New Video: How I Teach Math & Dance at the Same Time

There's a cool new international math education project on the interwebs.  It's called Mathagogy: Two Minute Math Education. Peps McCrea, the instigator of this project, says on the site: "Our aim is to slowly gather a diverse collection of short ‘approaches to teaching mathematics’ videos from practitioners around the world."

He asked for submissions. Fueled by John Golden's support, I complied, and now my just-under-three-minute video is up and running on the Mathagogy site along with some other rather fantastic videos. (Although, now I need to give John himself a little nudge!)

This has been the year of videos for me, but I think this one is the best quick, visual description and reasoning of my work out there right now. (However, stay tuned for a new article from me, to be published in the Teaching Artist Journal in October, which pushes forward on what it really means to teach and learn in this kind of interdisciplinary setting. Much of my thinking in this video includes excerpts from that piece of writing.)

Feedback and questions on this video are welcome and encouraged!



If you'd like to leave a comment but don't see a way to do it, chances are my blog template is getting in the way.  Try going back to the home page and refreshing your browser.  If that doesn't work and if you still want to get in touch, feel free to e-mail me or contact me via the Math in Your Feet website.

Chicken or the Egg? A Math Integration Tale

I recently had the opportunity to have my teaching work critiqued by a group of colleagues.  They viewed a ten-minute video I produced which illustrated what success looks like in my classroom. The feedback I received was all at once enthusiastic, thought provoking and puzzling.   

I teach elementary students the elements of percussive dance and then, within a structured framework, give them the freedom to create their own percussive patterns.  Along the way we use and talk about a lot of math which both describes their patterns and informs their creative choices.  It seems straightforward to me, so I think that is why I was flummoxed by a question they all had:

“When your students are choreographing their percussive dance patterns, how much of that activity is about their math understanding?”

I can answer that question.  The answer is, “All of it.”  I don’t see a separation between the two.   In fact, I think the dance and the math are essentially the same activity.

Here is an example:  a video of some traditional Irish figure dancing with accompanying percussive footwork.  You only have to watch a minute of the dancing to notice it is full of geometry and symmetry and all sorts of other wonderful kinds of math:

The shifting, curving patterns move through space and time while undergoing symmetrical transformations.  The dance choreography explores permutations and combinations of moves and steps by arranging and rearranging dancers at a dizzying rate in time to the music.  The footwork traces invisible maps on the floor.  The math in the percussive footwork is a reiteration of the figure dancing, but on a smaller scale with more specific and precise patterns.  Unsurprisingly, precision is a hallmark of mathematics which has, by a popular meme, been called ‘the science of patterns’.  

All this is well and good, but what my colleagues really wanted were more specifics about my evaluative criteria.  How exactly do I gauge my students --within the medium of percussive dance or with regard to the math?  Again my, possibly controversial, answer:  Both.  

And a question back: Why do we think of them as separate activities?  I think part of the issue might have a lot to do with how we, on the whole, perceive mathematical activity.

Generally conceived, dance is a three-dimensional, kinesthetic endeavor.  Math is rote memorization of algorithms and concepts and inhabits a two-dimensional symbolic realm.  Everything we’ve learned in school bears this out, except that it’s really not true!  When I started to really investigate what it means to do math I found that it’s completely different than what I did in school when I was a kid (and you too, probably).   

And, as I dug deeper, I also realized I had been thinking mathematically all my life – I just never recognized it as a mathematical activity.

One of the things I’ve come to realize is that, really, people who do math don’t spend a lot of time plugging numbers into memorized algorithms.  Instead,they formulate and/or approach questions that don’t have immediate solutions.  They spend time thinking, talk to others, sketch out ideas on napkins (or whatever), and build models.  And then, when they think they’ve got something that resembles a solution, that’s when they start writing it down.  The notation is the end result of a process of questions, trial and error, and conversations.  Sounds a lot like what we do in Math in Your Feet, actually.  Take a look:

When I first started wondering about whether or not there was math in the dancing I did with students, I knew I needed an interpreter, someone who really understood math and how it was taught to children. I was lucky to be connected with Jane Cooney, a classroom teacher with deep experience and love for teaching math.  Our collaboration in creating Math in Your Feet included long discussions about the best ways to retain the integrity of both content areas.  We weren’t going to make up the dance to fit the math and I wasn’t going to make up the math to fit the dance.

We didn’t and I haven’t.  There was no need. There is enough overlap between the two that, if you hit it right, you often can’t tell where one starts and the other ends.  However, I have consciously created specific lessons to identify and learn the math that we’re going to use in our dancing.  Not only is math a tool we need to understand in order to use it properly, but I think it’s also important to know exactly how math is involved in our physical and creative work.     

Like the old chicken/egg conundrum, it really doesn’t matter which one comes first because they’re both part of the same process.   And that is why, when I watch my students share their work throughout the week, I can see clearly if they have both the dance and the math and to what degree.  But that’s another story!

[This story originally posted in the Teaching Artist Journal's ALT/space, 11/28/12]

Friday (Video) Fun: This is How We Fly on RTE

The fabulous Nic Gareiss and the rest of This is How We Fly.  Feet visuals at around one minute in.  Enjoy!

Video: (Percussive) Dance Forms of Mexico's Son Huasteco

I was searching for Mexican son jarocho dance and found this! I'm enamoured with the soft little sounds they make with their feet, as well as the singing style. The dancer, Artemio Posadas, does a little demonstration in the middle of the video that shows the softer sounds very clearly.



...and here's one more, this time of Irish sean nos (old style) step dancers. The video had disabled embedding, but here's the link! See what you think in terms of similarities and differences between the Mexican and Irish percussive dance styles.

A Sunday Video Treat

Here's my current favorite fiddle/feet duet...enjoy!

Jump Patterns: The Full Story!

I'm am thrilled to announce that my article, Jump Patterns: Percussive Dance and the Path to Math, has just been published in the Teaching Artist Journal, the only peer reviewed publication for my (still very new) profession.

The article focuses on how my approach to teaching percussive dance led me to search for, and find, relevant math connections.  I outline how I developed and formalized 'Jump Patterns,' a teaching tool which illustrates the elements of percussive dance (similar to how creative movement teaches the elements of other formal dance styles like ballet or modern dance).  I also describe how this tool has helped children become creative in my art form and make many meaningful connections to math topics at the same time.

Although I have shared much about my work in this blog over the last five months, the newly-published article is the first time I have provided a comprehensive, detailed description of Jump Patterns and how they are used in the classroom.  The article can be found here. 

I am very interested to hear your thoughts, observations, and questions about my approach as well as any similarities to other approaches out there.

Ode to A Dance Board

LuAnne's dance board.  I am completely covetous.

My friend LuAnne recently started learning how to clog.  She had a friend make her a dance board so she could practice at home. 

Being the wonderful multi-talented artist that she is, she decorated it.  Now the board is magically practical.

My own board is not nearly as beautiful as LuAnne's.

In Math in Your Feet, children do their dancing and creative work inside taped 2'x2' squares that creates a similar dance space to the dance board that I use.  These boards are sometimes called step-a-tunes. 

At traditional fiddle festivals around the country, where old-time musicians gather in the summer, dancers often carry their step-a-tune around until they find a jam they like.  Then, they put down their board (in the dirt, in the mud, in the grass) and are able to join the music.

Here is LuAnne's recent ode to said dance board which I think perfectly celebrates this seemingly limited, yet completely freeing, dance space of the step-a-tune.  Enjoy!

Representing Math Concepts Through Percussive Patterns

Not quite congruent.  One partner has landed while the

other 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!

Jumping for Joy!

Oh, I'm excited!  My article, Jump Patterns: Percussive Dance and the Path to Math is on track to be published in April 2011 in the peer reviewed publication the Teaching Artist Journal.  From the journal, "The Teaching Artist Journal is a print quarterly (also available online) that serves as a voice, forum and resource for teaching artists and all those working at the intersection of art and learning."

Not only will it be exciting to be able to share my work with colleagues in a formal way, but I'll be able to share it with you, too!  The article focuses on how my approach to teaching percussive dance led me to search for, and find, relevant math connections.  I outline how I developed and formalized 'Jump Patterns,' a teaching tool which illustrates the elements of percussive dance (similar to how creative movement teaches the elements of other formal dance styles like ballet or modern dance).  I also describe how this tool has helped children become creative in my art form and make many meaningful connections to math topics at the same time.

More Than The Sum of It's Parts

I am always thinking about better ways to describe what exactly is happening in Math in Your Feet.  It's actually been quite difficult for me to explain because, in the end, the total experience is more than the sum of it's parts.  Think about it -- this program brings together two subjects which communicate, in their own mystifying language, about space, time, and movement.  Teachers who have been through it once often advise first time teachers that they'll "understand it after they're done," which is not ideal.  Luckily, I'm meeting with some teachers tomorrow to plan for an upcoming residency.  While preparing for the meeting I took the opportunity to update my thinking about what is really going on while a bunch of kids jump around in small boxes taped on the floor.  Here's what I came up with:

Specific Learning Areas in Math in Your Feet (Upper Elementary)

INTEGRATION
Both the dance and the math content are focused on equally; finding connections between the two creates a stronger understanding of both content areas.

KINESTHETIC LEARNING
Engaging the vestibular system through intentional cross lateral and patterned movements improve learning.  Math concepts are experienced first through the body.  Words are connected to the movements and then used in reflection journal entries, word studies, and in the process of recording patterns on the page.  This everyday language is then converted to a more abstract symbolic language in the mapping activities.

REFINE/STRENGTHEN/REMEDIATE UNDERSTANDING OF SPATIAL RELATIONSHIPS
Firm grounding in spatial relationships (best learned through the body) is vital to a strong understanding of math concepts. 

INTENSIVE STUDY OF PATTERNS
Higher order thinking and problem solving skills are strengthened during the process of creating, manipulating, combining, observing, transforming and analyzing foot-based dance patterns.

MATH VOCABULARY LEARNED IN CONTEXT
Teachers consistently report that their students use new math terminology and vocabulary appropriately and with ease in conversations about their work in the program.

CONCRETE GRADE-LEVEL MATH TOPICS
This program is not about numbers, formulas, or procedures, but there are discrete math topics learned within the experience.  Angles, degrees of turns, directions, basic fractions, symmetries, reflections and rotations are all covered in the dance class.  Extension activities in the Student Workbook also touch on combinations, tangrams, lines of symmetry, lines of reflection, scale drawings, and perimeter and area.

IMPROVED ATTITUDES TOWARDS PROBLEM SOLVING AND MATH
At the center of the students’ experience is their role as creator, using just the elements of percussive dance and a few guidelines.  There is nothing quite so empowering as being able to create something by yourself out of (almost) nothing.

What do you think?  Does this answer any questions you may have had about the how's and why's of this program?

Video: Bloomington Dancers in a Groove

Video: Mary Devlin -  Welcome Table Dress Rehearsal - February 2010

Choreography by Abby Ladin, with contributing footwoork from me, to the tune Mary Devlin, by Sam Bartlett. Moira Smiley belting it out on vocals along with Malcolm Dalglish and others. 



*If you have a Facebook account you'll be able to view this video. My apologies if you're not in that category.  It may take some time, but I'll work on getting it up on YouTube.

Video: Two of My Favorite Dancers, Together!

Here are two of my favorite traditional percussive dancers. I love how they are each so tuned into and connected to the music, especially in improvisational settings like this one. 

In this video, Melody Cameron of Mabou, Cape Breton Island, Nova Scotia, Canada (all of that is important!) and Nic Gareiss of Michigan (and many place beyond that) are caught on tape having an impromptu, probably late-night, exchange/playtime/conversation.  They were at the 2010 North Atlantic Fiddle Convention in Aberdeen, Scotland this July.  Later in this video they are joined by two other Cape Breton step dancers Mats Melin and Brandi McCarthy.

Cape Breton step dance was the first percussive dance style I learned, and is still my first love.  A 'neat and tidy' and 'close to the floor' tradition where most dancing is improvised on the spot in response to the music, the aesthetic is to wear shoes that have some snap to them but not taps (which I learned the hard way, but that's another story!).  In this video Melody also throws some Appalachian style clogging steps into the mix. 

Nic was just a kid when I first met him more than a decade ago, but had already been dancing longer than me.  Always an inspiration, his blog Dance is Music is, I think, the best way to describe his dancing.