Contribuições das atividades de ensino para a compreensão do conceito de porcentagem

Abstract

Currently, it is usual that children experience situations related to Financial Mathematics, monetary adjustment, investments and another types of operations in which percentage is present. Furthermore, the incentive, by the mass communication, to consume and to acquire material assets constantly conducts these individuals to handle money: discounts, tax rates, statistic studies and many other dairy situations that involves percentage. We, as educators, frequently neglect the appropriation process of the percentage concept, and, instead to proceed in this way, we develop this theme during classes about fractions and decimal numbers. Thus, this research aims to investigate this following question: Which are the contributions of teaching activities to the comprehension about the concept of percentage by students of the 8th degree from an elementary school? Considering this question, this study is underpinned by the Historic-Cultural Theory, that postulates that the human being, when constructs knowledge, transforms his environment and, at the same time, changes itself. In this regard, these ideas guide our methodological approach as well the data analysis process in this research. Therefore, the main goal of this study is to analyze potential contributions of teaching activities to the understanding of the percentage concept by students of the 8th degree from a public elementary school in Uberlândia – MG, Brazil. In order to attain this aim, we have researched about the origination of the concept of percentage in Rome and have analyzed how the teaching of percentage has been discussed in the specific literature and in the federal educational document Parâmetros Curriculares Nacionais (BRASIL, 1998). In addition, this research is based on the Historic-Cultural Theory (VYGOTSKY, 1991, 2000, 2001, 2002), on the Teaching Activity (MOURA, 2000, 2002, 2004, 2011, 2016) and its relation with the Activity Theory (LEONTIEV, 1978, 1983). This research has started in the realm of a collaborative group of studies titled ―Group of Studies and Research on Mathematics Teaching and Pedagogical Activity‖ (GEPEMAPe, in Portuguese) that works since 2015, in the Federal University of Uberlândia – MG, Brazil. The produced and analyzed data were obtained from individual and collective registers about the activities executed by the students; registrations in the dairy notes of the researcher; audio and video files of discussions that occurred among the main actors in these process and the production of activities and recordings of the students actions (pictures, filming, and notes). In order to analyze all these files produced during the development of the proposed activities, is used the concept of ―episodes‖ (MOURA, 2004), that suggests the selection of some moments – written or verbal sentences, gestures and actions – that demonstrate revealing actions of the education process of the participants. In the episodes analysis, some important scenes that permit to comprehend the entire path taken by the students during the process of the construction of percentage concept are emphasized. Likewise, some considerations that possibly contribute to the teaching of this concept and to the Mathematics teacher formation are highlighted. From the analyzes carried out it was possible to infer what is one of the concepts of reason, of proportion and also operate as four essential elements for the concept of lower order. They are essential if the concept of percentage is to be seen only as a fraction being part of the whole.