Given the recent debates about teacher pay, a recent NBER paper by Harvard Economist, Roland Fryer, throws a wrench into the debate. His study finds that providing incentives (ie money) to teachers for improving math and reading scores in NYC had no positive impact on their students test scores, and if anything led to slight declines.
This article has a good overview of the study. In short Fryer hypothesizes the payment may have been too small and that the relationship between teacher effort and student achievement may have been unclear.
Another issue is that teachers split bonuses among all faculty in their school not just those that led to the improvement. Fryer sites other work that this shouldn't matter, although I find that hard to believe.
Economists always say that incentives matter, but this result shows how difficult it is to really improve test scores and achievement.