Proporção Áurea e Geogebra no Ensino de Matemática: visualizando conceitos à luz da Modelagem Matemática

Abstract

This study aims to develop two teaching sequences based on Mathematical Modeling and created with the aid of GeoGebra software for teaching the Golden Ratio at the high school level. The research is grounded in the issue that traditional mathematics instruction prioritizes the memorization of formulas and abstract concepts, leading to a lack of interest and comprehension difficulties among students. To support the development of these teaching proposals, the study addresses historical aspects of the golden ratio, its properties, and its manifestations in various fields, as well as the theoretical foundations of Mathematical Modeling and the use of GeoGebra in mathematics education. As a result, two teaching proposals were developed, structured around the stages of interaction, mathematization, and mathematical modeling. The first proposes exploring human facial proportions by marking points and calculating dynamic ratios in GeoGebra, leading to the formalization and understanding of the golden ratio. The second proposal focuses on the geometric construction of the golden rectangle overlaid on works of art and the façade of the Parthenon, enabling hypothesis validation and the development of students' critical thinking regarding mathematical models. The study concludes that integrating these methodological approaches can foster contextualized and participatory learning, promoting student autonomy and bridging the gap between mathematical concepts and real-world reality.