Configural Reasoning and Geometric Workspace in the Proof's Problem Resolution

Abstract The transition from the first justifications of geometric properties in the school environment to the mathematic proof in a deductive context is an issue widely studied. From the Theory of Paradigms and Geometric Workspace, which provides a framework regarding the institutional environment in which the geometric activity is developed, we use the model of Configural Reasoning to study the resolver's geometric workspace when facing a task of proving a geometric property. We describe the discourse organization of high school students' responses to a four-task questionnaire in which they were asked to prove a geometric property, and we determine the configural reasoning that led them to those responses. This analysis allows us to provide evidence on the transition that students must undergo from their first experimental justifications in Natural Geometry to the valid mathematical reasoning proper of Natural Axiomatic Geometry. The Configural Reasoning is shown as a theoretical model with a great capacity for addressing the articulation between visualization and reasoning.