A MATEMÁTICA DO ENSINO DE FRAÇÕES NA COLEÇÃO 'MATEMÁTICA, METODOLOGIA E COMPLEMENTOS' DE RUY MADSEN BARBOSA (1966).

Abstract

This dissertation aims to identify elements of the mathematics of fractions teaching in the collection of textbooks "Mathematics, Methodology and Complements for Primary Teachers" by Ruy Madsen Barbosa published in 1966. We delimited a period for this study, namely 1960 to 1970. This demarcation is due to the creation of the Law of Directives and Bases of Education of 1961 and a year before the unification of primary education in 1st grade by Law Nº. 5.692 of 1971, both considered important milestones in the history of Brazilian education. The studies were guided by the following questions: What guidelines were conveyed, in the collection "Mathematics, Methodology and Complements for primary teachers" by Ruy Madsen Barbosa (1966), concerning the teaching of fractions? The theoretical and methodological framework is based on the socio-historical perspective, considering elements such as: History of Mathematics Education (COSTA, 2017); knowledge to teach and knowledge to teach (HOFSTETTER and SCHNEUWLY, 2017); mathematics to teach and mathematics to teach (VALENTE, 2017); and teaching mathematics (MORAIS; BERTINI; VALENTE, 2020). The collection of sources was carried out in the Institutional Repository of the Federal University of Santa Catarina on the page of the Research Group in History of Mathematics Education (Ghemat/Brazil). After asepsis of the sources found, we selected the collection "Matemática, Metodologia e Complementos para professores primários", published in 1966, by Ruy Madsen Barbosa, containing three manuals for teacher's training. We considered as categories of analysis: knowing how to teach, knowing how to teach, sequence, grading, meaning, didactic devices, and exercises and problems. From the studies carried out, it is possible to infer that, in the analyzed textbooks, the teaching of fractions starts from the concrete to the abstract, using manipulative materials; the fractional numbers were presented before the content of decimal numbers; the textbooks present a well-defined mathematical language, in the sense of a language using symbols, definitions, etc., using set theory; emphasis on equivalent fractions for the teaching of operations; the exercises and problems with repetition characteristics, among other points that we discussed during the preparation of this dissertation.