Summary This article explores how students can learn mathematics by physically reenacting a large dance performance from the 2016 Rio Olympic opening ceremony. In the study, groups of four participants watched a short video clip and then used a large square sheet to recreate the movements they saw. As they worked together, ideas like symmetry, reflection, rotation, and transformation naturally emerged through their coordinated actions. The authors argue that mathematics does not only happen in symbols or written work—it can also emerge through shared bodily movement and interaction with materials. They also suggest that reenacting the performance helped not only the learners but also the researchers better understand the mathematical ideas involved.
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One moment that made me pause was when a group of 8th grade girls argued about whether the shape they folded was a right triangle or an isosceles triangle. One student said, “In math, you don’t turn the math book,” meaning that in school, shapes are usually shown in one fixed position. But in this activity, they could walk around the large shape on the floor and see it from different angles. This made me think about how much school mathematics depends on having one “correct” viewpoint. When students move their bodies, the idea of a single correct perspective becomes less clear.
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Another powerful moment happened when a group of STEM teachers accidentally created a movement that resulted in a 180-degree rotation of the sheet. They described it as “cool,” but they could not explain how they did it. Later, the researchers realized that the group had physically performed a mathematical idea: combining two reflections creates a rotation. What stood out to me is that the mathematical idea appeared in their movement before they could explain it in words. This suggests that understanding can sometimes begin in action, not just in formal explanation.
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I was also struck by the idea that the large sheet itself played an active role. Sometimes it twisted or tangled and “refused” to move the way participants expected. This shows that materials are not just tools—they shape what is possible. The mathematics that emerged depended not only on people’s ideas but also on how the sheet behaved. Learning happened through the interaction between bodies and materials.
Discussion Questions
1. In school mathematics, we usually assess individual written explanations. How might ensemble, embodied learning challenge that norm, and what risks or tensions might it create?
2. If students physically demonstrate a mathematical idea (for example, enacting two reflections that create a rotation) but cannot yet explain it formally, should that count as evidence of understanding?
Hi Amy, thanks for your reflection and discussion questions! I think ensemble and embodied learning challenges the idea that students only deeply understand a concept if they can explain or prove those concepts on paper through equations or linear, step-wise processes. While this offers another opportunity for students to show and develop their understanding, there will always be a risk that some students in the group will not participate fully, leaving those that value and benefit from the activity at a potential disadvantage.
ReplyDeleteFor your second question, this is something I really struggle with because it is so different from my own educational experiences. I've internalized the idea that if students cannot explain what they are doing then they do not understand something fully - which is why I value open-ended or word problems so much in my classes. However, physically demonstrating the ideas are a means of explaining them without formal language, so I believe it depends on what exactly is being assessed. Written explanations can be useful for assessing a student's understanding of the vocabulary (which may be necessary for future mathematical endeavours), while embodied demonstrations can be useful for checking for conceptual understanding. Both assessments should be equally valued and be given their own time and emphases in the classroom.