Virtual Reality and Augmented Reality in the Math Classroom.

 

Virtual Reality (VR) and Augmented Reality (AR) are powerful tools that can transform abstract mathematical concepts into immersive, interactive learning experiences. They bridge the gap between two-dimensional representations in textbooks and the three-dimensional world, helping students visualize and understand complex ideas in a way that traditional methods cannot. Virtual Reality creates a fully immersive, computer-generated environment that a user can explore. In the math classroom, VR can be   used to bring abstract concepts to life. 

VR can allow you to explore 3D Geometry.  Instead of looking at a flat image of a cube or a pyramid, students can step inside a virtual space and manipulate these shapes in three dimensions. They can walk around a geometric solid, see its different faces and vertices, and even "disassemble" it to understand how its volume and surface area are calculated. This hands-on, spatial understanding is crucial for students who struggle with visualization. Imagine a student being able to walk inside a virtual prism and see its base and height clearly, making the volume formula $V=\text{base}\times \text{height}$ intuitive.

It also allows you to walk through statistical graphs since VR allows students to "enter" a statistical graph. Instead of just seeing a bar chart or a scatter plot on a screen, they can walk down a data axis and see the height of each bar representing a data point. This can help them grasp concepts like data distribution, outliers, and trends in a tangible way. For example, a student could walk through a VR scatter plot to understand the relationship between two variables, or stand inside a histogram to see the frequency of different data ranges.

Augmented Reality overlays digital information onto the real world. Unlike VR, which requires a headset for full immersion, AR can be accessed through a smartphone or tablet, making it more accessible. AR brings concepts to life.  AR can overlay 3D models of geometric shapes onto a physical desk. A student can use their device to project a virtual cone onto their textbook and then rotate it, slice it, and see how its cross-sections change in real time. This allows them to see how abstract concepts like conic sections relate to a physical object

 AR can be used to create interactive puzzles and challenges. For example, a problem on a worksheet could have an AR component that, when scanned, projects a virtual equation or a geometric figure for the student to manipulate. They could physically move their device around to find the correct angle or solve for a variable, making problem-solving a more engaging and physical activity.

Both VR and AR offer a unique way to engage students, moving them from passive observers to active participants in their learning. By making abstract mathematical ideas tangible and explorable, these technologies can reduce math anxiety and help students build a deeper, more intuitive understanding of the subject. They turn the question "Why do I need to learn this?" into a quest for discovery.  Let me know what you think, I'd love to hear. 

VR And AR In Math

 Over the years, I've been following VR(virtual reality) and AR(augmented reality) especially as it applies to math because I love having an excuse to play with technology in order to figure out the best way to use it in the classroom.  Most of the apps that are classified as VR or AR generally deal with showing shapes in Geometry.  I did see one example where they had the busts of mathematicians. If you clicked on the bust, you'd bring up information on that person but I've not found a good use for it in math.  The only other ones were geared for elementary students, not for middle school or high school students so I decided it was time to revisit the topic to see if things have become more applicable. (All links go to the web page of the company so you can find more information.)

One of the biggest arguments for using VR in the math classroom is that this technology allows students to "see" math in a new way.  Virtual reality especially provides a new way of immersing students in their learning.  It helps students block out both auditory and visual distractions of their surroundings so they are able to focus more on the topic at hand. It can help them connect with the material in a new way, especially when the new material involved spatial relationships such as volume, surface area, edges, etc.

When students use virtual reality, it helps provides opportunities for students to improve their spatial awareness, while at the same time, it presents materials in a three dimensional form such as volume that makes it easier relate to and calculate.  They can rotate the object to see all three dimensions necessary to calculate volume.  Furthermore, the use of headsets to create the environment, means that students who have not developed their fine motor skills can still participate fully.

The University of Illinois at Urbana-Champaign has a wonderful list of programs and apps that can be used in the classroom.  They've reviewed a variety of programs, provide the location you can get the program, cost, and the date they looked at it.  I'll do a full column on why VR and AR are good in math but in the meantime, we'll look at a few apps and programs out there that can be used in class right now. They cover math from middle school into high school and even up into college.  

Geogebra does have a Geogebra AR app that can be downloaded and used in the class.  The directions to set it up and use it are quite clear and can be used on both apple and android operating systems. Furthermore, Geogebra has multiple AR activities available including domain restrictions, tornado inside a cone, and so much more.  

I'm starting with the ones you don't find in the App Store. Lets start with Calcflow that is designed to use with certain VR head sets and requires the use of a specific software program called Stream which is a desktop gaming platform.  You have to install Stream to use CalcFlow.  CalcFlow allows students to explore vectors using hands, learn more about vector addition and cross multiplication, check out certain types of graphs and so much more but it does appear it is only available for windows operating systems.

As far as apps go, there are several possibilities but not all are totally free.  For instance, there is a program called Math VR which goes with something called ACE-Learning systems. The app is free but to use the models, you have to have a subscription in Singapore dollars which is on their web page. They say they have an educational subscription but the cost is not listed. You have to contact them.   It covers topics such as simple and composite solids, volume, inequalities, graphs of trigonometric functions, trigonometric ratios and so much more.  They claim to have over 100 models available to use in class.  The app works on the iPad, iPhone or on an android operating system.

For Calculus, one can download CalcVR which stands for Calculus in Virtual Reality. The app can be found for both apple and android operating systems. This app works with google headsets or VR headset that is google headset compliant so you don't need to invest much to get started.  It works on a smartphone and is designed to have the person sit rather than move around. The nice thing about this site is that they include lessons to go with each topic and each lesson includes the objectives, pre-class activities, and uses Desmos lessons to help students learn the material better. I do not know what it costs but the app seems to cover so much material for Calc 1, 2, and 3.  Although it looks as if it is more for college, it could easily be used in a high school calc class and works for Analytical Geometry too.

Yes, most of these activities are designed for upper level students so on Wednesday, I'll be exploring VR and AR games and activities for middle school and high school students.  Let me know what you think I'd love to hear. Have a great day.