Geometric constructions using the régua and the compass in the environment paper and pencil: a study in the light of Van Hiele's theory

• Autor(a) principal: Pachêco, Franklin Fernando Ferreira
• Data de Publicação: 2019
• Outros Autores: Pachêco, Gisele Ferreira, Silva, Anderson Douglas Pereira Rodrigues da
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Revista de Educação Matemática (Online)
• Texto Completo: https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/159
• topic: Triangle Equilateral; Square; Van Hiele theory; Triángulo Equilátero; cuadrado; teoría de Van Hiele; Triângulo Equilátero; Quadrado; teoria de Van Hiele.

The present research aims to analyze geometric constructions produced by students of the 8th year of elementary school in a municipal public school through an AB straight line segment using ruler and compass, and from them identify if the participants fit the level of analysis through the Van Hiele Theory. As a theoretical contribution, the development of the geometric thought proposed by the Van Hiele, in particular the levels of understanding that support the verification, identification and framing of the geometric knowledge that each individual possesses through a study on geometry was used. In methodological terms this is an exploratory research with a qualitative approach in which 28 students belonging to the 8th grade of Elementary School participated in a municipal public school located in the city of São Vicente Férrer, located in the Zona da Mata Norte of the State of Pernambuco. For data collection, a test involving two questions was used. The first objective was for the students to perform an equilateral triangle with the AB segment and with the aid of the ruler and the compass. The second one approached the students to construct a square with the segment AB. Through the analyzed protocols, it was noticed that the students used the geometric instruments to respond to the applied test. It was verified through the categorizations that the students submitted to the applied test obtained a higher index of correct answers in the first question, in which it contemplated the construction of the equilateral triangle. It is noteworthy that there was no total error of the test, that is, the students who miss the first question, hit the second and so vice versa. Thus, those students who partially fulfilled the test fit the level of comprehension of the analysis using the Van Hiele Theory, at least in the geometric figure constructed correctly in the study. Therefore, it was evidenced that these students of the 8th year of elementary school conceive geometric knowledge that correspond to the level of comprehension of the analysis through Van Hiele Theory.