As contribuições da geometria dinâmica no processo de ensino e aprendizagem de geometria espacial por meio do software GeoGebra 3D e de atividades investigativas

Abstract

This master's thesis proposes the creation of activities based on mathematical investigative learning and problem solving, centered on Spatial Geometry, using the Geogebra 3D software. The study aims to analyze the advantages and disadvantages of this approach in a public-school classroom. Initially, the work conducts a literature review on the interpretation of Spatial Geometry in official Brazilian documents, seeking theoretical basis and curricular contextualization. Next, a study is conducted on active methodologies, focusing on investigative learning and problem solving, aiming to understand the foundations and benefits of these approaches in teaching mathematics. The research includes an analysis of resources available in Geogebra, especially applets that can be used for investigative activities in Spatial Geometry. This survey aims to identify suitable tools for creating dynamic and interactive activities, favoring the exploration, and understanding of geometric concepts by students. Based on this theoretical basis, specific investigative activities on Spatial Geometry are developed, using Geogebra as the main tool. These activities are designed to encourage active exploration by students, promoting the construction of knowledge through investigation and problem solving. Furthermore, the advantages and disadvantages of using Geogebra 3D in Spatial Geometry classes are identified. Aspects such as technology accessibility, ease of use, student motivation, interactivity of activities and integration with the school curriculum are considered. Finally, the dissertation presents conclusions and recommendations for the effective use of GeoGebra 3D as a tool for teaching Spatial Geometry in public schools. Strategies to overcome challenges and maximize the benefits of this approach are discussed, aiming to contribute to improving the teaching and learning of mathematics in this specific context.