GEOMETRIC THINKING, VISUALIZATION AND IMAGINATION IN THE TEACHING OF GEOMETRY:

CONNECTIONS AND STRATEGIES FOR LEARNING

Abstract

Graphic representations have been fundamental in the transmission of ideas and in human development. In Geometry teaching, they play an essential role, especially in learning concepts such as quadrilaterals, by promoting geometric thinking. This study aims to investigate how doctoral students in Science and Mathematics Teaching in a Geometry subject apply these skills in practical activities of geometric creation and analysis. The research adopts a qualitative and exploratory approach, with eight participants. Practical tasks and electronic forms were used to collect data, ensuring sequential and authentic responses. The activities included the formulation of conjectures, initial imagination and the use of concrete materials, such as strips of paper, to stimulate the construction and analysis of quadrilaterals. The results indicated progress in the development of geometric thinking and visualization, and also revealed challenges such as predicting geometric relationships and identifying properties. It is concluded that interactive activities, combined with the use of concrete materials, are essential to enhance geometric learning, integrating theory and practice. The study reinforces the need to train educators who are able to explore methodologies that promote visualization and imagination, strengthening the teaching of geometry.