Reflections on 'Dancing Euclidean Proofs'
In the video, the dancer and mathematical choreographer, Samuel J. Milner, provides an insightful thought on why we want to embed aesthetics, especially artistic choreography, into mathematics: “When you see it on the page, it’s all there at once. But when you go through it mentally, you need to go through it step by step. So doing it as a dance, which takes time, somehow makes a little bit more mental sense… [1]” Back to the ancient time, the process of establishing the truth of a mathematical statement is torturous but exciting. Designing the dances to recreate and visualize those hot inventions is a valuable opportunity for our students to dissect the process of proofs step by step. Dances anthropomorphize mathematical ideas and make rigid proofs more vivid and memorable.
Moreover, the article written by Samuel J. Milner, Carolina Azul Duque and Suan Gerofsky also bring out an innovative platform on which we can meld land-based learning and decolonization with mathematics learning [2]. During my short practicum, I was always wondering what could be an optimal way to incorporate all of the first people’s principles of learning into mathematics. Now I am inspired by the idea of dancing Euclidean Proofs, and start thinking of how I can design a lesson which can be delivered on the land belonging to indigenous people and where teaching and learning experiences can take place outside of the confines of the classroom walls. It would be a great opportunity for both instructors and students to create their own dances and demonstrate mathematical ideas through their dances, meanwhile feeling the connection between the land and human beings, as learning ultimately supports the well-being of the self, the family, the community, the land, the spirits, and the ancestors.
My own experience of dancing Euclidean proofs in the class on Monday, November 7th reinforces my passion for taking students outside the classroom and teaching mathematics in dances. After witnessing a variety of performances that were done by my mathematics cohort classmates, I also realized that a mathematical idea can not only be represented by dances but also be rendered by singing or other types of artistic performances. Nevertheless, I have to admit that there will still be many constraints and challenges we might confront as a teacher if we want to incorporate artistic performance into mathematics. For example, dancing on a beach will only be feasible if the school is near the location; safety issues might also need to be considered. Moreover, time constraint is another factor that needs to be taken into account; it might be time consuming if we want to give students time to design their performance and rehearse plays, especially given that curriculum content has already been very compact.
[1] Susan Gerofsky. Dancing Euclidean Proofs. Video: https://vimeo.com/330107264
Moreover, the article written by Samuel J. Milner, Carolina Azul Duque and Suan Gerofsky also bring out an innovative platform on which we can meld land-based learning and decolonization with mathematics learning [2]. During my short practicum, I was always wondering what could be an optimal way to incorporate all of the first people’s principles of learning into mathematics. Now I am inspired by the idea of dancing Euclidean Proofs, and start thinking of how I can design a lesson which can be delivered on the land belonging to indigenous people and where teaching and learning experiences can take place outside of the confines of the classroom walls. It would be a great opportunity for both instructors and students to create their own dances and demonstrate mathematical ideas through their dances, meanwhile feeling the connection between the land and human beings, as learning ultimately supports the well-being of the self, the family, the community, the land, the spirits, and the ancestors.
My own experience of dancing Euclidean proofs in the class on Monday, November 7th reinforces my passion for taking students outside the classroom and teaching mathematics in dances. After witnessing a variety of performances that were done by my mathematics cohort classmates, I also realized that a mathematical idea can not only be represented by dances but also be rendered by singing or other types of artistic performances. Nevertheless, I have to admit that there will still be many constraints and challenges we might confront as a teacher if we want to incorporate artistic performance into mathematics. For example, dancing on a beach will only be feasible if the school is near the location; safety issues might also need to be considered. Moreover, time constraint is another factor that needs to be taken into account; it might be time consuming if we want to give students time to design their performance and rehearse plays, especially given that curriculum content has already been very compact.
You highlight some great points about dissecting the steps of a proof through dance. Taking dance outside with your class is a wonderful idea!
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