If it were ADHD then it is likely that you would have similar impulse issues at home.

Sounds like he is trying to fit in, but not quite hitting the mark.

How far ahead is he in his school work? Is he being challenged or is he just completing what is asked of him and then acting up because he is bored? Have a look at some gifted children sights and see if you think that might be a thing to consider. A lot of gifted kids don't seem to fit in socially.