Didactic analysis of the modality of study of the real numbers in the Degree in Mathematics (2509.20023v1)

Abstract: To conduct a didactic analysis of the current modality of study of real numbers in the Bachelor's Degree in Mathematics, we rely on the notion of didactic paradigm and employ a novel research methodology within the framework of the Anthropological Theory of the Didactic. This methodology proposes that, in general, analysing a modality of study of a field of knowledge, currently implemented in a certain didactic institution, consists of modelling, through respective didactic paradigms, not only the current modality of study but also: (1) an alternative modality of study (a possible future) whose didactic ends include attempting to avoid certain current phenomena considered ``undesirable'' from the perspective of research; and (2) an antecedent modality of study (a possible past) that allows us to explain the emergence of current phenomena as a reaction to the existence of certain antecedent phenomena.