Rethinking DFW in Gateway Mathematics: Preserved, Disrupted, and Dissipated Momentum Pathways to Student Retention

Abstract This study examines how disaggregated first-year mathematics outcomes, including failure, low-passing grades, course withdrawal, and no attempt at a credit-bearing mathematics course, are associated with second-year retention at a large, diverse, urban public university. The study extends academic momentum theory by positing and operationalizing preserved (marginal passing), disrupted (failure or withdrawal), and dissipated (non-enrollment) as qualitatively distinct momentum states rather than a single condition. Using a segmented binary logistic regression model with more than 26,000 first-time, full-time students across ten entry cohorts (2012–2021), we estimate differences in retention by mathematics outcome, course type, and cohort context. Results show a pronounced discontinuity between failure and marginal passing: students earning even the lowest passing grade were more likely to be retained than students who failed, and withdrawal was also associated with lower retention. Students who made no attempt at credit-bearing mathematics had the lowest predicted retention. Retention additionally varied by course context, with higher rates in courses that embedded supports, including College Algebra with supplemental instruction. Because institutions increasingly rely on gateway-course performance indicators to guide intervention efforts, findings underscore the value of treating failure, withdrawal, marginal passing, and no attempt as distinct momentum conditions and aligning supports to each pathway.