A geometria espacial em questões do ENEM e vestibular: algumas análises segundo a teoria dos van Hiele

Abstract

This dissertation focuses on the teaching and learning of Spatial Geometry, with an emphasis on high school students' learning. The objective is to understand, based on van Hiele's theory of geometric thinking levels, how third-year high school students learn and develop their knowledge of Spatial Geometry through exercises from external assessments, such as the National High School Exam (ENEM) and college entrance exams. To achieve this, the methodology involved the application of ten questions from these exams to third-year students. The questions and solutions were analyzed and classified according to van Hiele's levels of geometric thinking. The results indicate that students are situated between levels 1 and 2 of geometric thinking, below the expected level (level 3) for this educational stage. As an educational product, a didactic sequence was developed that incorporates questions from ENEM and college entrance exams—given the centrality of these exams in students' lives—to assist mathematics teachers in identifying and teaching Spatial Geometry using the contributions of van Hiele's theory. Additionally, based on the reviewed literature, suggestions are proposed to address contemporary challenges in the teaching and learning of Spatial Geometry in Brazil.