Mathematical reasoning and Generative AI: an audit-to-repair experience in elementary number theory

Abstract

This descriptive instructional case examines an AI-mediated proof-validation activity implemented from September to November 2025 in Principles of Mathematics in Education (MAT105) at the University of Panama. Participants were 58 preservice preschool teachers from two intact groups (n = 31 and n = 27). The focal task asked students to determine all positive integers n satisfying 3ⁿ−1 = k³. The instructor submitted the same neutral prompt independently to ChatGPT and DeepSeek, after which students completed independent exploration, guided auditing of the AI arguments, and collaborative reconstruction of a deductively complete argument. Documentary and interpretive analysis compared the instructor-documented mathematical content of both outputs with a verified benchmark and examined how the task sheet, evaluation guide, and four-level rubric operationalized critical AI literacy. Both systems supplied the correct factorization and candidate n = 2 but omitted the exact divisibility warrant required to establish uniqueness. Cross-model agreement therefore did not constitute independent mathematical confirmation: both systems converged on the same productive idea and the same hidden deductive gap. Because timestamped verbatim model transcripts, item-level student work, and completed rubric records were not retained, no learning-gain or response-frequency claims are made. The study contributes a transparent audit-to-repair design for treating convergent model outputs as fallible mathematical texts requiring human verification and justification.