The authors report insights, based on annual site visits to elementary and middle schools in three states from 2004 to 2006, into the incentive effect of the No Child Left Behind Act's requirement that increasing percentages of students make Adequate Yearly Progress (AYP) in every public school. They develop a framework, drawing on the physics concept of an attractor basin, to relate to theoretical literatures in economics and psychology the experiences that teachers, principals, and parents are having with the law. The authors anticipate--and find evidence of--very different incentive effects of the AYP requirements on schools of different initial achievement levels. (Contains 3 tables, 1 figure, and 7 notes.)