MODELAGEM MATEMÁTICA E ETNOMATEMÁTICA NO CONTEXTO DA EDUCAÇÃO MATEMÁTICA: ASPECTOS FILOSÓFICOS E EPISTEMOLÓGICOS

Abstract

This dissertation turns for two trends in Mathematics Education: 1) the Mathematical Modeling and 2) the Ethnomathematics. The choice is justified because these trends, at current time, are focus of discussion and use within the teaching and learning in mathematics and more specifically by being present in the world-life of the researcher, since about four years, from graduation to post-graduation. The generator question of research was: What are the philosophical and epistemological aspects shown in Mathematical Modeling, in Ethnomathematics from the point of view of Mathematics Education? This issue, formulated and reformulated during the research process, guided our look over the trends as they were, in a first time for, posteriorly, from the descriptions about them, we establish interpretations of the philosophical and epistemological aspects. It was studied five authors who work with Mathematical Modeling, with different ways of conceiving it, they were chosen because of their outstanding academic recognition. For Ethnomathematics, it was opted predominantly, by the writings of D'Ambrósio that is considered the main theoretical and founder of this trend. The research outline was in a qualitatively, theoretical and bibliographic way. It was oriented by the Phenomenology, which is a Consciousness Philosophy and a rigorous method of research for the Human Sciences and Education. In Phenomenology is not sought to confirm hypotheses, nor it is chosen a theoretical referential a priori for the interpretations, the phenomenon is focused as he shows, always related to the question. In such case, elapsing phenomenon events, we looked their meaning and significance in Science, History and bibliographies, to allow clarify these senses and meanings. The interpretations, concerning the philosophical and epistemological aspects of the two trends were concreted by means of the development of units of sense, which emerged with some of the following denomination: Mathematical Models; Conception of Knowledge; Conception of Education, Curriculum and others. These invariants were those that repeated in the descriptions of the ways of conceiving Modeling and Ethnomathematics, even those who were idiosyncratic, but considered equal in importance. Thus, it elaborated a triangulation among the invariants of the two trends from the point of view of Mathematics Education. As result of the interpretations of this research, it was shown that there is a tendency for an approximation between Modeling and Ethnomathematics when the ways to conceive Modeling are in accordance with the Epistemological Social Sciences Statute. It unveils a distance when Modeling orients itself by the philosophical and epistemological presupposed of Exact and Natural Sciences. This “unveiling” extends to what refers the construction of models, and to the ways of think the curriculum and other aspects out.