@ Bostonian — I couldn't tell from your comment whether you think that the correlation between spelling bee performance and going into / succeeding in medicine is causal...is that what you meant?

@ ultramarine — Thanks for sharing your experience! Looking back over the different extracurriculars that you were involved with, does participation in the National Spelling Bee stand out as among the best, or are there others that you found more enriching and/or enjoyable?

As for girls/women assessing their abilities more accurately than boys/men, this may be true in general, but I think that it's less likely to be true for gifted populations. I've seen a number of examples of gifted girls/women underestimate their intelligence by ~1 standard deviation (~15 IQ points) roughly speaking, and fewer instances of gifted boys/men overestimating their intelligence by ~1 standard deviation.

@ master of none — I'm glad to hear that things have been going better, and am sympathetic. Has she thought about going to a math camp for middle school students like MathPath (where I worked for three summers)? A lot of the girls there had very good experiences meeting other girls who share their interests. Art of Problem Solving also has some very mathematically talented girls.
Advising for gifted children available at Cognito Mentoring.