Análise das questões de geometria do ENEM 2020, sob a perspectiva de Van Hiele e a de Raymond Duval

Abstract

The main objective of this work is to present the resolutions of the Geometry questions in the area of Mathematics and its Technologies of ENEM 2020, through analyzes carried out under the perspective of Van Hiele Theory and Raymond Duval Theory. Both theories focus on teaching and learning Geometry, seeking to help the teacher, reduce their possible difficulties in the teaching process of this content, and direct the development of student learning. So, the work had as methodology to seek a theoretical framework of the two theories, through the Semantic Fields Model, which allowed us to have a plausible reading when solving the selected questions, under the eyes of Duval and Van Hiele. Using the Theory of Semiotic Representation Records, the types of records used to solve each question were cataloged, the types of looks we had to identify the objects brought by each problem were analyzed, and the necessary apprehensions to find the solutions for each question . According to Van Hiele's theory, the questions were solved by the necessary skills of each level required for each problem, according to the characteristics of their respective levels, as shown in this theoretical model. As much as the two theories approach the teaching of Geometry, each has a different look; in this way, it was shown how each resolution behaves towards each theory. Therefore, the catalogings of ENEM questions were analyzed, which were resolved considering Van Hiele levels and Duval's Theory, showing and identifying the differences that each model has from one another. Thus, the considerations obtained in carrying out the work are brought up, raising questions that involve the teaching and learning of Geometry in the face of both theories, addressing its advantages and disadvantages that we found when working with both models.