Originally Posted by GinaW
The gifted child without appropriate challenge learns different lessons. He learns that a typical learning experience should involve no effort. He learns that challenge can only be found by attempting perfection. What you end up with is a kid who may be years ahead of his peers when it comes to intelligence but behind when it comes to work habits.
Thank you GinaW - that is one of the most illuminating posts I have ever read on underchallenged gifted kids.
OP, we had the same problem. My child was accelerated 1 grade ahead and it was still useless. He started developing an arrogance that he was very good at everything compared to peers (his verbal abilities alone was a light year ahead of his peers and he could do multiplication and divison of 2 digit numbers in K). He also started developing a very poor work ethic. And he was looking for ways to while away his time in the classroom - not disruptively, but more on the lines of a caged wild animal that goes round and round and round for the lack of anything better to do - he was sharpening pencils, going on bathroom breaks, singing songs out loud for entertainment, chatting up his neighbors, pretend playing in the middle of a classroom session - the list go on. I volunteered in his classroom to observe him and I know quite well what happened there.
Here are some strategies that helped immensely:
1. We afterschooled intensively using rich curriculum and enriched him in his areas of interests - I can post what we used for each subject if you are interested.
2. Involved him in many enrichment activities where he needs to develop a work ethic, study skills and learn what losing and not being the best feels like. We did this with intensive piano studies, a serious chess club and martial arts. They have helped teach him that there is always room for improvement even if one is good at something. And he spends a lot of time each day poring over chess tactics, piano practice etc.
3. We found a tutor for the Japanese Sorban mental math technique (anzan) for which he has developed an obsession. It requires intense focus and concentration.
4. We read aloud literature to him that is way above his level and have deep discussions on them - as a way to improve his language comprehension, vocabulary and exposure to styles of writing.
5. I sarted a blog for him - he can make posts on topics of interest with parental supervision.
6. I started him on Mindstorm robotics, Scratch programming and Logo programming.
7. Got him educational math, reading and science program subscriptions for his computer.
These are some things that you can explore to see if you can implement them. Don't depend on the school to provide for 100% of his educational needs. If you feel that they are slacking, you can make up for that in your own time - atleast that is how it has worked out for me so far. Good luck.

PS: We are in a private school that is advanced in academics, and still, I afterschool intensively.