Thanks for all the thoughts and help. I think I should clarify a bit that the way DD gets the answers is not intuitive but the way DH and I were taught in school. She can show her work, but she does not do it the way her teacher does. So the first issue is the way she calculates is different, but acceptable in the math world. I think that her "quickness" and the fact she had already mastered this causes DD to work ahead and while the teacher is giving instruction DD may be completing the whole page. And when the work looks different, she gets asked "how did you get that answer?". DD can explain how she did it, but it's not the long way other students do it.
I don't know if DD comes off as a know it all, but I'm sure she is proud of herself for finishing the problems quickly. She is also very talkative and last year she had problems remaining quiet when she was finished ahead of others. Her teacher has not been in touch, so I think DD reads into the situation more than necessary. She is extremely sensitive and often seeks her teacher's approval. When she is questioned, she may think she is not doing it right.
I figured though that this problem creeps up with others too as my generation learned to calculate things differently (just as with cursive styles). Since I have a curious child, we don't teach her at home, but will explain things as she asks. DD has many books and websites she likes to explore and asks questions when she wants to learn more. I agree with the thought that it's good to learn different ways. We have done that before with other things, but as DD showed me the teacher's way, it seems very long way around to get to the same answer. But again, I may not know what it builds upon.
