Uma proposta de ensino de Geometria Hiperbólica : "construção do plano de Poincaré" como uso do software Geogebra

Abstract

This research aimed at developing a Didactic Organisation and identify possible obstacles that appear along the construction of the Poincaré model plan using Geogebra software with the use of a short course in Hiperbóica Geometry applied to students of 4th year degree in mathematics from University State of Paraná. The thesis intended to contribute to the teaching and learning of Geometry, specially of Hyperbolic Geometry, and to serve as research material and application for teachers and students of secondary and even higher education. The survey was divided into two parts. The theoretical part presented the history of Euclidean Geometry, from the attempts to demonstrate his fifth postulate to the starting of new geometry or just it is called now Non-Euclidean Geometry. We presented the model of the Poincare plan, used in the experimental part. Still in the theoretical part, we discussed elements of Anthropological Didactic Theory by Chevallard and Bosh and discussed the concept of teaching the didactic obstacle proposed by Brosseau . In the experimental part, the preparation of activities, implementation, research participants and the categorizations of the items collected were presented. We used content analysis of Bardin for information processing and obstacle detection in the construction of concepts relating to the construction of the Poincare model. The conclusions were that it is possible to teach Hyperbolic Geometry using dynamic geometry software like GeoGebra, if the contents of the school grades of apprentices were considered and respected and that there is the necessity of being careful during the building of metric concept.