Licenciandos e professores de matemática interagindo no VMTcG em atividades de semelhança de triângulos

Abstract

This exploratory research aims to analyze interactive processes of prospective teachers in an online and collaborative context and propose a didactic sequence on similarity of triangles for implementation in the virtual and synchronous environment Virtual Math Teams with GeoGebra (VMTwG). The data (graphs, tables, textual transcripts, constructions on screens) were generated in the environment itself and served as a basis for the re-elaboration of tasks and for the analysis of interactions. The pilot implementation made it possible to reformulate the tasks to better adapt to GeoGebra in VMT. The second implementation allowed a different design of the tasks in relation to the proposed task type, from a closed nature to a more open scope. At first, we analyzed one of the groups, identifying the interlocution properties involved in their records. With that, we ratify the interrelationship between the written chat and the graphic zone, we investigated the continuity of the interaction of the participants in the VMTwG and some aspects of the mathematical reasoning evidenced in their speeches. We also identified the different uses of the drag resource and the notes of these uses for the subjects' cognitive process. Among them, we highlight the wandering drag and guided drag that worked as an empirical-perceptive control in the exploration of properties and relationships of the figures built in GeoGebra added to the VMT. In a second moment, we selected the groups that discussed the objects, the properties, the relationships and the dynamics of the relationship between the objects. We selected and analyzed one of the rooms whose use of the checkered mesh was frequent, and another room highlighted by the use of the slider. We analyzed the ways of using the checkered mesh and the slider. We highlight the role of icons (task script, chat and measures) that compose, together with the checkered grid, a set of components of the semiotic mediation process. We consider that the mesh task enabled the group to explore more global aspect properties of triangle congruence through an upward reflective process (from construction to theory). We consider that the task with the slider made it possible to explore from more global issues to more specific intervals and values related to the similarity of triangles by ascending and descending thought processes. In this dynamic, we identified three types of drag with the slider: wide drag, local guided and control test. The VMTwG proved to be an environment that allows individuals to work collaboratively, constantly interacting and interpreting their ideas and those of colleagues. This reflective and feedback process is important in teacher education as it develops different ways of reacting to emerging and under construction ideas. The educational product is a didactic sequence of activities on the concept of combining triangles and a guide to setting up and using the VMTwG.