Math for Dance, and Dance for Math

By Malke Rosenfeld

In my new book, Math on the Move: Engaging Students in Whole Body Learning, I bring together the dancing body and mathematics, to the benefit of learning in both disciplines. As a percussive dancer my preferences are traditional Canadian step dance from Cape Breton Island and old-time Appalachian flatfooting and clogging, both highly rhythmic and improvisational foot-based dance styles. I provide learners (elementary students to research mathematicians) the opportunity to move math off the page and to harness mathematical ideas as potent choreographic prompts.

The basic tenets of my book are threefold: Math is more than memorization; the moving body is best conceptualized as a thinking tool for making sense of math; and amazing learning can happen when we bring math, making, and movement together in the classroom, especially for young learners. But how can we make math and dance at the same time?

Traditional academic curriculum presents subjects in isolation, but there is great benefit in curious explorations of where ideas, topics, or disciplines overlap in a genuine way. Although much of mathematics is in the details, the big picture of math is about exploring relationships between one idea or object and another, finding and harnessing the power of patterns both simple and profound, and playing around with rules and constraints. Math educator and professor Deborah Ball has written that math pedagogy “must be based on the structures of the discipline in order to avoid corrupting or distorting its content”(1990). This statement rings true for the discipline of dance as well and, most importantly, has implications for how we conceptualize, create, and execute interdisciplinary or arts integrated curricula. We shouldn’t trivialize or make up the dance to fit the math, nor should we do the same to make the math fit the dance.

To create Math in Your Feet, upon which a good portion of my book is based, I formalized a tool I had been developing in the program’s first iteration, “Drum with Your Feet.” The Movement Variables system breaks down the highly technical and precise nature of percussive dance into the core categories of foot position, type of movement, and direction. Children create their own original foot-based choreography and become familiar with the elements of percussive dance while they use the Movement Variables within the spatial constraints of 2’x2’ taped squares. What I didn’t know until much later was that the Movement Variables tool is, in and of itself, highly mathematical.

After many years of refining Math in Your Feet, I began to feel that I needed a way to better communicate the learning and thinking I saw happening in my work with children. After hearing “That looks like fun” multiple times from teachers, it became clear that there was something more I needed to do to support them in seeing the activity as real learning. I needed to make better, more explicit connections between math on paper and the activity of exploring and expressing math in the kinetic, temporal, expressive space of a dance system. This was not an easy task. Writing my book was very much a process of translation, taking my non-verbal understanding of what I see, feel, and understand happening in a moving classroom and interpreting it into a form others could access.

I knew this meant I needed to write a book. With actual words! I also knew I needed the benefit of others’ work and thinking about teaching and learning to help make a case for this generally unorthodox way of learning math.

My focus in the book is on how we can harness our students’ inherent “body knowledge” to help them develop new understanding and facility with mathematical ideas that often seem remote and impenetrable as presented in their textbooks. The phrase “body knowledge” was coined by the late Seymour Papert, a protégée of Jean Piaget. In the 1980s Papert’s work at MIT focused on developing “objects to think with,” including the Logo computer programming system for children. His intention was to harness a child’s own lived experiences in the world (what he termed “body syntonic”) as a way to investigate more formal mathematics via the programming of a little metal object called the “turtle.” Much of what we do in Math in Your Feet is similar to what children do with the LOGO turtle – working independently or in teams within a specific system/constraint, investigating and creating units of commands or patterns in a spatial and geometric language and, along the way, fine tuning their intentions and results. 

Similar to Papert’s work, Math on the Move is about math, but it is also about the nature of learning by actually making something and the need to develop strong pedagogy for interdisciplinary, movement-based curriculum beyond the preschool years. In the first chapter I provide an overview of what meaningful whole-body math learning looks like in my own and others’ math-and-dance classrooms. I clarify the body’s role as a thinking tool and its use within a purposeful making and learning context. I also provide a conceptual framework and pedagogical base for any educator wishing to do similar work with his/her own students.

In the second chapter I address the question I imagine most people are thinking but are likely too polite to ask directly: How is this math? Then, in later chapters, I focus on small steps to get started with learning/teaching math off the page, detail the progression of Math in Your Feet lessons, and share how this work can be adapted to the primary grades. I also provide detailed explanations for facilitating a moving math classroom. The final chapter is one of my favorites: How do you assess the work and integrated learning of moving students? Finally, to my great delight, my publisher spent three days with me to capture video footage of me working with four classes of fourth graders. As a result, there are over 40 videos of classroom action embedded throughout the text, to be accessed via links and QR codes.

I have been delighted by the diversity of educators who have reviewed my book. Their varied perspectives show the different shades and nuances of how and where this work can be applied and adapted. One review in particular clearly identifies our dance work as mathematical, and mathematics itself as a creative endeavor. David Butler, an Australian mathematician at the University of Adelaide, Australia writes:

“The dance moves within the tiny square spaces [used in Math in Your Feet] are abstract mathematical ideas that are explored in a mathematical way. We ask how the steps are the same or different from each other, identifying various properties that distinguish them. We investigate how these new objects can be combined and ordered and transformed. We try out terminology and notation to make our investigations more precise and to communicate both current state and how we got there. These are all the things we pure mathematicians do with all our functions, graphs, groups, spaces, rings and categories. The similarity of this to pure mathematical investigation is striking.”

More than anything, I wrote the book as a conversation starter. Please get in touch with any thoughts, questions, concerns, new perspectives or resources!

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More information on Math on the Move, including a sample chapter, can be found on the book’s product page on the Heinemann website.

www.malkerosenfeld.com
www.mathinyourfeet.com
Twitter: @mathinyourfeet
Facebook: Math in Your Feet
Book blog: www.mathonthemovebook.com
Other blog: www.mathinunexpectedspaces.wordpress.com

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