What do course trajectories look like? Do career paths intersect? Do courses assume distinct roles in educational careers? What factors lead students to adopt various curricular moves? This article addresses these questions by examining the structure and dynamics of participant flows across courses in two high school math curricula. Drawing on Markov models and network analytic methods, it examines the length, rate of progression, volume, and direction of multiple trajectories in math and identifies certain courses as important career turning points. The findings suggest that schools can design a variety of mobility systems by altering course offerings, prerequisites, and grading policies. Analyses of individual curricular moves show that nonsanctioned moves, such as leaving school, are guided by students' background characteristics, while sanctioned moves, such as course transitions, are guided primarily by structural constraints and adaptations to signals about classroom performance.
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