Prediction in Transition: Continuities and Discontinuities Moving from the Paper-and-Pencil to the Dynamic Geometry Environment

This article focuses on the possible relationship between predictions, developed during the resolution of geometrical tasks within a Paper-and-Pencil Environment (PPE), and subsequent explorations within a Dynamic Geometry Environment (DGE). Building on Fischbein’s Theory of Figural Concepts, and to gain insight into the transition of predictions from the PPE to the DGE, I introduce an analytical scheme that includes the identification of the solvers’ figural concepts in focus and geometric predictions; dragging modalities that solvers make use of in the DGE; reactive and proactive dimensions of the interaction with dynamic objects in the DGE. I present a fine-grained qualitative analysis of data collected during task-based interviews as high school students reason about a geometrical task—first on paper-and-pencil and then in a DGE. The analyses of three representative examples show that the interaction with DGE objects can lead students to rethink the geometrical configuration and renegotiate predictions, depending on the circumstances that offer the opportunities to experiment with continuities or discontinuities during the transition of prediction from one to the other environment.