Geometria espacial de posição sob a ótica dos registros de representação semiótica: um estudo com licenciandos em matemática

Abstract

This research aims to analyze figurative treatments mobilized by undergraduates in Mathematics when studying concepts/contents of Position Spatial Geometry. For this, the theoretical assumptions of the semiotic representation registers were adopted. The study is qualitative, following the principles of Content Analysis. The data production considered four works that stand out in bibliographies of curricular components related to the teaching and learning of Geometry that make up the curricular matrix of Mathematics Degree courses, offered by federal institutions in Brazil. In addition, it has the development of three structured tasks from the reorganization of activities presented in the analyzed works, in view of the discussion about concepts / contents of Position Spatial Geometry. Given the analyzes performed, it was found that the activities proposed in the works emphasized the registration in natural language to communicate their statements and, in most cases, remains in this representation, evidencing a treatment activity. In contrast, the figural record and the dimensional deconstruction are little explored. As for the figurative apprehensions, the analyzed activities can enable the mobilization of the perceptive and discursive. Following a readjustment of some of these activities to the ideas of Raymond Duval, they were developed with seven undergraduates in Mathematics. The accomplishment and analysis of the task block showed that the students were removed from their comfort zone at different times, sometimes by different representations of the cube, sometimes by descriptions that required the use of results from Position Spatial Geometry. This movement caused the subjects to mobilize different types of cognitive transformations and distinct figurative apprehensions, which contributed to the movement of dimensional deconstruction and the spontaneous functioning of visualization. In addition, it was observed that participants demonstrated knowledge about concepts / contents of Position Spatial Geometry and that stimulated the action of seeing in Geometry when developing organized activities. It can be said that the figurative treatments contributed in an integral way to the visualization in Geometry, considering the pertinent solutions presented by the academics. In view of this result it can be stated that the figurative treatments are a means that contributes to the learning of visualization in geometry, considering the solutions presented by the academics in carrying out the proposed activities. Given the above, the importance of exploring this type of activity during any level of education is emphasized.