Approaching Secondary School Geometry Through the Logic of Inquiry Within Technological Environments

Abstract

The chapter illustrates a pedagogically innovative way of using mobile technology to support the transition from an empirical to a more theoretical and logical approach to geometry. We propose an approach that shows the possibility of discovering geometric theorem statements and appreciating their universal truth using a suitable pedagogical design that draws on the work of the Finnish logician J. Hintikka as well as on Dick and Zbiek's notions of pedagogical, mathematical and cognitive fidelities. We implement it through game-based activities, namely group activities in which, first, students play a game in a dynamic geometry environment (DGE) and then, guided by the questions contained in a worksheet task, investigate the geometric property on which the game is designed. In the worksheet task, students are asked to act as detectives using the game to investigate, formulate and check conjectures. In order to analyse the students' productions we use a cognitive model elaborated from Saada-Robert's psychological model, which properly describes the cognitive modalities and the empirical versus theoretical and logical approaches to geometry.