The Correlation between Figural and Conceptual Properties of Angle and Cube in Pre-Service Teachers Geometric Reasoning - Olivera J. Đokić; Mila S. Jelić; Svetlana M. Ilić (University of Belgrade, Teacher Education Faculty, 2020)
Drawing upon Fischbein's theory of figural concepts, the starting point of the paper is the use and value of the history of geometry in mathematics education - first point that we make historical reference are theorems of Eudemus of Rhodes and Thales of Miletus and the second one is elaboration of these theorems in work of Serbian mathematicians Mihailo Petrović Alas. Fischbein's theory is mainly based on a hypothesis that geometry deals with mental entities, the so-called geometric figures, which simultaneously possess conceptual and figural properties. Fischbein called the geometric figures figural concepts because of their nature. We have analyzed the internal tensions of the concepts of angle and cube, which may appear in figural concepts because of their double nature, developmental aspects and didactical implications. The goal of the research was to examine the pre-service primary school teachers' geometric reasoning regarding the correlation between figural (pictoral) and conceptual properties of geometric objects (angle and cube) in order to obtain a framework for creating didactic situations that reduce the gap between figure and concept. The results of this study show that the figural (pictoral) structure of an angle (and cube) dominates in the geometric reasoning of the pre-service primary school teachers over its formal conceptual constraints. There were some differences in situations when an image is helpful in solving tasks involving the concepts of the net of the cube and the cube itself.