Dancing Euclidean Proofs

When the topic was introduced, I was quite skeptical of dancing math as an instructional tool. It is not a style of learning that I find personally useful, so I dismissed it as something I wouldn't want to try. But the article made me appreciate that, even if mathematical dance does not help build technical understanding, it bridges the gap between mathematical beauty and the physical beauty of movement and dance. Since conscious sensitivity to mathematical beauty is quite rare in high school students, being able to translate that beauty into a form that more students are familiar with could be very valuable.

It was striking how difficult it was to visualize the steps of the dance from the written description, even having seen the dances performed in the video. It reminded me of the difficulty in understanding a complex proof of abstract material: we have concepts that don't quite map naturally onto human language or human cognition, and so the process of understanding requires a sort of translation or visualization. For abstract concepts like this, and especially in teaching them, we need to reach for whatever representations or analogies make this translation the easiest - and for some, it may be embodied math.

The third thing that struck me was the connection between "local" in the mathematical sense, and "local" in the geographic sense. Since we live on a sphere, on a large-scale model spherical geometry is the accurate choice, but in our daily lives, we don't really live on sphere. We live locally, and locally the earth is flat. Euclidean geometry was developed first, and used for thousands of years, because we understand best the things that are close to us. I think it's quite beautiful that, mathematically, we need completely different paradigms for thinking globally and thinking locally, because the same is true for other concepts, such as sustainability. I think this would be a very interesting discussion to have with a class, making connections between math, geography, human communities, and the environment.