Subject Area
Education
Abstract
This dissertation explores the integration of embodied extended reality technologies with mathematics education and problem-posing practices, particularly within the context of geometry. The research is driven by three primary questions: (1) How is student performance on assessing and advancing mathematical problems affected when engaging with geometric simulations in Augmented Reality (AR) versus Virtual Reality (VR)? (2) How is student performance on assessing and advancing mathematical problems affected after Problem-posing versus after Problem-solving? (3) How do students’ individual gestures, collaborative gestures, manipulations, perceptions of usability, and feelings of immersion compare when engaging with geometric simulations in AR versus VR?
The findings reveal that AR and VR are not interchangeable tools in mathematics education, each carrying distinct pedagogical affordances. AR uniquely supported higher-level geometric reasoning on advancing questions requiring abstraction and generalization, as well as individual and collaborative gestures associated with embodied sense-making. VR, by contrast, elicited more object manipulations and was perceived as more immersive and usable within a hand-tracking context. Problem-posing emerged as a more effective pre-activity than problem-solving for application-level geometric reasoning, suggesting its benefits extend into immersive technology contexts. Overall, this dissertation contributes to the understanding of how AR and VR can be purposefully integrated into geometry education, offering actionable guidance for educators, researchers, and developers of immersive learning experiences.
Degree Date
Spring 5-16-2026
Document Type
Dissertation
Degree Name
Ph.D.
Department
Teaching and Learning
Advisor
Candace Walkington
Second Advisor
Anthony Petrosino
Third Advisor
Kelsey Schenck
Fourth Advisor
Mina Johnson-Glenberg
Acknowledgements
Partially supported by the Moody School of Graduate and Advanced Studies at Southern Methodist University. The opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the funding organization.
Number of Pages
292
Format
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Recommended Citation
Washington, Julianna C., "Augmented Reality versus Virtual Reality Intervention With and Without Problem-Posing Effects on Mathematics Learning" (2026). Teaching and Learning Theses and Dissertations. 26.
https://scholar.smu.edu/simmons_dtl_etds/26
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