Reconstructing Undergraduate Real Analysis in the AI Era: The QADAN Instructional Model

Résumé fourni par la source

Undergraduate Real Analysis is usually presented in the logical order of the finished subject, even though this order does not always make visible the mathematical problems that give rise to new concepts. This paper examines an alternative way of organizing the course: beginning with questions that expose a limitation in students’ current mathematical language or methods and using the resolution of one question to prepare the next. On this basis, we developed the QADAN instructional model, in which a learning unit moves through Question, Analysis, Discovery, Answer, and Next Question. The model was used to reconstruct a 32-hour Real Analysis course into 64 connected units covering sets, measure, measurable functions, Lebesgue integration, differentiation, and Lp spaces. Rather than treating generative AI as an additional instructional stage, the design assigns it a supporting role in selected activities, while mathematical interpretation, proof, and validation remain the responsibility of learners and teachers. The opening sequence on set language is examined to show how a local QADAN cycle can function as part of a longer curriculum-level question chain. The resulting framework offers a concrete way to connect mathematical dependency, intellectual need, and lesson design in a proof-oriented undergraduate course. Because the present study concerns curriculum development and theoretical coherence, claims about its effects on student learning await classroom-based empirical investigation.

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