Estrutura e interpretação de situações-problema em matemática: uma análise baseada na semântica formal

Abstract

This dissertation investigates the difficulty of interpreting mathematical story problems, considering the semantic relations established between the natural language in statements and the meaning in the mathematical language. The research was divided into two moments: firstly it has been a contact with four students of the junior school in order to understand how they have interpreted and how they related the meaning and reference in situations considered as simpler; secondly it has been the analysis of six story problem of three differentiated junior school years books with the thematic percentage. In this way, we had investigated the difficulties that occasionally arise in the interpretation of the statements of story problems, since the solution requires a logical-formal thought constitutive of the mathematical language. In order to avoid common sense, we have searched to understand and to analyze the various linguistic and structural reasons and aspects, which cause challenges, as well as competent individuals in mother tongue and mathematics. In addition, we had noticed that there was remarkable importance in the construction and form of the commands, sometimes composed by questions and others by imperative sentences, since they are always in search of a fulfillment to his x. Thus, some linguistic phenomena students can deal with in the wrong way, such as synonymy, paraphrase and logical entailment, have been worked on and can also be used in the interpretative process of the utterance. The analysis was based, firstly, on the questionnaire applied to some students, so that later it was possible to examine the statements of textbooks with a closer look.