Week 8 Reenacting mathematical concepts found in large-scale dance performance can provide both material and method for ensemble learning-- Summary

This paper explores the intersection of dance and mathematics through the analysis of quartets engaging with video recordings of choreographed performances from the 2016 Rio Olympic Games. It aims to enhance ensemble learning by dissecting and reenacting performances to explore their mathematical potential.

In the introduction, the authors highlight the importance of reenactment as a method to supplement Interaction Analysis (IA) in understanding quartets' actions and exploring the potential of ensemble learning. They emphasize the creative re-use of public media for mathematical exploration and the hybridization of dance and mathematics in ensemble learning.

The methods section details the approach taken in the study. Quartets participated in 90-minute video-elicited interviews where they watched and discussed the Rio performance recordings, engaged in mathematical activities with a square sheet prop, and created their own performances. The interactions were captured using multiple cameras and screen capture software to analyze the quartets' work and interactions.

The results of the study show that quartets explored symmetries and transformations of quadrilaterals and triangles through their reenactments and creative activities. By engaging with the prop and the choreographed movements, participants were able to learn mathematical concepts embedded in the dance performance. 

Dissection and reenactment helped to provoke fundamental questions about knowing and interpreting mathematical figures. The participants at first encountered complexities in coordinating phrases, such as flipping a square like the Rio performers did. Through dissection and reenactment, they discovered new units for action and engaged in ensemble performances that transformed familiar mathematical objects in innovative ways. The hybrid space created by dissection and reenactment pushed the girls to invent new practices and negotiate shared approaches to interpreting and enacting mathematical concepts.

Props can act as partners in generating ensemble mathematical performances. The educators engaged in improvisational work, developing complex performance sequences that showcased the prop as a key participant in their collaborative exploration. Through collective experiences with dissection and creative play, the educators were able to leverage the prop to enhance their ensemble reasoning and generate innovative mathematical performances.

Reenactment can be a method to make discoveries and systematize ensemble performances mathematically. Through repeated enactments and collaborative analysis, the scientists discovered new facets of interaction with the prop, leading to a deeper understanding of the mathematical concepts involved. By engaging in ensemble reenactments, the group identified key elements that contributed to successful performances, allowing them to explain and replicate complex mathematical actions.

Furthermore, the study revealed the significance of ensemble learning in hybridizing dance and mathematics. Quartets' coordinated movements and interactions with the prop demonstrated a form of collective action that went beyond individual capabilities, emphasizing the importance of collaborative exploration in understanding mathematical concepts through embodied experiences.

Stops: 

"While beyond the scope of this paper, these exchanges of partner positions can be described from the perspective of academic mathematics as transpositions. Just as partner exchanges were basic phrase units for the quartets’ explorations in our interviews, transpositions are basic units for analyzing the structure of mathematical groups" (p.345)

I was astonished at the similarity between the strategy the girls adopted and the terminology used in abstract algebra. I think this is the power of reenactment, which allows people to reconstruct their perceptions of a design and generate new understandings through creation. I think there's also a lot of implicit and hard-to-characterize growth or new cognitive structures in the girls' reenactments. In addition to the videotaping perhaps the open-ended interviews will help us discover these interesting results.

Question: What do you think about the contribution of reenactment to the discovery of math in dance performance?