What TED-Ed, Math-Ed and Arts-Ed Have in Common

I just presented at the Young Audiences National Conference.  Their theme this year was STEM to STEAM, exploring ways to add the arts to the STEM (science, technology, engineering and math) initiative.  I shared my process for integrating math and percussive dance with executive directors and program staff from Young Audiences affiliates from around the country -- people who work every day to bring teaching artists like me into educational settings.  When I told them that just two weeks prior I had presented a 90-minute, hands-on workshop of the same material to 130+ math teachers from around the country (at the NCTM annual meeting) they CHEERED!

Here's what I know: The math education folks WANT math to make sense to their students.  They WANT their students to understand and apply and maybe even enjoy math, and they are looking for effective tools to make this happen. 

Here's what I know: The arts education folks know without a doubt that the arts are a perfect vehicle in supporting learners in the process of understanding and connection making. 

Liz Lerman, dancer/educator/human extraordinaire who was also at the Young Audiences National Conference, shared the work she's been doing with scientists.  Later in the day she lead a workshop in which she said multiple times:  "There is always a structure we can put in place to help solve a problem."    Today I found a structure that has great potential to bring the teachers, the artists, and the organizations together to realize our common goals toward a real, engaging, fulfilling education for all:

"The TED-Ed Brain Trust is a private online forum created to shape and accelerate TED's push into the realm of Education.  We aim to assemble a new archive of remarkable educational videos designed to catalyze learning around the globe. TED is seeking the expertise of visionary educators, organizations and creative professionals to help guide, galvanize and ultimately lead this exciting new initiative."

Here's the video that introduces this incredible moment in education:



You might also be interested in the conversation the math-ed folks are having right now about what they might contribute to this effort: Making mathematics real: A TED-ED series proposal

Perfect Reasoning: The Right Brain Initiative (Manifesto)

Looking Forward...to the NCTM Annual Meeting!

The 2011 Annual Meeting of the NCTM is coming up in about three weeks, and it happens to be in Indianapolis, IN this year, about an hour from my home. 

I'm starting to get excited!  There are many things to look forward to including (but not limited to):

• the possibility of meeting Keith Devlin, NPR's Math Guy
• the possibility of meeting Scott Kim (one of the MathDance guys)

Both Keith and Scott are presenting.  Also:

• the possibility of meeting other really interesting people, still to be discovered but no less exciting
• the sheer volume of workshops on interesting arts connections to teaching math

And, last but not least:

• a chance to share my own work, and to give teachers some concrete experience with integrating percussive dance and elementary mathematics as well as tools and lesson plans that they can take right back to their classrooms after the conference is over!  And all in 90 minutes.  

You gonna' be there?

Divided Loyalties?

In the process of exploring the intersections between math and dance I find that I seem to camp out in one subject for a while, and then pack up and move on back to the other camp.  Frankly, it leaves me feeling a bit fractured, which is interesting since I have declared in the past that in Math in Your Feet the two subjects come together 'seamlessly.' 

Maybe for the kids, yes, but not for me.  So let's focus on me for a moment.

This issue shows up in my teaching.  When I am thinking too closely about the math, my feet don't move in class.  They don't talk.  I forget to use the one great attention getter I have that nobody else does -- my tap shoes!  I forget to start our sessions with the art and instead hurry forward to the math. 

My most recently completed residency at Christel House Academy has made me think of this.  The residency was part of a pilot project by Young Audiences to evaluate the structure of their new Signature Core Services and the elements that interact to create a quality arts learning experience.  They wanted to know if and how these elements were brought out in this particular arts-based programming.  But me? I was worried about how I was teaching the math and was surprised that they didn't even care about that (for the purposes of the pilot).  That shows you where my mind is these days, doesn't it? 

I've also spent a lot of time overly focused on the dance (mostly in the first few years of developing the program) but these days?  These days, as I teach, I have mostly been taking the dance for granted.  I am quite surprised and somewhat alarmed to realize that I've been seeing dance as a means to an end.  I'm horrified, actually! This is not really supposed to happen in an integration and I'm really supposed to be on the side of the dancing right?  Yes, we're dancing and moving our bodies at least two thirds of each workshop, but I am realizing now just how much my mind has been over at the math camp.

I think this might be because I've been spending much of my creative work time this fall focused on learning about math.  I've been trying to figure out what math means:  What is math really?  What other kinds of math are we doing in this program besides the ones I know about already?  What kinds of conversations are these kids having about the math while they're dancing?  The learning I've engaged in, I believe, has been a full out creative process, one full of questions, dead ends, frustration, problem solving (What don't I know?  Where do I need to go to find out?  What sorts of questions do I need to ask?  Am I asking the right questions?) and 'aha!' moments. 

My intellectual explorations have affected my teaching in the past as well.  Earlier in the development of Math in Your Feet, when I was still trying to figure out how the dance and math fit together I was deeply engaged in exploring the integration aspect of the program and  my teaching at the time reflected this.  Although I did have questions about the value of teaching the integration (and still do; mostly I think it's a good tactic) I was working it out in the classroom none-the-less.

So here's a question: If the basic flow of the residency content stays the same, does it matter if my interests bias our focus, even if slightly?  Does it matter if I'm over in the math camp while teaching a dance-based program?

Maybe my loyalties to both camps are like siblings vying for their mother's attention.  I am essentially acting as the content specialist for both camps simultaneously and it's hard to pay attention to both equally at the same time. 

Maybe I embody the reality of integration and the inherent tensions therein?  It's interesting to reflect on this question because, since it's just me responsible for both content areas, we can't blame the tension on personality conflicts between teaching artist and classroom teacher.

Maybe none of this matters because one's best teaching comes when you're enthusiastic, engaged and truly interested in the subject matter. 

Maybe it doesn't matter which camp I'm in on any given day or year because the truth is the kids are moving, they're dancing, they're thinking intensely with their bodies and they're learning a whole lot of math, all at the same time.

I've been told on numerous occasions that I think too much, but who was it that said an 'unexamined life is not worth living'?  (I just Googled it, it was Socrates.)  I think it is important for me to ask questions about where my loyalties lie even if, in the end, it doesn't matter.  I'm a process person, I live in the moments between.  And, I know I'm a better teacher when I'm inspired, whether it be by math or dance or reading Carla Hannaford's book Smart Moves like I did in the Fall of 2009.  Hopefully my dance friends will put up with my math obsessions for a while.  I'll be back soon!

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!

Making Things

Curried red lentil soup with sweet potatoes and greens.

I know a lot of people who make things -- dinner, for example.  I know people who grow their own food, make their own music, build their own rock walls, design and build their own houses, decorate their homes with their own artwork, sew their own quilts, and bake their own bread, all as a matter of course.  I know people who knit their own socks!

Then again, when I go into schools, I meet legions of children who never even considered the possibility that they could make something, let alone their own percussive dance patterns.  Here the thing, though -- most kids, even if they don't regularly engage in making things, get excited when it's their turn to make their own dance patterns in class.  It's amazing and energizing to watch, honestly.  It's like I'm giving them permission to take their rightful place in the human race.

I have been reading back issues of the Teaching Artist Journal and finding common themes emerging in what I read.  One of the things that comes forward is that many Teaching Artists (like myself) teach with less of a focus on the technical aspects of their art and put more emphasis on helping their students make things within the structure of an artistic practice and process.  When a Teaching Artist takes their art into the classroom (or community center, or after-school program, or a nursing home, or wherever people are)  they work with people who may have never taken a dance class or made music or used paint in a meaningful way in their entire lives.  They usually have limited amounts of time to work with a group of students and so they become masters at helping people make personally relevant art with a limited vocabulary of skills.  

This is what I do in Math in Your Feet.  In an upcoming article to be published in April 2011 in the Teaching Artist Journal, I go into detail about a teaching tool I created which I call 'Jump Patterns.'  Essentially, Jump Patterns are to percussive dance what creative movement is to ballet or modern dance.  Jump Patterns reflect the elements of percussive dance and allow children to be creative and successful in this particular dance style, but without great need for technical development. 



Don't get me wrong, skill development is important, but sometimes a focus on technical issues creates a huge obstacle to experiencing the incredible joy and importance of just making...things.  Art.  Ideas.  Music.  Shoes out of paper plates.  Even having this particular discussion is part of the cultural baggage we carry, a particular mindset that gets activated and reactivated whenever we think of art solely as something to be 'good' at  instead of an opportunity to make things.  And that's a pity, because I believe that making things is one of the most meaningful activities in which a person can engage. 

An 'old fashioned dress' the creation
of which was facilitated by safety pins and
some adult modeling.

Right about now you might be asking yourself, 'Just how can someone make something without skills?'  The answer is facilitated making.  Kids are like everyone else, you do have to give them something to work with before they can begin to create.  But, in the end, all you really have to do is help kids explore the medium, find a way for them to  investigate the processes of the art form, help them formulate some questions or just wait until one is asked, and, when it's time, add instruction on specific skills when the student is ready for them.

Here are some examples of what I mean by facilitated making:

Example I:  In Math in Your Feet, Jump Patterns are the tool that facilitate the making of foot-based dance patterns.  Once a kid learns three of the four elements of percussive dance (leaving out the most technical aspect, parts of the feet) they are then ready to experiment and create their work.  They become participants in the traditional aesthetic -- everyone has something to offer, everyone has their own style or take on the dance, everyone is welcome.  Not everyone is good but, more importantly, everyone participates.  Without participation there is no form.

Example II: A Teaching Artist friend of mine works with kids who, more often that not, have no formal music training.  When he sets up digital recording studios in their schools they are able to get immediate feedback on their own ideas and find ways to evaluate and adjust their ideas to make real, and often interesting, music and lyrics in a collaborative way with their friends.  He spends parts of each class talking about the science of sound or new techniques for using the equipment but mostly the kids experiment on their own and come to him if they have questions.  In this case, the facilitation is the TA's approach to using the equipment with his students. 

Mermaid's Tail

Example III: My daughter, who is five, has always had many ideas and many of them get expressed through her art supplies.  When she was two, she wanted paper cut into shapes so she could make something with them.  She had an idea but still did not yet have the skill to cut the paper the way she wanted.  Did I say, "Sorry darlin'.  You'll have to wait until your hand muscles are stronger and more coordinated before you can get that idea out of your head"?  Nope.  I cut the shapes for her and she did the rest.  Did it change the fact that it was her artwork?  Nope.  A few years later, when she was a few months shy of her fourth birthday, she had an idea for a mermaid's tail.  By then, facilitating her making process simply consisted of making sure the tape was secure so all those little pieces stayed together.

Making things is not rocket science...well, unless you're trying to build a rocket.  But what comes before that rocket?   All the times when kids get a chance to ask questions, experiment with materials, find their own answers and get some help and guidance from adults along the way.  We can sometimes get wrapped up in giving kids what we think they need to learn, but it's in the doing where the meaning is made. 

And Now? A Standards Antidote

Okay, here's my special challenge (and I take comfort in knowing that out there are other people who understand exactly what I am about to say).  I am an artist.  I am a teacher.  I am a teaching artist, curriculum developer, website designer, market research specialist, performer, agent, writer, editor, math student, calf wrangler...I am going insane!  Well, not really, but I do feel like I exist in multiple worlds simultaneously, sometimes to the point where I can completely contradict myself and agree with myself in the same moment!

Today I was all over those Common Core State Standards I wrote about yesterday.  I just spent the better part of the afternoon working with the new language.  I'm not making anything new up, just translating what I do, what I've always done, into the language of the most current stated education goals.  I've also been working on a grant project for the second pilot stage of Young Audiences, Inc. Signature Core Services program, which has meant working with new forms and terminology.

Along parallel lines, I have been spending the better part of my after-the-kid's-in-bed time systematically reading all my back issues of the Teaching Artist Journal (I'm into year five at this point).  I started this particular project in December because I figured that, as a recently appointed Associate Editor for this publication, I should probably have a working knowledge of what kinds of articles, topics, research etc. have been published in the past before I move forward with my new position.

Re-reading TAJ's has actually been really interesting and inspiring, and much less an exercise than my husband thought it might be.  It's been interesting because the process of reading them one after another is bringing me the big picture I never had getting each new TAJ one at a time, three months apart.   I'm learning a lot!  And, it's been inspiring, because I've been running into really great thoughts like this one (below), which balance out all my standards-based wonkyness of late.  So, without further ado, here's my standards antidote for today:

"Although making art does encourage curiosity, critical thinking, and empathy -- necessary tools in today's world -- these very qualities may also demand that one speak truth to power or insist on beauty.  Nourishing imagination may inspire one to declare along with Blake: Everything that lives is holy.  Such a vision might make one less suited for production lines, prison cells, or political speech.

"So how do we, as human beings and as artists, speak honestly about art?  I'm glad that we talk about the connection between art-integration and academic progress, art's value in passing down community wisdom, and the transferable skills that making art develops.  But I hope we also remember to say that making art is a voyage into the unknown and, therefore, not a process inherently practical, polite, predictable, or proper."

From Judith Tannebaum's article"Oh How We Sparkled: One Vision, Two Themes."  Teaching Artist Journal 4.4 (2006): 248-9.

Digging Deeper: Math and Dance, Dance and Math

I am always on the lookout for connections and commonalities between mathematics and the arts, dance in particular.  In my on-going survey of math/movement/dance approaches out there, most of what I've found seems focused on numeracy and procedural concerns; these are not necessarily wasted efforts, but why stop there?  There is also a lot of illustration of math concepts using dance, but the two subjects stay on parallel tracks with no real connections between the two.  Overall, approaches like these never get to the deeper commonalities between math and dance because they are often more focused on memorization or performance of prescribed movements than understanding and application.

The main focus of Math in Your Feet is a thorough exploration of patterns.  Since my dance form is based in making foot-based dance patterns, it is a natural and meaningful connection, especially if the goal is to develop mathematical thinking and not simply working to improve skills or memorization of procedures or formulas.  After patterns, another commonality between math and dance is certain habits of mind and flexibility of spirit in the process of finding solutions.  With that in mind, I submit to you two diagrams, one from a math point of view, the other from an arts perspective. 

When I look at this diagram from the blog Keeping Mathematics Simple each one of the intersecting circles could describe what I do as a dancer including, I think, even the theoretical.    


From the blog Keeping Mathematics Simple

Coming from the other perspective, when I look at the next diagram, from the article Defining Arts Integration, I think about how mathematicians go about posing and solving problems and definitely see connections to this arts-based diagram of the creative process.  The creative process is a hallmark of artistic activity and, I'll argue, a hallmark of mathematical thinking as well, just not labeled as such. 

From the article Defining Arts Integration

Be you mather or dancer, what say ye?  (Alternative and/or opposing viewpoints welcome!)