Iterative Use of Mixed Methods for Addressing Inequalities in High School Mathematics Course Taking

• In Event: Successful Mixed-Methods and/or Multidisciplinary Team Approaches to the Study of Racial Justice/Injustice in Education

Abstract

Prior longitudinal multi-site ethnographic studies have provided valuable insights into the educational experiences of underrepresented minoritized (URMs) and low-income students in urban schools (Authors, 2022; Authors, 2015). These studies have revealed that such students often undergo non-linear progression during their high school years, with variations observed across different cities that have distinct policy contexts in terms of state-mandated graduation requirements. In urban schools, it has been observed that high-achieving students interested in STEM fields often enroll in "fun" classes, hoping for an easier senior year and higher GPA (Authors, 2022; Authors, 2016).
While previous qualitative studies have speculated on the association between state-mandated high school graduation policies and students’ math course-taking patterns, it remains challenging to determine why URMs exhibit non-linear progression in mathematics throughout their high school years.
This study builds upon existing qualitative studies and aims to address two key questions: (a) whether students follow a hierarchical sequence of mathematics from less to more difficult (“on track”) throughout their high school years or deviate from a consistent linear progression (“off track”), and (b) whether the presence of high school exit exams is associated with students' mathematics course-taking patterns, including linear progression throughout their high school years, which has received less attention from researchers. To conduct this investigation, the study utilizes the High School Longitudinal Study of 2009 (HSLS:09), which is a nationally representative high school cohort dataset.
Employing cluster analysis, the study identifies eight distinctive course-taking sequence typologies. Approximately 45% of students follow a linear sequence of mathematics, while others discontinue taking math altogether, repeat coursework, or regress to lower-level courses. Only about 14% of students follow the expected four-year linear sequence of Algebra 1-Geometry-Algebra 2-Advanced Mathematics. The membership in different typologies is found to be related to student characteristics and school settings, including race, socioeconomic status (SES), and high school graduation requirements.
By employing multilevel models and inverse probability weighting, the study discovers that the presence of exit exams is associated with a lower likelihood of taking mathematics courses that involve upward progression over the four years of high school. Moreover, the associations between high school exit exams and mathematics course-taking patterns vary significantly depending on student prior achievement and socioeconomic status, often resulting in disadvantaged underachieving students being left behind in mathematics course-taking.
This study demonstrates how the findings from prior qualitative studies can inform the generation of research questions and hypotheses aimed at mitigating challenges and enhancing opportunities in mathematics education for underserved populations. It also explores the generalizability of interactive findings (Gamoran, 2019). By building upon previous qualitative studies, this research contributes to examining the extent to which low-income underrepresented minoritized students consistently scaffold their learning in hierarchically-based math courses over the four years of high school, and whether the findings from qualitative studies hold true on a national level. Additionally, this study contributes to understanding the link between state-mandated high school graduation requirements and consistent upward moves in mathematics nationally.

Authors

• Seong Won Han, University at Buffalo - SUNY

• Chungseo Kang, Korean Educational Development Institute