Funções monotônicas: alunos da 3ª série do ensino médio frente ás Olimpíadas de Matemática das escolas públicas

Abstract

The goal of this research is to analyze the performance of 20 high school seniors in the State Public School System in the resolution of four problems involving the concept of monotonic functions (increasing and decreasing). The selected problems were proposed in the Public School Mathematical Olympiads (OBMEP) of 2005, 2006, 2007, and 2008. The study has a qualitative approach. The theoretical reference for analyzing the performance was Raymond Duval s theory of Registers of Semiotic Representation (2003). The analyzed protocols contained both the resolution of the problems and the justifications presented by the students for their responses. The analyses indicated difficulties in interpreting the problem statement, as well as in the activities related to handling and changing the Registers of Semiotic Representation. This study also performed an analysis of the errors, which allowed the questions to be classified in groups based on the types of answers. The results revealed that most of the students were not familiar with the proposed problems, which required them to move among the different representations of a single mathematical object