Geometric Transformations in Geometry Teaching: different appropriations in modern mathematics

Abstract

The present work establishes a study within the scope of a broader project on the relationships between the History of school geometry and the Modern Mathematics Movement (MMM). We analyzed how a particular knowledge – geometric transformations (GT) – circulated in the Brazilian context during the mentioned period. From a historical perspective, we investigated four textbooks produced between the 1960s and 1970s by MMM leaders. The guided questions of this study were the following: what are the similarities and differences in the approaches to GT between the different books? How did the articulation between GT and Euclidean Geometry (EG) happen? The process of insertion of GT through textbooks was diverse, highlighting the complexity of the dialogue and the prediction of reconciling demands arising from specific cultures: the academic one, as a representative of scientific production, and the school one, representing experiences of professional practices.