Synthetic Fluency and Epistemic Offloading in Undergraduate Mathematics in the Age of AI

Abstract: The rapid adoption of generative AI tools in higher education is transforming how students engage with undergraduate mathematics, raising concerns about learning and assessment validity. This study examines the impact of AI accessibility across a two-semester, multi-course dataset including Business Calculus, Linear Algebra, and Calculus III. By comparing unproctored homework and proctored exam performance, we analyze how student learning behaviors shift in AI-accessible environments, particularly through epistemic off-loading of mathematical work. Guided by a sociocognitive framework, we employ complementary measures -- performance gaps, homework-exam correlations, and Wasserstein distance -- to characterize divergence between practice and mastery. Results reveal a growing integrity gap as course content shifts from procedural to conceptual and spatially intensive mathematics. In both Business Calculus and Linear Algebra, differences in homework format (online versus hand-written, TA-graded) do not yield substantively different performance patterns, indicating that paper-based homework is not inherently more resistant to AI-mediated offloading. While homework retains partial predictive validity in procedural courses, upper-division courses exhibit a collapse in alignment between homework and exams, indicating that unproctored assessments increasingly reflect synthetic fluency rather than internalized understanding. These findings highlight the need to rethink assessment practices in the AI era.