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Using the PerFECt framework to invent playful learning activities for exploring the binary system

Moumoutzis Nektarios, Rigas Apostolos-Nikolaos, Xanthaki Chara, Maragkoudakis Ioannis, Christodoulakis Stavros, Paneva-Marinova Desislava, Pavlova Lilia

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Περίληψη

This paper presents a learning community building framework and how it is being used to establish a learning community on the mathematical foundations of computer hardware, namely the binary system. The work builds on previous research efforts targeting gamification of mathematics and is seen under new light offered by the Theatre in Mathematics (TIM) Methodology. The result is a combination of a theatrical game and a board game to teach the binary system to children. The two games are closely related: The theatrical game uses the children's bodies to enact the mechanism of the board game by employing simple rules for interacting with each other. Following simple rules the participants embody the operation of a calculator that is able to transform integers into their binary representations and compute the result of the four arithmetic operations (addition, subtraction, multiplication and division). A simulator of the theatrical game is also offered so that learners can explore it for themselves and discover how the arithmetic operations are done, even when they are not in the same physical space with their peers. The board game is essentially a binary version of a counting table or abacus. It offers an alternative mechanism for understanding the validity of the rules of the theatrical game and makes these rules more concrete and accessible to the children. This way they can explore on an individual basis the way that the four arithmetic operations are performed. Both games offer new learning opportunities, when compared with previous work related to game-based teaching of the binary system. The games surveyed mainly focus on the binary representation of numbers without engaging students in active exploration of arithmetic operations in the binary system. Another important aspect of this work is its unplugged nature that enables students to engage their body in a playful inquiry of mathematical ideas. The knowledge developed can be transferred to other number systems and in particular to the decimal system, thus contributing to a deeper understanding of the mechanisms of number representations and arithmetic.

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