- Thurston Domina
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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.
We identify 510 California public middle schools (and 753 school-years) that use a 7th grade achievement threshold to place students into 8th grade Algebra, and we use these schools to estimate fuzzy regression discontinuity effects of 8th grade Algebra placement. We find that enrolling in 8th grade Algebra boosts students’ chances of taking advanced math courses in high school by 30 percentage points in 9th grade and 16 percentage points in 11th grade, as well as boosting achievement on the 10th grade math California High School Exit Exam by .031sd (ITT) and .053sd (LATE). Eighth-grade algebra has a smaller, positive effect on student ELA achievement in grades 9 through 11. Importantly, we also find that the effects of 8th grade Algebra vary substantially across students and schools. Encouragingly, women, students of color, and English-Language Learners benefit disproportionately from access to accelerated coursework. However, school-level decisions about how to implement accelerated coursework in middle school appear to matter. In particular, we find that the benefits of 8th grade algebra are substantially larger in schools that enroll students whose 7th grade math scores are at least “Proficient” (or grade level).
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.