O desenvolvimento do pensamento geométrico nos anos iniciais do ensino fundamental a partir da Teoria de Van Hiele: contribuições de um curso de formação de professores

Abstract

This research aimed to investigate the contributions of a continuing education course, about the development of geometric thought according to Van Hiele’s Theory, to the pedagogical practice of teachers who work in the Early Years of Elementary School. In this ambit, a collaborative work and the use of manipulative material was proposed as pedagogical resource; in addition, a proposal for teaching plane and spatial geometry, and didactic material to be used in the classroom were developed, in order to encourage the development of geometric thought according to the levels of thinking of Van Hiele’s Theory . The course was organized in three stages: theoretical foundation regarding the teaching of geometry and Van Hiele’s Theory; elaboration of tasks on plane and spatial geometry based on levels of thinking and learning phases systematized by and based on Van Hiele’s Theory; and application of tasks for validation, discussion and reformulation. The participants were two trainer teachers, three teachers who act in Early Childhood Education and seven teachers that work in the Early Years of Elementary School from a private school in the North of Paraná. Data were collected through questionnaires, applied before and after the course, video recordings of meetings he ld via Google Meet and a field diary. The proposal to develop and apply geometry tasks, in this research, gave the participating teachers the opportunity to relate theory with practice and thus understand Van Hiele’s Theory. The data analysis, guided by a qualitative approach, revealed as contributions of the course that: the teaching of geometry became more meaningful, that is, the teachers understood the need to explore the previous knowledge of each student; they were able to know, study and apply Van Hiele’s Theory; they also acquired knowledge to design and apply tasks according to students' thinking levels; they recognized the importance of using manipulative materials in geometry teaching, considering them since task planning; and constituted a new look at the assessment of students, with tasks that can lead to questions and reflections relevant to the development of geometric thought. The results of this research, in confluence with others present in the specialized literature, emphasize the importance of continuing education actions, such as the proposed course, as a way of dealing with the teachers’ difficulties in mathematics, resulting from their initial formation, especially regarding geometry and the development of geometric thought. In view of t he results obtained, as an educational product resulting from this professional master's research, a continuing education course was reorganized, with a description of the development of geometric thought according to Van Hiele’s Theory, so that teachers have subsidies to identify, mobilize and/or promote geometric thought and go further on the basic concepts of plane and spatial geometry. In this material, we provide suggestions for tasks, which we call exploratory tasks, prepare d by the researcher in collaboration with the participating teachers, emphasizing pedagogical practices that can favor the student’s learning in geometry.