HowlerKarma - we've had the same sort of thoughts about our DD12 a few times. No idea where she gets the idea that she is a fraud, but it is definitely there.
I have also seen it often in my students. One in particular was so convinced that she was a fraud she stopped being able to function in class because she was convinced that she shouldn't be able to do things as easily and as well as she could. It was very sad, and she is still working through these issues.
I think that middle school girls benefit so much from being told how smart they are AND how this effects others' perceptions of them before they start puberty. Because once puberty starts they seem to have an even harder time understanding that they really could be as smart as they are. I think this is one reason why so many girls opt out of science and math at this age - they no longer believe that they should be able to do those subjects and no one is explaining that they should be able to and that they can do it. I have colleagues who just take girls' sudden lack of confidence in themselves at that age as the norm and nothing to be concerned about. When I have explained why it is important to support them and help them through they call me crazy and walk away! Needless to say, I continue to pester them.
I have a master's degree in physics, so I have lived similar situations of having people shocked that I am a female physicist and can carry on conversations about complex physical situations. It is a drag, and does make you feel embarrassed and frustrated. I have had many times when I have thought of great comebacks later on. However, over the years, I have learned how to respond in the moment. The interesting thing is that it doesn't always help - it has ended up with the other person deciding I was being a bully or worse. (A reaction that they would not have had if it had been a male questioning them.)
