Week 6 Reflection - Mathematics & dance, movement, drama and film

 “Meet mathematics in a different way” (von Renesse, 2019, p.133)

b) Julianna Campbell and Christine Von Renesse (2019) Learning to love math through explorations of maypole patterns

The most provocative and inspiring part of this article for me was the discussion around classroom pedagogy. The inquiry and problem based, constructivist pedagogy in the class, resulted in deep mathematical learning and experiences for the non-math major students taking the course. 

This article is about a mathematics exploration class for first year students with non-math majors. The students explored mathematics within the ribbon colours of maypole dances. The article explores “how seeing maypole dancing through a mathematical lens can excite liberal arts students to deeply explore mathematics” (Campbell & von Renesse, 2019, p. 131). The question the students chose to explore is, “how many non-equivalent ribbon patterns are there, given the number of dancers and the number of colours (of ribbons)?” (p. 132).  

Working together as a class, the students developed shared vocabulary, along with other advancements, allowing them to create representations of the mathematics (ribbon patterns) evident in maypole dancing. In this article, von Renesse and Campbell describe students evolving understanding as they develop these representations and capture mathematical ideas embodied in various iterations of the dance. Rather than inhibiting or limiting their mathematical thinking, the development of representations opened up new possibilities and ways of thinking for the students. An example is evident in this statement, “the students first invented the tree representation since it was the easiest to conceptually make sense of” (p. 136). The article goes on to explain several definitions developed by the students before stating the theorems and proofs the students created about various patterns created through different dances with different coloured ribbons.   

Here is a short 44 second video that shows one of the dances in action. Maypole dance in action

The problems encountered were tackled in community, ideas built upon ideas. For example, language used to explain the activity included, “the first mathematical problem the class encountered…” This shows the social nature and shared engagement with the mathematics, and the acceptance of problems as opportunities to be solved, not work to be overcome. The problems were the work. 

Although not all the examples we have seen in this course of embodied, arts-based, outdoor mathematics are from an Inquiry-based pedagogical stance, the pedagogy and the mathematical opportunities inherent in these embodied activities are complementary, bringing an alternate perspective to the industrial model of the past (hopeful thinking here!). Even the simple idea of mathematics as a social activity, rather than an individual, competitive discipline, is a divergence from the traditional, industrial model. When I think back to my own K-12 mathematics education, I cannot think of even one activity (besides playing games) that was done with others. This paper by Campbell and von Renesse, highlights the value of wrestling out the mathematics in community; relationships with content enhanced by relationships with people (and I would suggest we can expand on this by including relationships with land and the more-than-human world as well).

I felt so lucky this week to connect with the grade one class I had at the beginning of the year before starting my new position in the district. I used the lesson from Malke Rosenfeld’s website, Clap Hands: A Body-Rhythm Pattern Game. As students represented patterns with body movements, I could ‘see’ their brains working to remember and incorporate the movements. Those who understood the pattern, were sometimes searching their memory for the proper movement. Other students, simply participated in the movements, paying little attention to the correct order of the pattern. There was discussion in one of the groups of who should be the leader… navigating the social elements. One boy felt that he should be the “leader” because he knew the pattern and could help people stay on track. One boy yelled excitedly, “it’s like a chain reaction!” Each student was engaged in adding an element to the pattern, when it became their turn. Students were helping each other remember the moves. As a teacher, watching students participate in this activity gave me insight into their understanding of pattern, in a different way than a pencil and paper activity would. It was super valuable, although a bit tricky for me as I swooped in to do the activity and had only a short amount of time. 

At the end of the lesson, I asked students to tell me about their experience with the activity. The answers included, it’s in a circle (I asked groups to form a circle while doing the activity so they could go around the circle), "it started going faster", "it was going a pattern", "it was all going really silly", "you did different actions", "we were making up things that aren’t even real". I then asked the students what this activity had to do with math. Answers included "patterns with people and movements", "each time we added a movement", "there was one movement, then two then three… and math has something to do with numbers and patterns", "you could count how many times the person did it…" 

We did this activity on a Thursday afternoon before a 4 day long weekend, just before students were to go to centres. We could have spent much more time unpacking the activity, but centres was calling and so I dismissed students one at a time to go play and I asked them to give me a word to say about the activity that we did. The words (often students gave me phrases) included: "circle in math", "math comes in numbers", "actually a little fun", "I’d like to do it again", "very, very fun to do the activity", "I really, really like it", "a lot of fun", "we were going in a pattern", "like a circle for math", "everyone in the circle was different", "something was the same- the pattern", "everyone has a different movement", "chain reaction", "like exercise", "the same – we were all in the circle doing different actions", "a circle of people", "it was like going over and over again", "it’s a pattern". (I recorded this debriefing conversation and wish I could upload it for you to hear but I’m having trouble figuring out how to do that.) There was a lot of focus on the idea of the circle, which was interesting and something I would revisit if we were to do the activity again. How would it be different if we did the activity in a line instead of a circle etc? I saw this as a connection to something Dr. Gerofsky wrote in the introduction. “Mathematics deals in abstract forms that are not always easy to realize in the physical world.” These six year olds were working out the abstract movement patterns in the physical world with their bodies. A complex task, indeed, of representing mathematics in the real world.

I was reminded how differently lessons translate when working with actual students, as opposed to trying the lessons out with adults or simply reading about the ideas. I loved doing this activity and saw lots of potential for learning. If I was in the classroom full time, I definitely would have slowed it down, probably done the lesson over a few sessions etc. There was a lot of learning to draw out from this one simple activity, a myriad of potential mathematical concepts to explore.

What I loved is that, as the quote from von Renesse above stated, students were invited to "meet mathematics in a different way".

Here is a short little clip of one student during his turn playing the game. If you could see his eyes, his deep thinking would be even more evident! You can 'see' him thinking through the actions to determine what comes next, as he talks himself through the actions.

The course description (of the class in which the maypole dance exploration occurred), on which the article by Campbell and von Renesse is based, was described as a course "based around meta-goals and doesn't require specific content goals" (p. 132). My questions this week are revolving around these ideas. "How can we teach K-12 with this type of inquiry pedagogy while confidently covering the content of the curriculum?" "How can non-math teachers be supported to integrate content and embodied arts based mathematics, system wide?" "What is an effective way to support teachers on this learning journey?"

Julianna Campbell (one of the authors) was a student in the class. In talking about her mathematics experiences, Julianna said that, "K-12 education failed me" (p.134). She stated that math had "always been a source of struggle, insecurity and general annoyance for me" (p.133). She felt that during this time she was, "faking my way through math, neglecting my natural instincts toward curiosity and inquiry" (p.134). 

What can we do so that students no longer experience this "misperception of math" (p. 134) and instead encounter mathematics in school to be authentic, and a way to foster curiosity?