She could grow up to write a graduate math textbook. Flip through one of those--there are hardly any explanations there because they assume by that stage the reader can fill in on their own.
Hmm. IMO, this is a serious weakness in mathematics textbooks (and is a reason for why there's a huge market for books with "For Dummies" or "Idiot's Guide" in the titles). A lot of textbooks fail to teach because they don't explain stuff properly.
I agree with Dandy. It's very important to be able to prove how you arrived at a conclusion. This is an important way to convince other people that you're right, after all. It's a skill like any other and it helps to develop ordered thinking for those times when you can't just intuit the answer.
I also understand the frustration of feeling like the world moves in slow motion at times. Yet I also know that I'm the one who's different. I need to be aware of that fact and operate so that others can understand me.
Also, I am my son's math teacher. I cajole him about showing his work. It's a long-term lesson. Say he has a moderately complex problem and he does it in his head. If he gets the answer wrong and didn't write out any steps to his solution, I have no way of knowing where he made his mistake(s). Was it a computational error? An error with a fraction? Or did he really not understand what he was supposed to do? When all he wrote was "42," I can't help him understand where he went wrong. Your DD's teacher may feel the same way.
The approach of showing your work carries forward. I'm a scientist. When I do benchwork, I'm obsessive about writing down details in my lab book, including calculations, etc. This way, when something goes wrong, I have lots of information in the lab book to help me understand what happened. As in, "Oh crap; I was supposed to dilute that stuff by a factor of ten and I diluted it by 1000 instead. That explains why I didn't get a reaction."
ETA: your DD may have at least two different challenges here: development of a particular skill and a need to interact with people who also think at warp speed. If she qualifies for the DYS program, it might help with the second need.
