Do Schools Matter for High Math Achievement?: Evidence from the American Mathematics Competitions
By Glenn Ellison and Ashley Swanson
American Economic Review, 106(6), 1244-1277, 2016
Abstract: This paper uses data from the American Mathematics Competitions to examine the rates at which different high schools produce high-achieving math students. There are large differences in the frequency with which students from seemingly similar schools reach high achievement levels. The distribution of unexplained school effects includes a thick tail of schools that produce many more high-achieving students than is typical. Several additional analyses suggest that the differences are not primarily due to unobserved differences in student characteristics. The differences are persistent across time, suggesting that differences in the effectiveness of educational programs are not primarily due to direct peer effects. (JEL H75, I21, I24, I28, R23)

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I think section C on "Informal Evidence on High-Achieving Schools" is especially interesting:

Quote:
Comparing the summary statistics we note several differences between the high-achieving schools and the matched comparison group. One clear difference is that the high-achieving schools were much more likely to have “star” math teachers. In some cases star teachers seem extremely important (and impressive).

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There also appear to be differences in the curricular offerings. In looking at the most standard high school courses, geometry and algebra II, we found that the high-achieving schools tend to stratify their math offerings more finely: they typically offer three levels of these classes whereas the comparison schools usually offer two. They are also more likely to offer multivariable calculus: we found such courses at five of the high-achieving schools and just two of the comparison schools. The final column records observations of additional special curricular offerings. The “−1” notation marks five schools which offer some type of additional math course which includes problem solving and/or math competition in its description. Often the descriptions indicate that the classes offer a variety of types of enrichment. The most striking example is that of the top ranked school, Vestavia Hills HS, at which students may in addition to their regular math course enroll each year in an extra one-half or full-credit “Honors Math Theory” class that meets every day before school and/or during lunch. The “−2” notation marks schools that offer classes to prepare students for research competitions, which is something we found at two high-achieving and one comparison school.