Hi Eleanor - I think the decision depends on the kid and the family. I have a DS6 who just skipped 1st. He refuses to ever learn anything at home, along with not complaining while he's in school. We hear about how easy things are at home. We have seen evidence that he would rather pick the easy route if given a choice at school. Since our DS6 won't do anything that appears to be learning at home, we rely on the school. Luckily, they are willing to work with us. They are giving him pretests and are trying to give him work at his level (it's not perfect yet). Last year, in kindergarten, he was given 2nd grade math. If my son were in your situation, I would worry about him becoming complacent in school, and thinking that school is not for learning. But your DS is getting some work at his level at home, so maybe that's not a concern.
