PRATICANDO UM EXERCÍCIO DE HERMENÊUTICA DE PROFUNDIDADE NO LIVRO ELEMENTOS DE GEOMETRIA PLANA "COMPILADOS" DO PADRE ALBERTO JOSÉ GONÇALVES (1885)

Abstract

This research was developed in the Graduate Program in Mathematics Education (PPGEduMat), in the master's course at the Federal University of Mato Grosso do Sul (UFMS), at the Institute of Mathematics (INMA), linked to the Group History of Mathematics Education in Research (HEMEP) and aimed to develop an analysis using Depth Hermeneutics (HP) of a Geometry compendium from the 19th century (1885), prepared by Father Alberto José Gonçalves, which was used in the Episcopal Seminary of São Paulo. As already mentioned, our analysis is based on the methodological theoretical framework of Depth Hermeneutics according to the proposal based on John Brookshire Thompson (1995) for the analysis of symbolic forms, as well as HP, we also make use of Gerard Genette's Editorial Paratexts (2009 ), which states that everything that is part of a book, in addition to its content, says a lot about its relevance, dissemination strategies and importance of the author in his time, as well as the target audience of the work. We also analyzed the content of the book, inspired by the work of Moreira (2018), which was based on Ludwig Wittgenstein's Language Games (1999), we observed the language and the axiomatics of the work, eventually comparing contemporary books to the analyzed one, looking for possible similarities and dissimilarities. This research permeates three HP movements: the socio-historical analysis, in which we observe the social contexts in which our author and work were inserted, the life of Father Alberto, the magazine to which the priest contributed at some point, the Episcopal Seminary of São Paulo, confessional teaching, and the teaching of Geometry in our country; Formal analysis, focused on elements contained in the work itself and their relationships with the context of the time. Thus, we sought help in Gerard Genette with the Editorial Paratexts, still in this movement, we made an analysis of the language and axiomatics of the work, inspired by the work of Moreira (2018), which uses Wittgenstein's language games to compare two teaching textbooks of Plane Euclidean Geometry. The third movement is that of interpretation/reinterpretation, in which we place our vision on what was found in the course of our research, although our author did not leave clarifications or writings about his book, our work allowed us to produce interpretations about it, the which are most directly manifested in this movement. We believe that our study makes a significant contribution to the History of Mathematics Education and Geometry teaching in our country, reaffirming HP as a methodological possibility for research aimed at investigating old textbooks.