JaneSmith,
You have already lots of good advice.
Fear these may sound harsh but they are to the point and I believe many now-adults remember their painful piano lesson days and wished some of these ideas for when they were children. (You probably do these things already so this is just a list.)
- let the teacher be the one to criticize and correct the child
- the parents/family - to cheer on any little success at all, yay, you did 20 minutes today, yay you finished that piece, yay I've never heard that piece played so fast but it sure sounds neat and different
- ask your gifted child, what do they think, how do they feel about their playing?
- what songs would you like to try?
- lets explore the different kind of music out there, which type do you like?
- for something completely different, lets look up what a blues scale sounds like
- there are some simple workbooks, 1-2 pages a week, for example, some comes with CD that work through music theory (very easy stuff for child to think they're are mastering it)
My child plays / practices with the piano, creates own music, and "plays" and learns for about 2-4 weeks, then we're on a sabbatical. The interest for us is not a serious passion but an interesting hobby. For those children who love it, they will practice on their own, but even then they may need a pause. Some parents have their children in lessons for 1 term, then off 1 term, on another term.
My gifted child is very sensitive to criticism but is able to handle it from gentle caring teachers quite well. Do you sense your child might be also? However, if I told my child played too fast or the beat is off, etc, it seems to immediately pierce the heart.
Instead, I just ask, what does the child think of their playing? And when the child is honest with themselves (this takes time) and acknowledges their own imperfection, I think we are really making strides. Then I say, you are very insightful and understand yourself. Keep at it. I don't catch the child for not admitting it, because not everyone is ready every time to admit their own mistakes.
Just one last thought. Do you sense your own intensity in the matter? Do you think your children sense your intensity?
Best of luck.
