How can VR bridge the gap between formal and informal mathematics learning?

3D thinking is crucial for understanding many mathematical concepts, as it involves visualising and manipulating objects in three-dimensional space. Research indicates that students with strong 3D thinking skills tend to perform better in mathematics. However, traditional teaching methods often rely on 2D representations, which may not fully develop spatial reasoning abilities. Virtual reality (VR) offers a promising solution by creating immersive environments where students can explore and interact with mathematical concepts in 3D. This makes abstract ideas more concrete, helping students understand relationships between mathematical elements. By providing insights into spatial relationships, VR can support deeper learning in mathematics.

Games and VR, in particular, have a huge potential to facilitate experiential learning in worlds that cannot be experienced otherwise. As experience and imagination are the major limiting factors of our thinking, using VR as an educational tool can help us to transcend our limits. Indeed, our experience and therefore our thinking is largely dominated by the classical Newtonian physics we experience in everyday life. To escape that many great thinkers and scientists of the past have been using mind simulations. The most prominent one being Einstein, for example, who came up with Special Relativity by imagining what it would be like to chase a light ray. VR allows us to do such "Gedankenexperiments" more easily and in a controlled way.

I'd personally like to see how each student can create their own virtual world using VR technologies. I think understanding the underlying concepts of, for example, geometry and trying to construct the mathematical world based on what is learned but with each personal perspective. This would be supervised with the teacher, but imagine, for example, that someone interested in medicine can generate a geometric image of the brain and understand how to change its shape based on function parameters. Or someone interested in managing a business can create, with the help of someone interested in architecture, an infrastructure with both employers managing the finances or flow of resources with applied mathematics.

VR’s contribution to learning mathematics is truly impressive! This technology makes math more engaging and enjoyable by connecting it to real-world scenarios. It also fosters creativity and allows students to express themselves in unique ways. It's a fantastic tool for boosting motivation and interest in the subject!

In my experience,VR platforms can adapt to individual learner preferences and abilities, providing personalized learning experiences tailored to each student's needs. They also offer opportunities for experiential learning, allowing learners to explore mathematical concepts through immersive experiences and hands-on activities.

VR indeed helps foster collaboration and game-based methodologies in fields such as probability when playing with dice that can be modified within seconds to study different scenarios. In my personal experience within an online school environment, it provides the opportunity to feel part of a nice community where our characters represent ourselves and we can interact with each other and the teacher without any limitation. It is as if we all share this attribute of learners, and you do not feel intimidated to ask questions to the teacher, but instead empowered. It creates a safe space for discussions, where we also learn to communicate our ideas and articulate them visually with tools such as virtual whiteboards or shapes.

Other challenge to discuss is how to make VR possible for students with visual impairments. My current understanding implies that VR technology employs the use of visual experiences to generate this virtual world that also uses indirectly the sound that is generated and the physical reactions based on the equipment used. However, what if we encounter some problem with vision? VR would have to evolve to not be dependent on visual education. I am open to read if this aspect is being addressed somehow.

Providing timely feedback within the VR environment is crucial because this actively results into reinforcing learning and also in line with this, there needs to be a very good balance between the use of VR with traditional instructional approaches since this will greatly help in the maintenance of a comprehensive and balanced learning environment.

A major challenge of experiential learning through games and VR, in particular, is to develop understanding based on the experience made. Based on my own teaching experience this amounts to explore the mathematics that is behind the VR experience and to link its visualisation to the VR experience made as clearly as possible. This link is crucial as, otherwise, the experience made will not facilitate learning and understanding of the subject effectively. Afterall, the VR experience is not everyday experience, so will not lead to any form of encoding of information in long term memory, unless experienced on a regular basis, which is unrealistic. However, connecting the experience with theory facilitates higher level encoding and thus learning

I would like to see VR versions of games/simulations that allow us to experience higher dimensional spaces or non-euclidean geometries. One example, for the former is the 4D puzzle game "Miegakure", and "Hyperbolica" for the latter. An example for teaching Special Relativity is a "Slower Speed of Light", which allows one to experience the effects of Lorentzian geometry when moving through space at speeds in the order of magnitude of light speed. I would love to see a VR game that allows one to experience the world of atoms and molecules based on Bohmian Mechanics. As teaching tools these would really help the learner to experience the realms that lie outside of what they (can) experience in everyday life, building intuition effectively.