Comparing Inductive and Deductive Geometric Reasoning in Augmented Reality

This study compared how students engage in inductive and deductive geometric reasoning using augmented reality (AR) by analyzing their geometric thinking elements, gestures, and cognitive functions of actions while collaboratively producing geometric proofs. High school students (N=14; seven dyads) completed inductive (pyramid) and deductive (cylinder) tasks using AR. Students’ speech and actions were coded for geometric thinking elements (operational, logical, and generalizable), action types (pointing, depictive gestures), and cognitive functions (pragmatic, epistemic, complementary), then analyzed using Epistemic Network Analysis (ENA). Results revealed distinct reasoning patterns: inductive reasoning relied more on external resources through pragmatic actions and pointing gestures to generate insights and form logical and generalizable thought, while deductive reasoning involved complementary actions and dynamic depictive gestures that externalized mental processes to construct logical and operational thought. These findings illustrate how AR interactions differentially support inductive and deductive geometric reasoning, informing the design of AR-based learning experiences.