Investigative tasks of spatial geometry with GeoGebra software in the mathematics teacher education process
The present study presents a qualitative research, in which we analyze the process of construction of spatial geometry tasks, using GeoGebra-3D, by mathematics teachers who are in a training process, and the execution of these tasks in the classroom of class. For the data production, we made video and audio recordings of three moments of the teachers participating in an extension course on geometric constructions, using the Geogebra software, for Basic Education. This dissertation was prepared in a multipaper format and structured in five chapters. The first chapter was intended for an introductory section, presenting the academic and professional trajectory of the researcher, the theoretical justifications of the study, the three objectives, the structure of the dissertation and the methodological procedures adopted for the development of the research. In the second chapter we present the first article, which brings a meta-synthesis of articles analyzed in a literature review, aiming at (i) identifying and analyzing theoretical and methodological aspects of research that address the teaching of spatial geometry. The third chapter was intended for the presentation of the second article, which analyzes professors participating in an extension course, with the aim of (ii) describing the process of developing investigative tasks on teaching spatial geometry, using GeoGebra, by teachers of mathematics during a formative process. The fourth chapter, we designate for the third, and last, article of the dissertation, which presents the execution of one of the tasks elaborated by the teachers and aims to (iii) reflect on the process of carrying out investigative tasks of spatial geometry using the GeoGebra in the classroom. The fifth chapter will include the final considerations of the present study.