Tournament Mobility in Mathematics Course-Taking Pathways

Abstract

This visualization represents the structure of mathematics course opportunities as seen in the progress through middle and high school for one cohort of students in Texas. Trajectories are consistent with a tournament mobility regime in which there are repeated opportunities to fall behind but almost none to catch up. Pathways are also characterized by staggered starts, with differences in when students begin the mathematics sequence that have consequences for ultimate attainment. The structure of mathematics opportunities provides many points where trajectories diverge, and these branching points disproportionately sort economically disadvantaged students into less advanced pathways.

Mathematics attainment in high school is related to many important later outcomes, but ultimate attainment results from a series of individual transitions throughout students’ educational careers (McFarland 2006; Schiller and Hunt 2011). Figure 1 provides a parsimonious representation of mathematics progress for one cohort of students in public schools in Texas. The network of branching pathways traces how students are sorted from undifferentiated general mathematics instruction prior to 7th grade to many different destinations in 12th grade. In turn, these pathways reflect the ways that the organization of curricula—what and when opportunities are available as well as the rules for eligibility—structure school opportunities.

Figure 1.

Mathematics trajectories of one cohort of students in Texas (n > 300,000). The width of each line segment represents the number of students making this transition (e.g., Algebra I in grade 8 to Geometry in grade 9), and the color represents the mean economic disadvantage of these students. Mathematics courses listed with black text represent the typical sequence. Those listed in gray represent alternatives that often divert from typical progress. Paths for infrequent courses (Independent Study and Other Mathematics courses) are omitted for legibility. For a version that includes exits from mathematics coursework, see supplementary materials.

The most common mathematical careers, represented by three parallel diagonal lines, follow the traditional sequence of Algebra I, Geometry, Algebra II, Precalculus, and (if time allows) Calculus. But pathways diverge in two critical ways. First, typical progress is not certain. Students may repeat a level—represented by horizontal paths—or take a course that diverts from typical progress. For example, Mathematical Models and Application, a course reviewing algebra and geometry content, is a common alternative to Algebra II in 11th grade. Likewise, AP Statistics provides a less advanced alternative to Calculus. Notably, there are no countervailing accelerated pathways, meaning that students cannot move to a higher trajectory, nor can they catch up if they fall behind. ¹ These dynamics are consistent with a tournament mobility regime (Rosenbaum 1976); students face a series of uncertain contests in which “winning” enables them to move forward to the next round but losing means falling behind irreparably.

The second distinguishing feature of mathematics pathways is that students begin the differentiated mathematics sequence at different times. Most students start Algebra I in ninth grade, many begin in eighth grade, and some begin in seventh grade. Given the mobility dynamics in high school, these starting points strongly shape how far students can go. For instance, the selective group of students in Algebra I are on the clearest path to advanced calculus. Conversely, there is not a pathway to calculus for students who begin Algebra I in high school. Thus, the structure of mathematics opportunities creates a tournament mobility regime with staggered starts; earlier entry allows the possibility—though not a guarantee—of further progress. It is notable that pathways are “messier” for the students who start differentiated coursework late; this reflects that late starters face the greatest risk for horizontal or downward movement by the end of their educational careers.

Students do not navigate this structure of opportunities equally, and each diverging path represents a categorical educational distinction that may reproduce social inequality (Domina, Penner, and Penner 2017). As shown by the color of each pathway in the figure, almost all diverging paths serve to heighten socioeconomic disparities by sorting more affluent students to a more advanced pathway. This is the case both for initial starting paths and those that divert progress later. Economically disadvantaged students are especially overrepresented in lower courses in later grades, where the risks of falling behind are highest. Students with fewer socioeconomic resources are more likely to be in these pathways because of differences in prior academic preparation, less information about courses and policies, and weaker connections to institutional resources (Lucas 1999). This visualization highlights that the socioeconomic gradient in ultimate attainment outcomes is created by the series of sequential categorical distinctions that schools make throughout students’ educational careers.

Research Data

mathematics_paths – Supplemental material for Tournament Mobility in Mathematics Course-Taking Pathways

Supplemental material, mathematics_paths for Tournament Mobility in Mathematics Course-Taking Pathways by Paul Hanselman in Socius

This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage).

Research Data

mathematics_paths_by_eds – Supplemental material for Tournament Mobility in Mathematics Course-Taking Pathways

Supplemental material, mathematics_paths_by_eds for Tournament Mobility in Mathematics Course-Taking Pathways by Paul Hanselman in Socius

This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage).

Supplemental Material

mathematics_sequences_plot_20200402 – Supplemental material for Tournament Mobility in Mathematics Course-Taking Pathways

Supplemental material, mathematics_sequences_plot_20200402 for Tournament Mobility in Mathematics Course-Taking Pathways by Paul Hanselman in Socius

Supplemental Material

Tournament_Mobility_Visualization_Supplementary_Information_20200402_clean – Supplemental material for Tournament Mobility in Mathematics Course-Taking Pathways

Supplemental material, Tournament_Mobility_Visualization_Supplementary_Information_20200402_clean for Tournament Mobility in Mathematics Course-Taking Pathways by Paul Hanselman in Socius