O Cálculo no livro Matemática para o Ensino Secundário de Thales de Faria Mello Carvalho (1915-1961)

Abstract

In this work is it presented a historical research on the approach to fundamental concepts in the teaching of Differential and Integral Calculus (CDI) – function, limit, continuity, derivative and integral, in secondary education in the 1940s, using the textbook Mathematics for Classics and Scientific courses, by Brazilian author Thales de Faria Mello Carvalho, as its main analytical support. Through qualitative research, we adopted documentary analysis as a methodological horizon, with our main source of research being the book, and as a procedure for classifying and organizing the data for our analysis we chose the categorization method. In this way, we seek, in addition to analyzing the presentation of the fundamental concepts for teaching CDI, to identify and observe the exercises indicated in the book, and subsequently to outline a biography of the author Thales de Faria Mello Carvalho. To this end, a survey of research was carried out that addressed analyzes in textbooks and the CDI, we found support in the studies of Raad (2012) and authors such as Chervel (1990), Ludke and André (2018), Choppin (2004,2012), Bloch (2001) and Duval (2012) which served as theoretical references. The question that directs our investigation is: How the fundamental concepts of Differential and Integral Calculus are proposed in the book Mathematics for Classical and Scientific Courses, authored by Thales de Faria Mello Carvalho? We conclude that the author approached each content in a mixed way, observing the presence of arithmetic examples, symbols, different semiotic representations, and the mention of important mathematicians. The abundant number of exercises and definitions, accompanied by exemplifications for the most part, characterize the work as suitable for secondary education at the time. The work is in accordance with the official mathematics programs of the time.