Progressões geométricas através da resolução de problemas: contribuições ao licenciando em matemática

Abstract

This dissertation presents an investigation, as a case study, undertaken in the second semester of 2019, on the teaching of Geometric Progression (PG) using the Teaching-Learning-Evaluation Methodology of Mathematics through the Resolution of problems in higher education. The subjects were undergraduates in Mathematics from the Federal University of Santa Maria (UFSM) enrolled in the Complimentary Undergraduate Course (DCG) entitled Problem Solving. The motivation for this research was due to concerns regarding how to teach Mathematics in schools, as the memorization and repetition of exercises and/or formulas entails, to the students, a mechanical learning, to which, generally, they are not allowed to assign meanings. The main objective of the study is verifying what contributions are made to the teaching-learning of PG by the undergraduate students in Mathematics through the Methodology of Teaching-Learning – Evaluation of Mathematics through Problem Solving, proposed by Onuchic and Allevato (2011). The data collection occurred within seven meetings, each of which sought to contemplate a specific concept of PG. The research has empirical character and a qualitative approach, in which questionnaires, observations during activities, field diaries, audio recordings and registers of the students were used as data collection tools. From the meetings, three axes of analysis were listed: The previous concepts as a triggering agent in the learning of new concepts in the Teaching-Learning-Evaluation Methodology of Mathematics through Problem Solving, The collaborative and cooperative work in the construction of the personal and professional knowledge of undergraduates of Mathematics from UFSM, and Challenges and possibilities in the use of the Teaching-Learning-Evaluation Methodology of Mathematics through problem solving. Although the collaborative and cooperative work did not have its essence present in all the meetings, it was a fundamental part for the teaching-learning-evaluation process of the undergraduates in Mathematics, specially, the content of PG. Through this methodology, students were able to realize that memorizing formulas, theorems and/or axioms is not always necessary in the teaching of Mathematics.