I agree that gifted kids need to be told that they are smart/gifted/fast learners, whatever words their parents feel comfortable using. These kids know that they are outside the norm, and if they don't have a clear understanding of HOW/WHY they are different, they can jump to the conclusion that they are just odd, weird, or even stupid.
I completely agree with this statement. My DS realized by the time he was 3yo that he was gifted and it took me yet another year to finally realize it myself.
Very recently we had a conversation about how more typically able children often need or benefit from further explanation and examples after the directions are given. His response was, "They do?!" It had never occurred to him because he almost always "gets it" when the directions are given and he just want to get down to business.
Our other children noticed that our gifted son is very smart even w/o us saying anything. That prompted many discussions regarding talents. One of my children is a gifted athlete, another is showing great potential in artwork, and one happens to be gifted with things of the brain.... at least that's how we put it for lack of a better way to describe it. Our children all accepted it a lot better realizing that they all have something they good at, even if they are not expressly gifted in it.
But mostly he have to tame the lion in our gifted son because he forgets that his brain works faster and thinks more deeply than his same-age peers. We often caution him to slow down and look at it from their point of view while at the same time allowing him to be who he is. It's a delicate balance.
Okay, off to read the article.

[edited for spelling]