A noção de limite: um estudo da organização didática de um percurso formativo digital

Abstract

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 restrictions evidenced during the trajectory of experimentation. As an answer to our research question Q0, namely: how do didactic praxeologies contribute to the teaching of notions of limits of real functions of a real variable in a Bachelor's Degree in Exact and Technological Sciences in virtual learning environments? we have to R♥: the elements of formative assessment, when incorporated, promote dynamics in the didactic moments of a didactic organization capable of making the didactic system established by the teacher disappear and that the student has autonomy at the end of the study process, with other didactic systems being established by the teacher himself student, promoting other relationships with knowledge. However, we noticed that there is a didactic contract established, in which students usually do not resume the activities carried out to understand the feedback provided by the teacher. And, for student autonomy to be successfully established, there must be a rupture of the didactic contract, now established, and face the phenomenon of naturalization and automation of the evaluation process, examining the praxeologies constructed by the students. We highlight as one of the contributions, the reflections around the praxeologies of evaluation, observing the possible errors in the students' techniques, as they are their efforts to arrive at an institutionally expected technique. New works can be developed related to the phenomenon of automation and the naturalness of the evaluation process within the didactic moments, as well as related to the praxeology of evaluation. Furthermore, in our understanding, assessment for (formative) learning is at the heart of the didactic system, which is often not considered in this way, being only seen from the perspective of exams and tests to meet external interests such as external assessments (usually with the in order for the teacher to be accountable). Although assessment is at the heart of the didactic system, it has a close relationship with the entire didactic system ∑=S (x; y; φ), as it has a strong connection between knowledge (φ), the student (x) and the study advisor (y). In short, assessment cannot be the heart of learning, but the means that the teacher uses to evaluate the praxeologies constructed by the students, changing the direction of teaching if necessary, not being restricted only to the institutional pressure for results.