## Wednesday, January 26, 2011

### Representing Math Concepts Through Percussive Patterns

 Not quite congruent.  One partner has landed while theother is still up in the air.
This week I'm working at Christel House Academy, a charter school up in Indianapolis.  This is part of a grant-funded pilot project for Young Audiences' Signature Core Programs.  The fifth graders are fantastic!  They are perfectly perfect in all their 11-year-old-ness, and quite observant and thoughtful to boot.  They make connections easily and ask interesting questions that show they are really thinking about how this all works.

This is an interesting situation for me.  I am usually invited to schools where kids are at least a grade level or more behind in math and my role is to assist in catching them up.  At this school, the fifth graders know and understand quite a bit so we are in the position of applying what they know to a new situation instead of learning it for the first time.  But the really fascinating thing for me is that, although they 'know their math' they are still challenged by representing it physically.

In my reading about mathematics education, I've come across an idea called 'the power of three'.  Essentially, the idea is that to really understand a math concept a child needs to represent it in at least three different ways.   This would be through pictures or some other means.  I'm just beginning to realize that one of the strengths of Math in Your Feet is that it provides an opportunity to experience and represent math concepts in the kinesthetic realm.  Part of this challenge lies in the fact that these patterns are not static, but require students to literally be 'in' the pattern.  Just today I had an interesting conversation with some boys about whether to record a turn as being on the third beat or on the fourth.  We eventually came to the agreement that the turn was actually happening between the third and fourth beat, but that since third beat ended in one position and the fourth beat was in the new position, we had to record it as being on the fourth beat.  My system may not be perfect, but it does create a structure to ask these kinds of questions.

So, here's how it works.  Kids make up a four-beat dance pattern using the elements of percussive dance that I've outlined for them.  They learn to make their dancing congruent by producing (with pre-teen bodies!) the same tempo, foot placement, movement, and direction as their partner.  After that, we start transforming these patterns using different symmetries, starting with reflection.  At that point, all the pathways forged between the body and the brain have to be shuffled around as one partner dances the original pattern and the other (on the opposite side of the line of reflection) has to change the pattern by dancing the opposite lefts and rights.  For example, a turn to the right would be reversed to go left, or a right foot would be switched to a left foot.  This all sounds rather straightforward as I'm writing about it, but after observing the CHA fifth graders this morning, I realize that no matter how well they understand it in their heads, and no matter how 'smart' their bodies might be, it's still a challenge!  There's quite a bit of thinking going on here, in both body and brain, and it takes a lot of practice to remember a sequence of the four moves that make up their pattern.

This is only the third day and we have a couple more to go.  Things do get more interesting and more challenging when we start combining individual patterns into larger ones (i.e. start the second pattern where you ended the first, not at your original starting point and then try the reverse) and also when we transform the patterns using turn symmetry which seems rather straightforward in a static representation on paper, but is absolutely spectacular when you see it in motion.

I'll keep you posted!

#### 1 comment:

1. "Just today I had an interesting conversation with some boys about whether to record a turn as being on the third beat or on the fourth. We eventually came to the agreement that the turn was actually happening between the third and fourth beat, but that since third beat ended in one position and the fourth beat was in the new position, we had to record it as being on the fourth beat."

This issue actually comes up A LOT not only in music or dance, but also in measurement. Almost 100% kids get confused about rulers starting with 0 instead of 1, for example. Or they answer "how many inches between 2 and 5?" by counting "2, 3, 4, 5" and obtaining 4.

Anyone who has done any programming with cycles or lists can also relate to the confusion between the number of STEPS (between items) and the number of ITEMS.

Movement is a great way to notice and to discuss this issue. Thanks for sharing!