Summary: Berezovski, Cheng, and Damiano use the art and sport of a figure skating upright spin as a mathematical model for creating math tasks. Using the program, Geometer’s Sketchpad, the authors map the pattern of arm movements during a spin from a bird’s eye view. Two models are presented. Here is a snippet of the author’s Table 1, mapping the first aspect of a spin:
Model 1, designed for middle school, maps only forearm movement, and assumes a stationary upper arm. From this simplified model, math tasks have students calculating scale factors, collecting shoulder-to-hand distance data across varying elbow angles, and using scatterplots to determine a functional curve of best fit. Model 2, designed for secondary students, increases complexity by tracking both upper and lower arm segments in motion. Math tasks for this model include solving triangles at specific timestamps, analyzing the ratios of circular arcs, and investigating the symmetry and interior angles of the pentagon formed when the skater’s hands cross. Math tasks for both models require students to use the Geometer’s Sketchpad software.
Stop 1: The introduction to the article listed the criteria judges use to evaluate a spin in figure skating, and lists facts about fastest and longest spin from the Guiness Book of World Records. I think that this context could be quite engaging for students, especially if they were going to try some spins themselves (which they did not - more to come on that in later stops.) They could compare their time to the records, or look at aspects of the spin being judged and try to change their body to elicit more of those aspects.
Stop 2: This model/task was designed using Geometer’s Sketchpad software, and the software is meant to be used by students when they do the task (it is said that the map is dynamic, so maybe it moves?) Unfortunately, the links to the files for the task are no longer working, so I could not look at this aspect. Which may have hindered my understanding of the task, leading to my stop 3…
Stop 3: The math tasks used with this model are forms of measuring, calculating and graphing using the software. Students did not actually move their bodies. I chose this article because I thought that it would combine the art of sport with math, which I think would be engaging for many students. While I am taking away great aspects (modeling real-world scenarios) I am finding it lacking embodiment. Wouldn’t it be better for students to feel a spin? To move their arms at different angels to see what speeds them up or slows them down? It would be hard to measure this, but maybe filming and measuring angles or distances from their own body images could work? Many sports that students participate in involve mathematical structures such as angles, arcs, and symmetry. Opening up exploration of these aspects for students to experience these maths through their own bodies, and then use technology (video, still frames, measurement tools) to model and analyze what they felt might be more in line with what we are trying to accomplish with this course?
Questions:
- I have not used a software program in my math teaching like Geometer’s Sketchpad; the closest I have come is Desmos. Have you used a software successfully in a math context? I wonder if the addition of these technologies adds to, or takes away from, embodiment?
Hi Nichola,
ReplyDeleteI have not used software such as what is described here. I quite like this idea of students having an opportunity to experiment with their own bodies and see the results in some way. Given what they were measuring in this case, I also am struggling with how we could measure such things.
I have seen something similar to this done before where a teacher uses an office chair and alternates arm position to change the speed of the spin. This is a physics lesson looking at angular momentum. I think it could though be used to collect data that could be plotted in some way to be analyzed by a group of students.
I actually kind of like the idea of integrating the technological aspect of a software program with the embodied mathematics lesson (if we could find a way to make this more student centered instead of having them analyze the movements of someone else). I am becoming more and more open to fusing together pedagogies and opportunities for students. They are still experiencing the math, but then analyzing with a tool.
I cannot help but imagine how fun it would be to take a group to a skating rink and test this angular momentum out for themselves. Experiencing it.
Thanks for the thoughts this week Nichola.
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ReplyDeleteHi Nichola,
ReplyDeleteYour question about whether technology supports or limits embodiment is an important one; your response suggests that technology can be most powerful when it comes after movement, helping students make sense of what they have already experienced physically. I just love Amanda's idea of recreating the art on the ice. On the other hand, integrating the technology, to me, sounds very stressful with my limited technology knowledge.
Thanks Nichola, Amanda and Fiona! I agree -- this activity is so much more meaningful if the spinning is really experienced by students (on ice or on a rolling platform or chair). Interesting to hear your thoughts on Geogebra or Desmos (or the older Geometers' Sketchpad, Cabri , Cinderella, or other dynamic geometry programs). There is an element of movement in these, but it is several steps removed from the experiential movements of actually spinning on an ice rink!
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