Doctoral Colloquium—A Comparison of Teachers and Students in Categorizing and Representing Geometric Conjectures Using AR Simulations

Authors

  • Chaeyeon Kim University of Wisconsin-Madison, Madison WI 53706
  • Michael I. Swart University of Wisconsin-Madison, Madison WI 53706
  • Joel P. Beier University of Wisconsin-Madison, Madison WI 53706
  • Fangli Xia University of Wisconsin-Madison, Madison WI 53706
  • Matthew M. Grondin University of Wisconsin-Madison, Madison WI 53706
  • Doy Kim University of Wisconsin-Madison, Madison WI 53706,
  • Mitchell J. Nathan University of Wisconsin-Madison, Madison WI 53706

DOI:

https://doi.org/10.56198/3ad2ea07

Keywords:

Extended Reality (XR), Progressive Formalization (PF), Geometric Reasoning, Categorization, Representation, Four Stages of Representation, GeoGebra MR

Abstract

This study investigates how an extended reality (XR)-based learning environment, GeoGebra MR, supports progressive formalization (PF) in geometric reasoning by comparing the reasoning processes of high school teachers and students. This doctoral colloquium paper explores how participants categorize and represent geometric conjectures through XR interaction. Findings reveal that teachers categorize conjectures by emphasizing underlying principles and concepts, effectively constructing and connecting scientific and algebraic representations with their sensorimotor experiences using GeoGebra MR’s interactive features. In contrast, students tend to categorize conjectures based on surface-level details, often remaining at literal and naïve representations or prematurely applying incorrect formal reasoning, struggling to integrate abstract concepts with hands-on experiences. These differences highlight the challenges students face in engaging with PF and underscore the need for scaffolding strategies, such as embedding explicit operational cues in the literal elements of problems and visualizing algebraic features in XR environments. The results provide evidence-based design insights for XR-based learning tools to better support learners’ progression from concrete experiences to formal representations, ultimately enhancing geometric reasoning and educational outcomes.

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Published

14-06-2025

How to Cite

Doctoral Colloquium—A Comparison of Teachers and Students in Categorizing and Representing Geometric Conjectures Using AR Simulations. (2025). Immersive Learning Research - Academic, 1(1), 168-175. https://doi.org/10.56198/3ad2ea07

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