Matemática a ensinar e Matemática para ensinar temas de geometria a partir do livro “Didáctica del Cálculo (1969)”

Abstract

This research was developed in the line of History of Mathematics Education, using as a source of investigation the book Didáctica del Cálculo (1969), written by José Junqueira Muné. Having as a guiding question, “what professional knowledge is materialized in ‘Didáctica del Cálculo’ (1969) for the teaching of geometry, based on book I (methodology and procedure) and book III (didáctica del geometría)?” To answer this question, we set out the following general objective: analyze professional knowledge based on Book I and some aspects of Book III present in “Didáctica del Cálculo”, by José Junquera Muné. Therefore, for the development of this work, the study on Professional Knowledge, by Hofstetter and Schneuwly (2017), mathematics to teach and mathematics to teach by Bertini, Morais and Valente (2017) and a category of analysis, described with four stages of the process of acquiring knowledge by the child, identified as observation and manipulation, drawing, arithmetic representation, problems and exercises. These steps were identified by us from the analysis of Book I (methodology and procedure) and applied in analyzes in Book III (geometry didactic). This research contributes to the field of Mathematics Education when analyzing specific professional knowledge for teaching geometry, as outlined by Muné in his work. The relevance of understanding how the author articulates the knowledge to teach and knowledge to teach mathematics stands out. Therefore, we conclude that Muné's book presents objective knowledge that is intrinsically related, when the author provides the reader with didactic guidance on the geometry themes developed and analyzed by us in book III. In this way, the manual contributes to the condensation of knowledge by allowing us to identify a mathematics to teach and a mathematics to teach proposed by the author in the form of instructions for the teacher to develop the stages of didactic work in geometry.