innate/biological effect. But yeah, you go with your beliefs....and while teachers like you are ignoring the evidence and going with their beliefs, I'll be going with home education.
My DD used to wear a batman swimming costume. She got SO many questions from adults and children along the lines of 'are you a girl or a boy?' 'why are you wearing that then?' 'wouldn't you like a nice pink costume like mine?' and she didn't get ANY questions from lifeguards about whether or not she should be swimming out of her depth.
When it wore out, we went shopping and it turned out she mysteriously suddenly preferred a pink and orange flowery costume.
So now we get no comments querying her gender, and every single bloody week a life guard would be over asking if she was okay to swim our of her depth.
A month ago in the shower, an adult came over and said 'Ah, I thought it was you....what happened to your lovely batman costume? I loved seeing you play in that'. And guess what....now she wants to go back to super heros when her current costume wears out.
So....do you think her preference for super heros versus flowers is A) innate, biological and there since birth, B) imposed by what people around her tell her they think she should prefer?
And would you care to guess what all that querying her ability has done to her actually ability, let alone her confidence, in swimming? Yes, that's right, we are now about 3 months back from where we were when the batman costume died, all because of people assuming girls must be less able and less confident than boys.
That is exactly how adults (and other children) impose gender difference on children, where none existed.