Uma análise epistemológica dos trabalhos de Lazare Carnot sobre geometria de e suas potencialidades para o ensino

Abstract

This document results from research whose objective was to analyze the foundations and methods that Lazare Carnot elaborated in his writings about geometry to identify their didactic possibilities for a conceptual treatment of geometry in the late elementary and middle school grades. To attain our objective, we used contributions of the theoretical concepts, Saberes a ensinar e Saberes para ensinar (knowledge for teaching, knowledge to teach). Through our reinterpretation of these concepts, we identified emergent concepts and methods and epistemic approaches in Carnot’s writing about geometry as well as possible historical contributions and consequences for the teaching of geometric constructions nowadays in late elementary and early secondary grades. Therefore, in our investigation, we selected thematically from among four of Lazare Carnot’s publications, written between 1800-1806, with the tools of documentary research directed to historical-epistemological analysis, supported by content analysis. Thus, by analytically interpreting the problems described in his geometry, we were able to indicate potentialities for a didactical and wholistic approach, from geometric constructions connected to generalizations, representative models in solving problems, and expressions of correlation between figures. As such, it is possible to elaborate an educational approach that combines the history of geometry, geometric concepts, and information and communication technologies.