Exploring the concepts of polygons and polyhedra from Van Hiele´s model

Abstract

The objective of this study was to analyze the levels of reasoning manifested by a group of high school students when solving problems involving the concepts of polygons and polyhedra following the Van Hiele model. For the development of the research, a quantitative approach was chosen, with a descriptive scope. A bank of questions was designed and implemented as techniques to collect the information, using the educational software Viaje por la Geometría (Journey through Geometry). The results showed a good level of reasoning achieved by the students in recognizing, analyzing, classifying, calculating the number of diagonals of a polygon and using Euler’s theorem to establish the relationship between the number of faces, vertices and edges of the polyhedron. The formal deduction reasoning process corresponding to level four was not achieved by most of the students due to the difficulty in performing algebraic calculations to calculate the apothem of a polygon as a function of its side; they also had difficulty in calculating the diagonal of the parallelepiped.