I, too, think it is up to you. And I do not think the teacher has to overextend himself. My DD is turning 6 tomorrow. She is also high energy, squirmy, not great at listening. She should move into the Hot Shots at gymnastics but she is not behaving like a model student. She gets bored, wants to do more. That is not the teacher's problem. She has to learn to focus and listen and behave.
And why we are doing the CTY for math acceleration. Great if the school works with us but figure for DD, that is best option.
A high energy 6 year old is a handful and the 3rd grade teacher should not have to spend energy on that.
Ren