All my dd's were social butterflies in school. My oldest would finish her work and then go to help someone else with theirs-of course, she didn't ask the teacher if she could do that, so she was labeled a social butterfliy, but she did do her work.
My other two would talk before their work was finished, but they both grew out of it, as did my oldest dd. Of course we did have talks about talking in class without permission and they really didn't want to get on the 'bad' chart at school either so we got through those years fairly easily.
Some kids, even at age 6, are just not ready for sitting still for periods of time, boys usually have that problem more than girls but I think it's showing up in girls more and more at the early ages.
Good luck.