I am not sure if this is of any use. I see it as how they value themselves. If you value yourself as smart then the only reason you do not do well is that you are not smart. If the praise you get and the validation you get from others is based upon being smart then that is how you see yourself. It is better to praise only effort, then they value hard work.
But then if you only praise hard work, and the child does something amazing, but it felt easy to them, they see no value in it. If they have a talent or ability that comes naturally to them, they should be encouraged to exploit it, not avoid it.
Also, solving problems doesn't depend entirely on hard work... it also depends on one's faith in their ability to solve the problem if they keep working on it. Confidence and work ethic go hand in hand. Some of the hardest-working people in my company have very little confidence in their abilities, which cripples them in key situations, and the ones who rise to the challenge leave them behind.
So, we praise hard work, and we also praise being smart. We use a somewhat altered definition of "smart" though. It doesn't mean regurgitating facts. It means "figuring things out on your own" (which has an effort component), and it means "coming up with a new or interesting idea." In other words, "smart" isn't about knowledge acquired, it's about knowledge applied.
