Don't memorize theorem proofs! The Modern Geometry of Osvaldo Sangiorgi

Resumo

This paper aims to examine how deductive geometry was constituted in two didactic book collections by Osvaldo Sangiorgi — named by pre-modern (1950s) and the modern (1960s) ones. The guiding question of the study is: how does Sangiorgi change the proposal of a deductive geometry for the 3rd grade of junior Brazilian high schools in the modern collection compared to the pre-modern collection? Postulates, theorems, and demonstrations are examined in detail, emphasizing the quantitative and qualitative aspects, as well as the methodological recommendations. This analyzes shows that the modern collection brought about significant changes and contributions both in the scope of Euclidean geometry, of a geometry to teach, and in the methodological didactic aspects by proposing the insertion of exploratory and experimental exercises, different registers of representations, which means, in our point of view, a geometry for teaching, which can be interpreted as an intuitive geometry, taken from the 1st and 2nd grades of the Brazilian Minimum Program of 1951.