We've had some of these kind of issues. My 8 year old started piano at age 5.
When the teacher says he's moving too fast, does she think he is starting to play songs note wise that maybe he isn't ready for technique wise? We had an issue where a teacher let us move TOO fast. My son can learn notes and songs very quickly, but the technique of playing it well with lifts, tall fingers, dynamics etc take a little longer. We had to switch to a pickier teacher. Our "pickier" teacher doesn't demand perfection by any means. But if DS is going to play a song that is usually played by kids several year older, he is going to learn to play it as well as them. If the teacher just wants him to slow down because she wants to pigeon hole him with the rest of the 4 year olds, that's ridiculous. And I would find a new teacher. We've had 3 piano teachers. All 3 absolutely LOVED teaching DS because he learned so quickly and had no interest in slowing him down at all!
A nice compromise we have with our teacher is we have "sight reading" songs where we just read the songs for notes. Then we have technique songs that we really work on and try to prepare for performance. Even though you don't envision your child as a pianist as a career (I don't either - but it's his choice!), if they are going to continue on in piano to get more difficult songs the technique really does have to be there.
I also agree with whoever said that eventually most kids do hit a wall where they start to move at a more modest speed. Beginning music is usually very easy for these GT kids.
Good luck finding a new teacher!
It helps to observe the teacher and talk to other families of students. I had a frank discussion with our latest teacher about our GT issues that helped lay the groundwork for a good relationship as well.
