Do sensível às ideias: Um estudo de geometria a partir de atividades envolvendo espaço e forma

Abstract

My interest for, and my first ideas related to, this research area began during my initial teacher training. Today, I can verify some results from the reflections along this journey. They make us infer that if geometry is approached since the first years in school, initially through empiric ideas, and later on through the exploration of concepts of plane geometry, that would be a more coherent way for school children to develop geometrical concepts. However, the recognition of geometry was relegated by almost everyone for many years, which has damaged its teaching quality in the schools. Fortunately, during the last three decades, there is a tendency to recuperate and show the potential of geometrical knowledge for the development of a human being. In this context, we are searching for possible explications that lead us to the answer to our guiding questions: What effects are produced by a series of planned activities that favor the exploration of a concrete/sensitive geometry in order to approach notions of plane geometry with fifth-graders? To what extent does this classroom intervention, guided by the recommendations for geometry teaching to fifth-graders, contribute to the development of concepts of plane geometry based on the exploration of activities that involve the composition and decomposition of some representations of geometric solids? In order to discuss these questions, this study aims to investigate the effects produced by a series of planned activities that favors the exploration of a concrete/sensitive geometry in order to approach notions of plane geometry with fifth-graders, through situations that involve the composition and decomposition of some representations of geometric solids. We carried out a qualitative field study with an interpretative and naturalistic aspect, involving 25 pupils from a fifth-grade-class at a State school in the town of Monteiro, State of Paraíba, Brazil. The research structure was based on a set of eight activities related to geography that were denominated along the episodes of the text. These activities were thought in the light of a geometry that initially favors the concrete, sensitive character as a possibility to develop some tri-dimensional geometric concepts and, later on, approach elements of plane geometry in a constant dialogue between plane and spatial geometry. The data was gathered between the months of February and March of 2015. Various instruments were used in this task, among them the activity notebooks that were handed out to every work group during every episode, the film recording, the facial, corporal and gestural expressions along the process of achieving information, and commentaries said before or after the moments of construction of geometric knowledge. As part of the results, it can be highlighted that the activities developed in groups favored an interpersonal communication where the more skillful participants contributed to the learning of those that presented more difficulties.