Does class size have an effect on academic performance?

Responsible researcher: Viviane Pires Ribeiro

Paper Title: Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement

Authors: Joshua D. Angrist and Victor Lavy

Intervention Location: Israel

Sample Size: 62,000 students

Big theme: Education

Variable of Main Interest: School quality

Type of Intervention : Maimonides Rule

Methodology: Instrumental Variables

Understanding the relationship between class size and academic performance has motivated several studies that, until now, have reached inconclusive results. While some authors found results that indicate that smaller classes are associated with higher academic achievement, others refuted these results. In this scenario, Angrist and Lavy (1999) use Maimonides' 40 students per class rule to construct instrumental variable estimates of the effects of class size on test scores. Estimates show that reducing class sizes induces a significant and substantial increase in test scores for fourth- and fifth-graders, although not for third-graders.

Assessment Context

Class size is a variable that is at the center of political debates that deal with the quality of teaching and the allocation of school resources. Typically, parents and teachers prefer classes with few students because they believe that this type of class offers a more conducive learning environment. Furthermore, this variable is considered easy to manipulate by policymakers. It is observed that despite this broad interest in the consequences of changing class size, the causal consequences of this variable on school performance have been a difficult parameter to measure.

Although the level of educational inputs differs substantially between and within schools, these differences are often associated with factors such as training or students' socioeconomic background. Possibly for this reason, much of the research on the relationship between class size and performance is inconclusive.

Intervention Details

According to Angrist and Lavy (1999), the 12th century rabbinic scholar Maimonides proposed a maximum class size of 40 students. This same maximum induces a non-linear and non-monotonic relationship between grade enrollment and class size in Israeli public schools. Thus, the authors point out that this rule has been used since 1969 to determine the division of enrollment cohorts The maximum of 40 is known to teachers and school directors, and is distributed annually in a set of decrees from the Director General of the Ministry of Education. Furthermore, this rule generates a potentially exogenous source of variation in class size that can be used to estimate the effects of class size on the academic performance of Israeli students.

In this sense, Angrist and Lavy (1999) use the class size function induced by Maimonides' rule to construct instrumental variable estimates of class size effects. Although the class size function and the instruments derived from it are themselves a function of the size of cohorts , these functions are nonlinear and nonmonotonic. You can thus control a wide range of smooth inscription effects when using the rule as an instrument.

Furthermore, the authors point out that Maimonides' rule is not the only source of variation in Israeli class sizes, and average class sizes are generally smaller than would be predicted by a strict application of this rule. But Israeli classes are large by U.S. standards, and the 40-student-per-class cap is a real limitation faced by many school principals.

Methodology Details

Maimonides' rule of 40 is used by Angrist and Lavy (1999) to construct instrumental variable estimates of the effects of class size on test scores. The resulting identification strategy can be seen, according to the authors, as an application of Donald Campbell's regression discontinuity design to the question of class size.

The average class size in the study data is 31 students, with 25% of classes having more than 35 students and 10% having more than 38 students. A regression of actual class size at mid-year against predicted class size using beginning-of-year enrollment data and Maimonides' rule explains about half of the variation in class size at each grade level (in a population of about 2,000 classes per grade).

The test score data used comes from a national short-term testing program in Israeli elementary schools. In June 1991, near the end of the school year, all fourth- and fifth-grade students were given achievement tests designed to measure reading and math skills. The scores used in Angrist and Lavy's (1999) study consist of a composite constructed from some of the basic questions and all of the more advanced questions on the test, divided by the number of questions in the composite score, so that the score was scaled from 1 to 100.

As part of the same program, similar tests were administered to third graders in June 1992. The achievement tests generated considerable public controversy due to lower-than-anticipated scores, especially in 1991, and due to the large regional difference in results . After 1992, the national testing program was abandoned.

Results

Angrist and Lavy (1999) present a variety of Ordinary Least Squares (OLS) and instrumental variable estimates of the effect of class size on the reading and mathematics scores of elementary school children in Israel. Instrumental variable estimates constructed using functions of Maimonides' rule as instruments for class size, while controlling for student enrollment and background, consistently show a negative association between larger classes and student performance.

These effects are observed to be largest for the math and reading scores of fifth graders, with smaller effects for the reading scores of fourth graders. The results for fourth graders' math scores are not significant, although the pooled estimates for fourth and fifth graders are significant and accurate on both tests.

Public Policy Lessons

Angrist and Lavy (1999) point out that even though the effects reported in the study are mostly smaller than those reported in the Tennessee STAR experiment, they may represent important gains in relation to the distribution of Israeli test results. The authors comment that the Israeli Parliament has initiated a debate on a bill that would reduce the legal maximum class size to 30 students. cohort size distributions , they estimated that the new law would reduce the average elementary school class size from 31 to about 25 and reduce the top quartile from 35 to 27. These reductions would clearly be costly to implement, requiring something like 600 additional classes per series. But the results reported in the study imply that the resulting change in Maimonides' rule could have an impact equivalent to moving two “ deciles ” in the 1991 distribution of class averages.

Finally, it is worth considering whether the results for Israel are likely to be relevant to the United States or other developed countries. In addition to cultural and political differences, Israel has a lower standard of living and spends less on education per student than the United States and some Organization for Economic Co-operation and Development (OECD) countries. Additionally, Israel also has larger class sizes than the United States, United Kingdom and Canada. Therefore, the results presented may be showing evidence of a marginal return to class size reductions in a range of sizes that is not characteristic of most American schools. On the other hand, although classes as large as those in Israel are not typical in the United States, in 1991 the average eighth-grade class size in California was 29 students, not dramatically below the corresponding Israeli average of 32 students.

References

ANGRIST, Joshua D.; LAVY, Victor. Using Maimonides' rule to estimate the effect of class size on scholastic achievement. The Quarterly journal of economics , vol. 114, no. 2, p. 533-575, 1999.