My DD has always know she is very smart. She also knows she cannot take any credit for how smart she is and therefore it is nothing to brag about. She can feel proud (and even brag a bit) if she has worked really hard on something and she has learned/mastered a new skill. We always talk about the fact that we can only do our best and that our best is different for different kids.
We had some parenting classes last year at her school where the subject came up of just how much you tell your children about their giftedness. Some parents believed that they had to "hide" it from their neighbors/friends. I very strongly believe that kids need to know they are different. Not better, but definitely different than most kids. I feel that with self awareness they learn to become humble. My kid or your kid can be very smart, even profoundly gifted, but there is always another kid who is even more gifted/talented/tall/cuter (fill in the blank).
There is a quote on her baby book which I have tried to teach her to live by:
"Much is required from those to whom much is given, for their responsibility is greater."
Luke 12:48
It also helps that all the kids at her school are smart, so it would be sort of pointless to brag amongst each other about how smart they are!!
