Etnomatemática & história da matemática : movimentos de contraconduta na educação básica

Abstract

This thesis is part of two research themes present in the Mathematical Education: Ethnomathematics and History of Mathematics. Of the possible articulations between both, the thesis is concerned with those that contribute to reflect on the teaching and learning processes of Mathematics, in order to categorize pedagogical actions emerging from the articulation of the Ethnomathematics and the History of Mathematics and to analyze how such actions contribute for Basic Education students to understand the hegemonization of language games present in School Mathematics. As a theoretical support, it is anchored in the post-structuralist theorizations of the philosophers Michel Foucault, especially in the concepts of power, knowledge and conter-conduct, and Ludwig Wittgenstein, in relation to the concepts of language games and forms of life. Methodologically, it presents and analyzes, through openended questionnaires, seven teaching proposals carried out with 210 elementary and high school students from the cities of Porto Alegre and Rio Grande, both in the state of Rio Grande do Sul. To analyze the results obtained, the discursive genealogical analysis was used as a method, which is concerned with analyzing the conditions of possibility for certain speeches to come to the fore. As some results, some pedagogical actions are outlined: to start a concept with the resolution of historical problems; to present historical aspects related with the studied concept; to motivate the creation of the own way of solving exercises; to provide the opportunity to solve exercises without privileging a single language game; to request the research on the History of Mathematics highlighting the contributions of different civilizations; to use the historical material to approach a concept or part of it; to present different ways of mathematizing based on rules and language games that are different from school; to make the operationalization possible with the different ways of mathematizing; to discuss the similarities and differences between the different ways of mathematizing; to compare language games in the different ways of mathematizing; to relate the different ways of mathematizing their historical, geographical and social aspects; among others. The effects produced by these pedagogical actions legitimized the categorization process and enabled the construction of three categories. The analysis carried out shows that the results make it to be possible to defend the thesis that Ethnomathematics articulated with the History of Mathematics can be seen as a conter-conduct in relation to the hegemonization of language games present in School Mathematics, contributing to the learning of Mathematics.