Embodied Concreteness

Our paper, "Grounding Graph Theory in Embodied Concreteness with Virtual Reality", is part of TEI '23: Proceedings of the Seventeenth International Conference on Tangible, Embedded, and Embodied Interaction.

The figures contains three pictures, in doodle style. On the first figure, a character solves a graph theory problem on paper with an abstract representation. On the second figure, on tablet with an abstract representation. On the third figure, in Virtual Reality with a relatable and embodied representation. The graph is always the same and the character always interacts with the same edge.

Abstract

Abstract mathematics can be difficult to grasp, in part because it relies on symbols and formalisms that are powerful yet meaningless to novices unless grounded in concreteness. Although a wide corpus of research focuses on concreteness in mathematics education, the notion of concreteness can be apprehended in various ways and it is not yet clear which specific aspects of concreteness help the learners. In this paper, we explore embodiment as a form of concreteness to ground abstract mathematics. First, we designed and evaluated an embodied learning activity on graph theory. Through a user study with 89 participants, we then compared three approaches: abstraction, manipulated concreteness, and embodied concreteness. Our results show that, compared to abstraction, both forms of concreteness increase learners’ perceived attention, confidence, and satisfaction. However, only embodied concreteness increases perceived relevance and grounding. Moreover, unlike manipulated concreteness, embodied concreteness does not impair learning outcomes nor transfer abilities.

Video

User study

The figure contains 4 areas. The first area in the Week 1 and contains the demographics, body awareness, and math anxiety questionnaires and a duration of 10 minutes. The second area in week 2 and 3 contains a pre-assessment, the problem solving intervention on paper, tablet, or VR, a motivation questionnaire, a break, and a learning assessment and a total duration of about 70 minutes. The third area in week 4 contains the lecture and a duration of 30 minutes. The final column in weeks 4 and 5 contains a learning assessment and a duration of 1h.

Team

Acknowledgments

We would like to thank:

Chatain, Julia, Rudolf Varga, Violaine Fayolle, Manu Kapur, Robert W. Sumner. "Grounding Graph Theory in Embodied Concreteness with Virtual Reality". In TEI '23: Proceedings of the Seventeenth International Conference on Tangible, Embedded, and Embodied Interaction. (2023). (link) (pdf)