I will assume that most English schools outside the worst neighbourhoods are roughly comparable to my description of an ordinary American school. How much can an ordinary English school do to raise the academic performance of its students? If the question is framed in terms of teaching them bodies of factual material about history, politics and citizenship, science and the arts, the increases in learning across the board could be dramatic. But if the question is reading and maths, the answer is that the quality of the school makes surprisingly little difference.

This counterintuitive result was first exposed in the United States in 1966 with the publication of the Coleman Report. Named after the sociologist who led it, the magnitude of its effort remains unmatched by anything done since. The sample for the study included 645,000 students nationwide. Before Coleman's team began its work, everyone (including Coleman) thought that the study would document a relationship between the quality of schools and the academic achievement of the students in those schools. Any other result seemed impossible.

To everyone's shock, the Coleman Report instead found that the quality of schools explained almost nothing about differences in academic achievement. Measures such as the credentials of the teachers, the extensiveness and newness of physical facilities, money spent per student - none of the things that people assumed to be important in explaining educational achievement were important in fact. Family background was far and away the most important factor in determining student achievement.

The Coleman Report came under intense fire, but reanalyses of the Coleman data and the collection of new data over many years continue to support the core finding that the quality of schools just doesn't make much difference in mean student test scores. Move away from the awful inner-city schools to the schools that are ordinary or better, and much of the slack has been taken out of the room for improvement in academic achievement for the average student.