Variáveis complexas na licenciatura em matemática: o caso dos números complexos

Abstract

This work is the result of a research project carried out in a professional master's degree program in the Mathematics Education Postgraduate Program of the Federal University of Juiz de Fora/Brazil, inserted in the research line Teaching and Learning of Mathematics, Analysis of classroom conditions and Pedagogical Intervention in Mathematics. This investigation is part of the macro research project of the Linsiano Research Program entitled Mathematics Education in Schools in the 21st Century: the training of students and teachers of Basic Education, being one of the subprojects that deals with the initial training of mathematics educators in mathematical disciplines, more specifically in disciplines aimed at discussing topics related to complex numbers and complex variables. Characterized as qualitative research, its objective was to investigate what the characteristics of a discipline of complex variables should be, within the set of disciplines of a Bachelor's Degree in Mathematics, so that it is at the service of the training of future mathematics teachers, and to delimit such characteristics as a classroom proposal, in line with the theoretical methodological framework used, the Semantic Fields Model, proposed by Romulo Campos Lins. We defined characteristics for a discipline of complex variables after analyzing the curricular matrices and pedagogical projects available for access at eleven Federal Universities in Minas Gerais, reviewing the literature related to mathematical training in the Mathematics Degree Program, and reading the enunciation residues obtained after field application of the Educational Product formatted in our research, consisting of Worksheets with texts for discussion and tasks with the intention of introducing students to a methodological proposal based on the concepts of the Semantic Fields Model, providing experiences to teachers in training that go beyond mathematical knowledge, related to future teaching practice as methodological and pedagogical experiences in the face of complex variables content. We conclude by reinforcing the need to construct texts that are sufficient to integrate the basic bibliography of syllabuses of disciplines with mathematical content, making it necessary to conduct more and more research with the objective of creating materials for the mathematics degree program with a different perspective from that already presented by mathematicians.