I now realize how lucky we were to have an insightful kinder teacher for my older son. When he started to misbehave (tying other kids' shoes together in circle time...), she asked if we'd considered getting him screened for gifted. She set up the screening appointment with the school's evaluator and delivered the news that he'd topped out on the screening test. We chose to pull him from public school and put him in a more rigorous academic private school, something we would have never done without her intervention.
Misbehavior can be from boredome, and it is worth exporting if he's unhappy.
Good luck!