MODELO GEOIA-M PARA LA MEDIACIÓN DEL RAZONAMIENTO MATEMÁTICO EN CÁLCULO UNIVERSITARIO CON INTELIGENCIA ARTIFICIAL GENERATIVA Y GEOGEBRA

Abstract

The integration of generative artificial intelligence (AI) into university calculus teaching has advanced rapidly, yet many observed practices remain instrumental and answer-oriented, which encourages students to delegate their reasoning to the tool. This theoretical-methodological paper proposes and grounds the GeoIA-M Model, a didactic architecture for mediating mathematical reasoning in differential and integral calculus courses, in which generative AI acts as an interlocutor that problematizes and GeoGebra as an environment for exploration, representation and validation. Drawing on a narrative and critical review of recent literature and on the analysis of calculus tasks, the model is organized into five dimensions: exploration, visualization, argumentation, metacognition and ethical reflection and seven implementation phases, placing student reasoning at the center of the process. Two university calculus examples are developed, on optimization with derivatives and on the definite integral and accumulation, including dynamic construction protocols, Socratic querying prompts and process-oriented assessment criteria. The main contribution is an initial didactic architecture to guide classroom practices and teacher education in university Mathematics Education, open to subsequent empirical validation.