We are home schooling, but the psychologist who tested our DS gave us some good advice that might help you, too. He told us that DS needs to do something he loves every day.
Maybe rather than the more traditional afterschooling, you could tell your DS that he has two assignments: 1) learn something new every day, and 2) do something he loves every day. (And video games don't count!) The quicker he completes both assignments, the sooner he gets to his beloved video game. But that's not a bribe--just the facts of time management! If he can do something that meets both goals at once, so much the better for him!
Oh, and our local gifted enrichment group just had a speaker who said that 3rd grade is often the point at which GT boys begin to have gender-based reasons for resisting the "smart kid" label. Maybe part of this is that he's struggling to fit in and be a "real boy" (as he sees it)? I guess 3rd grade is often the time when underachievement kicks in for boys. The main recommendation for fixing this is to make sure he has plenty of opportunities to pursue his particular interests and to have male mentors.
And maybe I missed it, but I didn't see any mention of advocating for more challenging work with the teacher. I'd certainly recommend that you do this. It's very hard to make up for 7 hours of school-time boredom with any activity after school. Something is going to have to change there, I think.
I'm sorry. I know how awful it is to watch this happening. Hang in there!
