I actually have experience on both sides of this issue. My principal would not allow me to skip 3rd grade, despite my teacher's and parents' requests. On the other hand, in junior high, I was allowed to test out of three years of math.
I can assure you that any negative effects of skipping grades are far outweighed by the effects of holding students back. The latter fosters resentment and frustration, which doesn't help social aspects much. For the former, as long as you're sharing classes with advanced students in higher grades (and why wouldn't you be?), the older students are very welcoming.
Also, arrogance isn't a negative quality in talented math/science students -- it's essential. You just can't get really good at math unless you believe you can figure out difficult problems yourself. Maybe you don't have to admit it, but there's a point where denying your abilities looks foolish. The "I've played a lot of Number Munchers" line only works for so long.
I can assure you that any negative effects of skipping grades are far outweighed by the effects of holding students back. The latter fosters resentment and frustration, which doesn't help social aspects much. For the former, as long as you're sharing classes with advanced students in higher grades (and why wouldn't you be?), the older students are very welcoming.
Also, arrogance isn't a negative quality in talented math/science students -- it's essential. You just can't get really good at math unless you believe you can figure out difficult problems yourself. Maybe you don't have to admit it, but there's a point where denying your abilities looks foolish. The "I've played a lot of Number Munchers" line only works for so long.