- Thurston Domina
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How should schools assign students to more rigorous math courses so as best to help their academic outcomes? We identify several hundred California middle schools that used 7th grade test scores to place students into 8th grade Algebra courses, and use a regression discontinuity design to estimate average impacts and heterogeneity across schools. Enrolling in 8th grade algebra boosts students’ enrollment in advanced math in 9th grade by 30 percentage points and 11th grade by 16 percentage points. Math scores in 10th grade rise by 0.05 standard deviations. Women, students of color, and English-language learners benefit disproportionately from placement into early Algebra. Importantly, the benefits of 8th grade algebra are substantially larger in schools that set their eligibility threshold higher in the baseline achievement distribution. This suggests a potential tradeoff between increased access and rates of subsequent math success.
Estimates of teacher “value-added” suggest teachers vary substantially in their ability to promote student learning. Prompted by this finding, many states and school districts have adopted value-added measures as indicators of teacher job performance. In this paper, we conduct a new test of the validity of value-added models. Using administrative student data from New York City, we apply commonly estimated value-added models to an outcome teachers cannot plausibly affect: student height. We find the standard deviation of teacher effects on height is nearly as large as that for math and reading achievement, raising obvious questions about validity. Subsequent analysis finds these “effects” are largely spurious variation (noise), rather than bias resulting from sorting on unobserved factors related to achievement. Given the difficulty of differentiating signal from noise in real-world teacher effect estimates, this paper serves as a cautionary tale for their use in practice.
Schools utilize an array of strategies to match curricula and instruction to students’ heterogeneous skills. While generations of scholars have debated “tracking” and its consequences, the literature fails to account for diversity of school-level sorting practices. In this paper we draw upon the work of Sørenson (1970) to articulate and develop empirical measures of five distinct dimensions of school cross-classroom tracking systems: (1) the degree of course differentiation, (2) the extent to which sorting practices generate skills-homogeneous classrooms, (3) the rate at which students enroll in advanced courses, (4) the extent to which students move between tracks over time, and (5) the relation between track assignments across subject areas. Analyses of longitudinal administrative data following 24,000 8th graders enrolled in 23 middle schools through the 10th grade indicate that these dimensions of tracking are empirically separable and have divergent effects on student achievement and the production of inequality.