Balance Board Math Project

Balance Board Math (BBM) aims to foster new forms of inclusive math pedagogy by incorporating learner’s experiences of balance. Learners rock on wooden balance boards to explore a range of mathematical concepts including functions, negative numbers and equations.

Design Team: Sofia Tancredi, Helen Li, Julia Wang, Carissa Yao, Kimiko Ryokai

Research Team: Genna Macfarlan, Yuqian Liu, Johnny Serrano, May Sar-Israel, Evelene Zhang, Katie Macfarlan, Melissa Rubusch

Research-Practice Partners: Elizabeth Dutton, Kiara Danavaro. Read about some of our work together in this research-practice brief.

Project Rationale

Some forms of movement, such as rocking, are common means of sensory self-regulation yet are discouraged in classroom contexts. This classroom conflict between self-regulation and student-regulation disproportionately affects sensory seekers: individuals who require high sensory stimulation through movement in order to regulate and attend. In parallel, recent developments in cognitive science suggest that moving in new ways forms the basis for conceptual learning (Varela et al., 1991), and the balance sensory system has been specifically implicated in cognitive development and conceptual reasoning (Antle et al., 2013; Hitier et al. 2014). As such, we seek to foster opportunities for the regulatory movement of rocking to serve as a resource for exploring mathematical concepts and representations.

Tancredi, S. (2024). Balance Board Math: Exploring the sense of balance as a basis for functions and graphing and number line concepts. Digital Experiences in Mathematics Education 10, 202–227. https://doi.org/10.1007/s40751-024-00140-1

Tancredi, S. & Abrahamson, D. (2024). Stimming as thinking: A critical reevaluation of self-stimulatory behavior as an epistemic resource for inclusive education. In B. de Koning, S. Sepp, & S. Zhang (Eds.), Human movement and learning [Special issue]. Educational Psychology Review 36, 75.https://doi.org/10.1007/s10648-024-09904-y

Balance Graphing

Screenshot of a display labeled "Frequency matching!". The display shows a black grid with a rainbow colored sinusoidal horizontal graph showing 10 peaks and valleys. At the top of the graph is written "Current frequency: 10 cycles/second, goal frequency: 5 cycles / second".

Two girls rock front-to-back seated on large rockable boards, looking up at two projected graphs they are making. The graphs are sinusoids of different frequencies and similar amplitudes and show green stars at peaks and troughs.

Balance Graphing cultivates embodied understandings of graphical representations and function equations. Learners generate dynamic graphical displays by rocking on the balance board, “being the graph,” not just “seeing the graph” (Gerofsky, 2011). Balance Graphing activities present discovery-based challenges where children discover and control critical function parameters such as the frequency and amplitude of sinusoidal graphs.

Tancredi, S., Wang, J. X., Li, H. L., Yao, C. J., Macfarlan, G. L., & Ryokai, K. (2022). Balance Board Math: “Being the graph” through the sense of balance for embodied self-regulation and learning. In M. Horn, M. Giannakos, & T. Pontual (Eds.), Proceedings of IDC ’22: Interaction Design and Children (Vol. “Full papers”, pp. 137–149). https://doi.org/10.1145/3501712.3529743

Tancredi, S., Li, H.L., Wang J.X., Liu, Y., & Serrano Rodriguez, J. S. (2023). Beyond ‘just sitting there’: Function addition through collaborative balance sensory activity with Balance Board Math.. American Education Research Association – AERA 2023. Chicago, IL.

Tancredi, S. & Serrano Rodriguez, J. (2025). Becoming the graph: Changes in children’s gestures following dynamic, whole-body graphing activities. American Education Research Association – AERA 2025.Denver, Colorado.

a child rocks front to back on a wooden balance board, generating a digital graphs on a screen in front of him. He is attempting to trace his graphing line over an existing graph on the screen.

a child rocks front to back on a wooden balance board, generating a digital graphs on a screen in front of him.

The Balance Number Line

The Balance Number Line introduces negative numbers and the additive inverse principle through balance experiences. Learners sit on a balance board and move their hands along a number line in front of them. The shifting weight of their hands controls the tilt of the board. In this context, negative numbers are the counterbalancing points to their positive counterparts. Learners solve movement problems such as figuring out how to move both hands while staying balance to plan, explore, and analyze relations on the number line.

A large flat-topped balance board with a carpet on top in front of a wooden number line with a magnetic surface.

Using this set-up, kids then create their own movement compositions, writing them with math arithmetic expressions, and get to “play” other kids’ mathematical moves.

A child's playful movement composition, titled

Balancing Equations

Learners reason about equations and inequalities challenges by using weighted unit and variable blocks to tilt the board they are sitting on.

Photograph of a balance board with wooden beams extending from each side. At the ends of the beams are plastic bins containing weighted wooden blocks. In front of the board, wooden numerals document the number and comparison of the amounts on either side of the bin: 3 > 1.

Open Access Code

All BBM code is open access. We invite you to use and remix this project. Get started with this tutorial written by Julia Wang.

Screenshot of the landing page for the BBM web version: 6 rectangles in rows of 3, each showing a symbolic representation of a BBM activity, such as graphs (multiple overlapping sinusoids; a graph with stars at apex points), rectangles of different colors, shapes, and a coordinate grid.

Recorded Presentations

Presentation at the Interaction Design and Children 2022 conference titled “Balance Board Math: “Being the graph” through the sense of balance for embodied self-regulation and learning”

This is an excerpt of a talk titled: “Getting up to SpEED: Special Education Embodied Design for sensorially equitable inclusion” given at Inclusion Week at University of Macerata, Italy on March 16, 2021 with Rachel Chen, Christina Krause, and Dr. Dor Abrahamson.

Other Related Publications

Zhang, F. & Tancredi, S. (2025). Predicting electrodermal activity from conceptual and physical activity in an embodied learning environment. Proceedings of the Cognitive Science Society 2025 (Cogsci 2025) (Vol. “Posters”). San Francisco, CA.

Sar-Israel, M., Zhang, F. E*, Liu, Y., & Tancredi, S. (2024). Tracking sensory regulation during embodied learning with electrodermal activity. Proceedings of the 18th International Conference of the Learning Sciences – ICLS 2024 (Vol. “Short papers”). International Society for the Learning Sciences (ISLS), Buffalo, NY.

Tancredi, S., Chen, R. S. Y., Krause, C., & Siu, Y.–T. (2022). The need for SpEED: Rationale and guiding principles for Special-Education Embodied Design. In S. Macrine & J. Fugate (Eds.), Movement matters: How embodied cognition informs teaching and learning. M.I.T. Press. https://doi.org/10.7551/mitpress/13593.003.0021

Tancredi, S., Wang, J., Helen Tong Li, Yao, C. J., Ryokai, K., & Abrahamson, D. (2022). Graphing with Balance Board Math: Critical embodied design for regulation and learning. In C. Chinn, E. Tan, C. Chan, & Y. Kali (Eds.), “International collaboration toward educational innovation for all: Overarching research, development, and practices”—Proceedings of the 16th annual meeting of the Learning Sciences (ICLS 2022), Hiroshima, Japan (online) (pp. 1181-1184). ISLS.

Tancredi, S., Chen, R. S. Y., Krause, C., Abrahamson, D., & Gomez Paloma, F. (2021). Getting up to SpEED: Special Education Embodied Design for sensorially equitable inclusion. Education Sciences and Society – Open Access, 12(1). https://doi.org/10.3280/ess1-2021oa11818