Mixed Reality Can Reinvent How We Learn Math

by Angela Loh

The entire realm of mathematics is built upon imagination. From Euclid’s creation of geometry during Greco-Roman antiquity to Newton’s conjuration of calculus in the fifteenth century, mathematics continues to challenge the human race with its infinite mysteries. Unfortunately, despite the historical precedence of mathematics, many today view math as a subject inundated with stone-cold rules and untouchable manifestations of foreign taboos. People make the disheartening statement that math is just not their “thing.” They dislike math because there is apparently no room for differing opinions or individualistic thought. However, math completely debunks this widespread notion. The concepts of math are actually similar to the game of Jenga. As more ideas are aggregated to the list of preceding theories, the proofs of certain concepts begin to lose their stability, resulting in a growing number of exceptions. In The Joy of X, Steven Strogatz writes, “Math swaggers with an intimidating air of certainty. Like a Mafia capo, it comes across as decisive, unyielding, and strong. It’ll make you an argument you can’t refuse. But in private, math is occasionally insecure. It has doubts. It questions itself and isn’t always sure it’s right” (Strogatz, 236). Math is not the unforgiving subject many people think it is. As Strogatz has stated, the mathematical concepts that help us discover patterns within our chaotic universe  are fluid and malleable.

The discomfort math causes many people does not entirely stem from the subject itself, but rather from the imagination it requires. Mathematics involves a large amount of abstract information, and the main problem many students struggle with when it comes to understanding math is its “relevance” (Bujak). When students are taught math, they are simply shown a concept without any social or environmental context and are expected to automatically draw the connection between math and the real world themselves. Students continue to struggle with creating mental images within their heads and tend to fall back on the dangerous comfort of memorizing the process of doing specific math problems, rather than truly understanding the ideas behind them. However, due to the rapid advancements in technology, the possibility of integrating mixed reality into mathematical learning might just be the solution to the age-old problem of visualizing abstract concepts with which millions of students struggle . 

On the virtual spectrum of reality-transforming technologies, there exist two extremities: augmented reality and virtual reality. Augmented reality is a 3D technology that “enhances the user’s sensory perception” of reality by adding digital objects over a real-world view, while virtual reality completely immerses the users within the digital environment (Ibáñez, 109). Microsoft recently developed the concept of mixed reality (MR) in 2016, which encompasses the features of AR and VR, producing a “hybrid” environment that both “overlays” and “anchors virtual things in a real world” (Colagrossi). Although augmented and virtual reality may seem to be groundbreaking  advancements in technology, the latest invention of mixed reality is predicted to surpass the other two reality-shifting technologies with time. 

Envision this: students a in a science classroom are learning about the position of planets, and they are able to actually analyze the three-dimensional simulation of the solar system by only wearing a head mounted display. In another classroom,  students watching the atoms split as blood pulses through a simulated, multidimensional recreation of a human heart. Somewhere else, students create virtual pop-up storybooks and settings to the stories in a way that was not formerly possible (Kapp). Within the field of mathematics, it is often difficult to understand a concept without being able to see or imagine it. To alleviate this problem, the educational curriculum can use mixed reality as a stepping stone to bridge the students’ personal experiences with the mathematical concepts. Often times, students succumb to the belief that they are not “smart enough” to be good at math. According to Junior Achievement, a global non-profit youth organization, the number of teenage boys who want to pursue a STEM career in 2018 has dropped from “36 percent to 24 percent,” and the level of interest among teenage girls remains at the unchanged low rate of “11 percent year-over-year” (Kim). Looking on the more optimistic side, mixed reality will not only  provide students with the opportunity to understand the application of the mathematical concept within the real world, but it will also inspire students to use their imagination when it comes to learning math. Math was created on imagination, and even though studies have shown a dwindling amount of teenagers interested in pursuing math or other STEM careers in recent years, mixed reality has the potential to ignite students’ enthusiasm for math again.

Today, there are a growing number of companies and projects addressing how mixed reality can enhance the learning experience for many students. Mina Khan is the founder of Mathland, a project that seeks to translate the metaphysical realm of mathematics into real world applications through mixed reality. As I am personally interested in learning more about the role technology can play in mathematics, I interviewed Khan about her work. As a current research assistant at MIT, Khan believes that in order for people to enjoy and truly understand math, they must experience it through “play” (Khan). She explains how users can use this new technology to physically interact with the mathematical concepts and make their learning experience less about crunching numbers and more about fostering the logical structure of thought and theoretical connections the human brain can make. While using the Mathland application, the user or student wears a Microsoft Hololens headset and body trackers that trace the user’s movements, virtually displaying mathematical concepts in front of the user. The student is able to see the physical environment of the real world while also being able to interact with the virtual world’s graphs and equations, which is impossible for those who are not wearing the headset. With this technology, users can throw balls, visualize graphs, rotate objects, slide weights down ramps, and create art with geometry. 

Pearson Education, a  leading global education company, announced at the EDUCAUSE conference of higher education its official collaboration with Microsoft to explore “the power of mixed reality to solve real challenges” in the different fields of learning, ranging from “online tutoring and nursing education to engineering” (“Pearson”).  Mark Christian, the Global Director of Pearson Immersive, claims, “Until now, we have been teaching the same for the past 30 years.” Even though our world has “newer technology, the teaching process is the same.” Christian believes that Pearson’s collaboration with Microsoft to bring “holographic imagery and 3D modelling” together with the power of mixed reality will create a “new way to leverage the best of classroom teaching” (“Pearson”). 

Texas Tech University and San Diego State University are both part of the Pearson mixed reality program that aims to solve challenges in nursing education through mixed reality (“Pearson”). Similar to mathematical concepts, the scenarios that nurses face in the real world are difficult to control and replicate. The Microsoft HoloLens allows the faculty and students of the universities to participate in simulations to gain “real world experience” with diagnosing patients and building the “confidence and competence” for their future careers (“Pearson”). Even though Pearson has not announced any designs of the future mixed reality math curriculum, they are one of the world’s leading companies in applying modern technology to solve real world learning problems. This suggests that there is a rising push for today’s classroom to evolve from one that focuses on explanations and readings to one that encompasses a more interactive and visually based environment. 

With the technology optimists also come the wave of pragmatists—people who have raised genuine concerns about how mixed reality might be potentially harmful to the education sector.  Mounting unease has emerged in response to the way in which using mixed reality and wearing the headsets naturally assumes that the skills of the users, such as “attention and spatial cognition” are already “developed enough” for user interactions, which proves to be an issue with younger children (Bujak). Because many children continue to develop their “hand-eye coordination and fine motor skills” throughout their middle and late childhood, it will be more difficult for them to “intercept moving items with their hands” or “move in indirect motions” (Bujak). These specific physical limitations may influence the ability for the children using MR-based educational content, which places children who develop their coordination later than other children at a disadvantage. On the contrary, because this problem is more concerned with the development of younger children’s cognitive development, it will most likely not affect students of greater ages who have stabilized their states of coordination. 

Furthermore, as more mixed reality applications develop into tools that students can use to advance  their math education, the technology can also widen the achievement gap between families of different socioeconomic statuses. Over the past 20 years, numerous studies have shown that in the American education system, “inequality is winning” (Porter).  A 2018 report from the National Center for Education Statistics revealed that poor kids participate in fewer “educationally enriching” activities than middle class or wealthy kids. Poorer and less educated parents are not able to keep up with the wealthier families, who are spending large amounts to ensure that their children “end at the front of the rat race,” suggesting that integrating mixed reality into the educational curriculum will only widen the achievement gap between  rich and poor students (Porter). The New York Times reveals that on the very first day the children enter kindergarten, the children from families of low socioeconomic status are “already more than a year behind the children of college graduates in their grasp of math” (Porter). The current Microsoft HoloLens headset that projects or companies like Mathland and Pearson are testing their virtual simulations with is worth $3,000 for the “development edition” and $5,000 for the “commercial suite” (Microsoft). If mixed reality applications are integrated into the classroom, income inequality and the educational disparity between  will only continue to grow at a higher rate. Whether or not mixed reality will be integrated into the educational curriculum is still a work in progress and is only of speculation today. However, if mixed reality enters the educational market or classroom, the children of wealthier families who can afford this new technology will be able to foster their imagination and creativity with the mixed reality tools, while the students from lower socioeconomic families will be at an educational disadvantage. 

The biggest criticism toward mixed reality raises  the question, “Is this technology really worth it?” A simple Google search will deliver users a list of websites that have 3D models of mathematical concepts, making the use of mixed reality seem unnecessary and financial burdensome for many people. Lorraine Bardeen, general manager for Microsoft Windows and the HoloLens Experiences, makes the argument that learning through holographic computing in mixed reality provides students with experiences that “they can bring into their real-world interactions” (McNeill). The images of graphs or objects on a flat computer screen may finish the job of delivering what the mathematical expression may look like, but it does not have the enhancing hands-on experience that mixed reality encapsulates. Researchers have stated that “students remember concepts better” when they “physically interact” with them (Bujak). For example, with mixed reality, students can personally change a graph with their own hands, allowing them to develop a deeper sense of understanding of how stretching the graph will alter the original function. Subash Chandar K, a Microsoft Innovative Educator Expert, is exploring the possibilities of using the Microsoft HoloLens with his math students inside the classroom. After using the technology in class, one of his students claimed that using mixed reality and playing with virtual simulations helps students “rediscover the touch of ingenuity” that was lost through “the boring, old methods and disconnected learning environments” (McNeill). Another one of Subash’s students who played around with mixed reality expresses how the technology gives students “so much freedom to experience,” where the “only limits are [the students’ own] creativity and imagination.” He claims that  mixed reality is not “changing what [students’] learn, but how [they] learn it” (McNeill). This reveals how today’s generation of students learn through visual examples grounded in fun, gamified experiences, which encourage students to understand contextualized mathematical answers. There is a sense of freedom and possibility that surrounds mixed reality, allowing students to explore their own potential by breaking the boundaries of old-school learning and venturing into the realm of unprecedented innovations.In today’s society, there is a growing number of people who dislike learning mathematics, and the main problem the majority of our population faces when it comes to learning math is the way it is taught. We live in a society that often cherishes quantity over quality, leading to an educational curriculum that places too much emphasis on getting as much information into the students’ brains as possible within a short amount of time. The traditional lecture-based style rarely gives students opportunities to explore why or how some concepts work the way they do. Mixed reality is the catalyst that can push students who are initially unable to picture an abstract concept to the step where they can use their own critical thinking to navigate their way to the correct solution of a problem, because mixed reality visually projects the virtual simulation of the concepts in front of the students. When students are able to contextually see and physically interact with the virtual simulations of the math problem, they can think more critically and come up with solutions through creative ways that may deviate from the conventional way of solving problems. As mixed reality applications continue to develop, and companies or teams like Mathland and Pearson furthers the coalescence of reality-transforming technologies within the world of math, the possibility of a classroom that is built upon the principles of in-depth understanding, creativity, and critical thinking will become more predominant. Mixed reality will not only transform the way technology is fused into the classroom, but it will also revolutionize the entire structure and mission of the educational curriculum.  

Work Cited

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Ibáñez, María & Delgado-Kloos, Carlos. (2018). Augmented reality for STEM learning: A systematic review. Computers & Education. 123. 

Kapp, C & Balkun, M. (2011). Teaching on the virtuality continuum: Augmented reality in the classroom. Inclusive Scholarship Pedagogy. 22. 100-113.

Khan, Mina. Personal Interview. 20 Oct. 2018.

Kim, Stephanie. “New Research Shows Declining Interest in STEM.” Government Technology: 

State & Local Government News Articles, Emergency Management, 11 June 2018, www.govtech.com/education/k-12/New-Research-Shows-Declining-Interest-in-STEM.html.

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Porter, Eduardo. “A Simple Equation: More Education = More Income.” The New York Times, The New York Times, 11 Sept. 2014, www.nytimes.com.

Porter, Eduardo. “Education Gap Between Rich and Poor Is Growing Wider.” The New York Times, The New York Times, 23 September. 2015, www.nytimes.com.