Geometric prediction: A framework to gain insight into solvers’ geometrical reasoning

This paper focuses on the theoretical construct of geometric prediction (GP): a cognitive process through which a geometrical figure is manipulated, and its variations imagined, while certain properties are maintained invariant. The aim is to gain insight into this process as it is accomplished by solvers during the resolution of geometrical tasks within the domain of Euclidean Geometry. Interpreting geometrical reasoning in terms of a dialectic between the figural and the conceptual component of a figural concept, I introduce a framework of geometric prediction that I elaborated cyclically by observing, analyzing through a microgenetic approach, and re-analyzing solvers’ resolution of prediction tasks in a paper-and-pencil environment. The framework provides deep insight into geometric prediction, a specific and fundamental process in geometrical reasoning.