Matemática e linguagem: um enfoque na conversão da língua natural para a linguagem matemática

Abstract

This research aimed to identify and analyze which possible difficulties that come from the language students face in the conversion from natural language to mathematical language. The investigation was carried out during the school year of 2008 in high school groups of two public schools in the city of Belém, where information has been collected through mathematics registers produced by the students through tests and assessments performed every two months. To assist such investigation, the ideas of Raymond Duval were used as a theoretical reference about the theory of the mathematics registers of semiotics representation; the concept of meaning connected to the philosophy of language according to Wittgenstein; also some considerations by Gottlob Frege about the distinction between meaning and reference and other ones by the philosopher Gilles-Gaston Granger concerning the problems of meaning and the formal aspect of mathematical language. The analyses of the information collected during the period of investigation revealed that, in the students’ perspective, the conversion of natural language to mathematical language faces four types of difficulties: the first one has pointed out the fact that there are, in each record of representation of the same mathematical objective, different contents to be mobilized; the second one has shown that the students fail when they perform the conversion of natural language to mathematical language, when they do not interpret correctly the mathematical rules implied in the proposition of a situation problem; the third one has appeared from the fact that there are, in the text of a situation problem, words that the students do not understand the meaning of or may have an ambiguity of senses; the fourth one has appeared from the fact that the students do not understand the mathematical meaning of the letters used in the problem situations.