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A reflection on "Dancing Euclidean Proofs"


Both the video and the paper on "Dancing Euclidean Proofs" brought several interesting ideas to light. The notion of embodying mathematics is not one that I have encountered before, and it certainly provides new ways to engage with math. In particular, I found their discussion about the differences and similarities between constructing proofs with pencil and paper compared with using bodies. While I immediately recognized the imagination and simplification that is required when embodying the proofs, it was helpful to be shown how those same elements apply to a proof drawn on paper. The points we draw aren't infinitely small, the lines we draw don't extend infinitely, and the circles we draw definitely aren't perfect circles! In both cases of embodiment and 'empaperment' (is that a word?), we are simply representing abstract ideas in a concrete way. This limits how "exactly" we can show these abstract ideas, but both methods encapsulate the concepts.

Another point that stood out to me was the mention of how embodying the proofs embedded the ideas deeply in ones memories, more deeply, perhaps, than if one had simply drawn them out on paper or on a whiteboard. The need to memorize dance movements, coordinate with another person, and know the order of the steps of the proof arguably can lead to a deeper understanding of the proof itself. 

My own experience in class embodying of one of Euclid's proofs reinforced for me the ideas brought up in the video and the paper. By enacting the steps of the proofs, I feel as though I more fully understand and likely will longer remember the proof itself. This certainly could bring the idea of embodied math into the forefront of a discussion around how to support long term mathematical thinking in students. Internalizing and 'relevantizing' (is that a word?) math continues to be an issue at schools, and perhaps embodiment may be one way to solve these problems.

Comments

  1. Amanda FritzlanDecember 19, 2022 at 4:50 PM

    You've beautifully articulated the ways in which embodiment and empaperment are both performances and visual representations. Several people in this course have mentioned their immediate association with Euclidean proofs is lots of memorization. Embodied memory is still work, as you point out, but it sits with us in a different manner.

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