A noção de limite: um estudo da organização didática de um percurso formativo digital ; The notion of limit: a study of the didactic organization of a digital formative path ; La notion de limite: une étude de l'organisation didactique d'un parcours de formation numérique

The current work is inserted in the field of Mathematics Education, more specifically in the area of Didactics of Mathematics and has as its object of knowledge the notions of limit of a function of a real variable. In the Differential and Integral Calculus course, the notions of limit are important, as they imply a better understanding of the ideas of other concepts related to this object of study, such as derivatives, integrals, convergence of series, among others. The research had as a problem the difficulties that students have in the institutional relationship with the notions of limits and in the disarticulation between the intuitive notion and the definition épsilon-delta of limit. In addition, normally, in the didactic organization there is a naturalness and automation in the teaching process (on the part of Mathematics teachers in our context) which, many times, only signals the student's failure to do the proposed tasks, failing to promote reflection. and analysis of such errors or mistakes, thus not showing the reasons for not learning so that the student can progress in his studies. Our objective is to investigate how didactic praxeologies contribute to the teaching of notions of limits of a real function in virtual learning environments. We used the methodology of research praxeology that, through the herbartian system [S (X ; Y; Q0) ➦ M] ➥ R♥ and with the help of the study supervisors (Y) (supervisor and co-supervisor), allowed us to create a M formed by the secondary questions Qn, secondary answers Rm◊, consulted works Wn, interviews, questionnaires and experimentation Dp, producing an answer R♥ (expected answer). This Methodology contributed to guide our ideas so that the chapters and sections were able to be delineated with our research object. As a methodology for experimentation, Didactic Engineering was adopted, because, in our view, it provided us with conditions to reach the observables and answer our research question, so that we were able to observe and analyze the conditions and ...