A representação semiótica e os conceitos da geometria euclidiana plana: o processo de ensinar e aprender nos anos finais da educação básica

Abstract

According to the BNCC (2018), geometry is an essential field of mathematics because it fosters the development of geometric thinking and critical thinking skills, and is applied in a variety of social and academic contexts. However, it still presents gaps in teaching and learning, especially in the transition from elementary school to high school, which requires innovative methodologies and teaching resources to make the process more meaningful. This study aimed to analyze how graphical representation can contribute to the appropriation of geometric knowledge in the teaching of Plane Euclidean Geometry, considering the principles of Didactic Engineering. The qualitative research involved a literature review of academic databases and a case study with 11 first-year high school students at a state school in Luís Eduardo Magalhães, Bahia. Diagnostic questionnaires, an introductory class, a practical workshop with manipulative materials, and an online game were administered to assess students' perceptions and evaluate the effectiveness of the developed teaching sequence. The data revealed significant conceptual difficulties, especially in distinguishing between perimeter, area, and angles. The GeoBasic workshop, combined with visual and digital resources, enabled students to understand fundamental geometric properties, such as the sum of the interior angles of a triangle, in addition to developing greater confidence in using instruments such as the protractor. The interactive game reinforced the content, promoting engagement, logical reasoning, and active learning. It was found that graphic representation, when combined with Didactic Engineering and active methodologies, helps overcome difficulties in teaching geometry, making the process more dynamic and meaningful. The research indicates the need to broaden the scope of future research, including systematic reviews and diverse educational contexts, to consolidate the contributions of this approach to mathematics teaching.