Análise do livro "elementos de geometria" de Clairaut como um estudo dirigido

Abstract

The present investigation analyzed the book "Elements of Geometry", by Alexis Claude Clairaut (1713-1765), from the perspective of Depth Hermeneutics (DP) by Thompson (2011). Simultaneously, we designed and applied a targeted study (our educational product) with activities to an exercise in historical analysis of that book. This product has been tested with students from an undergraduate math teacher course. We conclude that Clairaut's text had a great impact on the teaching of mathematics at the time of its first publication: the book presents a “break” and a methodological innovation for the teaching of geometry from the selection of the work's contents to its organization and, mainly, for its conception of geometry based on human needs of terrain measurement. We note that Clairaut presents an almost reactionary proposal, in our view, in relation to the teaching model of mathematics marked by Euclid's “Elements”, something that was also experienced by other nineteenth-century authors. This change of direction for teaching this content was noticed by the students who participated in the application of the activity we developed, especially because they were able to compare the work to other geometry books from different periods. These students also considered it possible to implement a teaching of elementary geometry with the valorization of experimental, natural and problematic activities, as proposed by Clairaut, depending on the level of education in which it is applied.