Theoretical Frameworks for the Learning of Geometrical Reasoning

With the growth in interest in geometrical ideas it is important to be clear about the nature of geometrical reasoning and how it develops. This paper provides an overview of three theoretical frameworks for the learning of geometrical reasoning: the van Hiele model of thinking in geometry, Fischbein’s theory of figural concepts, and Duval’s cognitive model of geometrical reasoning. Each of these frameworks provides theoretical resources to support research into the development of geometrical reasoning in students and related aspects of visualisation and construction. This overview concludes that much research about the deep process of the development and the learning of visualisation and reasoning is still needed.