Ballroom dancing and mathematics

Summary:Ballroom dancing allows students to approach mathematics in a variety of ways.

Ballroom dancing, considered sophisticated for its elegance, is a style of choreographed dance showcasing not only the dancers’ technical skill but also their poise and style. Originally danced primarily at balls for the social elite, ballroom dancing has become a competitive sport. Dancing allows students to approach mathematics in a variety of ways, from the basic arithmetic of the beats per minute (bpm) to the geometric spatial relationship with respect to the other dancers. Choreographers Erik Stern and Karl Schaffer have created a dance called a “math dance.” The purpose is twofold: to use mathematics to create dance, and to help students learn mathematics concepts through the movements of the dance. Some of the topics explored in math dances are the mathematics of rhythm, polyhedra, symmetry, and dissection puzzles.

History

The phrase “ballroom dancing” derives from the Latin word ballare meaning to sweep or to dance. Now considered historical dances, the original forms of ballroom dancing included the minuet and quadrille. Some steps performed in the quadrille, such as the entrechats (crossing the legs one in front of the other multiple times) and the ronds de jambes (circular movement of the leg while it is extended, toe pointing to the floor), have disappeared from the modern ballroom yet still exist in the ballet world.

In the early 1800s, the waltz made its appearance; the distance between dancing partners was considered scandalous at the time since the waltz required the partners to dance in close proximity. The early 1900s brought the birth of jazz and new dance styles as dancers moved together yet independently of each other. In addition, lively dances such as the Foxtrot, otherwise known as the one-step or two-step, moved away from the traditional placement of feet being turned out and instead called for dancers to have their feet parallel to each other. While many people are unfamiliar with any ballroom dances besides the waltz, competitive ballroom dancing has gained notoriety; it has been showcased on the ABC television show Dancing with the Stars and has become an Olympic sport as well.

Beats

Ballroom dancing consists of a series of dance moves, where more complicated dance steps are called “figures” or “dance figures.” Each of the formally named dances has a variety of dance moves that can be put together to form a personalized performance. Determining the dance moves to use involves more than merely counting the beats. One can calculate the total number of beats that will occur in a song and then determine how many different dance moves would be necessary. For example, if one hears 12 beats in a five-second segment of the song, it can be calculated that the song has 144 bpm. If the song is exactly two minutes long, one can calculate there are 288 beats to work with for the whole song (2×144=288). Since each dance move is typically 8 beats, dividing 288 by 8 beats indicates one needs 36 dance moves. The moves can be repeated, using, for example, 9 moves 4 times each or 11 moves 3 times each (the second option gives the dancer three fewer moves than needed, requiring a dramatic flourish to end the dance). The total number of beats combined with the thematic moves of a particular dance and an individual’s personal signature steps form a composite whole.

Rhythm

One rhythm option for the American-style Foxtrot consists of Slow, Quick, Quick, or half, quarter, quarter in 4/4 time; this approach to the dance gives teachers the opportunity to teach fractions to students using dancing. By creating a dance of successive moves in which two basic steps make one whole move, students will use fractions—adding and subtracting in 4/4 time and introducing the family of fractions

This also can be done in 6/8 time with 1/2, 1/3, 1/6, and so on.

Geometry

As the lead dancer gauges the couple’s location within the coordinate plane of the dance floor, he or she keeps them spatially equidistant from other couples. In addition to the symmetry involved in the various dance moves on the dance floor, symmetry is considered within each dancer’s pose and posture (the form created by the two partners together—symmetrical or asymmetrical). This symmetry can lead to an understanding of angles and curves when various dance poses are examined, and allows students the opportunity to solve problems kinesthetically when they attempt to form a mirror image of their partner while executing the dance moves.

Bibliography

Hackney, Madeleine. “Dancing Classrooms Enhance Math Skills.” Connect 19, no. 4 (2006).

International Dance Sport Federation. http://www.idsf.net.

National Dance Council of America. http://www.ndca.org.

Watson, Anne. “Dance and Mathematics: Engaging Senses in Learning.” Australian Senior Mathematics Journal 19, no. 1 (2005).

World Dance Council. “Welcome.” http://www.wdcdance.com.