Divisão por frações: compreensão profunda da matemática fundamental de futuros professores de matemática

Abstract

The teaching of fractions is a very complex topic, it is located in a transition phase between the initial and final years of Elementary School, in which the routine and school context are different. As the teaching of fractions advances, it demands solid foundations to develop. The arrival of fraction division, an operation that encompasses fractional numbers and division, often becomes a major challenge not only for students but also for teachers. This research continues an investigation on the teaching of fractions that consists of the analysis of six collections of textbooks approved by the PNLD 2019-2022 for the fourth and fifth years of Elementary School, about the concept of fractions. As the main theoretical reference, a research by Liping Ma is used, in which she develops the concept of Deep Understanding of Fundamental Mathematics (CPMF). Focusing on the teacher's knowledge about the teaching of division of fractions, it seeks to provide challenges (contribute to) the knowledge about division by fractions from an investigation of what future mathematics teachers understand, allowing them to know another teaching role, that of a professor who has a deep knowledge of the subject. As it is a Professional Master's, one of the requirements for a degree is the production of an Educational Product (EP), in this case, a course intended for (future) teachers who teach mathematics. A prototype of this EP was carried out in a class of the Mathematics Degree at the University of the State of Rio de Janeiro (UERJ) that provided relevant notes for the course under construction. In the context and conditions (remote teaching and pandemic period) in which the meetings were held, no clear evidence of CPMF was found in the group of course participants.