My daughter has stopped doing any homework because she hates it. I have found homework with "hate" written on it with plenty of exclamation points. I told her she would have to explain to the teacher when it wasn't done (she tries to be a perfect student, which is an issue in itself, and I knew she would be unhappy with that). However, the teacher apparently doesn't care or just excuses it because her averages are all 99 or 100 percent.
My daughter was skipped one grade in kindergarten, which worked well because she hadn't had a chance to form close friendships. She has changed schools repeatedly but says she prefers her current school, where kids do individual work at their own pace, even though she has better friends at the public school.
Honestly, though, nothing has really worked and I don't know how much the acceleration helped in the long run (it was a huge help at the time, but only a temporary help as others have mentioned).
She is tested to determine placement and allowed to skip work if she does a few exercises to show she can do it. However, she still has to follow a standard spiraling curriculum ("didn't I learn this in second grade?") and to test on each section. She can go more quickly, but with no challenge and with no practice managing homework (not that I want her to have lots of homework). It's not harder work, just more advanced. She recently had to write a story and enjoyed it, writing and illustrating about thirty pages that her teacher bound for her and had her read to the lower grades. When I signed her up for an independent writing program because she loves writing, she was shocked to receive feedback for improvement of her story instead of just hearing that it was wonderful and receiving a perfect score. She just doesn't get the experience of handling difficult work even though she is allowed to work quickly.
So technically she should be in third grade but is placed in seventh grade math and high school English. It sounds great and is much better than any other options we have tried, but it still isn't a solution.
So we just try to work out ways to add to her school work, like the independent writing program, and hope it will be enough.