This project explores collaborative embodiment in the domain of geometric reasoning, leveraging Augmented Reality (AR) technology. AR is a technology that allows the layering of virtual components onto the physical world, such as projecting a three-dimensional hologram of a cylinder atop a real-world desk. Embodiment encompasses the idea that students can learn mathematics using physical motions, gestures, and their perceptions of objects and shapes. Theories of collaborative embodiment, i.e., theories that account for multiple people working together in an embodied way, are needed that take into account the multi-learner nature of mathematics classrooms, and how learners can jointly embody mathematical ideas using different tools and representations. 

Recent advances in multi-user instructional technology, namely shared holographic AR or shAR, allow for new and important hypotheses about collaborative embodiment to be tested. ShAR is AR technology where multiple learners can view and manipulate the same holograms together at the same time – in our case, holograms of different geometric shapes and solids. We hypothesize that different modalities for math learning (like a hologram, a set of physical manipulatives, a dynamic geometry system (DGS) on a tablet, or a piece of paper) have different affordances, including the degree to which they can represent dynamic transformations, can represent objects and operations in 3 dimensions, can support joint attention, and can provide situational feedback. 

This project is developing an experimental platform modeled after the Flatland novella, a piece of mathematical fiction from the 1800s about an imaginary world run by geometric shapes, to test our hypotheses. This platform will facilitate data collection from students, situate experimental tasks in an engaging narrative story, and allow for researchers to control key experimental variables. Our overarching research questions are: How do different modalities for collaborative embodiment, particularly shAR, impact student understanding of geometric principles? How are these effects mediated by gesture, language, and actions, and how are they moderated by student and task characteristics? This project is a collaboration between the Department of Teaching and Learning at SMU, the Guildhall at SMU, the Department of Educational Psychology at UW Madison, and a software company GeoGebra who will create the AR geometry environment.

QUESTIONS?

Contact excelprojectflatlandxr@gmail.com to get more information on the project.