Summary: Vogelstein, Brady, and Hall (2019) promote foraging in public media for performances with potential for exploring mathematics. This allows viewing mathematics within cultural contexts and opportunity to highlight the complexities of the work. They chose the opening ceremonies of the 2016 Rio Olympic Games to work with for their research. In this performance dancers worked in quartets, each holding a corner of a square piece of fabric (about 7’x7’) to create effects. The dance includes walking scale symmetries, rotations, reflections and translations. Here is a link if you would like to see, starting at 12:15.
In their study, authors invited learners in groups of 4 to dissect the performance by watching it together and analyzing the dancer's moves and resulting effects with the fabric. Then, learners reenact aspects of the performance, physically moving through different combinations to get the desired effects. Finally, learners create their own performance to culminate the activity. All the way through the process, learners are encouraged to describe their experiences mathematically.
The authors found that reenactment was pivotal to this process in two key ways. One, it developed understanding for what the performers did in the video in a way that just analysis when watching did not. Until learners tried certain moves, they could not be sure their analysis was correct. Second, reenactment also allowed learners to explore what could be done within the “people-plus-prop system” as there were physical limitations here that were not foreseen in the dissection stage. (p. 334) The authors also found the learning quartets had to undergo what they termed ensemble learning, needing to each move a corner of the sheet as an ensemble, or the movements could not be realized.
Stop 1: Foraging. I really like the idea of foraging media for mathematics connections. I think that this would be highly engaging for students, and agree with the authors that it could be a way to showcase cultures and complexities. Thinking of the current Olympic opening ceremonies, which I tried to stream part of in class, it could have been a great opportunity. Perhaps also the recent Superbowl halftime show which students chatted about the day after. Students could maybe even do their own foraging to bring in examples. It also makes the idea of bridging dance and math more do-able for me as a non-dancer. It feels OK to explore together with the students and not need to be an expert.
Stop 2: Reenacting as a way to strengthen understanding of processes and also of the limitations provided by reality constraints. One big question I had coming into this course was around re-creating. I wondered if there was as much learning value in re-creating as in creating something new or your own. During our week re-creating a Bridges piece, I answered this question for myself, noting that re-creation was valuable for me in that I had to slow down, think through and really understand the concepts to be able to attempt it myself. This article (and my activity experience this week) furthers my agreement and has expanded it to include the experience of limitations. I did experience the limitations of my person-plus-materials system during Bridges week, I just didn’t recognize it as such. Limitations are an important part of mathematics.
Stop 3: I love the idea of ensemble learning, specifically in comparison to group work. Ensemble learning is different from group work, because learners “need to act together.” (p. 332) In the case of this article, each quartet member needed to move a corner of the fabric. If one did not, the task could not be performed. This eliminates the group work scenario where someone can “participate” without really doing anything, or really understand what is going on. It builds in a whole new level of accountability. I am quite excited by this idea!
Question:
- How can we build in more ensemble learning in the classroom? Can we do it with a task that does not have a prop?
Reference:
IOC. (2016, August 5). Rio 2016 Opening Ceremony – Parade of Nations [Video]. YouTube. https://youtu.be/N_qXm9HY9Ro
Vogelstein, L., Brady, C., & Hall, R. (2019). Reenacting mathematical concepts found in large-scale dance performance can provide both material and method for ensemble learning. ZDM: The International Journal on Mathematics Education, 51(2), 331–346.
Nichola, this idea of ensemble learning is very interesting to me. From my understanding of your summary, it guarantees active participation from each party member or else the outcomes (visual or otherwise) can simply not be accomplished. In addition, the act of re-enacting will reveal limitations that would otherwise be hidden – this second part fascinates me because it essentially is the skill/technique involved in a magic trick, per se.
ReplyDeleteI can see what you mean about dance and ensemble learning going together. Without the body(bodies) physically present in the performing arts, the “scene”, snapshot or tableau is incomplete.
This is very interesting to think about: Other ways that we could do ensemble learning…
I imagine for elementary or middle grades, we would look at rational numbers by creating an L shape with our arms. All students L hands go into the centre, and R hands go onto the shoulder of a person in front of them. They could manipulate length of circumference R arms, number of students in circle.
I imagine it would be really cool to see marching bands on the field doing interesting shapes, then try to reenact the movement of the overall shapes. If students could figure out how to superimpose a Cartesian coordinate grid and provide instructions on movements, that would help to demonstrate their understanding. This could lead to linear equations.
I’ve noticed that something general when it comes to each of these reenactments is that it is geometry based. All shapes, and movement of those shapes. Maybe students can becoming sides and vertices of a geometric shape, and the investigation of sorting out what kind of shapes we can develop may be interesting. What 3D shape can we create with two students and all limbs connected to vertices (ie. No dangling or free-floating limbs)? What kind of symmetries would the shape have?
How about three students? Four? Is there a general rule?
That’s all for now, Thank you for the thoughts!
I love the idea of assembling learning. I learned about this in my undergrad. Instead of making a group and telling them to work together (this can be productive for some classes - perhaps those with more experience in group work), make small groups and assign tasks. Ex: Person 1 is the secretary (taking notes), person 2 is the calculator, person 3 and 4 are doing the activity. And then you rotate jobs for the next question. It is fun, and ensures that everyone is participating in some way for every part of the activity/project/experiment/etc.
ReplyDeleteIt's great to follow your train of thought here, Nichola. Very interesting line of thinking and experimenting with reenacting and re-creating, and with the exciting idea of ensemble work! And I like the idea of both teachers and students 'foraging' for interesting geometric movements, as in the Olympics ceremonies (note that Paralympics are coming up soon!) and the Super Bowl. Oliver's ideas about marching band patterns are also very intriguing.
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