O ensino-aprendizagem da multiplicação de números naturais no 5º ano do ensino fundamental

Abstract

This thesis exposes matters concerning the difficulties faced as a teacher who lectures Mathematics. Based on reflections and primarily on research, we present this work aiming to: comprehend multiplication and its process. The overall goal is to investigate the comprehension of the teaching and learning processes of natural numbers multiplication with students coursing the fifth year of elementary school. Furthermore, we seek to identify studies on natural numbers and natural numbers multiplication, in order to promote understanding of the subject matter itself and the exploration of different teaching possibilities; to problematize the proposed strategies; to analyze the procedures developed by the fifth year elementary school students when participating in and solving problems involving multiplication; and to analyze how interaction can contribute to the learning process. Our research is based on a qualitative approach, and, according to Penteado (2010), can be classified as a teaching-research - the type in which the researcher is also the teacher in the analyzed classes. Concerning the theoretical aspects, we address the evolution of numbers, as well as the characteristics of the Natural Numbers set; the ideas and characteristics of multiplication; the student as an active agent in the construction of knowledge; and also the methodologies that favor the pedagogic practices which allow such construction. Our data consists of nine meetings that totalize sixteen class hours, realized with three groups of students coursing the fifth year of elementary school, from which we picked one to compose our study’s universe. Our registered data is composed of photographed activities performed by the students, the impressions of an auxiliary researcher who acted on the unfolding of those activities along with the researcher, besides the impressions of the researcher herself - all documented on a field journal. Our results point that in spite of the high incidence of mistakes by students, who were still consolidating their knowledge concerning the subject matter - the developed work involving the four ideas of multiplication was adequate in favoring comprehension and the evolution of mathematics operation abilities, especially in regards to the students’ interaction, who played an essential role in setting up a collaborative learning environment, confirming that the relationship between teachers, students and knowledge is fundamental when students are active agents in the construction of knowledge. We present, as educational resource, the didactic sequence developed with the students, reformulated and enriched with relevant considerations that will be able to improve the pedagogic practices of other teachers.