Geometric Thinking: Reflections Manifested by Preservice Mathematics Teachers in van Hiele Model Studies

Background: The study of geometric thinking in the preservice education of mathematics teachers is an emerging theme that can reverberate in the teaching of geometry in basic education. Objectives: To analyse reflections manifested by prospective mathematics teachers (PMTs), working with tasks supported by van Hiele theoretical model to develop geometric thinking. Design: The nature of this study is qualitative and interpretative. Setting and participants: Twenty-four PMTs members of a geometry teaching subject were investigated in a mathematics degree course at a public university in Paraná - Brazil. Data collection and analysis: The data was collected from the video-recorded training sessions, the written production of the PMTs promoted by the tasks and the registers kept on the field diary. The analysis focused on the reflections expressed by PMTs regarding the work with tasks involving geometric thinking, considering the levels of reflection proposed by Muir and Beswick (2007). Results: The results show descriptive, deliberate, and critical reflections, with different levels of incidence, associated with (I) the levels of thought proposed in the van Hiele model; (II) the teacher’s role in classroom practice; and (III) the geometric concepts and properties of flat figures. Conclusions: The promotion of formative actions that privilege discussions and reflections on geometric thinking can allow PMTs to seek connections between knowledge of geometry, geometric thinking, and their future teaching practice.