Covariational Instruction and MWS-AI Integration: Modeling Teacher-AI Interactions in Math Education

In the era of Artificial Intelligence, mathematics education requires a profound rethink-ing [1,2] from an academic and ethical integrity perspective [3]. This research is grounded in the theoretical framework of Mathematical Working Space (MWS), which considers mathematical learning as a multidimensional process occurring between epistemological and cognitive planes [4]. It is also based on constructive alignment theory in technology-rich environments and on understanding AI not as a mere support tool but as an agent capable of promoting the development of critical thinking and metacog-nitive competencies [5]. We analyse not only how AI moves within the MWS components but also how AI participation in mathematical activities covaries with human participation through task-induced covariational instructions generating predictable patterns of group-AI covaria-tion. The introduction of the MWS-AI framework represents a first step for a specific theoretical-methodological framework to understand and design covariational interac-tions in AI-integrated mathematics education. We aim to: (1) develop a theoretical framework of constructive alignment for AI-integrated teaching environments within MWS [6,7]; (2) identify covariational patterns between student-AI interactions that foster meaningful learning across MWS compo-nents [8]; and (3) create and evaluate guidelines for modelling teacher-AI interactions in mathematics education [9].