Beyond Tracking: The Relationship of Opportunity to Learn and Diminished Math Outcomes for U.S. High School Students

Abstract

Background/Context: In this study, we draw on evolving definitions of opportunity to learn (OTL) to conceptualize mathematics OTL has having two main components: structural OTL, defined by gatekeeping access to specific mathematics courses through the process of tracking, and instructional OTL, defined by the learning experiences of students in their mathematics courses. We also conceptualize both of these aspects of OTL as occurring in the current educational milieu, where sociopolitical factors reward or punish specific school strategies. Purpose/Objective/Research Question/Focus of Study: This study seeks to examine, using an OTL framework, the relationship between high school math teachers’ instructional practices, students’ course tracks in mathematics, students’ perceptions of mathematics, and students’ distal measures of academic attainment, including completion of advanced math coursework and completion of a high school diploma. Research Design: Using latent class analysis, this secondary data analysis analyzed the 2009 High School Longitudinal Study data from the National Center for Educational Statistics to examine mathematics instructional OTL based on math teachers’ objectives of emphasis and its relationship to structural OTL in the form of course tracking. Findings/Results: We identified “Enriched” and “Rote Knowledge and Skills” latent classes of math OTL. Teachers providing Enriched OTL emphasize the widest variety of objectives, including cognitively demanding problem-solving and logic objectives and practical applications of mathematics, while teachers providing Rote Knowledge OTL emphasize basic computation, algorithms, and computation skills. Black students, Hispanic students, and students living in poverty were more likely to be in math OTL classes focused primarily on basic concepts, algorithms, and computation, with little to no emphasis in more applied and cognitively demanding math course objectives, and they were less likely to be enrolled in advanced ninth-grade math courses. Students in Rote Knowledge OTL courses with little to no emphasis in applied and cognitively demanding math course objectives had lower mathematics identity and self-efficacy, and math achievement. Conclusions/Recommendations: This study adds to the literature suggesting that students in the United States experience an opportunity gap rather than an achievement gap, and that opportunity gaps are both structural and instructional. This study also adds to the literature suggesting student sorting systems are inherently unequal and must be addressed through policy, leadership, and cultural shifts in both schools and districts.

Getting Students to (and Through) Advanced Math: Where Course Offerings and Content Are Not Adding Up

“…In a follow-up study, Schmidt, Guo, and Houang (2021) note that this effect is appreciably compounded by race-and ethnicity-based sources of OTL inequity within and across schools. This is because systemic inequities coupled with the practice of identifying students for advanced courses based on past achievement or more-subjective measures, such as teacher nominations, have historically led to the disproportionate assignment of students of color and students living in poverty into lower tracks where they have fewer opportunities to learn challenging math content (Hallinan, 1994;Wronowski et al, 2022;Schmidt, et al, 2015).…”

“…Previous studies show that year after year, lower achieving students tend to be assigned to classes where they spend less time on content-and that students from historically marginalized communities are more likely to have teachers with less content knowledge and experience who spend less time on instruction (Desimone and Long, 2010). One study that analyzed the course learning objectives of grade 9 algebra I teachers, for example, found that students who were enrolled in remedial classes, which focused on less cognitively demanding content (e.g., basic concepts, algorithms, and computation), were less likely to complete algebra II and had lowered perceptions of their own math identity compared with their peers in algebra I classes that incorporated more problemsolving and practical applications (Wronowski et al, 2022). The students enrolled in remedial algebra I courses were significantly more likely to be Black or Hispanic/Latino or economically disadvantaged.…”

Double jeopardy? Examining the influence of mathematics tracking on in‐school suspensions through an intersectionality framework

“…Another key difference between high‐track and low‐track classrooms is the quality of the teachers and instruction. Low track classrooms have less experienced teachers and teachers which use more ineffective instructional practices (Kalogrides et al, 2013; Mayer et al, 2018; Nirode & Boyd, 2023; Wronowski et al, 2022). Nirode and Boyd (2023) found that in one state, 70% of mathematics teachers were tracked with those in the lowest quintile of experience more likely to go to low tracks.…”

“…Nirode and Boyd (2023) found that in one state, 70% of mathematics teachers were tracked with those in the lowest quintile of experience more likely to go to low tracks. Students in non‐advanced tracks were more likely to have learning opportunities focusing on rote knowledge and skills and receive lower‐quality instruction (Wronowski et al, 2022). Mayer et al (2018) found that the same teachers provided less emotional, organizational, and instructional support to their low‐track classes when compared to their high‐track classes.…”

The American Mathematics Educator Study: Unraveling the Formula for Equitable and Excellent Mathematics Teaching and Learning

“…Furthermore, students tracked into higher-achieving classrooms typically receive more opportunities to ask questions, engage in mathemat- ics reasoning, and have access to more grade-level content than their peers in lower-achieving classes (Domina et al, 2019;Donaldson, LeChasseur, and Mayer, 2017;Gamoran and Mare, 1989;Oakes et al, 1990). Subjective factors in how students are identified to take one course versus another-such as teacher nomination, interaction with guidance counselors, or parental involvement-can lead to deep inequities in which students get placed on higher versus lower tracks (Hallinan, 1994;Schmidt et al, 2015;Stone, 1998;Wronowski et al, 2022). At the same time, students who are identified to receive remedial coursework based on test-based measures-which are often deemed less subjective-may potentially be placed in lower-track classes that inhibit their future success (Figlio and Özek, 2023).…”