Transformações de produtos notáveis em livros didáticos brasileiros do século XX - Eity Io, Leandro (2023)
The teaching of notable products has hindered the learning of mathematics at different levels of education. Throughout history, different forms of approach have been presented in textbooks, including algebraic and geometric approaches. Thus, having as a theoretical-methodological framework Cultural History and the History of School Disciplines, we seek new elements to compose the history of this content. This research aims to describe the historical course of the teaching of notable products and to investigate the processes of ruptures and continuities in the approaches to notable products in textbooks from three periods of the 20th century. The first period is marked by the New School movement; the second, by the Modern Mathematics Movement (MMM); and, the third, by the end of the Modern Mathematics Movement and the emergence of Mathematics Education. The works analyzed were: Mathematics 1st year (1934), by Cecil Thiré and Júlio César de Mello e Souza; Gymnasial Mathematics (1944), by Euclides Roxo, Cecil Thiré, and Mello e Souza; Gymnasial Mathematics course (1961), by Osvaldo Sangiorgi; Modern Mathematics course (1969), by Osvaldo Sangiorgi; Mathematics in the Renewed School (1972a, 1972b), by Scipione Di Pierro Netto, volumes 2 and 3; Mathematics for first-grade courses (1973), by Osvaldo Sangiorgi; Mathematics (1979), by Scipione Di Pierro Netto; Mathematics (1986), by Osvaldo Sangiorgi; and Mathematics Concepts and Histories (1998), by Scipione Di Pierro Netto. We used as main reference the works of André Chervel and the History of School Disciplines, as well as the analysis categories used by Morais, Bertini, and Valente (2021). As a result, we found that the geometric representation of notable products configured a movement of continuity in the works of the 20th century. However, for Osvaldo Sangiorgi, the main representative of the MMM in Brazil, it did not remain in the works of 1973 and 1986, as they marked the influences of the technicist movement in organizing the teaching-learning process. The works from the 1930s and 1940s showed less concern with the formalization of the content and more concern with communication in writing and the approach to remarkable products. From 1969 work onwards, the use of memory in using techniques and formality in the approach to notable products began to be referenced. We observed, in the works of 1973 and 1986, by Osvaldo Sangiorgi, the use of synthetic teaching approaches for remarkable products, and, in his contemporary Scipione Di Pierro Netto, the remarkable presence of geometric representation as a fundamental resource for interpretation in the learning of notable products