Introdução ao conceito de função: a importância da compreensão das variáveis

Abstract

This research aims to introduce the concept of function throughout the comprehension of the dependable and undependable variables, and of the relation between them. Its fundaments are on the Didactics Engineering principles by the creation and application of a teaching activity sequence and a posterior analysis of the collected data. It is based on Raymond Duval s Theory of Semiotic Representation of Register. The teaching activity sequence is derived from the research of Kieran & Sfard (1999) about the algebra school mathematics teaching and a Duval s research (1988) about the articulation between the graphical and algebraic registers. On of the teaching tools used during the application of the activity sequence was a software called Cabri-Géomètre II, besides paper and pencils. The activity sequence was applied to second-year-high school students in a private school in the city of Araçatuba, northwest of the state of São Paulo, Brazil. The protocols of six pairs of the participating students presents in every section were analyzed. The results convey the existence of a certain increase among the students of the development in understanding the concept due to the comprehension and the relation between the variables as well as to the corresponding articulation among the different representation registers of the function