O ambiente dinâmico GeoGebra para o desenvolvimento de aspectos específicos da aprendizagem em Geometria segundo Raymon Duval: olhares, apreensões e desconstrução dimensional

Abstract

Geometry consists of an area of mathematics which is rich in possibilities of cognitive development, but not always valued from this point of view. Raymond Duval's Theory of Registers of Semiotic Representations (2004, 2005, 2012, 2012a, 2012b, 2013, 2015) provides a description of cognitive activities related to the development of geometric thinking, serving as a support for possibilities of improving teaching and learning processes. An articulation of the geometry with a dynamic environment directs the present study in the search for the answer to the following question: In what way is it possible to stimulate the development of cognitive activities according to Raymond Duval using the GeoGebra dynamic environment in geometry activities? From this questioning, the objective of this research is to point out contributions referring to the use of this dynamic environment for the work with Geometry with respect to the stimulus of the visualization of characteristics involving geometric figures indicating which specific cognitive activities of the Theory of Semiotic Representation Registers of Raymond Duval were present. This study was carried out with 30 students from the eighth grade of elementary school of a public school in the state of Paraná, in which the subjects' digital and written productions were analyzed during the application of a workshop, whose theme was geometry, with activities involving polygons and polyhedra through the use of GeoGebra. As a result, it was possible to infer that the dynamism provided by the GeoGebra dynamic environment was a facilitator for the identification of characteristics of certain mathematical objects. The choice of contents involving regular and non-regular polyhedra and Euler's Relation, as well as the resumption of concepts of regular and non-regular polygons, provided a stimulus for dimensional deconstruction. The presence of the apprehensions was identified and the iconic views more evident. Through GeoGebra, the explorations of the geometric figures are efficient and favor the establishment of conjectures, consequently, the seizures, views and dimensional deconstruction are required.