Um estudo sobre o conceito de média com alunos do ensino médio - Stella, Cristiane Aparecida (2003)
The aim of this study is to identify interpretations of the concept of arithmetic mean held by High School students following the Brazilian curriculum. With this aim in mind, we investigate the characteristics of the concept of mean that are emphasised in the High School Mathematics Curriculum and in research studies related to understanding the teaching and learning processes associated with this concept. We begin our research with some considerations about the concept of mean from historical and epistemological perspectives. We go on to attempt to identify aspects of the concept emphasised in the following teaching instruments: official documents (PCNs), textbooks, and systems of curriculum evaluation (ENEM and SAEB). We also determine different approaches to the concept that are proposed in Mathematics Education research studies, choosing as a basis for our analyses the theoretical model of Batanero (2000). As a result of these investigations, we selected some questions to be used in interviews of students from the third year of High School, with questions chosen to take into account the different approaches associated with teaching instruments and the research studies. Analysis of the interviews indicate that, on the one hand, students perform well in relation to problems involving weighted means and in problems of construction (problems in which they construct distributions of data sets). On the other hand, most of the students interviewed see mean as algorithm and have difficulties in solving problems in which they have to calculate means on the basis of graphically presented data. These results suggest problems in the teaching and learning of mean that go beyond the student and are associated with structural questions which have their beginning in official documents, reaching the students by means of mathematics textbooks and forms of evaluation