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ARTS  INTEGRATION:
INSPIRING  STUDENTS  TO  LEARN

Below is a summary of some "Arts Integration" programs that can be run at any school.  These blend the study of Latin Dancing with standard concepts in Mathematics, Science, and Social Studies curricula.

For example, some dances such as Cuban Salsa, are performed by couples in a circle.  A line drawn between the leader and follower in each couple should be a tangent to the circle if they are positioned correctly. If extended, these lines would create an equilateral polygon.  Students can watch some dance shows and determine if the dancers got their geometry right!  Or they can compute the length of music needed to fit a dance performance of a given number of beats and a given tempo.  Then they can have fun testing if their conclusion works. 

Below are detailed descriptions of some arts integration programs with specific references to the common core principles that are covered.  To arrange a program for your school or group, please contact me, Dr. Barbara Bernstein (301-9806043; BarbBtalks@aol.com).

PROGRAM # 1.  (Grades 6-12)

Using Salsa Dancing To Teach Concepts In Middle and Upper School
                                 Mathematics and Physics 

A variety of principles in STEM subjects (Math/Science) can be illustrated by aspects of dancing Cuban Salsa, which I have taught for the past dozen years.  This dance is done by couples in a circle, with frequent partner exchanges.  It is the lively group form of Salsa that was featured in "Dance With Me."  Mathematics enters into many aspects of the dance, from how music is counted and cut for presentations, to how the circular formation of the dance respects the laws of Geometry and Physics, etc.

For example, I frequently remind dancers to watch their placement on stage so they remain symmetric---in a well formed circle, or in lines if the presentation is linear.  We also chant the rhythm of the moves so they are executed in tight synchrony.  All of these concepts use Mathematics.

For high school students, more advanced Mathematics can also used by featuring principles of high school Geometry. For example, if a line is drawn between each leader and follower in a Cuban Salsa circle, that line would be a tangent to the circle.  This means that if you drew a line from the center of the circle to the point half way between the couple, it would be at a 90 degree angle to the line connecting that leader and follower. 

And if you extended the line between all the leaders and followers, you would be drawing a regular polygon, meaning that all the edges of the polygon would be the same length.  In practice, all of this simply flows from the fact that the couples are spaced evenly around the circle.  This is in essence, a mathematically rigorous way of saying that. So if anyone isn't in exactly this formation, the circle will look lopsided. 

And by diagramming these lines and circles at the board, many other relationships can be observed.  Congruent triangles are created when radii to certain points on the circle are drawn, and students can prove congruence between some of the triangles.  The polygon constructed as described above would be an equilateral polygon circumscribed around a circle. But a polygon can also constructed by connecting the points (vertices on the circle) which represent the mid-point between each leader and follower.  This second polygon is also equilateral, and it represents a polygon inscribed in the circle.  The diagram will have some central and inscribed angles; and the measure of these angles can be computed, as well. 

Moreover, by altering the number of couples who are diagrammed dancing in a circle, you are essentially "doing the same problem with different numbers." So students can run through the exercise again and practice all the computations and see the concepts in a slightly different light--with new numbers.

To further expand the lesson, we then have the dancers create a larger circle, concentric to the original dance circle.  So for example, suppose we have five couples in a circle.  We keep the circle fairly small initially.  If we then create a circle with a bigger radius, the dancers will have a longer path to cover when they move to a new partner.  But they still have the same number of beats to move in.  So they have to move much faster. 

Specifically, if the radius were doubled, the line from the midpoint between one couple to midpoint between the next couple would also be doubled. This can be proven using laws of similar triangles.  Similar triangles are created since the radii on each circle are equal, and the angle between the radii is the exact same angle. Hence the relationship between the length of the corresponding sides are in direct proportion to each other. 

Thus doubling the circle's radius, doubles the path the dancer travels to the next partner. That makes stopping at the right spot more difficult, because dancers build momentum while moving.  This complies with Physics principles.  At the same time, the angle of the circle they are covering (the "arc") remains the same in a big or small circle. (It is one fifth of the circle with 5 couples. That is 360 degrees divided by 5.)  So Physics concepts of speed and momentum can be brought in. 

And the ratio and proportion relationship between similar triangles found in these concentric circles allows the teacher to cover somewhat simpler mathematical problems, such as solving for an unknown.  This is ideal for students in middle school who aren't yet ready for the more complex geometric relationships described in the several paragraphs above.

As you can see, many principles of Math and Science are very naturally illustrated by working with the music and dance moves in a Salsa circle.  I can present a program that would be fun and instructive, making Math and Physics principles come alive through dance. The program links STEM subjects to everyday experience and is suitable for children in grades 6 through 12.  There are two options: one geared to middle school Math students, and the other for high school Math and Physics students.
 
In addition, I produced a six minute documentary film on Cuban Salsa (Rueda) that can be shown to the students.  It's an inspiring film that underscores the universality of interest in this dance, all across the globe! To watch a trailer for the film, Click here.

For each program, a detailed lesson plan is prepared, including objectives, goals, procedures, evaluation methods, relevant hand-outs, and common core standards that the lesson addresses.  The exact content of the lesson plan will be determined by the students' grade level and their mathematical sophistication. But all of the lessons underscore the link between STEM subjects and the art of dance.

For more programs, click here…..






















Students at American University listening to Bernstein's lecture on Math Education and using the arts in Math instruction 2.13