Exploring visualization, geometric thinking and creativity

an experience with undergraduate students in Mathematics

Abstract

Teaching Geometry requires more than just conveying definitions and properties. It is necessary to stimulate visualization, reasoning, and creativity, and allow students to construct meaning from the investigation of practical situations. In this process, methodologies that encourage exploration and justification of strategies are fundamental to strengthening geometric thinking, especially in the initial training of Mathematics teachers. This study reports on a teaching experience with second-semester undergraduate students in Mathematics, aiming to develop geometric thinking, creativity, and visualization based on an investigation involving quadrilaterals. Using a qualitative approach, data were obtained from students' responses to three practical questions asked in a Fundamentals of Geometry class. The activities involved constructing quadrilaterals on dotted grids of different dimensions (3x3, 3x4, and 4x4), analyzing the ability to identify, justify, and explore different configurations. The results indicated progress, such as the distinction between convex and non-convex figures, but also revealed challenges, especially in formulating consistent justifications and identifying all geometric possibilities. There were difficulties in applying concepts such as rotation and translation, as well as limitations in scaling up solutions obtained in smaller meshes to larger ones. We concluded that pedagogical strategies that emphasize conceptual reinforcement, visualization, creativity, and reflective thinking are essential to enhance geometric learning. We believe that such approaches can contribute to the training of teachers who are better prepared for the challenges of teaching Geometry.