Designing a Mixed Reality Extension for an Educational Board Game on Fractions

Abstract

Fractions are one of the most complex and challenging notions for children and can often lead to frustration and a revulsion for mathematics in general. In this article, we present the Magic Cauldron, a Mixed Reality (MR) application, designed to help children apprehend fractions in a fun and interactive way. The proposed solution is a digital extension to a board game, called the Potion Workshop that is used to introduce fractions in more than 2000 schools in France. We put together a team, composed of the mathematics didacticians who designed the Potion Workshop, several teachers who use this game in their class, a multimedia designer and computer scientists, in order to create a MR game that would tackle several of the key notions that are still hard to grasp. In this article, we present the Design-Based method followed by this team. It offers insights on how to implicate non-computer scientists in the design of complex custom MR interactions. Through several cycles of collaborative design, involving three teachers and their students and the development of three prototypes, this method allowed us to produce a truly original MR application. 1. Fractions: a Complexe Concept to Master Math is an important discipline, right from the beginning of school. Studies show that succeeding in math usually implies success in reading and other disciplines (Siegler et al., 2012). Yet, many children in France dislike math and science in general (Perronnet, 2018). This aversion seems to appear, most often, in primary school, when fractions are introduced. Fractions are challenging mathematical concepts that are taught with many representations (Behr & Post, 1993). The ultimate objective is to understand the concept of fractions as rational numbers (p divided by q), that can be placed on a number line (Gunderson et al., 2019). However, this notion is too complex for children. Fractions are therefore usually presented, at the beginning, in terms of parts of an object (e.g. parts of pizza or cake). This simplified representation helps children grasp the concept but creates several didactic obstacles. Indeed, the representation of a fraction as a part of an object may lead to misunderstanding the fact that a fraction cannot greater than one. The fact that the objects are different can also lead to a misunderstanding of fraction equivalences. Indeed, a portion of pizza and a portion of cake do not feel the same, even if the pizza and the cake have the same weight. These notions are very complex for the large majority of children, who, at the end of the third cycle in France (CM1, CM2 and 6, from 9 to11 years old), still have not grasped the key notions of fractions. Children therefore need didactic tools that can help them understand the links between the various representations of fractions (Silver et al., 1983) to overcome these difficulties (Cramer et al., 2002). In addition, these didactic tools should be presented in a fun and empowering context, to motivate even the most reluctant children. In terms of motivation, the use of games seems to be a good solution. Teachers and game companies have created a large variety of math games, especially to learn multiplications and fractions, such as those found IJVR Volume 21 Issue 1