Do aprender ao ensinar álgebra: formação de futuros professores que ensinam matemática

Abstract

This Master's dissertation in Mathematics Education, from the Graduate Program in Mathematics Education and Physics Teaching at the Federal University of Santa Maria - UFSM, has as its theme the teaching and learning of algebra in the training of teachers who teach mathematics in the early years. Based on the researcher's concerns about this subject, this research has as main objective: to investigate training possibilities for prospective teachers who teach mathematics with regard to teaching and learning algebra in the early years of elementary school. Based on the assumptions that the human being develops through socialization and interaction with other subjects and thus produces culture, this study is theoretically based on Vigotski's Historical-Cultural Theory - HCT; in Leontiev's Activity Theory - AT; and in the Moura’s Teaching Guiding Activity - TGA. Understanding that the basic algebraic concepts, present in the early years, when worked efficiently, contribute to students' learning and development, it is essential to think about the forms of organization of this teaching in this school phase, in order to training the teacher that teaches mathematics to face challenges. For the development of this investigation, actions were developed in the perspective of a formative experiment, related to the algebraic conceptual nexuses, with students of the Mathematics Education B class of the Daytime Pedagogy course at the Federal University of Santa Maria, context of the formation of the prospective teacher who teaches mathematics in the early years. Based on the logical-historical movement of algebra, the actions were planned and based on the following nexuses: sequence, pattern, regularity, fluency, interdependence, variable, field of variation and relation of equality. The actions constituted a didactic unit composed of six teaching situations based on the perspective of Triggering Situations of Learning - TLS. The production of data took place through video and audio recordings, photographs, records and the researcher's logbook. It was possible to identify that, when planning actions based on the logical-historical movement of algebra and, more specifically, when exploring the conceptual algebraic nexuses through situations, there was an approximation with the essence of algebra, since academics were able to attribute meaning to such actions, coinciding with their historically and culturally produced meaning. The results confirm the importance of formative possibilities that guide prospective teachers to the learning of mathematical knowledge, as long as their organizer dominates mathematical knowledge and, more specifically, in this case, the algebraic knowledge, and can plan and organize teaching that aims to develop the theoretical thinking of Basic Education students. Thus, future teachers are set in motion to organize actions based on the ways in which they have learned certain knowledge.