# Virtual Reality in the Math Class: Moving from Abstract to Concrete

I have been thinking about Virtual Reality (VR) and how it could support math class. I think that we can help our students develop deeper conceptual understandings of math if we can provide opportunities to help students experience the math in multiple immersive ways. We know that students learn best when they can experience the solutions, versus merely given an algorithm or a rule.

What I also know is that Kyle Pearce has discussed the importance of concreteness fading in his blog, where he describes how students move from concrete to representational to abstract: https://tapintoteenminds.com/concreteness-fading/ – But as Kyle suggests, using manipulatives is still more abstract than what is actually being measured. This is where Virtual Reality can help. What if students had the opportunity to not merely use manipulatives to represent what is being measured, but could actually access and measure the actual object?

When students only have opportunities to memorizing the tricks, tips, algorithms, and rules only, they lack the depth of understanding of the mathematical concepts.

But if we are moving students to abstract thinking as shared in Kyle’s blog, we also have to acknowledge that if the goal is to help students transfer their knowledge abstractly to new math, this won’t necessarily mean that students will continue to be able to engage in adaptive reasoning, conceptual understandings, and further justify mathematically what is actually going on in new problems. Merely moving to the abstract is not sufficient enough. Staying abstract can and will likely greatly affect their ability to transfer knowledge to new mathematical problems.

Ruth Beatty addresses this very issue in here video, where she discusses the importance of not just moving from concrete materials to abstract, but also important to move from abstract to concrete:

Here, Ruth basically describes the importance of allowing students to construct their understanding of the world by actively constructing their own understandings of the math with multiple representations, with more interactions, connections and meaningful experiences.

I think that this is great support for why VR could work in the mathematics classroom. Students can use VR to NOT just replace concrete representations to manipulate, NOT just to build patterns, but to ALSO interact with a wider repertoire of experiences and representations.

Therefore, the concreteness comes from not just working with manipulatives, but from our multiple relationships and personal interactions with objects, patterns & ideas – so any concept can become concrete through the use of VR – to provide multiple models and ways to interact with the mathematical concepts.

If we construct our understanding with multiple experiences, the concepts can become concrete in the minds of our students. VR as a way to provide more experiences and representations, and ways to interact with to create lifelong and personal relationships with the concepts – not just with the mathematical terms and algorithms themselves. Therefore, we can have students move from abstract to concrete with VR.

Have you done this in your math class? If so, what did you learn?

Deborah McCallum

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