Well, I am with you and would definitely cringe if my children behaved that way. However, I have been told on occasion that I have gone too far the other way, but I make sure that my children knows and understands that as smart as they are, there are plenty of people smarter and more accomplished, etc. Even if they are above 99.99% of the population including all age groups, when you multiply by billions and billions, there is still a very large number of people. It also helps that being considerably older and better educated, it will be quite some time before they exceed my level. I also emphasize achievement over ability and remind them that it doesn't matter how smart they are if they don't use what they have.
I thinke age 6, particularly for a smart kid, is definitely not too young to understand. I explained to them that if you are smart, you don't brag about your intelligence because that would demonstrate a lack of social intelligence and also suggest that you were insecure in your abilities. My two younger ones seem to get that at a very young age, but then again they are socially savvy and don't have any medical issues like Aspergers. My oldest has some impulse issues even at a young age, but fortunately bragging type behavior wasn't one of his problems.
