Causes of behaviour problems in gifted children
I have heard that if gifted children are bored they can get themselves into mischief trying to entertain themselves.
I have also heard behaviour issues can stem from being bullied, not being understood or perhaps something is happening at home or in the child's life he or she cannot articulate into words his/her thoughts and feelings.
I'd talk to your child's teacher and together try to find out the best course of action to help your gift child.
The problem with gifted children is also the fact they have difficulty socializing with their peers and making friends.
As for me, as a child, I could talk to an adult much easier than I could a child my age. Many people see you as a "freak" or someone who boasts when, in fact, you are not. I was informed by a coworker once that if I am knowledgeable in an area or some areas, that I need to keep that information to myself because not everyone is like me and, those that aren't, find it offensive. So, I stay quiet. I have a bad habit of stating facts, even in cases of a joke. I take things literally as well. That is another issue with many gifted children. I was much like Spock in Star Trek (and still am).