Dancing Euclidean Proofs: Introducing Embodied Mathematics Into the Classroom

    The first think I noticed when watching the Dancing Euclidean Proofs video and reading the paper was my resistance to the arguments made therein. As I continued to read the paper, I also tried to consider where this resistance came from, and whether and to what extent it was warranted. 

    I think that part of my resistance comes from my long exposure to mathematics as it is currently done, and I think this impacted my reaction towards the video and article in two ways. First, culturally, I was very accustom to mathematics done the ‘traditional way’, with written or visual, but atemporal, representations. Because I am so accustom to the traditional way of understanding and of doing mathematics, I found myself resisting the idea that ‘dancing mathematics’ could be edifying, even in the face of evidence given in the paper that multi-sensory learning helps students to better internalize and understand mathematics. 

    The second way that my long exposure to mathematics coloured my initial opinion of embodied math is that, certainly relative to students, I have a lot of experience with math; I am very used to written mathematics, and to learning mathematics through papers and textbooks, and it has always worked well enough for me. As a result, I had a harder time seeing how embodying mathematics would be helpful to me personally. I had similar feelings when doing the activity in-class. Though it was an interesting change from the math learning I was used to, I don’t think I found it personally more enlightening.

    After having reflected, though, I think I can see clear value in having students engage in embodying mathematics. Essentially, I agree with what is said in the video and the paper about the learning value of having to choreograph and perform the proofs as dances. I think that it requires learners to spend a good deal more time carefully digesting the proof, deciding which steps are essential and why, why the steps must occur in a certain order, etc. Though dance is probably not the optimal vehicle for all, or even most, parts of the mathematics curriculum, incorporating multi-sensory, experiential ways for students to engage with the curriculum seems like and excellent way to enhance comprehension and retention of the material. 

    Finally, I think it was interesting that Samuel and Azul had to problem-solve how to actually embody the proofs using the spaces and material available to them. In generally, I think that one of the most important skills students should be learning in mathematics is how to problem-solve, and clearly a good deal of problem-solving was required on the part of the dancers in this project. Aside from having to figure out how to choreograph Euclid’s proofs, they also had to work with the constraints of their environment to produce their dance (using shells and sticks, drawing with their feet in the sand, etc.).  


Comments

  1. Amanda FritzlanDecember 19, 2022 at 2:39 PM

    I appreciate that you are noticing and writing about the tensions that you feel in relation to this piece. Enhancing comprehension is an interesting notion for mathematics. Deeply learning, through embodiment is different than most abstract written work, as you point out. Value for spending time with a mathematical concept is not usually found in schools which prize quantity and efficiency.

    ReplyDelete

Post a Comment

Popular posts from this blog

From the Eye of Horus to Grothendieck Primes: Math and Mythology

According to the Encyclopaedia Britannica, the Eye of Horus is a symbol of mythological significance, originating in a story in which the Egyptian gods Set and Horus clashed, and Set damaged or destroyed Horus’ eye. The eye was later restored by another of the gods (according to Wikipedia, most often Thoth, though the Encyclopaedia Britannica says Hathor); as a result, the Eye of Horus took on meanings of health and restoration. In fact, the association with health may have been so strong that the image has been passed down to the modern day: according to some sources, the ¼, 1/64, and 1/32 segments of the eye can still be seen today in the Rx symbol, used to denote a medicine prescription. Numerically, it is interesting to note that the fractions present in the eye represent the first six terms in the infinite series \sum 1/2^n. It doesn’t seem like a coincidence that this series sums to 1, given that the Eye of Horus symbolizes wholeness and restoration. This raises the question of w...
Read more

Reflection on Assignment 1

My biggest takeaway from last week’s presentations was the potential value of using historically-inspired geometry problems in a contemporary mathematics classroom. I want to start out this blog post with a quote by the Fields Medal-winning British-Lebanese mathematician Michael Atiyah. Speaking on the topic of contemporary algebra, he claimed that “ Algebra is the offer made by the devil to the mathematician. The devils says ‘I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine.’” While intentionally provocative, I think that Atiyah’s observation contains an important nugget of wisdom: modern algebra, while extremely powerful, is also very abstract and formulaic. I, for example, remember having to memorize the volumes of a number of 3-dimensional shapes, and besides rectangular prisms, these formulas often remained unmotivated and unexplained.  Looking specif...
Read more

What's in a Name: On the Acknowledgement of Non-European Mathematical Traditions in the Classroom

I want to state from the outset of this post that, by necessity, I come to this question from a position of relative blindness. While I can speculate all I want about the benefits of acknowledging non-European mathematicians and mathematics, I have neither the evidence base nor the lived experience that would be required to more strongly ground my musings. What I can speak to, however, is how I have benefitted from the heavy acknowledgement given to European and Western sources of mathematics. To start with, I have never felt culturally out-of-place is a mathematics classroom or venue; while certainly a large portion of this must have to do with the current demographics and culture of mathematics, I was also brought up (as were many if not all of my peers) with the idea that mathematics was mostly the product of white Europeans. Implicit in this view is that me, and people like me, were natural inheritors of our ancestors’ mathematical legacy. At an even more fundamental level, even wh...
Read more