Someone (I confess I can't remember who) had up a link to this New York Times Magazine article titled How Not to Talk to Your Kids, about the effects of different forms of praise on young (and also older) children.
Essentially, a number of studies have produced some pretty conclusive results that if children consistently receive praise that "You did great. You must be really smart." they tend to become risk averse and drop things which they don't immediately excel at, declairing "This is just something I'm not good at."
If, on the other hand, children receive praise along the lines of "Great job. You must have worked really hard on that." they tend to be more willing to accept difficult problems and work through them, even if they at first don't do very well. The explanation that the researchers suggest is that "You must have really worked hard" gives the recipient of the praise an implicit action plan for how to achieve similar results in a more difficult situation in the future. "You must be really smart" on the other hand, suggests that good performance is the result of innate ability, and there's little that the child can do about it, except try to preserve the appearance of intelligence by avoiding failure.
In a study with high school age students, a class of under performers in math were divided into two groups, each of which received identical drill in basic study habits, discipline, and math concepts. One group received an additional two 25 minute sessions on how intelligence is not innate, but can be built up through hard work. In subsequent instruction and testing ove the course of several months, the group which had received the sessions on the ability to improve intelligence and knowledge performed significantly better on average than the group which did not recieve those extra sessions. Classroom teachers (who did not know which students had fallen into which group) consistently were able to identify which ones had received the "intelligence can be improved" lessons based on how hard the students worked.
However, the someone disturbing thing in light of all this is that there is actually a certain amount of evidence that intelligence (measured in absolute terms) cannot actually be increased, at least past the age of 10 or 12. This post on GeneExpression provides a summary of the work on g, which is taken to be the measure of general intelligence possessed by an individual. Research has generally shown that increased study can make only marginal measurable improvements in g in adults and teenagers.
I'm certainly not a neurologist or psychologist, but to the extent that I can get away with opining on such things (why not, I'm an amateur at pretty much everything else I write about) it seems to me that the truth of the matter is to an extent illuminated by these apparently contradictory results. I think most people degree of absolute intelligence/intellectual ability is probably pretty much set by some (have no idea what) combination of genetics and early rearing/environment up through age 7 or 8. However, even given that intelligence itself becomes essentially set after a certain period, the extent to which people successfully utilize their intelligence varies widely depending on dedication, study habits, quality of learning tools, cultural environment, opportunity, etc.
Given that most people are performing well below the maximum level allowed by the degree of intelligence that they possess, it makes sense that increased application would generally attain dramatic results. The question, it seems to me, is how wide the actual range of absolute of intelligence is for the middle 90% or so of the population. Is there enough of a range that the bottom 20-30% of performers really can't reproduce the results of the top 20-30%, or at least the middle 40-50%? I suspect that probably they can.