Conceito de área de figuras planas: elaboração e análise de um teste-piloto para alunos do 6º ano do ensino fundamental

Abstract

The goal of this research is to survey and analyze the main phenomena that affect the construction of concepts related to the area of plane figures in elementary school. To this end, a pilot test of a didactic sequence was designed which considered the main variables related to the topic. The activities were designed to promote the coordination and dissociation of the geometric and numerical magnitude by searching for methods and strategies that can minimize the major sources of students' difficulties. The work also proposes a reflection on significant issues involving the construction of meaningful mathematical objects, since professionals who do not consider them do not allow learners to develop the skills needed to apply their knowledge in new situations. It can be observed that when appropriate activities facilitate relations between the tables involved, it can enable students to understand and differentiate the surface area, area measurement, contour, length and girth. The survey was conducted according to the principles of didactic engineering proposed by Artigue (1988). In the trial, 33 students of grade 7 from a school on the outskirts of Sao Paulo participated, however, for the purposes of gathering data, only two groups of three individuals each were considered. To offer reasonable grounds for this research, the use of Douady’s theoretical frameworks such as "Tool-Object Dialectic," and "Tables and Game Tables" were applied in addition to the "Records of Semiotic Representation" and "The Figural Seizures" by Duval