Examining new ways to help students more easily learn mathematics is nothing new for education researchers. The drive to innovate is constant and has been ongoing for decades.
One area of study that has garnered close attention in recent years, however, is the role our bodies — and particularly our hands — play in changing how students think about and understand math concepts. Research by UW–Madison’s Mitchell Nathan in this realm over the past five years has shown how gestures not only represent ideas but can actually influence mathematical reasoning.
This groundbreaking work has led to a collaborative new project between researchers and educators at UW–Madison and Southern Methodist University that will build upon this research and utilize augmented reality (AR) and virtual reality (VR) in an effort to help students improve their mathematical acumen through movement, spatial reasoning, and imaginative thinking.
This project, backed by nearly $1.4 million in support over the next four years from the U.S. Department of Education’s Institute of Education Sciences (IES), is called “Exploring Collaborative Embodiment for Learning (EXCEL): Understanding Geometry Through Multiple Modalities.”
“Embodied learning of mathematics is helpful for all students, but may be especially helpful for students who are English language learners and who may be struggling to communicate verbally to their classmates or teacher because they do not share a common language,” says Nathan, a Vilas Distinguished Achievement Professor of the learning sciences and a faculty member with the School of Education’s departments of Educational Psychology, and Curriculum and Instruction. “Embodied learning can also make mathematics more engaging and more fun.”
Candace Walkington, an associate professor with SMU’s Simmons School of Education and Human Development, is the principal investigator (PI) on the grant, while Nathan is the co-PI. The project involves partners from SMU’s Guildhall (a graduate-level video game development education program), Upward Bound SMU, the open-source mathematics software GeoGebra, and the Madison Metropolitan School District.
Previous research conducted by Nathan and his colleagues shows that math education depends on embodied learning, which occurs when the meaning of what is learned is grounded in body movement and perception.
“When students and teachers use their bodies to explore and express how they think mathematically, for example when they gesture, our research indicates that they demonstrate higher-quality thinking,” says Nathan. “Specifically, embodied learning encourages people to use action to simulate mental imagery that stimulates their ability to make logical inferences and form provable generalizations.”
The researchers explain that much of science, technology, engineering and mathematics (STEM) education depends on spatial skills and geometric reasoning.
“These skills matter anytime you make things,” says Nathan. “Today, for example, many scientists and technicians are exploring how to disrupt the pandemic by studying the geometry of viral transmission, designing materials for masks, figuring out how to optimally arrange students and workers, and examining ways to improving ventilation.”
The new EXCEL project is made possible, in part, due to the recent improvements in motion-capture technology for tracking body movement. These advances, notes Nathan, made it possible for the research team to design an entirely new class of learning experiences.
Previously, Nathan received funding in 2016 from IES to develop and test an embodied video game called “The Hidden Village.” This game allowed groups of students to explore high school level geometry by prompting students to move in mathematically relevant ways by interacting with characters in the game. “The Hidden Village” used the Microsoft Kinect sensory array to track players’ movements in real time and give them immediate feedback as to whether they are moving their bodies in ways that helped them understand the geometric relationships.
The new project is examining how augmented reality and virtual reality technologies can be designed effectively for collaborative learning, and how these designs can influence students’ cognition. Project EXCEL will utilize the Microsoft HoloLens 2, a head-mounted, mixed-reality headset that delivers rich holographic imagery right to students’ visual fields. It is a self-contained device that performs real-time hand and eye tracking without extra controllers. The unique technical advancement is that HoloLens users can be interacting with the same virtual objects using only their hands, even though they are in different locations. Being able to have this kind of interaction with remote collaborators has the potential to change the fundamental nature of shared virtual learning and teaching.
(To get a better sense of how students can utilize virtual reality to manipulate holograms and better learn about geometry, check out this video showcasing a project EXCEL prototype.)
“The use of AR/VR for geometry learning is new enough that it’s not clear what features, interactions, or kinds of activities are most powerful for learning,” says Walkington. “That’s what we want to try to figure out.”
The research team hypothesizes that different modalities for math learning — like a hologram, a set of physical manipulatives, a dynamic geometry system (DGS) on a tablet, or drawings on a piece of paper — have different affordances. To study this, researchers are developing an experimental platform modeled after the “Flatland” novella, written in 1884, that will facilitate data collection from students, situate experimental tasks in an engaging narrative story, and allow for the researcher to control key experimental variables.
“It’s important for students to be able to directly manipulate mathematical objects using their hands, allowing them to build a repertoire of gestures that they can use across contexts for geometric reasoning,” says Walkington. “These gestures can offer a whole new way for students to communicate and refine their thinking.”
There are two overarching research questions that will be explored via this work. How do different modalities for collaborative embodiment, particularly shared AR, impact student understanding of geometric principles? How are these effects mediated by students’ gestures, language, and actions, and moderated by student and task characteristics?
The EXCEL project’s research will work with high school students in Texas and Wisconsin, and at a university in Wisconsin.
Nathan notes that much of this research is early, basic science — but that this work offers tremendous potential to open doors to new areas of inquiry.
“This research can give us further insight into how people process spatial information and how we share embodied forms of thinking with others,” says Nathan.
This project is funded 100 percent through the Institute of Educational Sciences, U.S. Department of Education, in the amount of $1,398,245 (Grant R305A200401 to Southern Methodist University).