Grounding Abstract Mathematics through Embodied Interaction in Virtual Reality

Introduction

Mathematics is a useful skill to learn, even for students who do not wish to become mathematicians. One of the goals of mathematics is to gain understanding of the patterns of the world, in order to model and predict future outcomes. Recent years shed light on the importance of mathematics, for example to understand and take action during the COVID-19 pandemic or the general climate crisis. However, most students find mathematics useless and disconnected from the real world, and several countries are witnessing a worrisome decline in mathematics ability. This means, we argue, that we should challenge our assumptions about how to teach mathematics, specifically as the way we teach mathematics currently does not enable students to understand it well enough to transfer their skills to other classes, nor outside of the classroom setting.

Researchers and educators tackling this issue have argued that, although mathematics is often considered as a Platonic ideal that cannot directly be sensed or manipulated, mathematics rather is a social and malleable process that arises from our sensorimotor experiences of the world. For example, arithmetic can be seen as manipulation of object collections. Similarly, the concept of infinity can be related to our way of expressing something too large for our senses to perceive, while continuity may arise from sequences of elements too small for us to sense. Simply put, mathematics is embodied, and, although not all experts agree on the implications of this theory, there is undeniable evidence that our bodies play an important role in learning mathematics. As a consequence, when designing learning activities, we need to facilitate gesture production, and support sense-making of bodily actions.

Meanwhile, Virtual Reality (VR), a technology heavily focused on bodily movement and manipulations, became more affordable and widespread. Using a wireless Head-Mounted Displays, VR can immerse learners’ sensory channels into another world, digitally manufactured. Using hand-tracking technologies, VR seems particularly suitable to support embodied learning activities. With VR, we could create the MathLand imagined by Papert, a world of mathematics where learners can explore and manipulate mathematical objects. But is VR truly the solution to support the transition towards embodied learning of mathematics?