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

 “We tend to think more effectively with spatial imagery on a larger scale: it’s as if our brains take larger things more seriously and can devote more resources to them.”  William P. Thurston

“Mathematical thinking can be tied to symbols but it is not necessarily.” Erik Stern

    I have a fairly extensive dance background and I do love to dance even though I haven’t been lately (pandemic, bike crash, undiagnosed foot injury (hoping this will change on February 28)). I did ballet from when I was 4 until I was 17 and jazz dance as well for the last 3 years of my teenage dance life. About 6 years ago, one of my ballet school friends recruited me to do adult ballet with her and I did that for about 3 years with the odd drop-in class after that pre-pandemic. My enjoyment from dance comes from moving to music rather than being technically strong. What I am very good at though is remembering steps/choreography (show me once and I’ve got it) and my teenage dance teacher thought this was connected to my strong math skills; I think it is to my love for patterns. In the Dances with Math interviews, Schaffer talks about how mathematics and dance are connected and that “you can’t pull them apart.” I appreciate this idea because it makes a lot of sense in my soul – dance and math live together and thrive together.

(Sorry, the first paragraph is what I addressed in the Zoom meeting and all of my reading group was there! Hope it doesn’t seem repetitive!)

Dancing feet in the
parking garage

I drew on my dance experience and memories this week when I engaged with the Math in Your Feet task. I took the first lesson plan, Math in Your Feet Starter Kit, printed out the dance moves, and recruited my boyfriend to dance along side me. We went downstairs to the parking garage after trying the first one (4 jumps in place) and realized it was not going to be downstairs-neighbour-friendly. After 2 sequences my injured foot was talking to me and asking me not to jump, not even the tiny jumps I was doing. So, I had to adjust my engagement. However, I found that I could feel what the 4 beat sequences would be like if I had been jumping, even with the little bit of bounce I put in my body as I moved. I could imagine how my body would twist in the air to do a 180-degree turn, for example, even though all I did was bend my knees, stretched up and swiveled around, and bent my knees again. Is this an embodied memory? I connected this to the reading I did with the student’s who were blind and engaging with symmetry and how they drew on previous experiences (visual memories or physical memories) to perform a new task. In a comment on my week 3 reading summary, Susan notes that some of our students will have lots of embodied experiences to draw upon (from dance, sports, etc.) and others will not. How might I have experienced these dance sequences with a foot injury if I did not have a dance background?

    In my reading, Reenacting Mathematical Concepts Found in Large-scale Dance Performance can Provide Both Material and Method for Ensemble Learning (Vogelstein et al, 2019), I learned a definition of ensemble learning. As the authors define it, this is “learning that is fundamentally collective and performative, where learners recognize the need to act together” (p.332). This was a “stop” for me and I scribbled “orchestra and dragon boat” next to the authors’ example of marching bands. I taught orchestra grades 4-12 for five years and ensemble learning was integral to the experience. It was interesting to see the grade 4s develop from trying to be the first one finished a song to understanding it sounds much better if everyone finishes at the same time. I was recruited to help coach the high school dragon boat team because many of the team members were either orchestra students (and band students). One year at one of the regattas, one of our boats of all music students had a terrible first race. During the break between races, they got together to figure out how to make their strokes synchronize. One said, “Wait, you know how Ms. Fox and Mr. Reid (band teacher) say we need to sub-divide the beats in our heads to be more accurate? Let’s do that with our counting!” So they pulled together and practiced counting “1 and 2 and 3 and 4 and…” and did that in their next race – winning by more than a boat length! This understanding of dividing beats into smaller pieces, which is mathematical, contributed to the ensemble working and learning together to improve their performance. Again, these students had other experiences of ensemble learning to draw upon and was maybe enhanced by it being the same experience. Like I find dance and mathematics to be inseparable in how I understand choreography, I wonder if mathematics and ensemble learning weave together similarly so each helps the other.

    Vogelstein et al (2019) speak to how the props in the dance-based interviews connected participants so ensemble learning had to take place for both the dance and the mathematical thinking. They noted that the quartet of grade 8 students “acted and reasoned as an ensemble to resolve difficult challenges” but in another activity, the girls put down the prop and then “became disconnected and largely worked individually, talking over one another and using incompatible schemes of reasoning” (p. 338). The authors also note that a prop becomes a partner in the ensemble learning in generating mathematical performances. I connect the swords in the longsword dances to these ideas. The dances have the props/swords and by holding the swords, they are connected to one another in creating the mathematical formations. I can imagine that in practicing, they must come to jointly understand the mathematics of the patterns for the dance to work out and that they are connected in this ensemble learning through the swords. The swords are integral to the dances and are partners, just as the sheets of plastic were partners in the Rio Olympic inspired dances in the study.

    My final “stop” and connection for this week is about how movement/embodiment can assist understanding. Vogelstein et al (2019) had participants recreate dance sequences with a prop from a video as a way to understand the choreography and the mathematics that supports it. The authors found themselves getting up and re-enacting a movement that the STEM educators created but then could not recreate; the authors had to experience the movement to try to understand the experience of their participants. When I printed off the Math in Your Feet movement ‘instructions’/challenges, I was first looking at them and imagining what the four-beat sequences would be like. Then I found myself moving my hands, as ballet dancers do to ‘mark’ steps, to think more complicated ones through. Finally, I danced them out and they made the most sense, especially the ones involving 90-degree and 180-degree turns. However, this stop also had me wondering about students with physical disabilities in an inclusive classroom. If movement of the core/spine/etc. is important as a way of understanding, how do we provide access to embodiment with similar learning effects to children who are quadriplegic, for example?

Oh! My notes have me wanting to keep writing but hopefully I can weave in some more of my thoughts in discussion with others!  Lots to notice, wonder, and experience this week!

Questions to ponder

How do we address the variety of embodied experiences backgrounds our students have so the ones who have less experiences can be just as successful in connecting math and dance as students who have lots of experiences (with dance, sports, etc., even if they haven’t been explicitly connected to math)? (I am making a perhaps incorrect assumption that those with experiences say in dance might have an easier time with connecting with math in dance because they might not need to devote as many mental resources to engage with the dance elements.)

What mathematical ideas can be explored through ensemble learning with props? What are some extensions of this idea outside of mathematics to other curricular areas?

How can we provide inclusive embodiment experiences to our whole class so students with physical disabilities have the benefits of embodied learning/embodied ensemble learning?