Abstract
The aim of this paper is to reflect on the importance of the students’ game-strategic thinking during the development of mathematical activities. In particular, we hypothesise that this type of thinking helps students in the construction of logical links between concepts during the “argumentation phase” of the proving process. The theoretical background of our study lies in the works of J. Hintikka, a Finnish logician, who developed a new type of logic, based on game theory, called the logic of inquiry. In order to experiment with this new approach to the teaching and learning of mathematics, we have prepared five game-activities based on geometric theorems in which two players play against each other in a multi-touch dynamic geometric environment (DGE). In this paper, we present the design of the first game-activity and the relationship between it and the logic of inquiry. Then, adopting the theoretical framework of the instrumental genesis by Vérillon and Rabardel (EJPE 10: 77–101, 1995), we will present and analyse significant actions and dialogues developed by students while they are solving the game. We focus on the presence of a particular way of playing the game introduced by the students, the “reflected game”, and highlight its functions for the development of the task.
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Notes
The relationship which exists among: the distance between the centres of circles and the sum/difference between the radiuses; the length of a chord and the distance between the chord and the centre; the angle at the centre and the angles at the circumference which exist on the same arch; the tangent straight line to a circle and the radius which has its extreme in the tangent point; the perpendicular bisectors of a polygon and its inscribability.
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Soldano, C., Arzarello, F. Learning with touchscreen devices: game strategies to improve geometric thinking. Math Ed Res J 28, 9–30 (2016). https://doi.org/10.1007/s13394-015-0166-7
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DOI: https://doi.org/10.1007/s13394-015-0166-7