In this study, the authors make use of an unusual property of a data set from Bogota--whereby some teachers teach math to more than one group of students--to determine the roles of teacher quality, peer group composition, and class size. They show that all three have effects on student achievement. They also show that the average attributes of public schools and private schools differ markedly in dimensions that affect student achievement. Finally, they show that differences in student achievement among schools in the public sector, and especially among schools in the private sector, are much larger than the average difference between the achievement of children attending public schools and those attending private schools, net of family background influences. The implication for parents is that the decision to use public or private schools is much less important than the choice of school within either sector. The implication for governments is that the details of subsidy programs are extremely important. (Contains 3 tables, 2 figures and 68 footnotes.)