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Anthropological didactic theory (ATD) is one of the most widely recognized approaches in didactic research at the international level. Within the framework of ATD, didactic researchers have developed a reference didactic model in order to analyse, study and evaluate the didactic issues. Thus, for both mathematical activity and didactic activity there exists the notion of praxeology, in one case mathematical praxeology and, in the other, didactic praxeology. In addition, the strong interrelation that exists between both types of activities within a didactic system is emphasized. A didactic system is designated by S(X; Y; O) where the pair (X; Y) forms the study community of the work O. The set of people who want to study O is represented by X, while Y is the set of people who want to help X study O. An example of a didactic system is what we all know as a school didactic system where X is the set of students in a class and Y is usually made up of a single teacher, the teacher of the subject of which the work they want to study forms part. One of the tasks to be carried out by the researcher in didactics is to analyse the dominant model of the didactical system present in current educational institutions. This analysis will allow us, on the one hand, to detect some of the most important didactic phenomena related to the study of a given work. And on the other hand, to elaborate an alternative model of didactic system that allows facing these identified phenomena. Thus, many of the didactic phenomena detected in different investigations carried out within CAS are related to a dominant didactic paradigm that Chevallard (2013) calls the paradigm of the visit to the works. This didactic paradigm is characterised by the fact that the study of the works is carried out in such a way that the teacher presents them as if they were monuments that the students should admire and enjoy, and even “love”, even if they do not know which are the questions to which they respond. To describe this paradigm the herbartian scheme is used: S(X; y; O)  My  R Here the study community is represented by the pair (X; y) where X is the set of students and y the teacher who presents the work O to the students through a speech. In order to do so, the teacher y had to previously elaborate the answer R to which the work O responds, using the medium My. In addition, O as any human work has always had to arise as an answer to one or several questions, but in this case these questions are absent.

educação matemática pesquisa

The paradigm of questioning the world in research and teaching &lt;br&gt;El paradigma del cuestionamiento del mundo en la investigación y en la enseñanza