RATIONALITY IN GEOMETRIC AND MATHEMATICAL THINKING FOR TEACHING

Abstract

Rationality in geometric and mathematical thinking is a fundamental aspect that must be integrated into teaching processes to foster meaningful learning in students. This type of thinking is based on the ability to reason logically and in a structured way, allowing for the resolution of complex problems through the application of geometric and mathematical principles. In contemporary education, it is essential that students not only memorize formulas and theorems but also understand the "why" behind the concepts. Therefore, the objective of this article was to analyze how rationality influences geometric and mathematical thinking for teaching. Based on this, a process of discussion and hermeneutical understanding will be undertaken regarding the construction, creation, and representation of human life within the social phenomenon and the current known as postmodernity, characterized by its immediacy, volatility, diversity, and global nature—conditions that cannot be ignored in educational processes today. The results showed that one of the key elements in developing rationality in geometric thinking is visualization. Geometry, as a discipline that deals with shapes and spaces, requires students to be able to imagine and model abstract concepts. Through tools such as drawing, manipulating three-dimensional objects, and using dynamic geometry software, learning experiences can be facilitated that promote a deeper understanding.