CARNOTIAN GEOMETRY: POTENTIALITY FOR BASIC EDUCATION
Carnotina geometry. Position Geometry. Knowledge to teach. Knowledge to teach.
We seek, through this study, to analyze the foundations and methods of Carnot's geometric production and its didactic potential in the conceptual construction of Geometry for the teaching and learning process in Elementary School - Final and High Years. For this, we used the theoretical contribution related to the Knowledge to teach and the Knowledge to teach (HOFSTETTER & VALENTE, 2017) and we had, as objectives, to identify the methods and theoretical approaches that are contemplated in Carnotian Geometry; to verify the historical contributions of Carnot's writings on geometry and the developments that fall into the teaching of mathematics today; establish a relationship between the trajectory of the ideas contained in these writings and the History of Mathematics for teaching; discuss the pedagogical potential for teaching content related to geometric constructions in Basic Education. Thus, we developed the research in the scope of the four texts of Carnot on geometry, understood between 1800 to 1806, with the apparatus of the documentary research, of the aspects directed to the investigation and the historical analysis. Thus, from the interpretation of the problems described in our object of study, we found that the potential for a didactic and integral approach to the contents of Geometry in the course of Elementary and High School, from the geometric constructions connected to the generalization aspects, representative models in problem solving and expression of correlation between figures are effectively guaranteed and their use can provide more meaningful teaching.