Unfolding Joy: Expressive Mathematics in Ensemble Performance

• In Event: 51.027 - Pedagogies of Joy :) Joy as Resistance at the Intersection of STEM Learning Pathways

Abstract

Introduction
Billions of people watched performers execute large-scale-choreographed routines with dynamic geometric forms during the 2016 Olympic Opening ceremony (Figure 4). Our research engages with this cultural form, under the premise that ensemble performances hold rich relations to mathematics (Hall et al., 2014; Ma, 2016). We aim to understand how participants from different backgrounds used their bodies and similar props to demonstrate their understandings of this performance. We examine the potential of choreographed ensemble performances as a context for expressive mathematical activity where joyous interactions become instrumental to investigations of symmetrical performances.

Framework
We draw on Jaber and Hammer’s epistemic affect and motivation framework (2016), in which emotional affect is shown to be instrumental to science learning. We also brings in Goodwin’s concept of affective stance (Goodwin, 2007), looking at how changes in affect allow for changes in participation structures through the physical reconfigurations of bodies in space. These two frameworks have enabled us to see how positive effects of joy through laughter have enabled certain participation structures, which in turn positioned ensembles to engage in expressive mathematical explorations.

Methods
We collected video data of four 90-minute interviews. The interviews involve showing and discussing the Olympic performance (Figure 1), asking participants to reenacted moments with a similar prop (7’ x 7’ Mylar square) and then creating their own performance with the Mylar. The participants included quartets of professional dancers and 8th-graders. Analyzing these recordings is done using interaction analysis (Jordan & Henderson, 1995), allowing us to focus on multimodal forms of interaction. We focus on two quartets: professional dancers iteratively folding the Mylar-square into a right-scalene-triangle, and 8th-graders choreographing their performance.

Analysis
For the dancers, laughter marked their professional practice in which mistakes are acceptable because there is an understanding that iteration over time is necessary in order to properly execute performances. Moments of laughter loosened the Mylar between them, which facilitated new ideas as they worked backwards from a proof of concept to a fully choreographed folding sequence.
The 8th-grade girls accompanied their choreography with a song, which made them laugh and also helped coordinate their movements. This playful environment also allows the girls to try out ideas while one girl leads the group (Figure 5). Their infectious laughter and joyful affect opened up a playful space in which they tried out multiple ideas in order to clarify shared understandings.

Discussion
In these cases the Mylar extends an invitation to play. Participants’ expressions of joy involved physically interacting with each other and the Mylar and enabled them to try new ideas multiple times and work collaboratively as they explored geometric properties of the square. For these participants, epistemic affect and motivation took physical form as they sang, spun, waved, and folded the Mylar together. At the intersection of ensemble mathematics learning and joyful expressions of laughter lies important learning pathways with the potential to broaden who and how people participate in mathematics.

Authors

• Lauren Vogelstein, Vanderbilt University

• Rogers P. Hall, Vanderbilt University

• Corey Brady, Vanderbilt University