To Each its Own: Targeting My Professional Development Workshops

In the last couple months I've had whole bunches of fun presenting professional development workshops in a variety of settings, to a variety of people.  Let's see...math teachers from all over the U.S., PE teachers from across Indiana, classroom teachers from Indianapolis, fellow Teaching Artists from a variety of disciplines, and arts education administrators from Young Audiences affiliates from around the country. 

Each session bore the title 'Math in Your Feet' and was a combination of big picture information and hands-on experience, but that is where the similarity ended and my job got really interesting!

For the classroom teachers I started by focusing on the challenges of using movement in a classroom setting.  As they started to move and experiment with foot-based percussive patterns they became more comfortable and sure in their own movement.  This approach usually leads to a greater willingness to embrace, sometimes for the first time, the possibility of leading their own students in movement-based learning.  To some extent I am also encouraging them to have fun with math, many for the first time.  I consider the 'doing and making' of percussive dance patterns in this program the same as the 'doing and making' of math so, in every teacher workshop I do, I walk them step by step through the intersection where math and dance meet.  We're so used to focusing on the symbolic, static realm of mathematics that we don't always recognize when we see math happening in front of our eyes.  It helps to have a guide.

For the self-identified math teachers at the NCTM annual meeting I also started with a message of 'anyone can lead movement in the classroom and here are some tools' but then quickly moved toward 'here is an opportunity for your students to represent their math understanding in a new way within the kinesthetic realm'.  I also drew their attention to the fact that the processes of solving a problem in both math and dance (choreography) are often similar -- question, understand what tools it might take to answer the question, experiment with ideas, use your resources, find an answer that seems to work, evaluate and then ask more questions. 

The group of 80 or so PE teachers was a new one for me simply because there was not one bit of trepidation or reluctance to get up and move!  Not all of them were comfortable with the idea of dance, at least initially, but they were definitely game.  I was only with them for about an hour, and I couldn't go very deep, so I stuck with active modeling of the bridge between my particular brand of movement with an academic content area.  If I had had more time with them, I would have focused on the  process for moving the dance to the page -- speaking the words that describe aspects of our movement as we move, writing those words down, turning these words into symbols, and graphing foot positions on a coordinate grid.  I did the point that Math in Your Feet can be a collaboration between classroom and specials teachers, just like it is when I lead my residency.  The concrete movement and math activities can be done in PE or music class which then build the bridge to the formal, written, symbolic realm of math back in the regular classroom.

At their conference the arts education administrators were focusing on how to add the A in arts to STEM topics (STEM to STEAM).  I gave a general overview of the program and laid out my process for building the program and integrating the dance with the math.  The most important issue for me is that when you are thinking about integrating any art form with another content area you really need to be honest with yourself and ask 'is it a good fit?'  If the answer is no then it is not worth forcing the issue.  If you think 'maybe' then do a little more work to explore the connections.  In the end, though, the connections need to be more than skin deep.  Just because we count our beats in this program doesn't mean I consider that a good example of what math and dance have in common.  I also gave a similar account of how I combined math and dance to my fellow Teaching Artists.

My favorite moments while teaching teachers are when they ask me questions that show me they are imagining how they will do this work with their own students.  It's similar to house hunting, I suppose.  The minute you start imagining where you're going to put your furniture the realtor knows you might really be serious!  I love hearing all the different ways engaged and caring education professionals imagine tailoring my ideas for their own particular learning environments. 

You Can Count on Monsters

You Can Count on Monsters, by Richard Evan Schwartz
Paperback, 244 pages, A K Peters

I happened to be listening to NPR's Weekend Edition recently and I heard a conversation between Scott Simon and NPR's math guy Keith Devlin about this new book You Can Count on Monsters by Richard Even Schwartz.

From Schwartz's website:

"The book starts with a 20 page introduction, written at an elementary school level. After explaining multiplication, prime numbers, and factoring, the introduction lays out the general idea for the rest of the book, as I'll now describe. To each prime number, we associate a pattern of dots and a monster.

"There is something about each monster that has to do with the prime. Part of the fun of the book is figuring out how the monster is related to its prime. For each composite number, we factor the number into primes and then draw a scene that involves those primes. We also show an arrangement of dots and a factoring tree that helps explain the picture. (A factoring tree is a kind of diagram that shows one way to factor the number into primes.)"

Near the end NPR piece, Devlin said about the book:

"The thing that distinguishes mathematicians is that we, at some stage in our development, we develop this understanding that numbers do have personalities, they have structures, they have relationships.  We form that, but most people don't manage to get it.  What Schwartz has managed to do is use his own skill as an artist to bring out some of the personalities, and the point is that what he brings out through his art is actually the structure and the personality that those of us in the business have always seen, we just haven't got the tools and the ability to make it accessible the way Schwartz [has].  It's his skill as an artist that makes this work [emphasis mine]." 
-- Keith Devlin on NPR's Weekend Edition, Saturday, January 23, 2011

As a dancer who integrates percussive dance and elementary math, I am in the business of making math accessible. I work to illustrate math concepts through a thoughtful sequence of activities; the children build original percussive dance patterns and learn and apply the math that arises naturally from this creative process.  I have spent many years learning and building my own understanding of the math content and practices that relate to this work.  And, I have carefully built a learning bridge that makes meaningful connections between the two subjects.

Now that I have built my bridge and my curriculum is where I want it, for now, I have become fascinated with searching for and finding examples of other kinds of bridges to math.  I am also trying to figure out just what it is that mathematicians see that the rest of us can't.  I'm coming at this task from a couple angles (no pun intended). 

First, going on some information I heard recently that it is most effective to learn a new language like a baby does (there's been some research findings about this, but I can't locate them right now), I'm working on (re)learning math myself alongside my five year old daughter by exploring math concepts through hands-on experience.  And, because I'm not five, I'm also looking ahead to where we might go next.  A few years down the line we might both be ready for You Can Count on Monsters. 

I'm also finding articles and online communities that are focused on how to teach math concepts for comprehension (not just for memorization of procedures) and learning from others' descriptions of how they teach and the kinds of questions they ask students.  I'm also on the lookout for quality examples of how art in general can help build a bridge to real comprehension of math concepts.  Schwartz's monster book seems fit perfectly into the bridge category, in a big way!  By the way, not only does Schwartz appear to be a working artist he is also a Chancellor's Professor of Mathematics and Director of Undergraduate Studies, Department of Mathematics, at Brown University.

So, happy reading and happy learning!  I'm off to the library to find myself a copy!

Statement of Purpose: The Nature of Bridges

"But there are bridges between the one sort of thought and the other, and it seems to me that the artists and poets are specifically concerned with these bridges.  It's not that art is the expression of the unconscious but rather that it is concerned with the relation between the levels of mental process...Artistic skill is the combining of many levels of the mind -- unconscious, conscious and external -- to make a statement of their combination.  It's not a matter of expressing a single level."

--Gregory Bateson, Steps to an Ecology of Mind, page 464

Building a Bridge

I am not a math teacher. 

I am a traditional percussive dancer (Appalachian style flatfooting and clogging and Canadian step dancing) who has spent a lot of time learning about all the math that relates to percussive dance, with the support and help of master educator and friend Jane Cooney.  I have also spent years figuring out which areas of math make the best fit with my art form.

I am not a math teacher, but I do teach math.

Is this creating some cognitive dissonance for you?  I did for me too.  I had to think about this a lot before I could finally come to peace with that statement. 

How does that actually work?  Well, first that non-math teacher (me) had to work with an interpreter of sorts (Jane).  I told her how I worked with kids, and described my workshops and the focus of my work up to that point in time.  Then she told me all the math connections she saw.  It was that easy.  And, it was that hard, too.  She gave me a huge list.  It took me a whole year, on and off, to figure out where to focus my efforts at integrating the two subjects.   Here is what I came to:

I teach the math that directly relates to the process of making rhythm and patterns with the feet. 

When talking about integration I should first mention that there are a few different models for arts integration out there.  The Chicago Arts Partnerships in Education (CAPE) has a really effective model, one they've written about in a wonderful book called Renaissance in the Classroom: Arts Integration and Meaningful Learning.  In this model (as I understand it) there is a classroom teacher (the academic content specialist) and an artist (the arts specialist) working together to find an 'elegant fit' between two different content areas (academic and arts based), but taking turns sharing the instructional time.  In my case, I worked with a math specialist (Jane) to build the program but it was my job to bring the dance/music content and the math content together in cohesive way during the instructional time.  Essentially, I was the one to teach the dance, the related math, and the connections between the two.

I am not a math teacher, but I build a bridge to math.

I may be the one who makes the connections between the dance and math clear for the students, but their classroom teachers also have an important role both in the dance workshops and back in the classroom.  In order for the math understanding that emerges during dance class to stick with the students there are two things that need to happen. 

First, the classroom teachers need to be present and observing their students' efforts.  Teachers do not have to dance, but they can still help the kids iron out any rough spots during their creative work.  Teachers are also learning about the connections as the week progresses.  Second, if the math instruction that I am offering is going to have any lasting value, the kinesthetic learning needs to come back to the page. 

And now, I can finally resolve for you this issue of not being a math teacher who is teaching math.  This is how it works:

I identify and illustrate the connections between math and dance through a meaningful creative process.  I use my voice, their dancing, some humor, and lots of chart paper to make this happen.  On any particular day I use the necessary time between bursts of moving and activity to make clear the elements of both subjects that we are using.  The kids see the words/concepts written on the charts, the kids use this terminology while they are dancing and giving each other feedback, and then...

...and then I hand them back to their teacher!  Back in the classroom, the kids open their specially designed workbooks and reflect on their activity and learning through daily journal prompts.  They have a daily word study section to explore their perceptions of the new vocabulary they are learning.  They also find more recognizable 'math problems' on those pages which relate to and extend the math they learned in dance class.  For example, their personal dance spaces are 2'x2' squares.  In their workbook there is a page that asks them to create a scale drawing of their dance space on the page.  I love the relevance of this! 

So, there you have it.  I am not a math teacher, but I am a bridge builder.  Through the process of revealing the connections between two seemingly disparate subjects, I am able to illuminate certain elementary math topics in new and meaningful ways.  Tah dah!