Tradução interna e jogos de imagens na matemática

Abstract

This research has as primordial foundations Language and Mathematics in the context of Mathematics Education. The scope of the reflections that permeate the text comes from the perspective of the Mathematical Texts Translation, aiming to characterize intratheoretically the conceptual notions of Internal Translation and Image Games in Teaching Mathematics. To do so, I direct the discussions in two lines of thought: one philosophical and the other theoretical. The first emphasizes the expression language game coined by Ludwig Wittgenstein in Philosophical Investigations. The second highlights the epistemological contributions of Gilles-Gaston Granger on Mathematics and Language (form and content). Arley Moreno, Brazilian philosopher and disciple of Granger, elaborated the Epistemology of the Use, theory that unites philosophy and scientific knowledge. I sought theoretical support in Jakobson's Semantic Structuralism, in Gadamer's Hermeneutics, and in the lectures on the translator's practices of Ricoeur, Benjamin, and Steiner. In the course of the thesis, I emphasize the importance of looking at the constitution of mathematical concepts in teaching as an activity intrinsic to language. In this sense, I raise the hypothesis that teachers, in addition to reading and interpreting specific codes and symbologies in the classroom, make the transition from mathematical language to natural language through a translation. Therefore, the methodology used in the research gives it the status of an Epistemological Discussion, which is characterized in analyzing how the role of images in Mathematics (graphics study) takes place, observing connections between the languages of algebra and geometry. A part of the analysis had as technological contribution the use of GeoGebra software tools in the elaboration of hypotheses and inferences about the importance of elucidating complex concepts in mathematics, due to the formal and abstract treatment provided in teaching. Inferi, as scientific contributions in the field of Education, among other observations, that translate in Mathematics consists of understanding (master) the grammar and syntax of this language; translate in Mathematics is not equivalent to interpret, they are different language games; the games of images bring perspicuity to the understanding of graphs and the domain of specific rules makes explicit the meaning of concepts and symbologies of Mathematics; it still subsists in the language of teachers, a kind of internal translation in what concerns the teaching of mathematical concepts. I therefore point out that the internal translation in Mathematics can be seen as teaching activity that expands the frame of reference about language games and can contribute to the learning of mathematical concepts in Education.