Playing with Geometry: An Educational Inquiry Game Activity

Abstract

In this study, we present a new approach to teaching based on the Logic of Inquiry (Hintikka in The principles of mathematics revisited. Cambridge University Press, Cambridge, UK, 1998), which develops students’ investigative and reasoning skills and may promote a deeper understanding of the meaning and the validity of mathematical theorems . Starting from a game played in a Dynamic Geometry Environment (DGE ) and guided by a questionnaire, students discover and become aware of the universal validity of the geometric property on which the game is based. In this paper, we present two game-activities. The first is an activity in which students play the game against a schoolmate and use a worksheet questionnaire to reflect on their findings. The second is an online game-activity in which the students play the game against the computer and reflect their findings in an online questionnaire. Using the theory of didactical situations (Brousseau in Theory of didactical situations in mathematics. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997) we describe and analyse the work, diagrams , dialogue, and question responses, showing the importance of the strategic thinking activated by the game-activity for students’ mathematical inquiry and reasoning development.