A logical-historical movement of geometry and training actions in a Mathematics Club

Abstract

The text aims to share results of the study of the logical-historical movement on geometry and highlight contributions to teacher training processes from a collective perspective. This training is carried out at the Mathematics Club of the Federal Institute of Espírito Santo and the investigation of this process is developed in Ph.D. research, that has as theoretical-methodological foundation the Historical-Cultural Theory, Activity Theory, and Teaching Guided Activity. Based on these assumptions, teacher training is understood as a social, dialogic process marked by the needs and demands of pedagogical work, synthesizing debates and actions that involve teaching activity, the teacher's main activity. It stands out that the training movement in the Mathematics Club is based on the need for participants to appropriate historically accumulated knowledge, when studying a logical-historical movement of concepts, in this specific case, of geometry. The study highlights geometry as a human production, and, to approach its development from a logical-historical perspective, it becomes necessary to discuss the relationship between man and nature, attracting attention to the work processes and production of instruments, because the processes of perception of form, location and displacement in space change with the relationship between man and work. Furthermore, it is highlighted that theoretical study in the collective training process makes it possible to understand new ways of organizing teaching, approaching geometry through the perception of shapes, identification of figures, communication of their properties, different representations and establishing an organization of actions in the training process in an intentional way.