What Really Determines Math Placement? Evidence from a Massachusetts Public School District

• In Event: Friday Poster Reception

Abstract

High school mathematics attainment carries significant consequences for postsecondary access and labor-market outcomes (Altonji, 1995; Goodman, 2019), yet enrollment in advanced math courses remains starkly stratified (Ayalon and Gamoran, 2000). Prior academic performance is widely recognized as a major placement input (Loveless, 2009), but how it interacts with teacher grading practices, family override processes, and course-offering constraints to jointly shape placement decisions in practice remains thinly documented.

This study examines a public school district in Massachusetts, drawing on student transcripts, formal override filings, and the school’s published Program of Studies (POS) rulebook to surface the factors co-shaping placement recommendations and final decisions, a process involving students, caregivers, teachers, and department chairs.

I begin with a simple question: how strongly does prior final grade predict next-year advancement? The district sorts students into four math tracks: College Prep 2 (C2), College Prep 1 (C1), Honors (H), and Advanced Placement (AP). Stratified logistic regressions on 9,823 student-years across three within-track transitions (C2 to C1, C1 to H, H to AP Calculus) yield per-point marginal effects of 0.70, 0.84, and 1.47 percentage points (all p < 0.01), with pseudo R-squared of 0.17, 0.22, and 0.07. Despite AP carrying the highest grade prerequisite, the H-to-AP step has the lowest pseudo R-squared, indicating that other factors explain more of the variation where the grade bar is highest.

That uneven pattern motivates the rest of the analysis. The override records include 72 math filings, and the rulebook specifies 70 minimum-grade rules for advancing in each course sequence. Across 14,278 student-year enrollments, I classify every rulebook-covered enrollment against the published threshold.

Strikingly, 94 percent of below-threshold advancements carry no formal family override, and these cases concentrate at the AP Calculus AB gate, suggesting the threshold is not strictly enforced. One potential factor behind this pattern is teacher grading: below-threshold students disproportionately come from prior-year teachers with harsher grading practices. I establish this by estimating a two-stage fixed-effects model that recovers each teacher’s grading residual and links it to next-year advancement. Grading practices vary substantially across teachers (6.6-point spread, SD = 1.66), and the placement process partially compensates for this variation, most visibly at the H-to-AP transition, where each one-point increase in strictness is associated with a 2.24 pp higher advancement rate (p < 0.001), after controlling for student grades. A second potential factor is class size: AP Calculus enrollment is surprisingly stable regardless of how many students meet the threshold in a given year, suggesting that maintaining a viable section also shapes admission alongside prior grades and teacher recommendations.

Although descriptive and not causal, this study shows that math placement decisions reflect multiple interacting factors rather than any single mechanism such as prior grades. The findings open several avenues for future research, most notably the role of teacher grading strictness.  Linking these placement-stage mechanisms to downstream outcomes such as postsecondary access would clarify whether the influence of a strict prior-year teacher dissipates once a student advances or persists into longer-run trajectories.

Author

• Yuxuan Zhuang, Boston College
  Presenting Author