Monitoria de cálculo e processo de aprendizagem : perspectivas à luz da sócio-interatividade e da teoria dos três mundos da matemática

Abstract

In this doctoral thesis we seek for an understanding of how learning Calculus takes place in a context with instructors assisting professors, from two theoretical axes: Vygotsky’s social interactivity and David Tall’s three worlds of Mathematics. The investigation was carried out with a qualitative approach, as a case study, and the corpus was analyzed from the methodological perspective of Discourse Textual Analysis. The thesis we support here is that the tutoring Calculus’s can make a significant contribution for the learning of the Mathematics if the pedagogical proposal is guided by the theory of Three Worlds of Mathematics and supported in social relationships established between the peers. In that search, a study was carried out in 2 phases at Higher Education Institutions in the state of Rio Grande do Sul. On phase 1, we contacted the institutions in the state that have Calculus as a subject in their programs and who have instructors to assist professors and qualify learning. The most representative institution regarding the presence of interactive movements and of the theory of 3 worlds of Mathematics, participated in Phase 2, which was a return to the research field, and where we could dedicate a more specific look to the case. Professors and their instructors were interviewed. From the results obtained, we highlight the social relationship among subjects as a significant factor in learning Calculus. Team work can contribute for that to occur and the institution has to organize instructors’ activity so as to make that action possible. We also identified that proximity between the instructor and the student can provide a tension-free environment, where communication takes place easily with a closer language, enhancing chances of building mathematical knowledge. Another finding was the fact that acting as an instructor can contribute to form a future teacher, incentivating students who are not in a teaching major and promoting articulation between learning theories discussed in classes with practical situations for those in a teaching major. The relevance of analyzing the mistakes students make and the need of mapping what has already been found to trace educational actions is another finding. In addition to that, we realize that digital technological resources can be allies for the instructor, favoring the path through the three worlds due to the possibilities of manipulating, visualizing and exploring, and their use is necessary in line with pedagogical practices aiming at autonomy and criticism.