Belcastro, S.-M., & Schaffer, K. (2011). Dancing mathematics and the mathematics of dance. Bridges: Mathematical Connections in Art, Music, and Science, 99–106.
In this article, Belcastro and Schaffer explore the connections between mathematics and dance by showing how dance movements can express mathematical ideas. Multiple aspects of dancing are analyzed mathematically, including symmetry, transformations, patterns, permutations, and spatial reasoning to explore the connections between dance and math.
STOP 1: “Karl often uses simple props as giant math manipulatives. He recently created Fragments, a dance involving. oversized tangram pieces that are a serious exploration of the fragmentation and destruction of war. He has explored polyhedral in dance using various props: PVC pipes, loops of string, and even fingers”.
One question I wondered about last week was how to engage students who are not good at dancing in “dancing activities”. I used my personal example: I’m not good at dancing or making body movements, so many mathematical dance activities are extremely hard for me to try. I asked in my last week’s post how we can adjust the activities to be accessible and inclusive to everyone. In this week’s article, I found this amazing idea that answered my question very well! Karl developed activities that can be done with various accessible materials, and even just fingers! Those are good starts for students to collaborate and be engaged in the activities without being left behind. I’d like to try one or two examples introduced here and see how it goes!
STOP 2: “This pattern can be demonstrated by having one person clap a five-beat. rhythm and another clap a seven-beat rhythm with the same tempo, and at the same time. Both people clap loud sounds on beat 1of each phrase. This is a way to create interesting syncopations in which the accented beats don't fall in the expected place.”
Connecting to the previous week’s reading on how the use of different senses can be applied to math learning, I remember we discussed that sound may be something hard to apply to math. However, here in the article offers a great example of math rhythm. The picture I attached is a record of one person clapping a third beat against another person clap eight-beat. At the 24th time, both of them are clapping together since 24 is the lowest common multiple of both numbers. Many students are confused about how to find the lowest common multiple of two numbers and why we need the lowest one. This would be a good activity for students to try so that they can clearly see the multiples between two numbers, and the first time both of them clap together is the lowest common multiple.
Questions:
1. Can dance also be connected with functions (i.e. linear, quadratic, etc.)? If so, do you have any creative ideas on that?
2. What challenges do you anticipate during the dancing activities?
Activity:
I chose to try the activity "Making Stars" by Scott Kim this week. In the video, three people altogether used both their hands and fingers to create a five-pointed star. I want to connect this idea with “symmetric dancing in front of a mirror” introduced by Belcastro & Schaffer (2011).
Thus, I tried to do a “solo finger geometry” by using the mirrors to create the symmetric parts from reflections.
TWO fingers in front of ONE mirror --- a two-pointed star.
TWO fingers in front of TWO mirrors --- a three-pointed star.
We can develop from this and let students observe what happened. By getting different numbers of mirrors, the reflections will be different, so there must be a pattern!
Ask students to take a guess: What will happen if I put two fingers in front of three mirrors? If I want a five-pointed star, how many mirrors do I need? Are you able to conclude any patterns?
1. Can dance also be connected with functions (i.e. linear, quadratic, etc.)? If so, do you have any creative ideas on that?
ReplyDeleteI do believe dance can be connected with linear and quadratic functions. For quadratic functions, because they are mirrored across the vertex, two students could work together to represent this. Whatever they represent would need to start slower and increase in frequency to demonstrate the shape.
For linear equations, any dance that has a recurring pattern or other ratio would work. Even the ones we watched last week where one arm does one number and the other arm does another could also be graphed as a linear equation. It works very nicely because the dancer is representing the slope.
2. What challenges do you anticipate during the dancing activities?
Since you have asked about linear and quadratic functions, this means the dances are being completed by teenagers and grade 9 in particular seems to be peak self-conscious age.
Sunny,
ReplyDeleteI really appreciated your focus on accessibility. I relate to your hesitation around dancing. I also have two left feet and very little natural rhythm. Full-body movement can feel intimidating, especially for students (and teachers!) who don’t see themselves as “dance people.”
I really like the idea of starting small, clapping patterns, finger movements, simple arm rotations, and gradually building toward larger movements if it feels comfortable. That feels much more inclusive and lowers the barrier to entry. It also mirrors good pedagogy in general: start with something manageable and build confidence.
In terms of challenges, I agree that participation could be a big one. I see it even with math songs that I have used in the past. Middle schoolers can be quick to scoff or opt out because it feels “uncool.” I sometimes get that reaction even with math videos like Math Antics. I do wonder if starting these embodied experiences in younger grades would normalize them so that by the time students reach middle school, movement-based math feels natural rather than awkward. I also always tell my classes that just because the song or video (or in this case, movement) doesn't work for them, it might for someone else and help them so they need to be respectful of others learning.
ReplyDeleteSunny,
I really appreciated how you revisited your accessibility question from last week. Your honesty about not feeling confident with dancing made your reflection even more meaningful and I completely relate. I’m not a dancer either and would find full-body choreography very challenging. That’s why I loved your insight that movement can start small fingers, props, mirrors. That shift makes embodied math feel inclusive rather than performative.
Your LCM rhythm example was such a clear connection. Feeling the beats align makes the “lowest” common multiple make sense in a way worksheets never quite do.
I also thought your mirror exploration was clever. Starting with curiosity “What happens if…?” invites real mathematical thinking before vocabulary shows up.
Your post made embodied math feel thoughtful and accessible, even for those of us who aren’t dancers.
The mirror finger stars are very interesting! You learn something about mirrors as well as about geometry. Cool idea!
ReplyDeleteAnd it's always good to start with something that you feel comfortable with. String, props, familiar motions and gestures are good starting points for sure. Once you and your students feel quite comfortable and can use this movement to explore mathematical ideas, you might try making the moves bigger -- for example, longer pieces of string, more participants, etc.