Improvisational Thinking in the Classroom: A Dance with Mathematics
In experiential learning, the ability to improvise is as vital as structured lesson plans. This essay recounts an unexpected math lesson during a Dance and Movement Experience Studio class, modeling improvisation during facilitation of an experience.
During the fifth week of this seven-week course, students were tasked with prototyping their own movement activities, ranging from Rhythmic Gymnastics (Figure 1) to Physical Comedy Improv to inventing New Games (Figure 2). Each student led a movement activity and participated as peers in others, providing feedback.
Unlike typical presentations, their prototypes required research, planning, and a new skill for many: improvisation while facilitating others in an experience. While our course gives students practice with a framework for awareness, reflection, and creation of several aspects of experiences, I noticed that we were less explicit in developing the art of improvisational adaptations.
During one session, I was struck by the combinatorial math involved in grouping students for their activities. Energized by this realization, I decided to share my thoughts on the fly. We needed to ensure each of our six students led one activity, participated in two others, and experienced fresh group dynamics each round without repeating any group compositions.
Using a whiteboard, I intuitively assigned students to groups for three rounds. As I moved between classroom and outdoor locations, I pondered: Were these the only possible group combinations? Could combinatorial mathematics provide an answer?
I posed the problem: “How many combinations of three can be chosen from six?” The formula from my high school and college days was simple:
Where n is 6, k is 3, and the notation n! means n(n-1)(n-2)…1.
This suggests 20 possible combinations, but since two groups are chosen simultaneously, only 10 distinct pairs of groups are possible.
Surprised by the richness of this simple task, I was compelled to share this insight. Without planning, I gathered the students and explained the math behind our grouping, highlighting that this was not part of the day’s planned content but an improvisation prompted by my reflections.
This impromptu lesson turned into a lively discussion. Students eagerly shared their familiarity or new understanding of factorial notation. Some expressed surprise at seeing math they recognized from previous curriculum come alive in a real-world scenario in which we were participating together. Several took the opportunity to discuss differences between high school math subjects experienced by our highly diverse international community.
Through this experience, I shared with the students not only a mathematical concept but also the essence of improvisational teaching: enjoying the process, being transparent about the improvisation, and adapting well-constructed plans to spontaneous directions. My hope is that this offered a lively glimpse into the experiential journey of creating a learning environment, offering a meta-level understanding of teaching as a responsive and creative act.
For me as an educator, this improvisational moment remains, months later, an object to think with. It brings up questions I have yet to answer: In what ways are students and teachers aware of the relevance and importance of improvisation outside performing arts? What frameworks are available, or might we construct, for its value in experience facilitation, in teaching, and in everyday problem-solving?
As a facilitator, I remain delighted that I could share “being a mathematician”, and in particular, that I could share a mixture of confident understanding along with more brittle knowledge. While intuitive reflection on this particular experience seems to center being receptive and ready to transform a routine plan into an unexpected engaging moment, I go forward in search of ways to obtain more feedback on such an approach.
Through this dance with mathematics encountered during an evening of prototyping movement experiences as a class community, we hope to evoke questions and frameworks for considering the role of improvisation.
Margaret Minsky is a Visiting Arts Professor of Interactive Media Business at NYU Shanghai. Her early research in haptics was conducted at MIT and the University of North Carolina. Her recent investigations are in whole-body interaction with computing, electronic textiles, and learning environments. She is also an amateur trapeze artist and aerial choreographer.
