On Friday, April 19th, 2024, the TEIL Seminar Series wrapped up a successful year-long series with a talk presented by Candace Walkington, PhD. Her discussion delved into enhancing students’ mathematical reasoning with virtual and augmented reality technology.
Dr. Walkington received her PhD in mathematics education from the University of Texas at Austin. Before her post-graduate work, she earned a Bachelor of Sciences degree and a Master of Science degree in mathematics from Texas A&M University. At Southern Methodist University, she holds the titles of Professor, Annette and Harold Simmons Centennial Chair, and Gerald J. Ford Research Fellow in the Department of Teaching and Learning. In her research, Dr. Walkington seeks to increase mathematical understanding by leveraging augmented reality and virtual reality to make complex, abstract ideas feel tangible and approachable to her students. Her talk examines her investigation of physical movement and augmented and virtual reality as a means of teaching mathematics.
One key assumption underlies and drives Dr. Walkington’s work: how we perceive and understand mathematical problems reveals an embodied understanding. She defines embodied learning to be tied to the physical world, entangled with movement, action, and spatial awareness. If mathematics is an embodied science, she believes that we can harness this intuitive physical awareness and translate it to enhanced mathematical reasoning.
In contrast with a concept-based learning environment, which does not lend itself a physical approach to learning, Dr. Walkington explores how she can augment current methodologies to encourage an immersive, effective mathematical pedagogy. Students, she believes, have a natural inclination towards exploring the mathematical world through physical means.
In her discussion, she gives the example of two students, allowing the audience to watch them reason through mathematical conjectures with the use of complex gestures to enhance their understanding. The two, reasoning whether diagonals on a rectangle are always congruent, utilize physical movements to communicate the abstract concept to one another, visualizing their answer. Collaborating, largely without speech, the two students arrive at their conclusion, highlighting that physical gesture in the mathematic process serves as an intuitive language with which students can convey ideas.
According to Dr Walkington, embodied cognition employs three key elements: movement, the congruency of this movement to relevant ideas, and a perceived immersion in the simulated ideas. In the context of virtual and augmented reality, she is interested in gestures as well as epistemic or functional movements, which accomplish a goal-driven manipulation of physical or virtual objects.
She highlights that this movement-based processing is collaborative, fostering the dissemination of ideas through gesture-based communication to enhance group perception. By echoing, mirroring, and building upon the physical movements of one another, students strengthen their understanding of mathematical concepts.
In collaboration with the SMU Guildhall, Dr. Walkington has developed a virtual reality game centered on geometric problem-solving. The immersive simulation titled “The Hidden Village” encourages the use of physical motions to teach mathematical reasoning.
Expanding on this work, Dr. Walkington conducted a study in math tutoring. After reviewing currently available literature, research demonstrates that post-COVID online mathematical tutoring is significantly missing the mark, with many students falling behind. Dr. Walkington feels that the popular disembodied approach to math learning is a key shortcoming which may be stifling student success.
Dr. Walkington developed a virtual reality tutoring simulation investigating the embodied learning approach and its effects on math performance. Via a series of seven VR sessions of no more than an hour in length, Dr. Walkington measured the impact of embodied tutoring on academic performance in 38 middle-school-aged children. As compared to the control group, who participated in a non-math-based virtual reality program for the duration of the session length, math performance within the experimental group dramatically improved by approximately 0.79 standard deviations.
Additionally, Dr. Walkington’s lab conducted a second study using MathFinder, a mobile phone app designed to offer an immersive learning experience. The app, a research-practice partnership in collaboration with SMU Guildhall, talkSTEM, and local learning centers, allows students to find and learn from geographic features in their community. Users’ environments are overlayed with augmented reality mathematical prompts, teaching students how to apply math in everyday life.
In Dr. Walkington’s study, 44 middle-school-aged students were split into two groups; the experimental group used MathFinder, while the control group used the same app without augmented reality features. In a combined nine hours of sessions over three days, each student was tasked with developing a “math walk” at the local zoo, turning their surrounding environments into unique math problems they could then solve. Student feedback supported the use of augmented reality technology, with many participants expressing that they could understand mathematical concepts in new and immersive ways. Results demonstrate a significant decrease in math-related anxiety. Ultimately, participants were engaged and excited about learning math, with many utilizing gesture-based communication as well as recognizing mathematical problems in their physical environments.
To conclude her discussion, Dr. Walkington emphasizes that virtual and augmented reality can be leveraged to enhance mathematical pedagogy. The learning process, she believes, is embodied, harnessing physical motion to increase conceptual awareness. This embodiment should be both distributed, encouraging collaboration across the learning group, and situated, deriving meaning from the learner’s environment. By utilizing VR and AR systems to develop embodied, distributed, and situated math learning, she believes we can enhance student performance outcomes and encourage engaged learners.
Dr. Walkington’s presentation concluded the 2023-2024 TEIL Seminar Series. If you are interested in collaborating with peers in technology-enhanced learning, immersive learning, and AI/machine learning spaces, join us next year. Information on the 2024-2025 series will be posted at smu.edu/teil.