As faces dos sólidos platônicos na superfície esférica: uma proposta para o ensino-aprendizagem de noções básicas de Geometria Esférica

Abstract

The aim of this study is to present a sequence of problem solving activities through a qualitative approach whose aim is to study how this sequence can allow high school students to learn basic concepts of Spherical Geometry while reviewing Plane Geometry. That is why we are trying to respond to the following basic question: What contributions a sequence of activities that has as a proposal the tessellation of the phases of the platonic solids on superficial sphere can allow for the teaching and learning of basic notions of Spherical Geometry? We appeal to the passion of the Brazilian people, soccer, in order to contextualize the topic in an ordinary way for the learners. In this ordinary example, not only a soccer ball is included, but also a tennis ball, volleyball, etc. The use of tangible materials such as polystyrene spheres, flexible rulers, colored pens, compasses, strings, pins and other materials that are easy to find, in addition to the traditional pen and paper, can all be used by students in learning about the phases of platonic solids, basis for understanding this task, to tessellate a soccer ball on a spherical surface. We formulate the hypothesis that the utilization of these materials and the departure from traditional methods that have been used will stimulate the interest of the students and create more understanding not only of Plane Geometry, but also Spherical Geometry as in the example above. We have compiled in this study a theoretical reference that includes socioconstructivism, which we believe created more interaction, and therefore made the teaching and learning environment more effective. We ended, in the end of this research, exciting indications that it is possible the teaching- learning of the Spherical Geometry, as it was proposed