I am so glad that was useful and not offensive, I nearly deleted my post, I was so worried. Then my kids distracted me :-). I have spent a lot of time reading and thinking about the spikiness because I have one of my own - but not nearly so out there as your girl!

Have you done any reading about gifted girls and under achievement? There is a degree to which being socially aware that no-one likes a know it all is a useful skill, but when it inhibits achievement it becomes a problem... And it will make it harder for you to identify the difference between can't and won't.