The problem occurs when they incorporate "smart" into their identity, so telling them they're smart is a problem too.

From the article I linked:

> Since Thomas could walk, he has heard constantly that he’s smart. Not just from his parents but from any adult who has come in contact with this precocious child....

> But as Thomas has progressed through school, this self-awareness that he’s smart hasn’t always translated into fearless confidence when attacking his schoolwork. In fact, Thomas’s father noticed just the opposite. “Thomas didn’t want to try things he wouldn’t be successful at,” his father says. “Some things came very quickly to him, but when they didn’t, he gave up almost immediately, concluding, ‘I’m not good at this.’ ” With no more than a glance, Thomas was dividing the world into two—things he was naturally good at and things he wasn’t. [emphasis mine]