I agree with this post 100%. Just because she is using different notation does not make the answer wrong, and if the teacher can't provide empathetic feedback that is positive and useful, she does not sound like the teacher for your daughter. It strikes me that your daughter is probably far better at math than many of the other kids in that grade, and to punish her for having a better understanding of the mathematical foundations is unacceptable.
This reminds me of my brother when he was in 7th grade, and had a teacher who taught that "pi is the same as 22/7", which of course is wrong, and of course my brother knew that it was wrong. He argued with that teacher every day for two weeks, insisting that pi is an irrational number, and my mother was finally called to a conference with the teacher because he was "being disruptive" in class. When their complaints were explained, my mother just said, "Well, David is right, and you aren't." Then she arranged for him to go to the high school for math, where he met the teacher who would really become his mentor. He ended up heading to MIT at age 15, and now has a PhD in pure math. And he still knows that pi is an irrational number.
I guess my point is that you should insist that DD follows the rules, even if she finds them silly (e.g. using correct notation WHEN ASKED FOR), but stick up for DD when it is a question of right/wrong answers. It sounds to me like you may need to have a meeting with the teacher and the team leader to discuss the issues, and you may end up needing a teacher switch, if possible. It seems like the teacher is acting as though she thinks your daughter is "showing off", when in reality she is just trying to perform to a higher standard than perhaps some of the other kids.
Good luck. Sounds like you'll have your work cut out for you.
