How old is your son?
My daughter is 7 and takes Karate. She LOVES it. It is twice a week, in the evenings. However, IF she does not finish her homework, she knows, that she cannot make it to Karate. It is 'responsibility.' Because she loves Karate, this is an incentive for her. She cooperates.
For your son, did his bad behavior in school happen even prior to taking Karate?
if so, then I don't believe that Karate will, now so suddenly, "change" his overall behavior. It takes time and learning.....Because, his behavior existed PRIOR to taking Karate.
You could try and have the Sensei talk to him... as an incentive....
At my Daughter's Karate school, the Sensei's also, emphasize behavior in and out of school and at home, for example.
But kids have their own issues... which are not instantly 'solved' by Karate. But Karate is a good influence... and some of the kids in my daughter's class... are and were real 'trouble makers' and after a while of being in Karate... REALLY become outstanding young gentlemen. One of the Sensei's for example, is now a black belt and an Instructor there. HE was himself, a troubled child... behaviorally. Which Karate helped him.
Next, what is your son's Teacher, doing in class? For his behavior? Why the bad marks? Can the Teacher suggest anything? How does she discipline in class? Can he see the school Counselor????
Things like this, takes a variety of 'team effort' from a variety of people sometimes... ie: the school Teacher, at home, Karate class... but mostly it takes consistency as well.
Or does he have learning problems, hence his bad behavior in class???? Does anything trigger it?
Just some ideas...
all the best,
Susan