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February 1, 2019
Vol. 76
No. 5

"I Can See It!": Math Understanding Through Virtual Reality

Letting students engage with materials in a virtual environment can enhance math learning.

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Technology, used effectively, can dramatically affect student learning. Yet many teachers and administrators have difficulties keeping up with the continually evolving field of educational technology and ways new technologies can be used, as we've seen in our roles as a teacher and a professor teaching pre-service teachers. So it's helpful to explore in detail how educators are successfully integrating cutting-edge technologies to improve students' learning experiences, specifically in mathematics classrooms.
Virtual reality is one technology some schools—including Gavin H. Cochran Elementary School in Louisville, Kentucky, where Shannon teaches—use to support student learning in various math topics. For many students who struggle with spatial imagination, for instance, immersion in virtual reality provides opportunities to improve their spatial abilities (Kaufmann, 2011). We describe here how teachers at Cochran use VR to help students meaningfully investigate volume and other math concepts.

Revolutionary Potential

Virtual reality has the potential to revolutionize education because it literally immerses students in their learning in a way other methods cannot. By blocking out visual and auditory distractions in the classroom, allowing a learner to focus intensely on a structured virtual learning experience, virtual reality programs can help students deeply connect with the material they're learning in a way that hasn't been possible before (Gadelha, 2018).
Schools can leverage children's enthusiasm for entertainment technology into enthusiasm for infotainment technology. But it's not enough to simply equip schools with computers and tablets; the content on those devices must be meaningful to learning.

A Case Study in Tapping VR's Power

Gavin H. Cochran Elementary School is a low-income, urban school. More than half of Cochran's student body identify as African American, and 90 percent of students receive free or reduced-price lunch. As a Signature Partnership school with the University of Louisville, the school receives a yearly grant through the Oxley Foundation to use for whatever the school and university think will best support the professional development of the educators involved. Cochran decided to use the funds to integrate technology into its curriculum, particularly using virtual reality focused on mathematics instruction.
Math had been identified as a priority area because students' overall scores in mathematics were significantly lower than those in reading. In 2014, to address this issue, Cochran piloted the use of virtual reality with some students in math classes. Since 2016, the school's 5th graders have used virtual reality in math classes; they now spend 40 minutes a week using virtual reality headsets known as head-mounted displays (HMD). 
HMDs cover the headset-wearer's eyes, blocking out the physical world from direct view so that the wearer sees and experiences whatever virtual environment is selected. This might be a totally computer-generated environment or one composed of photographs or videos of "real-life" scenes, allowing a user to be immersed in videos or pictures captured using 360-degree technology.
Users interact with this artificial environment through a virtual representation of a specific body part (such as a hand) and tracked movement. Tracked movement is made possible by placing a sensor on a certain body part and tracking that body part's movement via the HMD. When a person lifts their arm, for instance, their virtual body lifts its arm.
Teachers at Cochran have used these headsets to help 5th graders understand the concept of volume. Some studies have demonstrated that using virtual reality improves students' ability to understand abstract concepts by making those concepts more concrete (Passig, Eden, & Heled, 2007). Volume is one such concept. When these 5th graders don the HMD as part of the lesson, they see a computer-generated scene that includes grass, trees, 3D shapes of different colors and sizes sitting on the ground, and a table that appears to be floating and holds the same 3D shapes that are on the ground. Students can pick up, throw, stack, or rotate any of the objects in the scene.
The environment simulates real-world gravity; for instance, if a student drops a block, it will fall to the ground. Other features of the environment make things happen that wouldn't if a kid were stacking real blocks. When a learner picks up a block, for example, that block changes to a particular color to signify that it's being held by a student. When two blocks are put together, they change to the same color and the "lines" where they join disappear, giving a more concrete example of how multiple blocks combine to create one volume.
Students work in pairs. First one student, wearing the headset, links blocks to make different block combinations and calculates the total volume that would result from each combination. As that student combines blocks, he or she says something aloud like "one small block, adding one cubic meter to the overall volume, bringing the total volume to four cubic meters." Their partner writes down and tracks the totals along with the active student, then the partners switch roles.
Students often struggle with the concept of volume because it requires them to imagine a 3D object. When this 3D object is presented in a two-dimensional way, such as on a worksheet or paper test, the student might not mentally supply the missing information. The virtual reality experience creates the 3D object exactly how it is organically. The student can maneuver a block and, as in this activity, see all the different sides, combine blocks, and effectively feel the volume being calculated.
Cochran teachers found that working within the virtual reality headsets supported students' understanding of filling shapes with n cubic units to calculate each shape's volume. The concept of volume is directly related to how much space an object occupies, so a deep understanding of spatial relationships is required. Manipulating blocks in the virtual environment supported students' understanding partly because blocks could be manipulated in ways the "real" ones could not. For example, students could more easily combine a small box with a big box to create a nonstandard shape, and then find the volume of each section and combine the two to tabulate the total volume. This is a higher-order skill because it adds an extra step to the rote method for calculating total volume; students can't just use the formula length x width x height for the object as a whole. In addition, virtual reality fosters a higher level of immersion than standard practice, which may facilitate deeper learning as kids experience positive emotions like curiosity and fun.
Virtual blocks also require minimal fine motor skills. Students simply use the hand controller to "pick up" the virtual blocks and touch them to combine them. This was beneficial for special education students with limited fine motor skills.

Higher Math

Virtual reality has been shown to enhance math instruction and learning in several ways. Engaging with virtual reality technology helps improve spatial cognition, making it useful for spatial instructions (Merchant et al., 2012) and for learning about overlapping and nonoverlapping objects, a concept connected to the Common Core Standards.
Cochran also uses virtual reality to teach students skills of distance measuring, directionality, and map skills. The default way to teach distance has been with a flat map or a grid on which students count the blocks—but this doesn't truly represent the distance. A 2D map can be challenging to make sense of, since the idea that miles of distance can be represented by an inch on a map is a symbolic concept. Instead, students can enter a virtual environment and actually "travel" a longer distance, walking through the environment for miles, passing landmarks and changes in scenery, feeling how far the distance truly is (as they can't do inside a classroom, obviously).
Virtual reality displays, such as head-mounted displays, also give people "superior spatial awareness by leveraging our vestibular and proprioceptive senses" (Krokos, Plaisant, & Varshney, 2018, p. 2), as compared to traditional desktop computer displays.
The 5th graders at Cochran seemed to learn the concept of volume better when using virtual reality. While we didn't conduct an official study, we compared outcomes for Cochran 5th graders who did the activity described earlier using the headsets (12 students) with outcomes of students who did the same activity using traditional handheld blocks (13). Nine of the students who used the virtual reality program outscored all 13 of those who used traditional blocks on the volume lesson's post-assessment. Allowing these students access to 3D figures during the learning process supported them when they later had to take a test that referenced 2D figures. The sides of the figures not shown on their test were no longer a mystery as students calculated the volume of shapes.
Students find virtual reality learning environments intrinsically interesting and intuitive. When we talked with a Cochran student about his experience doing the "virtual" volume task, he stated, "It was way more fun than the blocks we normally use … the box wasn't really there, but I felt like I was holding it. So, I could move it around and fill it with stuff that helped me find the volume." Another student said, "In class, the teacher tells us to imagine what would happen if we fill up a box. But, using this [technology], I can really see it!" Students were so engaged in the activity that they did not want to stop. One noted, "I forgot I was doing school work."

Supporting Teachers

Using virtual environments creates new and exciting experiences for students, but also constitutes new challenges for teachers. Teachers' personal willingness to adopt and integrate innovations into their classroom practice is crucial for any classroom tech initiative to succeed (Gess-Newsome et al., 2003). Cochran teachers showed that willingness, and they've seen firsthand the effects virtual learning tasks have on their students. As they listen to what students liked about the virtual tasks, teachers sensed excitement from these learners—when there previously was none. This has inspired many teachers to continue to use this new technology. One teacher stated:
I tried every single trick in my wheelhouse and could not get this one student to say a single positive thing about mathematics. After 20 minutes in virtual reality, she is asking for math practice. … I am a believer.
School leaders can take a few simple steps to support teachers who want to implement virtual reality technology to deepen learning. They should review the research carefully, investigating what products are available. Let teachers know that if they encounter any challenges while attempting to integrate a program, they should simply reach out for support: The virtual reality community offers countless free forums where people can connect with users, from novices to experts.
Helping teachers experiment with virtual reality shouldn't be too difficult. Virtual reality and the technical knowledge required to use it has become vastly simpler just over the last year. For instance, the Oculus Go standalone headset doesn't require a computer or even a phone to run, only an internet connection and a bit of open space for students to walk around.  There are no wires, so the students are free to move about and truly immerse themselves in their virtual world. A school can introduce its students to this technology in a matter of days.

Reaching Struggling Students

Virtual learning tasks give teachers an innovative way to present information to their students. Particularly in math, the technology allows educators to teach concepts in ways that are accessible and exciting, even to students who previously struggled. And increasing motivation is key: Students' motivation in math correlates strongly with math achievement, starting in the elementary grades (Middleton & Spanias, 1999). Cochran Elementary School created authentic learning experiences involving virtual reality that students want to participate in, shaping these urban students' positive attitudes toward math.

Lateefah Id-Deen has contributed to Educational Leadership.

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