Doctoral Colloquium—A Comparison of Teachers and Students in Categorizing and Representing Geometric Conjectures Using AR Simulations
DOI:
https://doi.org/10.56198/3ad2ea07Keywords:
Extended Reality (XR), Progressive Formalization (PF), Geometric Reasoning, Categorization, Representation, Four Stages of Representation, GeoGebra MRAbstract
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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