Reflection is Good for Everyone (Even the Teacher!)

I've just finished a five-day residency up in Indianapolis as the second part of Young Audiences' Signature Core Service pilot.  Most of the time it seems the dance and rhythm aspect of this program brings kids closer to the page by motivating them to write, sometimes for the very first time, multiple meaningful sentences about their experiences creating original dance steps.  The program can also help kids think of math as a friend, not a foe, also for the very first time.

The kids I just worked with, however, were already very comfortable in the symbolic realm of mathematics and also possessed strong verbal-linguistic skills and positive problem solving attitudes.  They were, however, still fourth graders in their bodies and feet (and I mean that in the best possible way).  In addition, they were good at following directions, and really dug into the activities I outlined but...

....upon reflection, I realize now they might have been bored. 

They might have been bored because they really knew their math, but at the same time they couldn't really do more than fourth graders normally can do with their bodies.  I think that if I had had more time with them, or could do it over, I would have found a way to get their brains more engaged while their bodies worked at age-level.

I would have challenged them to really play with their patterns.  For example, instead of just making a Pattern A and B and combining them into a third, 8-beat pattern (which is a great amount of play in itself), I would ask them how many different ways they could recombine the four beats that made up each pattern, and then encourage them to ask more questions along that line of inquiry: What if we reflected the pattern to itself, beats 1, 2, 3, 4, 4, 3, 2, 1?  What if we took our two favorite beats from the two patterns and traded them with someone else?  "What if...?" is one of my favorite questions, after all, because you never know where it will take you.

Despite these musings of mine, I think things went well.   Here are their perceptions and reflections of the first three days of the residency...

Day One: "You have a friend who was absent today and missed the first day of Math in Your Feet.  Tell that person about all the different ways you made patterns with your feet."

First, we had vocab words, such as hop, slide, clog, etc. then, we made and [sic] pizza, and used all of the dances.  For example, we did sausage as slide.  As it says, Math in Your Feet!

Today Ms. Malke came in and we learned all about dance steps.  This is called clogging.  Clogging and step-dancing are actually cousins!  When we were dancing sometimes we put our feet to a 90°angle and other times she told us to turn our feet to an acute angle.  We also used a lot of math vocabulary words.  We all had a great day full of dancing and math.

Today for an hour we did math in your feet.  We did clogging, and the chug.  We made a pizza in our mind and did different dances to represent what we put on the pizza.

We made patterns by dancing.  When we danced we also made rhythims [sic].  We also pretended to make pizza.


Day Two: "What did you have to do to dance congruently with your partner?  Using complete sentences, name at least three things that had to be the same.  What kind of challenges did you and your partner face to make your dancing congruent?"

To dance congruently with my partner we had to count out the four beats.  The timing, dance steps, and the beats all had to be the same.  One challenge we had was timing at first, but then we practiced and practiced and we finally got it at the same time.

My partner and I had to take one step with our right ft. 1st, then left, turn 180° right, then 180° left.  The kind of challenges we had to face are having to make sure we both knew what order our steps were in then we counted 1, 2, 3 to know when to start.

Do the same dance you have to keep a steady beat, go at the speed of the slower person, and practice.

My partner and myself really didn't have any problems, but if I had to pick three I would pick that 1. was that I could not get the steps right.  2. We could not stay together.  3. We could not figur [sic] out how we wanted to do are [sic] steps like for example speed fast, mideam [sic] or slow.

Me and my partner faced lots of challenges.  We did a 270° turn wich [sic] was hard to be congruent while doing.  The speed, movement, and moves had to be congruent.

To dance congruently, I had to say something to signal us to start dancing.  The 2 diagonal splits & 1 side split had to be the same so it would look good.

Day Three: "Write a friendly letter to your partner.  First, tell this person about what you had to do to reflect your dance pattern across the line of reflection.  Then, tell your partner what your favorite MIYF dance move is and why!"

I had to turn right instead of left to mirror your moves.  I love our Pattern A!  It's casual, but interesting.  I can't wait to see Pattern B.

To reflect our dance pattern across the line of reflection you had to do it in the opposite sides and I did it originaly [sic].  My favorite MIYF move is a slide, with our feet together, and back just because it's fun to do!

In Math in Your Feet we did a line of reflection and how we did it was we had to pick a person to be the original and the reflector.  The reflector had to do oppsite [sic] lefts and rights.  My favorite dance move was the cross because it is fun and it makes me feel like a real dancer!

I had to instead of going right diagonal at first I had to go left to right Diagonal.   I don't have a favorite dance move because I don't like to dance.

I love having you as a partner because you don't get mad when I mess up and you agree with anything we do.  I could go on with the tanes [tons] of things good about you but I'll stop there.

First, we had to pretend we were looking in a mirror. We had to  switch our rights with lefts and lefts with rights.  My favorite dance step is turn because I like getting dizzy.

I love fourth graders!

By the Book

I have to stop beating around the bush. 

You know, I know, and everyone knows that a chance to reflect on one's learning is where the learning actually happens.  That's why, when we were first developing the Math in Your Feet program, my wonderful co-creator Jane Cooney said, "We have to have a workbook to go along with the dance classes."

Yes, I know the label of 'workbook' has a lot of connotations, including busy work, and if you can think of a better name, please let me know.  Residency Journal?  That might be better.

Anyhow, Jane's idea was that the workbook would be the place for written reflection, word study (math and dance words/concepts), a record of the students' creative work (including mapping the patterns), and extension activities that look more like recognizable math problems related to the residency work.  For instance: "Make a scale drawing of the dance space you use in dance class."  As I've discussed elsewhere in this blog, I build the bridge between math and dance in my workshops, but it is up to the classroom teacher to make time to use the workbook and bring this learning back to the page.

Over the years, I've notice teachers becoming more and more stressed by the push of their district's curriculum and by testing, so much so that just bringing their kids to me for an hour a day for a week is now about all they can handle.  Maybe they get their kids to complete the daily reflection journal prompt and the word study, but that's about it.  Math in Your Feet, unfortunately, sometimes ends up being just a 'fun' event (and don't even get me started on 'fun'...).  There's also sometimes a perception that teachers carry that we're not doing any real learning while we're moving, the least of which would be math.  I once actually heard a teacher say to his students, when leaving my class, "When we get back to the classroom it's time for math."

An obvious sign that students are skipping the written work and reflection is when I start to hear the kids say, "Where's the math, anyway?"  Or, "Why are we doing this?"  Not every kid says that, and more often than not, kids still love dancing and making up their dance steps.  But I can tell they don't have the same kind of facility with the math and dance terminology.  I can tell they don't remember what we did the day before or why.  I can tell that they don't really fully understand the process and concept of transforming their patterns.

It's an opportunity lost, if you ask me.

Last week I was at Templeton Elementary School in Bloomington, IN where I live.  (Thanks to an Indiana University ArtsWeek 2011 grant!)  As the week went on I got lots of fantastic reports about kids who had never wanted to pick up a pencil who were excited to go back to their classrooms and write about their work in Math in Your Feet.  I've heard this before, actually.   Engage a kid's emotions, give them something real and personal to write about, and they'll respond.  And, along with that, REQUIRE that they complete their residency workbook assignments.  Even if it takes longer than expected.  Even if other things have to be pushed aside for the week.  Even if the math topics in this program don't align with your lesson plans for the week I'm at your school.   

There's the potential for deep, thoughtful engagement with both the math and dance content in this program, but it's all water through a sieve if kids don't get a chance to reflect on their learning and make it their own.

Learning to Listen

Are kids smarter than they were five years ago, or is it just that I've stopped looking for the 'right' answer?

Are my students more perceptive than they were, or is it just that I am more receptive to what they have to say, even if it's not 'time' for it?

Are fourth graders smarter than they used to be, or is it just that I am less interested in 'moving the lesson forward' and more interested in listening to their reasoning?

Are kids understanding the program better now or is it just that I'm finally really hearing what they have to say?

Have they always had insightful observations, or is it just that I am more open to multiple interpretations of the same event?

I think we know where this is going.  Kids have always been smart and I haven't always known what to listen for.  It's been really exciting this week to hear my students' observations, thoughts and insights.  I am, for the first time, really enjoying the process of teaching this program. 

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!

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!

Residency Reflection

I started this post a few weeks ago.  I guess I needed some time, space and perspective to finally finish it.  Here you go: 

I just finished a big week with four classes of fourth graders.  Their teachers told me they were a tough group on the whole, but of course it's only through experience that I figured out what that meant, exactly. 

I've had tough groups before, but these kids confounded me, actually.  There were bright spots in each class, and there was also some good thinking and creating, when it happened.  But, on the whole, they could barely stay in their squares.  They would forget any verbal instructions I gave.  I had to stay within two feet proximity to get any attention at all.  Most of them could not consistently find the center of their dance spaces.  They took every gentle reminder as a power struggle.  Transitions such as moving from sitting to standing or dancing to not dancing with control was a herculean effort for them.  

Don't get me wrong.  These were not 'bad' kids, just kids with a lot of challenges.  I've spent a lot of time over the years figuring out how to help kids control their bodies while moving and then again when the moving is done.  I've also spent many years helping kids become more aware of where they are in space and where in space they are intending to go, with good results.  But this particular week, none of my strategies seemed to work.

I often compare my week-long residency to the first week of school.  By the end of our time together I've figured out exactly what each particular class needs to be successful, but by then it's time for me to go on to the next school, or the next group of kids.  Not really understanding who I'm teaching and what they need as individuals and as a class is my least favorite part of the job.  If I had the week to do over, this is what I'd do:

• 30 minute class length, or less.  I am contracted to implement my program within certain parameters including the amount of time each class has with me (usually 60 minutes at a time).  Classroom teachers who implement Math in Your Feet in their own classrooms have the flexibility to work on it in ten minute chunks or whatever length they choose.  My 4th graders this week had to hold it together for a whole hour with me each day, which was a loosing proposition. 
• Take it out of the gym and find a more enclosed space.  The gym for this particular week was not a bad gym in terms of sound issues, but it was a gym none-the-less.  I never use the whole gym and always define the limits of our dance space (with tape!), but if we could have put walls around us to enclose the space somehow, it might have helped the kids feel safer and may have helped the focus issues. 
• Reduce transitions.  It's a hard reality, but we have to get up and move, and then we have to sit down and listen.  We do both in short bursts, which these kids needed, so I'm not sure exactly how I would have done this.
• Dance for them more to keep them focused on the reason for why we were together. 
• Teach one two-person team at a time. The only times they were really quiet, focused and, well, not argumentative and actually helpful, was when a team was up in front of the class showing work in progress or demonstrating a math concept through their dancing.  If I could do this over I'd take the plunge and just teach one team at a time while the others watched.  I think we would have gotten a lot more acomplished this way.
• Acknowledge the issue of 'first reaction' sooner and with all the classes.  I think I got this idea from a parenting book I read in the the last year.  Essentially, each one of us reacts in our own way to new situations.  We have either a negative first reaction or a positive first reaction.  Knowing how we operate in this regard can help us overcome the challenges each present.  For those with a negative first reaction (hold back, regard with suspicion, decline to participate, or exhibit unhelpful behavior) it just means making sure that they know that I understand they're not into it at the moment and that's okay with me.  At that point I usually outline what my minimum expectations are for participation-- stand when the rest of the class is standing and sit when the rest of the class is sitting, and that's it.  I've had success in the past acknowledging the reality that kids may not love what we're doing as much as me, but I still expect them to give it a shot.  By the time I realized what I was working with, it was too late in the week for this strategy to have much effect.   That usually gets us over the hump, but not this week. 

So, all in all, we did get through the week.  I suppose the bright side of all this is that I'm a little more ready the next time I encounter a group like this.  And, I'm still a big supporter of using dance and movement in integrated ways for all children.  Just because it didn't work for them the way I wanted this time doesn't mean that it can't.  It just needed to be different.  Too bad my time machine's in the shop, or I'd try again.

Like I said at the beginning, there were some bright spots.  This is what one girl wrote in response to a reflection journal prompt:

"Ten years from now I will remember how hard it was to learn and how much fun it was.  The challenges I had were putting pattern A and pattern B together.  The thing that helped me work through them were because I had D. as my partner and he was always hard working and an on task friendly boy. :)  I loved this program."

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.

The Power of Limits 4: A Jazz Metaphor in Mathematics Education

Stephen Nachmanovitch, in his book Free Play: The Power of Improvisation in Life and the Arts, includes a chapter titled 'The Power of Limits.'  This is the fourth in a series of posts inspired by this chapter, exploring how limits not only enhance creative problem solving but are actually a requirement of such a process.  

Today, however, my focus is on the idea about how 'playing outside' an established structure (e.g. a limit) is a way of exploring the limitations themselves, a process which can often lead to new innovations, strategies and ideas.  The article Playing outside: An introduction to the jazz metaphor in mathematics education is the inspiration for this post.

Stay with me here...

After debuting my blog in mid-October, an arts friend sent me a copy of an article, as referenced above, from the Australian Senior Mathematics Journal 18[2] authored by Jim Neyland, Victoria University, Wellington, New Zealand.

I read it and promptly penned (typed, actually) the post Building a Bridge which starts out "I am not a math teacher."  Since then I've been revising that particular view, but that's really the subject of a future post.

Today I picked up the article again because I needed something to read while the kid was jumping over alligators in dance class and found some very interesting ideas!  This excerpt from the article succinctly pulls together two of this blog's main topics -- connections between the arts (specifically music and dance) and mathematics education:

"It is becoming evident that experienced [math] teachers operate in a way that is better described by what is called a 'complexity' model, a radical alternative to the linear model...The teacher's role in the complexity model is that of an artist; but not any kind of artist.  The teacher is not the sort of artist that turns lumps of clay into pottery, or a blank canvas into a painting.  He or she is an improvisational artist who participates in the process of emergence, but in a special way.  The improvisational teacher uses an 'attractor' -- that is a technical term used by mathematicians when referring to the way some chaotic systems eventually settle to an emergent order, and in teaching can be taken to mean what is called a 'rich mathematical activity'...and watches what happens when the students engage with it." 

I read "rich mathematical activity" as something similar to a rich, productive creative process, one where ideas are experimented with, dropped, added, and revised in the process of becoming a fluent thinker within a discipline. I think that happens in my classes when children, after learning the basic vocabulary of percussive dance, are given the freedom to experiment and reach a level of comfort and fluency within a relatively short time frame of five days.

The author goes on to say,

"Much of what I have been referring to about the complexity model is evident in the way jazz improvisation occurs [...] In jazz, 'playing outside' refers to a radical form of improvisation that deliberately transcends the established [musical] structure [...] Why is playing outside done at all?  It creates a high degree of tension.  It is a way of exploring the limitations of the established structure.  It is a way of keeping the structure secondary to creative improvisation...Playing outside, to put it differently, is playing with [emphasis mine] the structure, not within it as happens in normal improvisation.  As such, playing outside is essential in the study of mathematics."

In reference to my own creative process of developing the program Math in Your Feet, I'm pretty sure I was 'playing outside' the traditional view of my dance form as I asked questions and, over the course of a couple years, experimented with the best fit between a rhythm-based dance form and elementary math topics.  There was actually quite a bit of tension as I did this -- a push and pull around what my role was as the artist in a math context, what kind of ratio of dance to math within my lessons, and whether or not what I was doing was 'real math' or not, etc.  In the end, I think I remained true to the spirit and the structure of the traditional dance forms I know and love, but the context for exploring the dance changed.

Also, because of the limited amount of time I have with kids, I'm not sure if I really 'play outside' the structure of what I am trying to teach; at the very least I am 'playing inside' (improvising) the structure of my lesson plans as I respond to the varied skills, experiences, and motivations of my students.  In terms of math education, however, the students' time with me may very well be the first time they have had the opportunity to 'play' with math ideas, free from procedural concerns, for a little while at least. 

It is possible that I will pick up this article again in another month and see something completely different, but equally as thought provoking.  For now, though, I'll leave it here as road marker on the path of this discussion about limits and creativity.  As always, your thoughts and feedback are welcome!

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?

More Than One Right Answer

There's a video showing up lately in the different places I'm visiting on the Internet.  It's an RSA talk by Sir Ken Robinson, world-renowned education and creativity expert, called Changing Educational Paradigms.  This is surely a subject that's outside the scope of my experience and this blog, but there are certain things he said during the talk that speak to what I think about when I'm working with or creating programming for children.

"Creativity is the process of having original ideas that have value.  Divergent thinking isn’t a synonym, but it’s an essential capacity for creativity.  It’s the ability to see lots of possible answers to a question, lots of possible ways of interpreting a question, to think laterally, to think not just in linear or convergent way.  To see multiple answers not just one."

There is also another interesting RSA talk I recently watched called The Surprising Truth About What Motivates Us.  It's a talk given by Dan Pink and although it is focused on workplace motivation, I think there are some parallels to a school setting. 

"[This study on what motivates people] has been replicated over and over and over again by psychologists, by sociologists, and economists.  For simple, straightforward tasks, those kinds of incentives, 'if you do this then you get that,' they are great.  For tasks that are an algorithmic set of rules, where you have to get a right answer [emphasis mine] if/then rewards, carrots and sticks – outstanding.  But when the task gets more complicated, when it requires some conceptual, creative thinking, those kinds of motivators demonstrably don’t work. […] There are three factors that the science shows that lead to better performance, not to mention personal satisfaction.  Autonomy, mastery, purpose."

My purpose in Math in Your Feet is to create opportunities for children to develop a level of mastery using the language of percussive dance to solve problems in a creative context. This context is naturally open ended and a place where there is more than one right answer, indeed an infinite number of right answers.  My philosophy is to give children limits (defined work space, four and/or eight beats only) and some tools (elements of percussive dance, a clearly defined process) and then let them work it out from there. 

The students work with a partner.  As early as the second day of our residency, students are taking control of their ideas, making choices, collaborating, and creating.  During their creative work time, I say over and over, "There are no right or wrong answers, only choices that have to be made.  What works, what doesn't work? Decide that and go from there..." 

What can you create within the limits that I set?  The 'answer' for each pair/team of students is two four-beat dance patterns sequenced into an eight-beat pattern and transformed with reflection or rotation symmetry or sometimes both.  In the many years I've been doing this, I've never seen the same pattern twice but they are all 'right' answers.  In fact, by the end of their time with me, many classes understand the potential of this structure so well that they still have ideas they want to try, directions in which they want to go. 

By the end of our week, children begin to understand and see that their ideas are ones "that have value."  I ask them if they are proud of the work they have done in their week with me (in both dance and math) and the answer is always a resounding

YES!

Going Local

For most of my career as a teaching artist I have had to travel hundreds of miles to get to work.  I'd spend a lovely week in some beautiful part of North Carolina, South Carolina or Kentucky and then drive home.  I loved the opportunity to work with all kinds of kids, but inevitably I'd miss my own bed and let's not even mention doing insane things to stay awake on the drive home after a busy week away (wasabi peas, anyone?).  Even now, having temporarily limited my travel closer to my current home, I usually 'only' go as far as the north side of Indianapolis and back in a day, and that's still three hours round trip from Bloomington, IN.

I have performed in Bloomington, but I have never worked in my capacity as a teaching artist here.  It is a fabulous town, full of arts and culture of all kinds with the Lotus World Music and Arts Festival being one of my favorites.  Indiana University is also a mecca for arts and culture, including the Jacobs School of Music and programs like the Department of Folklore and Ethnomusicology.  If you go hear to a show headlined by a 'local' musician, chances are that person has a thriving regional or national career, or is good enough to be considered for one.  Even without considering all this talent, Bloomington is truly a caring, involved and creative community. 

So, I do a lot of driving for work, but now?  Now I have a chance to reduce my carbon footprint and make a contribution to my own community with the receipt of a grant from....

Indiana University's ArtsWeek!  This year's theme is ArtsTeach and I'm completely honored and excited to have been one of the projects chosen for the 2011 ArtsWeek celebration.  In February, I'll get to drive approximately FOUR MINUTES down the street to Templeton Elementary School.  And when I'm done with my work, I'll drive four minutes back home.  Amazing.

I realize I probably sound more excited about the reduction of my commute than anything else, but I should assure you that I am thrilled beyond words to be able to bring Math in Your Feet into my own community.  In my collaboration with Templeton Elementary School, and their PE teacher Monica Chapin, we'll be offering a week-long residency, a family night focused on creative problem solving, and a no-holds barred traditional American music and dance performance to the Templeton ES community.  MY community.  I'll get to work with kids I have probably seen playing at Bryan Park after school, or in the audiences at the Farmers' Market when I busk there in the summer, or playing basketball at the Y, or whose teachers have taken a Zumba class from me.  There truly is no place like home and I, for one, am thrilled at this opportunity.  Thanks IU ArtsWeek!

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!

Teaching Below the Surface: Harnessing the Power of Tape!

In earlier posts I espoused my enthusiasm for using simple floor tape to manipulate an environment and encourage physical exploration of that environment.  It's a powerful tool for teaching below the surface, something that makes a bigger impact when you don't talk about it because it's just there.  The Reggio Emilia approach says that environment is the third teacher and I have found this to be true in my work.  How I set up a learning environment can have a large impact on the students, and I have pictures to prove it!

In my work with elementary students we have a group dancing time to warm up and learn clogging, a little each day until they have some mastery of basic steps by the end of the week.  The bulk of our class time, however, is spent with partners engaged in creative work.  This effort is done in what I call a 'personal dance space': a scaled down version of the portable square dance platform on which I teach and perform.  Mine is wood, theirs are tape.  Mine is brown, theirs are blue.  Mine is three dimensional, theirs is two dimensional. Mine is 3'x3' and theirs are 2'x2'.  Did I mention I love floor tape?

On the first day we work exclusively as a large group and the tape on the floor in our dance space is a simple three-sided rectangle.  The kids line up with their toes on the tape and face toward the center of the space.  This way everyone can see me and what my feet are doing.  By the second day of our work together I've managed to tape out about 15 pairs of blue dance spaces.  Inevitably, on that day the kids walk into the room and, knowing nothing about what is going to happen in our class later, they go directly to a box and sit down.  I have to redirect them to the large-group perimeter tape but there's something about having a space of one's own, and these boxes just pull them in.

We never talk about the set up of the room, but since we focus quite a bit on transformation and symmetry in this program I try my best to make sure that, if asked, I can draw an accurate line of symmetry down the middle of our dance space.  So, without further ado, here are some drawings done by fourth graders as part of a Thank You letter project their teacher had them complete at the end of the residency.  No one told them what to draw.

I'm obviously very welcoming!  This was drawn from memory, back in her regular classroom. 
Notice the basic symmetry of the space. 

This isn't exactly what the room looks like (not enough squares), but you can draw a perfect line of symmetry from top to bottom of this picture.

One of the other 'below the surface' learning tools in the program is that working with a friend and sharing ideas can lead to amazing results.  Not only are these two girls dancing together (and smiling), they're dancing in a space delineated by blue tape! 

Daily Creativity -or- What I Learned from Cooking

I would like to point out that we're all creative on a daily basis.  I never quite know what to say when someone tells me just how creative I am (and, reading between the lines, how not creative they are) as if creativity exists only in the realm of art making or that it's something that happens for just a few, select people. 

I also consider creativity and problem solving to be synonymous -- a series of actions and decisions made towards the goal of solving a problem, whether that problem be finding a cure for cancer or formulating ideas that end up as paintings in galleries or a concert on a stage.

In Math in Your Feet (elementary version) kids make up their own percussive dance patterns.  While we're engaged in this process I make the point that 1. both problem solving and the creative process usually don't occur with one action, but with a series of actions and choices that bring you to a solution and 2. sometimes, if things aren't going the way you'd like, you have to revisit a previous step of your process to refine or redirect your ideas. 

One of the other things kids experience in Math in Your Feet is the difference between choreography and improvisation.  Choreography is usually the end result of a lot of improvisation -- trial and error and trial again.  There are a lot of choices and decisions you have to make a long the way.  Sounds a lot like problem solving to me.

So, we are all creative, on a daily basis.  We all have multiple opportunities throughout the day to identify a need, make choices, and strategize about what to do next.  Not every problem needs to big and not every solution needs to be a work of art or cure cancer for us to engage daily in this wonderful process.

As an example of daily creativity, please consider Exhibit A: a list of ingredients for a recipe I used to make called Skillet Black Beans:

4 medium potatoes

1 1/2 tbs olive oil
1 med-large onion
2-3 garlic cloves
1 med green bell pepper

1 4oz can mild diced green chiles

1 16oz can diced tomatoes
2 tsp ground cumin

juice of 1 lime

6 6-inch corn tortillas, cut into narrow strips

This is a great recipe, don't get me wrong, but after eating it four or five times it just wasn't working for me.  I didn't like the potatoes or the bell pepper.  I'm not a fan of chiles.  We can't eat corn in our house right now.  So, I used the original recipe as a starting point.  I experimented and made adjustments.  It's still called Skillet Black Beans, but now it looks like this:

Oil (not measured, just eyeballed)
1 sweet onion
Lots of garlic
Half a small head of cauliflower, cut into small pieces
1 big can of fire roasted crushed tomatoes
2 small cans of black beans
2 tsp ground cumin
3 large rice tortillas, cut into small strips

It's still the same recipe, but different, and it suits my tastes and my needs.  I'll never be considered a gourmet (there are many, many better cooks out there than myself) but when I cook I feel a sense of my own mastery.  My food is the direct result of my choices, for better or worse.  If I don't like what I made, I get to try again to make my dish more the way I'd like it.

That's why helping kids create their own dance patterns is so satisfying for me. Once I figured out how to provide just the right amount of structure (which is really the topic of a future post) I found that kids had lots of ideas and were really excited to try them out, with only a minimum amount of struggle.  And, surprisingly, they were all happy at having a chance to solve a problem (a choreographic one, with limits, but still a lot of freedom for personal choice).

We are all creative, on a daily basis.  Maybe not in the kitchen or in a dance class, but in some other venue.  What's yours?

Looking Back Before I Start Moving Forward

From the first version of the Math in Your Feet Website back in 2004, under "Notes from the Artist":

April 12-16, 2004 was an exciting week for me.  The idea for this new program, Math In Your Feet has been germinating since I developed my first arts in education program, Rhythm & Dance (now called Drum With Your Feet!) back in 1997.  Over the years, as I gained experience working students, identified the what was important to me about my art form, and created study guides and extension activities to help solidify the dance and social studies concepts within my residency, I could just tell there was math in there somewhere, and the idea excited me.

I always wanted to understand math but there was only one time in my entire life where I actually did.  It was during my senior year in high school, in pre-calculus.  It was a grey day in western Oregon and I was sitting over my textbook completely confused. My teacher came over to help me, and all of a sudden I felt as if the sun was shining over me, full and bright -- I had grasped the larger meaning.  But in a moment, the clouds came back.  Over the years, I have held onto that experience, and used it as a beacon, knowing that there was hope that one day I would, and could, "get it".  

On Day Two of this first pilot week of Math In Your Feet! I wrote in my notes, "I can see the excitement in the kids when they see what they already know [about math] being used in this new situation."  That's what Math In Your Feet is: A crossroads, connecting previously unrelated ideas together to create a place of deep understanding, if even if for a moment.

In my mind, the connections are everywhere.  Thinking and dreaming and problem solving can occur using any language, whether it be spoken, or in your feet using the pattern of rhythm and movement, or in math.  At the end of this pilot week, one girl said to me, "I didn't like math, and I still don't, but I like it more."  I believe she "got it" this week -- that at some level, I was her ray of sunshine in an otherwise cloudy part of her mind labeled "math."