Gestures, embodiment, and learning the rate of change

ABSTRACT

Many researchers have stressed the embodied nature of mathematical understanding. Here we explore how embodied knowledge may evolve as students learn a basic calculus concept: the rate of change. We examined undergraduate students with different levels of calculus knowledge working in pairs to model the rate of change in an everyday phenomenon. Our findings revealed substantial differences between advanced and introductory students in how they represented rate of change with their speech and gestures. In particular, the advanced students’ embodied representations showed alignment with the formal symbolic process of integration and reflected more advanced ways to coordinate the relation between multiple changing variables. For example, advanced students often made gestures that represented a “disk” when explaining how the rate at which water rose in a bottle was related to the change in height. Thus, both introductory and advanced students demonstrated embodied knowledge through speech and gestures, but the advanced students constructed different concrete representations that reflected an advancement in their embodied knowledge. Our findings are relevant to calculus education and to the study of gestures in mathematics learning.

KEYWORDS:

• Gesture
• calculus
• embodiment
• representation

Acknowledgments

This research was supported by the NSF-funded Spatial Intelligence and Learning Center, Award #SBE-1041707.

We would like to thank the undergraduate students and research assistants in our lab for helping with data analysis, providing feedback, and assisting with figure production.

Additional information

Notes on contributors

Yanning Yu

Yanning Yu is a Ph.D. candidate in the Learning Sciences in the School of Education and Social Policies at Northwestern University. Her research interests include spatial reasoning and mathematical thinking. She currently investigates how young children learn mathematics by playing board games and how students represent mathematical ideas through gestures. 

David H. Uttal

David H. Uttal is a Professor of Psychology and Education at Northwestern University. Along with teaching, he leads a research laboratory of undergraduate, graduate students, and post-docs. His current interests include maps, symbolic representation, informal learning, & spatial thinking in STEM education.