Choreographing complexity: investigation of elementary preservice teachers’ quantitative manipulation in large group formations

Figures & data

Figure 1. Sequence of five preparatory activities with progressively more challenging mathematics.

Table 1. The Description of five preparatory activities.

Choreology Tasks	Learning objectives	Expected student actions
For a pair of dancers	Reflection and rotational symmetry	Execute duet dance based on reversed foot positions between the two dancers
For a group of four dancers	Addition and subtraction	Perform dance in opposite directions to represent the addition and subtraction process
For a group of six dancers	Multiplication and division	Manipulate number of dancers and movements of each dancer to represent multiplications
For a group of eight dancers	Concepts of variables	Perform dance with a number of dancers in specific regions on the stage as a way to represent constants and variables
For a group of 12 dancers	Concepts of functions	Change movement when dancers stand in certain regions on the stage to investigate concepts of function

Figure 2. Example of formation designs from one of the participants

Figure 3. Example of formation designs from another one of the participants.

Table 2. The definition of complexity in dance formation structures.

Foci	The Definition of Complexity in Dance Formation Structures	Counts (Rate)
On the Dancers	Boys and girls were not equally distributed/paired up	8 (12.9%)
	Boys and girls were mixed (beyond simple AB patterns)	30 (48.4%)
	Dancers spread out over the dance floor (less concentration)	11 (17.7%)
	Consists of more scattered groups/segments in formations	25 (40.3%)
	Dancers move in different directions and/or distances	10 (16.1%)
On the Shape	More diagonals were used	9 (14.5%)
	More curves/loop were used	12 (19.4%)
	Less reflectional symmetry was used	15 (24.2%)
	More rotational symmetry was used	6 (9.7%)
	More complex shapes were used	38 (61.3%)
	Shapes have more sides or overlap	8 (12.9%)
	More radial patterns were used	8 (12.9%)
	Figures with larger perimeters	5 (8.1%)
On the Equation	Smaller numbers were incorporated	12 (19.4%)
	More multiplication/division and less addition/subtraction	41 (61.1%)
	More odd numbers and less even numbers	20 (32.3%)
	Equations with more parenthesis (order of operations)	3 (4.8%)
	Equations with more than three components	14 (22.6%)

Table 3. Distribution of equations structures in simple and complex formations.

Equations Identified in Formation
	Simple Formations* (n = 372) Count (Percent)	Complex Formations* (n = 372) Count (Percent)
a+b+c	143 (38.4%)	2 (0.05%)
a×b×c or n(ab)	109 (29.3%)	27 (7.3%)
n(a+b)	75 (20.2%)	79 (21.2%)
n(a+b)+m(c+d)	32 (8.6%)	128 (34.4%)
n(a×b)+m(c×d)	13 (3.5%)	103 (27.7%)
n(a×b)+m(c+d)	0 (0%)	33 (9%)

Note: Simple formations refer to formations #1–6, and complex formations refer to formations #7–12 from each participant’s choreography design.