In the last week my 11 yr old dd said she though drs were men and nurses were women.
Told me her teacher had used the analogy of
"Most of you will be cleverer than your MUMS after the sats As it will be many years since they went to school 
Then today I was doing a bit of hand washing (we are camping) and a guy wa also doing his next to me.
A little girl of about 9 asked " how come you are doing the washing and not Claire?"
It seems the next generation simply aren't getting the message.
Dd was soley raised by me untill aged five.
I have always worked in a professional role, set good examples and since dh came along at aged five she has not been exposed to gender stereotypes.
We share childcare and housework and have independent lives.
What can you do?