Uma Proposta de Resolução de Problemas para Séries Iniciais

Abstract

This MA thesis consists of a pre-selection of problems that aim to contribute to the reduction of the gap of Mathematics students in Elementary School (6th grade) and to motivate them to study problem-solving. Even though it is designed for a specific grade, nothing prevents it from being applied on in the other grades. I separated the problems into 4 themes: “Logical Problems”, “Curious Problems”, “Pigeonhole Principle” and “Parity”. In the chapter “Introduction to Problem Solving”, suggestions are presented on how problems with students should be developed based on the book The art of solving problems: a new aspect of the mathematical method (POLYA; ARAÚJO, 1977). In the chapter entitled “Logical Problems”, I introduce some problems whose resolution does not depend on specific knowledge, or any solution technique, it just takes a certain mental effort and the good old method of “trial” and “error”. In “Curious Problems”, I present 35 problems and their respective answers that seek to address different resolution techniques. In the chapters entitled “Parity” and “Pigeonhole Principle”, their respective theoretical developments, some application problems and their answers are presented. In the chapter “The game of de Nim”, a winning strategy of the respective game is presented in a simpler way so that it can be uses the grades for which this research is intended. Certain selections were stimulated based on my experience in the classroom, and conversations that I had throughout my career with several colleagues in the profession in order to, whenever possible, facilitate the mediation between teaching and learning.