Vetores no Ensino Básico: proposta de intervenção em aula e novas perspectivas na visão de licenciandos em matemática

Abstract

In a context inserted within debates on Mathematics Teaching, in which the identified difficulties that many students have in understanding school mathematics, day-to-day mathematics and abstract mathematics are real, and identifying strong evidence that the use of vectors can contribute in Teaching, through its historical context and its versatility of application in several areas of mathematics and other sciences, the present work has as its axis the following questions: “Why not use such an important mathematical object in several areas of knowledge in Teaching of math? What is the understanding that undergraduate students in Mathematics, who have contact with such an object and who will be future teachers, have about the use of vectors in Basic Education? Could it be that this object does not help in Mathematics Teaching in the stages of Basic Education?”. Therefore, the general objective of the work is to describe the appropriation of a teaching methodological project, of an interventionist nature that emphasizes the use of the vector approach, by a group of Mathematics Degree Students. As for the theoretical basis chosen to achieve our objectives, we opted for the cognitive theories of Mathematics Learning by David Tall and Reymund Duval. The chosen methodology has a qualitative character, being typified as an action research with traces of a case study. The research resulted in a teaching intervention carried out in the Degree in Mathematics course at UERJ, where a total of 11 undergraduates participated in the research. The research steps boil down to exploratory research of the menus of the disciplines offered in the course, application of a questionnaire to identify the profile and the relationship that the undergraduates have with the vector approach; three face-to-face meetings, lasting 90 minutes each, to carry out activities, discussions, exchange of knowledge and other nuances regarding the vectorial approach and mathematics teaching; final questionnaire, applied with the aim of receiving feedback from undergraduates, contributing to individual self-assessment and to the evaluation of the proposed intervention. At the end of data collection, only 3 of the participants were selected as research subjects, and only 2 of the face-to-face meetings. The collected data indicate that the research subjects made use of the vector approach, working with multiple Semiotic Representation Records, and developed knowledge relevant to the Three Worlds of Mathematics. The data also indicated that, from the perspective of the ndergraduates, the vector approach can be useful in the Teaching of Mathematics in Basic Education. It is concluded that through the teaching intervention carried out, the undergraduates have a positive perspective of the vector approach, and that the use of the vector approach helped in understanding, learning and carrying out tasks related to Basic Education. The work hopes to ontribute to the debate on Mathematics Teaching.