Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2512.21045

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

Siyuan Wang·Qing Xia·Qiong Ye
View original source ↗Read source document ↗Export metadata ↓

Abstract

The rapid adoption of generative artificial intelligence (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.

Explore related subjects

math.HO

Keep this discovery

BibTeXRIS

Siyuan Wang, Qing Xia, Qiong Ye. 2025-12-24. Synthetic Fluency and Epistemic Offloading in Undergraduate Mathematics in the Age of AI. https://arxiv.org/abs/2512.21045

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Perspectives on the unit distance problem

This is a survey on an old open problem in combinatorics called the unit distance problem, and the field of mathematics around it, called incidence geometry. What do we know about the problem? Why is it difficult? How does it connect with other parts of math?

math.HO↗
arXiv2026

A Categorical Approach to Euclidean Ratios and Proportions

A categorial approach to the non-metric geometry in Books V and VI of Euclid's \textit{Elements} is presented. Specifically, we introduce a diagrammatic syntax that can be overlaid immediately on his diagrams, thus bridging intuitive presentation with fidelity to Euclid's arguments. This syntax makes complicated definitions like V.5, and indeed the arguments throughout books V and VI, including arguments about similar figures, intuitively clear. We show in an appendix that this syntax can be used to solve a puzzle regarding ancient mathematics. Finally, we offer evidence that this approach to Euclidean diagrams is rooted in the Aristotelian tradition itself, and that a similar syntax was utilized, in antiquity, for related questions of numeric and proportions. Thus the syntax is plausibly faithful to Euclid's own thought-world, and not an outside-imposition.

math.HO↗
arXiv2026

Some Early Results by Tutte Regarding the Cycle Double Cover Conjecture in 1948

OpenAI recently announced a proof of the Cycle Double Cover (CDC) Conjecture. Most media reports have characterized it as a 50-year-old open problem. In reality, according to a 1987 letter from Tutte to Fleischner, the Cycle Double Cover Problem has been open for at least 80 years. Two early results regarding the CDC conjecture were established in one of Tutte's 1949 publications.

math.HO↗