Examining and Representing Middle School Math Course Heterogeneity

• In Event: Systemic Factors That Limit English Learners' Access to Mathematics: Lessons From a Research-Practice Partnership

Abstract

This paper examines the class composition of middle-school math courses to investigate students' opportunities to learn. It builds on literature showing that class heterogeneity (student composition regarding gender, ethnicity, SES, test scores, etc.) may affect students’ academic performance. While some propose that a diverse student body is likely to be associated with positive effects because of possible complementarities in abilities, others argue that a heterogeneous class may present more challenges to teaching and peer interaction. Beyond academic performance, concerns with class heterogeneity also extend to student identity and civic engagement, resonating with the broader societal discourse on social justice. Examining class heterogeneity is one path to addressing fairness and equity in education and beyond. Proper visual representation of this heterogeneity is critical to effectively communicating school districts how they can improve practices concerning ELs. Examining data from the middle schools in School Districs A and B, for each mathematics class, we calculated a mean score and 95% confidence interval for student initial ability based on their CAASPP/SBAC math scores from the previous year. We used violin plots to parallelly display the distributions of student scores and their descriptive summaries. To investigate the association between students’ ability and English proficiency, we added language designation as another variable describing class heterogeneity. We differentiated the designations by color (Not-EL=green, RFEP=yellow, STEL=orange, LTEL=red) and annotated the violin plots. Random class assignments would be expected to result in similar mean value ranges and normal distributions, with balanced representations and dispersed spreads of colored dots within each violin shape. The violin plots allowed identification of different patterns of non-random class assignment concerning student ability and language designation. In general, biased placements (or potential tracking) appeared more systematically in Schools District A than in School District B, especially in some big schools where 30-40% of the student populations were ELs and 60-80% received free or reduced-priced meals. Tracking was less frequent in school district B, whose student body was 50-60% ELs and 90% free or reduced-priced meals. In both school districts, classes enrolled with fewer STELs and LTELs had higher mean scores. Moreover, students who scored higher and were not ELs were more likely to be placed in advanced math courses.

Author

• Hsiaolin Hsieh, Stanford University
  Presenting Author