Directed & Spontaneous

May 2024

Our paper, "Designing for Embodied Sense-making of Mathematics: Perspectives on Directed and Spontaneous Bodily Actions", is part of the Designing Interactive Systems Conference (DIS’24).

The left picture shows an anonymized participant representing a slope in the air using both pointing fingers. On their side is a picture of a function's graph that they are describing. The right picture shows a woman manipulating a function's graph on a tablet using both pointing fingers on a specific point of the function to adjust its slope. In the middle, there is a system representation with several elements. Learner in a circle with bidirectional arrows towards a bodily actions box. This box has bidirectional arrows towards a Concept circle. The box also has a double arrow towards a learning box. The arrow from the learner to the bodily action contains the label Design for spontaneous bodily actions, and the arrow on the other direction contains the label Design for directed bodily actions.

Abstract

While mathematics is conventionally viewed as an abstract discipline, contemporary perspectives on embodied cognition underscore the significance of integrating students' bodily experiences into the learning process. However, the efficacy of embodied learning activities, as compared to traditional methods, remains under scrutiny. We argue that both directed and spontaneous bodily actions should be considered when designing embodied learning activities, and explore such bodily actions through two studies. A quantitative user study involving directed bodily actions in Virtual Reality and on tablet reveals VR's support for math-anxious and body-aware learners, and distinct movement patterns related to varying mathematical abilities. A subsequent qualitative analysis identifies key characteristics of spontaneous bodily actions, namely coarseness, muscle tension, repetitions, anchors, perspective, and metaphors. Derived from both studies, we propose design recommendations, advocating for expanded embodied interaction design, consideration of embodied metaphors, coarse gesturing for deep features identification, supporting of sense-making anchors, and in-VR learning assessments.

Design Recommendations

Expand embodied interaction design beyond position and movement as learners also leverage muscle tension to represent mathematical concepts.
Consider embodied metaphors and embodied concreteness as learners spontaneously integrate metaphorical gestures, and sometimes adopt a relatable first person perspective.
Allow for coarse gesturing as it supports identification of deep features and is a sign of mastery.
Support and evaluate sense-making anchors by carefully considering which interactive elements should be visible and which should be imagined.
Integrate embodied in-VR learning assessments as these support math anxious and highly body aware learners, and allow identification of preliminary learning.

Materials

The teaser video for the DIS paper is available online:

Team

Julia Chatain - Implementation of the prototype for the first study, analysis for both studies, paper writing, supervision
Dr. Venera Gashaj - Quantitative study, paper writing
Bibin Muttappillil - Qualitative study, paper writing
Prof. Dr. Robert W. Sumner - Computer Science supervision
Prof. Dr. Manu Kapur - Learning Sciences supervision

Acknowledgments

We would like to thank:

Keny Chatain, Dražen Popović and Hanna Poikonen for their great feedback throughout this project;
all the participants from our user studies, as well as their teachers;
Charlotte Müller, Vera Baumgartner, Dominic Weibel, Chen Yang, Corinne Meier, Nadja Beeler, Samuel Tobler and Alex von Bergen for their help in conducting the study and transcribing the results;
Tanmay Sinha and Christian Fässler for their help with the sequence analysis;
Andreas Fender for the help with the teaser image;
David Sturzenegger for his support during the writing;
the Future Learning Initiative of ETH Zurich for their support;
the reviewers for their insightful comments.

Publications

Chatain, Julia, Venera Gashaj, Bibin Muttappillil, Robert W. Sumner, Manu Kapur. "Designing for Embodied Sense-making of Mathematics: Perspectives on Directed and Spontaneous Bodily Actions". In DIS ’24: Designing Interactive Systems Conference. (2024). (link) (pdf)

Chatain, Julia, Venera Gashaj, Bibin Muttappillil, Robert W. Sumner, Manu Kapur. "How do learners move when grasping derivatives?". In EARLI SIG 6 & SIG 7 Conference. (2024).

Chatain, Julia, Bibin Muttappillil, Robert W. Sumner, Manu Kapur. "How do students move when making sense of derivatives?". In Symposium "Embodied Learning in Mathematics: Nurturing Cognitive Development through Motor Skills, Finger-Based Strategies, and Bodily Actions" at the Mathematical Cognition and Learning Society conference (MCLS). (2024).

Julia Chatain