Using the PerFECt Framework to Invent Playful Learning Activities for Exploring the Binary System

Nektarios Moumoutzis, N. Rigas, C. Xanthaki, Yiannis Maragkoudakis, S. Christodoulakis, D. Paneva-Marinova, Lilia Pavlova
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Abstract

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.
使用完美的框架发明有趣的学习活动,探索二进制系统
本文介绍了一个学习社区建设框架,以及如何使用它来建立一个基于计算机硬件的数学基础,即二进制系统的学习社区。这项工作建立在先前针对数学游戏化的研究努力的基础上,并在数学剧场(TIM)方法论提供的新视角下被看到。结果是一个戏剧游戏和一个棋盘游戏的结合,向孩子们教授二进制系统。这两种游戏是密切相关的:戏剧游戏使用儿童的身体来制定棋盘游戏的机制,通过使用简单的规则来相互交流。遵循简单的规则,参与者体现了计算器的操作,能够将整数转换为二进制表示,并计算四种算术运算(加、减、乘、除)的结果。这个戏剧游戏的模拟器也提供了,这样学习者可以自己探索它,发现算术运算是如何完成的,即使他们不在同一个物理空间与他们的同龄人。棋盘游戏本质上是一个二进制版本的数数表或算盘。它为理解戏剧游戏规则的有效性提供了另一种机制,并使这些规则更具体,更容易被孩子们理解。通过这种方式,他们可以在个人的基础上探索四种算术运算的执行方式。与之前以游戏为基础的二进制教学相比,这两款游戏都提供了新的学习机会。调查的游戏主要集中在数字的二进制表示上,没有让学生积极探索二进制系统中的算术运算。这项工作的另一个重要方面是它不插电的性质,使学生能够将他们的身体投入到对数学思想的有趣探究中。所开发的知识可以转移到其他数字系统,特别是十进制系统,从而有助于更深入地理解数字表示和算术的机制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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