Cristian Nava Guzmán
The emergence of generative artificial intelligence (AI) in mathematics education poses challenges and opportunities that go beyond access to information, since they reconfigure the very nature of school tasks and the role of the teacher.This essay argues that prompt engineering should not be conceived as a merely technical skill, but as an extension of Pedagogical Content Knowledge (PCK) and a constitutive component of Technological Pedagogical Content Knowledge (TPACK).Drawing on the literature on questioning in mathematics, the design of open-ended tasks, and the Theory of Didactical Situations, we propose a model for designing educational prompts organized around three axes: cognitive intentionality, didactical constraints, and reflective iteration.As an original contribution, we present and analyze a conversational tutor prompt intended to foster covariational reasoning in the sliding-ladder problem, a classic dynamic situation.We conclude by underscoring the need to integrate prompt literacy into teacher education as a professional competence of a new kind.