Bruce Ferrington writes a popular blog about mathematics in Elementary Schools (http://authenticinquirymaths.blogspot.com.au). In July/August, he worked on a series of interviews with dancers & choreographers reflecting on how they use mathematics in their art and how it applies to their work. In August, he asked Ana & Joel Masacote to answer 10 questions about how mathematics relates to their passion – dance.
Other participants were Tommy Franzen, from “So You Think You Can Dance (UK), Alonzo King, from LINES ballet, Corey Herbert and Drew Hedditch, corps de ballet from the Australian Ballet, Elena Grinenko world champion Latin American Rhythm and Dancing with the Stars, Michael Apuzzo , dancer with Ben Wright, and Linda Gamblin, from the Sydney Dance Company.
Questions and answers from Ana:
Describe what math lessons were like for you at school.
Math was always one of my favorite subjects. With just a bit of problem solving, there was always an answer to every question. In high school, I was skipped up from geometry (later testing out) and placed in a new fast track math program in which you were taught your first two years of math in college (Calculus AB & BC) by the time you graduated. Eventually, my love of math (and computers) led me to study electrical engineering and computer science at Massachusetts Institute of Technology (MIT).
- When you left school, did you expect to be using any of the math that you were taught ever again?
In college, I switched into business when I decided I didn’t love engineering enough to do it as a living and wanted instead to build my own entertainment company. At that point, I figured I’d be using basic math through the business component of the company but never realized how much I would also be using it in my dance and movement.
- Do you divide dances or movements into parts or sections that might be expressed as mathematical fractions?
The co-founder of the company is also a musician, and he has helped us develop a musical foundation tied into our dance curriculum so they work hand in hand. We teach dance by breaking down the components of the music, odd timing variations, and notations. We explain the concept of whole notes, quarter notes, eighth notes, etc. We talk about the subdivision of time so dancers can fit steps within such rhythms as half beats and triplets, allowing them to stay better attuned to the music. For our dance company, this becomes even more present when working on choreography and staying in sync with one another.
- How aware are you of angles in dancing technique – angle of body, angle of arms and legs, angle of movements?
Angles are extremely important and emphasized both for social dance execution and performance presence. For social dancing, dancers must be aware of angles to partners at all times. Half the lead is signaled through the positioning of body in space rather than physically leading a move. Salsa can be both linear and circular. The style we focus on is linear, through which leaders must be aware of how to use the angle of the body to open up space for the followers while followers must be aware of the angle of the frame to the partners so as not to inhibit the lead. We often talk about 90 degree frame positions, 180 degree travel, and even some of our moves are called by names of angles, such as the 360.
Carrying that further into performance, lines become thoroughly emphasized when working on presence and synchronicity. We establish positioning of arm and leg styling by use of angles, body position by symmetry, presence by parallel and perpendicular forms, and other similar uses. In a show, I know exactly at what angle my arm, body, head, leg, etc. need to be.
- When dancers are moving in a performance, how much is “mathematical thinking and calculating where the space is” and how much is “feel for the space”?
Spatial awareness tends to be more of a feel of the space with set boundaries. For shows, we must decide center stage, stage boundaries, and in which portion of the stage we must begin, end, and dance within. For example, we might have a situation in which spotlight shines center stage, and when lights open fully, we must stay within a 2/3 area of the stage where lights are shining. After setting guidelines, the remainder becomes a “feel for the space” as we perform.
Formations require a really important feel of both the space and people around you. When you are developing shapes as a group, everyone has to be tuned into the distance of one person to the next and placement within the stage.
- Is estimation good enough or do you rely on accurate measurement of distances and times?
Accurate measurements are important in defining how much space we have to use to make sure choreographies are workable within the limits. Estimation is good enough for everything thereafter, unless we want a particular formation that involves set spotlights/ lighting requiring dancers to lead in an exact area.
- How aware are you of timing and beat in dance?
Timing is one of the most important subjects in our school. We actually teach music classes in addition to dance classes to keep people connected to what dancing “in time” really means.
Our style of dance uses syncopated counts in which dancers sometimes step between beats and not always right on top of pulse. This requires one to always be attentive to the present moment at which the count is happening and maintain an internal pulse (think of a ticking clock) while coordinating steps both on and between pulse at any given time. The body is maintaining a separate rhythm, and it is very common to switch from a syncopated time to one right on top of pulse, depending on the step, requiring the dancer to always be attentive to the space and duration of one beat to the next.
- Have you ever used math and physics to explain your technique, movement or choreography?
Although I loved math, I disliked physics. However, even then, I do use physics terms at times to explain connection to partnering, force applied in lead/follow, and execution of lifts and dips. Math (mostly geometry) terms are often used in explanation of movement, technique, and choreography.
- Do you look at statistics much to analyze your art?
I actually think statistics might be the one subject I don’t use in the explanation of my art, but then statistics and probability were my least favorite math subjects. LOL I love spontaneity!
- Do you have any other insights to offer into how you use mathematics in dance?
One of our company’s most famous choreographies is “Take Five”, danced to Dave Brubeck’s famous jazz song in odd 5/4 timing signature. To choreograph to it, we had to develop a way to dance salsa (normally in 4/4 timing) to it. We took 6 steps over an 8 count and adjusted them to 6 steps over a 10 count, requiring an upswing and tap of the step to fill duration of time. Since, we have experimented with different timing signatures and continue to explore new ways of movement in time.
Back in 2002, I was the Latin Dance Coordinator for a sister city project between the city of Cambridge, MA and Cienfuegos, Cuba. On this trip, I had the opportunity to listen to a kids’ band with a very unique teaching method. In an effort to help at risk kids who were having trouble with math studies, the teacher had developed a program in which he would teach them how to play music through the explanation of math. It was the 5th cycle of the program and had been very successful in getting the youth to become more interested in their studies and more understanding of math subjects. I thought this was a particularly profound and benevolent idea as he was helping them become successful students in a fun and yet systematic way. I hope more programs like this are eventually developed, but it is also a very innovative idea to try to find a similar approach through dance.