It can be a two-way street... the age-peers could be ostracizing the gifted child, and the gifted child can be ostracizing the age-peers.
Just as an example, my DD7 told us at the beginning of the school year that she didn't want any of her classmates knowing she was in the gifted program, because she didn't want to seem different and wanted to blend in. So whenever she had classmates over, kindly keep it to ourselves.
Fast forward four frustrating months of school for her, and DW and I mentioned this in an IEP meeting... and DD's teacher informed us that DD was openly declaring that she's gifted, making a huge issue of it, and putting off the other kids. This told us, in effect, that DD was tired of dealing with people she considered "little kids." DD's class just happens to be the collection point for the more difficult behavior cases, but she's a model citizen, and all the standing in line and being yelled at is driving her nuts. Her message to her classmates was "I don't belong here."
And then there are the situations where the gifted kid isolates herself with a behavior that nobody else can understand. For example, one of the kids in DD's gifted class cries every time she gets an answer wrong. That is a really off-putting behavior, enough so that DD mentioned it to us. We used it as a teachable moment about perfectionism, because she has her issues there, too. And because she has issues with it, hopefully she can understand her classmate a little better. But my point is that this is the kind of behavior that can cause a class to ostracize a student... even in the gifted environment.
Each case is different, and would need a different approach. In DD's case, the solution would be to put her in a more appropriate environment. In the other kids' case, it would be to work on the perfectionism issue.
