Geometria espacial de posição: do concreto ao raciocínio dedutivo com uma passagem pela tecnologia

Abstract

This study aims to present the development and the usage of a didactic proposal about spatial geometry of position in order to contribute to the learning of second year of high school students of the Military School of Santa Maria, through a a study focused on the theoretical aspects of spatial euclidian geometry. Before carrying out the study, it was done a research in seven schools which are part of the Military School System of Brazil, in order to verify how they are teaching the introductory part of Spatial Geometry and which didactic books are being used for this purpose. With these textbooks in hand, an analysis was made to verify the way each author has approached this topic and also to confront the ideas presented with the aims of the proposal. Once the didactic proposal was made, it was applied to the group of students aforementioned, during regular classes. It is important to highlight the presentation of a group of axioms as well as of the properties that derive from them, the tridimensional geometric construction and the use of group theory language as a way of representation. Some tridimensional building activities were carried out in the computer laboratory using the Geogebra 5.0 3D software. In addition, it was attempted to explore students visualization and perception in every step of the process, using concrete materials which represented the primitive geometric entities, their relations and properties. The data from this application were then put in a table and analyzed predominantly qualitatively, as well as the indices reached by the students in the evaluations concerning the objectives proposed. From the analysis made in the schools and didactic books, it was concluded that the emphasis in spatial geometry is not the positional and axiomatic one. However, after three weeks work with students and the analysis of the results, it was realized that it is possible to work the more formal and abstract aspects of spatial geometry, ones involving intuition, construction, deduction and representation.