Week 6: Mathematically Curious Dancers
Or 'Dancingly Curious Mathematicians', I suppose. I believe this to be the common denominator of all the readings and viewings this week.
I was in charge of the Campbell & von Renesse (2019) paper describing the mathematical exploration of maypole patterns by non-math majors taking a course called "Mathematics for Liberal Arts" at Westfield State University. One student in this course--Juliana Campbell--reflects on the experience of grappling with the creation of mathematical conjectures, proofs, and representations of a problem she found personally meaningful: woven ribbon patterns resulting from maypole dances. I can personally attest (from the perspective of 9-year old me) that it is both satisfying and magical to see the woven results of variations on under-over movement patterns. Groups of students enrolled in Mathematics for Liberal Arts not only found the ribbon patterns magical, but also the mathematical representations and proofs they created to help them predict and explain which ribbon patterns were equivalent and which were not. Julianna Campbell discovered her mathematical identity through the experience--one of curiosity, perseverance, and inquiry. She felt she had never once connected with her mathematical strengths in her K-12 education. This inquiry-based college course was life-changing.
I must admit that it was hard to follow the mathematical reasoning documented in the paper, although I can imagine that it was exciting to be a part of it. I love that kind of stuff too. By that, I mean making connections and experiencing the thrill of insight. What I am unable to do is represent insights mathematically in such a way that I have proven anything. The course's professor, Christine von Renesse, provided the expertise to enable the students to do just that.
Similarly, my mathematical ideas are constrained by my limited math skills. I'll look at something and think, "Gosh...that seems really mathematical. I'm sure that there is something interesting going on there" but the only mathematical connections I can make are related to basic pattern, symmetry, or maybe measurement and proportions. Not much else. So sad!
The other readings and viewings--the clog dancing, the hand clapping, the geometrical re-enacting--they all were exploring a variation on the question: "Is there math in what I love to do?" Knowing that there is indeed math in what they love to do, they were able to experience such things as symmetry, pattern, properties of numbers, and combinatorics. Their mathematical knowledge helped them explore more deeply and profoundly. Their love and knowledge of dancing and music gave them a focus for curiosity and insight.
I have enough basic dance experience that I have had no trouble choreographing elementary school dance numbers: voyageur paddle dances, "dances with basketballs" competitions, expressive choir movements, jump rope routines. I also occasionally made connections to pattern and symmetry (for sure), but the mathematics was a distant second to the choreography and movement practice. Having kids choreograph their own dances was always a challenge. Some children have tremendous dance or gymnastics experience and want to engage in some pretty complicated movements: flips and spins, and fancy leg-lifts. Others have very little experience with dance or very poor attitudes towards it. I wish dance were a big part of our culture, but it is not. Many children have never seen or participated in dance with the important adults in their lives. No community dances. No rituals. Dance is for dancers, and many children are not 'dancers'.
That is why I chose to play around with the "math in your feet" idea. I love the idea of simple patterns within the constraint of a small square. This seems much more doable and safe for kids: dancers and non-dancers alike. I also like that the mathematical exploration extends to representing patterns that then can be read and shared by others. I wish I could have tested this out with a class of students and would have been totally game to give it a shot. Alas, my week was packed. So! Here I am this weekend taping a square onto my floor, trying to persuade my husband to join my in my exploration. For the record: he is a staunch 'non-dancer'. I don't know how I ended marrying such a creature, but there it is.
I decided that I wanted to create a template for representing a dance that used much less paper. This may be too small to read effectively, but it may still be handy: Create your own dance within a square. Note that I included extensions such as reflections and canons (this was inspired by the belcastro & Schaffer article).
Next, I drafted a simple dance sequence. Performing it would not have been an issue, but jumping is hard on a 48-year old woman with weak pelvic floor muscles. I decided to film only my husband following my dance representation.
Fortunately, my husband was a good sport. Here is a video of him and my dog, who was evidently disturbed by the exercise:
Over all, it was a success! I definitely think intermediate students could manage the creation and practice of a dance within a square. I also think that my blackline master was handy. Next up is to have me and my hubby dancing in unison (or I can just have a glass of wine and pat myself on the back for having completed my homework...)
Hello Jen,
ReplyDeleteI feel you when you talked about the mathematical ideas are constrained by limited math (or other) skills. I have a similar experience to yours when it comes to recognizing mathematics in ‘non-traditional’ ways. It could be my lack of imagination or experience, I noticed most dancing videos lead to similar math learning concepts that are restricted to the basics of knowledge and I struggle to connect deeper learning. This gets me to think maybe one of the purposes of dancing and body movements was to increase students’ engagement and encourage their interest in math learning. It was never meant to replace classroom teaching. By moving away from traditional ways of learning, students are encouraged to use their creativity to represent math and collaborate with others to explore the concepts. But to dig deeper into the math concepts, I wonder the 'teacher teaching' instructions will be needed for that to happen. What do you think? I could be wrong, but I don't know how to teach Pythagoras theorem, which is what we are learning right now, to my grade 8 with dancing or body movements.
I am amazed to know your ability to choreograph dances with math and thank you for sharing your dance sequence. It is lovely to have your husband help you with it, I hope your dance in unison is a romantic way to celebrate your hard work this week!
I do agree that teachers need a little (or a lot) of help if they are to support students in digging deeper into the math using embodied approaches. If we invest the needed time and energy into it, it can't simply be for student engagement. Students won't take us seriously if we only use dance for engagement and can't actually connect it to deeper learning. You now have me pondering possible embodied approaches to learn the Pythagorean theorem, though.
ReplyDeleteHi Jen and Stella,
ReplyDeleteI really enjoyed reading the post and your comments. I guess the interplay between math and dance can be seen better in some topics. The one that comes to my mind that works best is rhythm and LCM. While using dance to demonstrate some basic math concepts can be engaging, whether or not it will help with the actual ability to do the math has to be assessed. Here I am thinking of the Dancing Statistics videos which I referred to in my post. In one of the videos, the concept of frequency distributions is demonstrated through dance. That is great. But can we study objectively if students’ ability to solve a statistical problem will be improved if they begin with using dance instead of traditional approaches while sitting at their desks. Obviously, student engagement and lesson delivery are very important, but we shouldn’t lose sight of learning outcomes and attitudes toward learning math (Jen’s point that “Students won't take us seriously if we only use dance for engagement.”) I am interested to find out if an enjoyable first learning experience (like learning frequency distribution through dance) leads students to pursuing more advanced topics in statistics, which may require tedious math procedures.
Stella, perhaps Pythagorean Theorem is a good math concept to teach by dance – Not the part that involves calculating square or square root. I am thinking in terms of the concept that for a triangle to be a right triangle there is a specific relation between the measures of the three sides. Let’s say, if we have 12 students, we know 3-4-5 will form a right triangle. But, 1-4-7 will be an obtuse triangle. How do we make sure each student measures one unit? Maybe they can hold a meterstick in front of them. Or better, for safety reasons, some kind of soft spongy foam tube. This activity can also include the Triangle Inequality Theorem (The sum of the lengths of any two sides of a triangle is greater than the length of the third side). Maybe Jen can help with the choreography and you will come up with a fantastic activity for this math concept.
Soft spongy tubes a meter in length is a great idea. I like the idea of exploring the triangles that result from different combination of 3 sides equaling 12 meters. I think that the biggest initial hurdle in all of this is classroom culture. I honestly think the ideas will come if we ready our students for engaging properly.
DeleteJen, I enjoyed reading your exploratory storying, with words like satisfying, magical, woven results of variations, curiosity, perseverance, under-over, flips, success providing honest and humorous connections toward insight.
ReplyDeleteTogether with your post and Stella, Magnus, and Zaman's responses, I’m considering whether recognising limitations may be a vital part of the learning journey.
Your comment Jen, “knowing mathematics may be a little like knowing a musical instrument deeply” stopped me in wondering. Then, Einstein’s fluency … and I was reminded of Maria Agnesi, a character in ‘The Witches of Agnesi’ play written by Susan Gerofsky, Witches of Agnesi musical math history play (2019/2021). Maria Agnesi made wonderful contributions to the work of Albert Einstein and Susan's play gives voice to this.
I expect Maria Agnesi would have celebrated your choreographing dance within a square and your husband’s performance. Though, I’m not getting a clear answer as to how to dance with him! All I’m hearing is: “Cheers, here’s to enabling constraints!”
Thanks for this conversation! When reading, the writings of Bill Doll came to mind. I remember being in a classroom and feeling enchanted by his considering the conditions for Pythagorean Theorem to really come into play. As an artist I was surprised to learn that Pythagoreanism, the basis of much of Plato’s sense of number, brings one into contact with mystical numerology, which fascinated scholars in the Middle Ages and is active today with card players and gamblers:
ReplyDeletePragmatism, Post-modernism, and Complexity Theory – The “Fascinating Imaginative Realm of William E. Doll, Jr” edited by Donna Trueit, 2012.