A geometria plana e espacial no ensino médio: um contexto formal e não formal como espaço de aprendizagem

Abstract

The objective of this study is to develop and analyze the present characteristics in the didactic strategies of teaching and learning Geometry in formal and non-formal spaces. The study was developed at a Ceres-GO High School Comprehensive Period Teaching Center (CEPI), with 28 students from a third-grade class and with the teachers the teachers who teach mathematics at CEPI, as above-mentioned. The research contains a bibliographic review about the subject and is composed of three other practical steps. The first step is an interview about the conceptions of mathematics teachers concerning the learning of Geometry in formal space; the second one is about the use of workshops in formal space as a methodology facilitating the teaching of flat and spatial geometry and the third, and last, is about the use of the ecological trail as a methodology for teaching learning Geometry. These steps were created in the form of chapters. During the practical activities the students discovered their potential interaction through visual perception and contact with nature revealing their interest in the activities developed. This contact with their potential reveals an increase in the students' self-esteem, creating more respectful relationships and, most importantly, the development of the cooperative spirit of solidarity with each other and the group's colleagues. Based on the methodologies used in the research came an education that stimulated collaboration and not a competition. The main results revealed that, although the theme related to Geometry teaching is remote, there is still a lot to be done, the difficulties encountered by teachers who teach Mathematics / Geometry in High School are many, despite the progress that has been made in the last decades. The training of teachers who teach mathematics is not sufficient, if you consider the non-training in the specific area; that many professors who teach mathematics expose resistance to the teaching of Geometry in a practical, playful way and with the use of diversified methodologies. The continuing education (role of the State) is an indispensable resource and capable of assisting teachers in the process of solving their difficulties with the subject matter. The reception by the students about the use of the workshops and realization of the ecological trail as innovative methodologies for the teaching of Geometry was very positive. The results also suggest a set of other issues that can and should be addressed in future research, including the initial and continuing training of teachers who teach Mathematics / Geometry, the methodologies to be used, the teaching resources available inside and outside school and classroom.