A teoria de Van Hiele no ensino de matemática: uma proposta de sequência didática para o Ensino Médio

Abstract

his dissertation aims to create a didactic sequence for teaching triangles to the 1st grade of high school, based on the Van Hiele Theory (VHT). The choice of VHT is justified by its significant contribution to the teaching of Geometry, considering that geometric thinking develops gradually, respecting students’ different levels of understanding. Although Geometry is essential content for mathematical education, its teaching still faces challenges in Basic Education, often being developed in an uncoordinated manner or sidelined. In this context, the research was guided by the following problem: how can we develop a didactic sequence for teaching triangles in the 1st grade of high school based on the levels of the Van Hiele Theory, in order to foster the development of students’ geometric thinking? Initially, a study on the teaching of Geometry in Basic Education was carried out to understand the main challenges highlighted by the literature and its importance for mathematical lear ning. Next, the foundations of the Van Hiele Theory were discussed, including its origin, levels of geometric thinking development, and phases of learning. Subsequen tly, a review of studies was conducted in the Catalog of Theses and Dissertations of the Coordination for the Improvement of Higher Education Personnel (CAPES), considering works from professional master’s programs published between 2020 and 2026. The search was performed using the descriptors “Van Hiele Theory”, “Geometry”, and “Mathematics”, initially resulting in 61 works. After defining the selection criteria, six dissertations were analyzed, allowing the identification of trends, contri butions, and possibilities for using the theory in Geometry teaching. The research is characterized as qualitative, of an interventional nature, and resulted in the deve lopment of a didactic sequence organized based on the levels of geometric thinking development and the learning phases proposed by the VHT. The activities were planned progressively, encompassing situations of exploration, investigation, mani pulation, and argumentation, in order to favor the construction of concepts related to triangles. As an educational product, the research provides a didactic sequence that can serve as support for Mathematics teachers interested in developing pedagogical practices aimed at strengthening geometric thinking in High School.