Desenho geométrico: a régua e o compasso como recurso didático na compreensão de propriedades de polígonos regulares

Abstract

The present work presents the development of a research carried out with graduates of the Degree in Mathematics at Universidade Federal da Paraíba / UFPB / Campus IV / Litoral Norte. The aim of the research was to investigate and identify the main difficulties of the graduates of the Euclidian Geometry Fundamentals in the Degree in Mathematics, in the understanding of the regular polygons properties by application of didactic sequences with the use of a ruler and a compass. In order to investigate the main difficulties of the graduates, two didactic sequences were applied that contemplated the geometric constructions of regular polygons inscribed in a circumference. After observing the didactic sequences, a diagnostic questionnaire was applied on the opinions of the graduates, regarding the use of the drawing instruments. From the general objective of this research and by describing our approach used to learn the properties of regular polygons and investigation the possible presented difficulties, we characterize our research as an exploratory-descriptive investigation. The research is a case study, as it sought to investigate the main difficulties of a particular class of Euclidean Geometry Fundamentals and to analyze the obtained data in the didactic sequences in detail. From the data collected with the answers of the didactic sequences it was possible to identify that the Euclidean Geometry Fundamentals of the Degree in Mathematics showed little mathematical knowledge regarding the properties of regular polygons (Equilateral Triangle, Regular Hexagon, Square and Regular Octagon), as well as little ability to handle geometric drawing instruments. With the data of the questionnaire it was possible to analyze the main difficulties presented by the graduates. To the analysis of the didactic sequences and the diagnostic questionnaire, the conclusions of the research point out that the use of the geometric drawing instruments (ruler, compass and transferor) inserted in an activity planning, as long as it is well elaborated, can contribute positively to the understanding of concepts and properties.