You might want to try playing board games where you have to all work together to win.. There are some good ones listed on the ultimate game thread. Forbidden Island is a good example of it.
We had to work on the "hi I am [name] I am smart social conversation status. When DS felt uncomfortable in new situations he lead with it so what I thought was bragging was actually trying to find a comfort space with kids in a non academic setting. Of course we still had to talk to him about what he was doing but it really helped to get to the why. With your DS why does he want to be first, what is he getting out it, what does he think the other kids feel when he he says those things, etc.
It might take awhile to deal with this but he absolutely can be led away from this behavior.
DeHe
