Developing Design Principles for an Augmented Paper-Based Mathematics Learning Environment from an Embodied Cognition Perspective: Focusing on the Exploration of the Volume of a Sphere

This study developed design principles for an augmented paper-based mathematics learning environment (APMLE) from an embodied cognition perspective and applied them to a lesson on exploring the volume of a sphere. The AR mathematics worksheet (ARMW), which overlays digital content onto static, physical paper-based worksheets, supports intuitive and immersive learning by integrating the advantages of paper media with handheld AR-based digital tools. This study investigates how such environments affect students' conceptual understanding in mathematics. Through a literature review, seven conceptual components were identified to form initial design principles. These principles were refined through expert validation and usability testing to ensure internal validity. The revised principles were then implemented in a classroom lesson and evaluated through retrospective analysis to examine their external validity. As a result, seven final design principles were developed: (1) the Principle of Mathematical Concept Orientation, (2) the Principle of Autonomy, (3) the Principle of Connection, (4) the Principle of Action Affordance, (5) the Principle of Perceptual Structure Formation, (6) the Principle of Reflection through Multiple Modalities and Formalization, and (7) the Principle of AR Tool Incorporation. In actual classroom settings, students engaged in embodied exploration by interacting with both the AR tool and the paper worksheet, using visual and verbal representations to construct mathematical meaning. The results demonstrate that APMLE can serve not only as a visual aid but also as a central medium for supporting embodied learning and conceptual development in mathematics. This study presents both theoretical and practical implications for the design and application of AR-based tools in educational contexts.