1 + 1 = Pas de Deux
Doris Humphrey derided symmetry in dance as boring. But perhaps she would have felt differently if she’d had math teachers like dancers Karl Schaffer and Erik Stern. They have an affinity for symmetry and other mathematical concepts and have developed a program that offers dance-based math lessons and math-based dance lessons for K–12 classrooms. Since their first foray into cross-curricular instruction in 1990, educators from around the country have signed on, incorporating exercises from Schaffer and Stern’s self-published handbook, Math Dance, into classes and inviting the pair to perform in schools and for education associations.
Though their program grew out of personal interests, it fits well with current educational trends to address different learning styles and make classrooms more exploratory. “We encourage teachers to use our activities—but also the whole program as a model for cross-disciplinary work,” says Stern.
Schaffer is on the math faculty at De Anza College in Cupertino, California, and Stern teaches dance at Weber State University in Ogden, Utah. They travel about six times a year for Math Dance workshops and performances, sometimes as visiting artists for the Kennedy Center’s Partners in Education program, which fosters relationships between arts organizations and schools.
Schaffer and Stern’s partnership began more than 20 years ago in Santa Cruz, CA. Stern, who has a BA in biology from the University of California, Santa Cruz, and an MFA in dance from Cal Arts, was dancing with Tandy Beal’s company. Schaffer was a grad student at UCSC who split his time between the dance and math departments, “which didn’t make either one very happy,” says Schaffer, who eventually earned his PhD in math from UCSC.
The two dancers immediately hit it off. “We found we shared a similar sense of humor and an interest in bringing philosophical concepts into dance,” says Schaffer. After choreographing and performing together for three years, they began creating work that explored the connections between math and dance. “Choreography is a way to identify, define and change a pattern in time and space. That’s a math problem,” explains Stern.
In 1990, the two created a performance piece for kids made up of a series of short acts that explored different mathematical ideas and included plenty of audience interaction. The performances were popular and before long the duo was touring schools and other venues around the country as the Dr. Schaffer and Mr. Stern Dance Ensemble.
Teachers soon began asking if their material could be used in the classroom. “Well, the answer was ‘sure’ but we had to figure out how,” says Stern. Schaffer had taught math to children and Stern had led dance workshops while working with Tandy Beal. But to combine the two subjects, they decided the best source of material would be their choreography.
Their first exercise, called Counting Handshakes, came straight from their performance piece and explores the mathematical concept of combinations. In pairs, students create a movement sequence by finding how many ways they can shake hands using one hand at a time (i.e., right to left, left to right, left to left, etc.). “At first, our goal was to get students to get the correct answer,” says Stern. “But over time we realized that the number you come up with depends on how you interpret the rules. Does a handshake performed over your heads count as a different one? Well, it can if you decide it does. What mattered was that the students understood the question and could explain their methodology.”
Another exercise on probability has each student create a movement. Then with a partner, they toss a coin 10 times. One person’s movement is represented by heads, the other’s by tails. Before doing the exercise, most assume that they’ll be doing roughly equal numbers of each movement. But they soon discover probability is counterintuitive, Karl says.
Looking at math and dance together “freshens up the ways you think about both,” says Stern. Dance sheds light on math but math frees up how you think about dance, too. Take symmetry. The typical way of approaching it in dance divides the body (or a group of bodies) in half. But in math, there are many ways of looking at symmetry. There is reflection symmetry, rotational symmetry, symmetry of scale. “Once you realize this, you can begin to see symmetry is really just about describing what’s the same and what is different,” says Stern. “You can move sharp, smooth, sharp, for example, and can think about dynamics in terms of symmetry.”
The idea of exploring connections between math and dance may seem new to many, but to teachers who use Math Dance it makes sense. Kathryn Irey, who teaches dance pedagogy to liberal studies students at San Diego State University, uses the book to teach her students about bridging K-12 arts and academics. But her college students often refresh their basic math skills in the process. “Some find that they never owned some of these principals,” she says, “until moving through them.” DT
Lisa Traiger, former president of the Dance Critics Association, contributes to The Washington Post, Dance Magazine, Pointe and other publications.