Reading: Berezovski, Cheng & Damiano (2016). Spinning Arms in Motion: Exploring Mathematics within the Art of Figure Skating. Bridges Math and Art proceedings.
Summary
This reading is based on a workshop presented at the Bridges Finland Conference, where the authors explore the mathematics embedded in figure skating, specifically focusing on upright spins and arm movements. Using a bird’s-eye view, the authors introduce two mathematical models that represent the motion of skaters’ arms during spins, with the intention of connecting these movements to middle and secondary school mathematics topics. The workshop highlights how concepts such as proportional relationships, regression, circular geometry, and trigonometry can be explored through the analysis of spinning motion. Rather than presenting detailed results or student responses, the paper primarily serves as an invitation to view artistic and athletic movement as a rich site for mathematical inquiry and classroom activity design.
Stop 1:
“Some of the mathematical topics used in these activities include proportional relationships, regression, circular geometry, and trigonometry. “
What stood out to me here was how many mathematical ideas can be embedded in something as brief as a single spin that may only last a second or two. While it is not surprising that movement involves mathematics, I was still amazed by how much mathematical thinking could be unpacked from such a small, focused moment of motion. This made me reflect on how often these mathematical opportunities go unnoticed in everyday life, especially when we observe movement passively rather than analytically. It also reminded me that mathematics does not always have to come from long, structured problems and it is sometimes hidden in fleeting moments that we usually take for granted.
Stop 2:
“Contexts of interest to students include art and sports. Figure skating is a captivating art and fascinating sport. One of the most beautiful required elements in a singles figure skating program is a spin. Being able to perform a spin requires the simultaneous interaction of multiple body parts in order to execute each movement within the spin.”
I strongly agree with the idea that art and sports can be powerful contexts for engaging students, especially during moments of shared excitement such as worldwide events like the Olympics. These contexts feel meaningful and relevant, and they naturally invite curiosity. Although I am not personally a figure skating fan, I have watched competitions during the Winter Olympics and found the sport visually captivating. When watching skaters spin, I often find myself wondering about the mathematics behind their movements like the angles of takeoff, the direction and speed of rotation, and how subtle changes in body position affect balance and motion. This reading encouraged me to think more intentionally about those questions and about how much mathematical reasoning and embodied knowledge must be involved and supported by extensive practice and precision
Discussion questions:
What are some practical ways teachers could adapt activities like the figure skating models described in this article for students who may not have access to specialized sports or physical spaces?
How might embodied activities like analyzing motion through dance, sports, or everyday actions support students who struggle with more abstract representations of mathematics?
Activity
https://gallery.bridgesmathart.org/exhibitions/2016-bridges-conference/dsthompson01
For this week’s activity, I created a hand-drawn art replication inspired by David Thompson’s maze artworks based on the Traveling Salesperson Problem (TSP), originally presented at the Bridges 2016 Conference. Thompson’s original pieces were generated using digital tools such as StippleGen 2, MATLAB, and Microsoft PowerPoint, combining mathematical algorithms with artistic design.
In my own attempt at replication, I chose not to use any software and created the maze entirely by hand. I selected the letter S as the frame for my design, inspired simply by the cup sitting beside my computer. I began by outlining the letter shape and then gradually filled it with continuous, maze-like paths, treating the process as a form of structured doodling.
Although my hand became a bit sore during the process, I found the activity surprisingly calming and enjoyable. My attention was fully absorbed in tracing the paths and maintaining continuity, which allowed my mind to slow down and focus in a different way than it usually does during academic tasks. This experience made me appreciate how mathematical thinking can support artistic creation, even when the math itself is not explicitly visible. At the same time, this activity made me reflect on how deeply technology has transformed both art and mathematics. Tools like software and algorithms not only expand what artists can create but also make complex patterns more accessible, precise, and scalable. This activity reminded me that mathematics and technology work together as powerful creative tools to express ideas and make meaning through art.
“This made me reflect on how often these mathematical opportunities go unnoticed in everyday life, especially when we observe movement passively rather than analytically”. I like your thoughts about how often people can ignore math around them and may view it as something far away rather than something that’s around everyone. Helping students discover math around them is a great way to engage their interest in math. Math concepts from the class may be too abstract for kids to understand, and kids will easily get lost and distracted if they can’t see the purpose of learning. Thus, I agree with your idea of linking the math concepts with everyday actions so that students can learn from their daily lives and see the use of math in various settings. To answer this question, we can start from some little things, like: how far can you run, how high can you jump, etc. This lets students know that every time they are thinking about those questions, they are thinking about math. Without math, we can’t get an answer!
ReplyDeleteI love your “S” maze! The inspiration from cup design is a great example of finding something little from your everyday life and transferring it into mathematical art! Since you created the maze by hand, I’m wondering how you designed your paths inside the maze? Is there a specific choice you make on purpose? Or did you draw the path freely? I guess the computer design always has a purpose, but human-design sometimes can go without any reason ---- which would be something interesting to think about, especially since we are in the world of AI development. Can people tell the difference between a human-designed maze and computer designed maze?
Your first stop is a great observation! Kristie and I are working on mathematical lessons based on historical swordplay. Like you said, the movement may last for a fraction of a second, but the complex math behind it is profound. This brings me to the idea of the complexity of our body and coordinated systems; mathematics is built into our body even if we cannot go about explaining, quantifying or teaching these concepts to others. Our bodies know what to do! I feel like doing math with our bodies is like having a mathematical discourse with oneself; it’s a way to create realizations.
ReplyDeleteIn response to your first wonder, I don’t think we would need to go far beyond the daily capabilities of our bodies. The students can practice these jumping twists on the ground/grass with and without arm movements and check for achieved rotational angles, or spin on the balls of your feet like a pirouette in ballet. If twisting may be too unstable, students can try a squat jump with and without arms. It could be modeled in two dimensions as well.
I think providing students with these physical first-order experiences to make solid memories may really assist for referencing when teaching students the complex mathematics involved.
I also enjoy your S maze! From further away, the maze becomes a plant-like texture with almost uniform distribution of protrusions like coral. Lovely!
Thanks for the contemplations on mindfulness here, Sukie and group -- the mindfulness on focussing on one small moment of movement and noticing so much within it, and the mindfulness of drawing by hand, in a very human and quite relaxed way, in whatever time it takes. Our society tends to rush us through everything, and this slowing down of perception and action becomes a very important contrast.
ReplyDelete