This week I read the article Dancing Mathematics and the Mathematics of Dance by Sarah-Marie Belcastro and Karl Schaffer, published in Math Horizons in 2011. Both authors have Ph.D.’s in mathematics and also consider themselves dancers, and have been interested in the connection between dance and mathematics for over 20 years at the time of publication.
The article presents and describes a number of examples of
mathematics in dance. Examples include
counting music beats and dance movements, arranging things in a line or with a
certain symmetry or other visual pattern.
Reflections, translations, rotations, inversions, are also discussed. Sometimes these mathematical patterns are
accomplished with a single dancer and their movements and body positions while
it can also occur in a pair or larger group of dancers working in coordination;
in some situations they occur spatially and in others temporally.
They also give examples of the mathematics of rhythmic sounds,
particularly polyrhythms such as 3 against 8 that repeat every 24 beats since the
LCM of 3 and 8 is 24. They also show
these patterns can converted into geometric shapes, for example a 5 against 7
polyrhythm could be diagrammed as a 7-pointed star. See the diagrams associated with these two
examples below.
Finally, they include some examples of more practical mathematics in dance, such as creating the curved or straight pathways dancers follow to dance across the stage, or using counting strategies so that each dancer in a row is equally delayed from the dancer in front of them.
Activity
From Malke Rosenfeld's Math on the Move website, I chose to
look at the lesson plan entitled Rope Polygons as I thought it might be used during
the scale factor and similar figures unit of math 9.
In the lesson plan, small groups of students are given a 12-foot
long rope with knots tied regularly every foot along the rope. With the rope they need to hold it in such as
way as to create a number of regular polygons and other shapes (see picture
from the lesson plan below).
The lesson as written is more for elementary age students,
but I think this type of activity could be adapted to be used with the grade 9
geometry unit on similar figures and scale factor.
I might give students a handout with a variety of polygons
drawn on it, and then they will need to measure the side lengths and then scale
up those measurements to accurately recreate the shape using the rope. They could then calculate the scale factor between
the shape on the paper and the shape created with the rope. Some of the shapes could be regular polygons (like the hexagon in the picture above) but I think I would also include irregular shapes as they would be more challenging for grade 9s.
Many of the units in math 9 are more abstract/conceptual in nature,
so adding in some lessons with embodied mathematics when possible would likely be
enjoyable for students.
Your article sounds like it connects well with mine! In mine, groups work together to recreate the various mathematics within dance sequences. They also have to make use of props, which requires a coordinated effort and lots of communication. Did your article mention the role of props? Or was it solely focused on the movements of the dancers themselves?
ReplyDeleteThank you for sharing the practical example of mathematics in dance. It is always intriguing to watch the the symmetrical and coordinated movement of dancers. The figure of seven pointed stars is a great example of how we can start of by drawing a design of position of dancers. I think this will be a good starting point for educators like me who are not very comfortable with dancing. Drawing and sketching the positions and movements of dancers before attempting the dance - this is definitely a food for thought for me if I ever think of bringing dance into my classroom.
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