Monday, December 27, 2010

The Mind/Body Split: A Guest Post from My Former Self

I found my former self in some files recently, but I wasn't sure what to do with her, until now.  Here's what happened:

A friend sent me a link to an article titled Children's Gestures and the Embodied Knowledge of Geometry.  This is an incredibly important finding.  Here's the abstract:

There is mounting research evidence that contests the metaphysical perspective of knowing as mental process detached from the physical world. Yet education, especially in its teaching and learning practices, continues to treat knowledge as something that is necessarily and solely expressed in ideal verbal form. [Emphasis mine.]  This study is part of a funded project that investigates the role of the body in knowing and learning mathematics. Based on a 3-week (15 1-h lessons) video study of 1-s grade mathematics classroom (N = 24), we identify 4 claims: (a) gestures support children’s thinking and knowing, (b) gestures co-emerge with peers’ gestures in interactive situations, (c) gestures cope with the abstractness of concepts, and (d) children’s bodies exhibit geometrical knowledge. We conclude that children think and learn through their bodies. [Emphasis mine.]  Our study suggests to educators that conventional images of knowledge as being static and abstract in nature need to be rethought so that it not only takes into account verbal and written languages and text but also recognizes the necessary ways in which children’s knowledge is embodied in and expressed through their bodies.

Reading this abstract I am reminded that when I was in college I was concerned with, among other things, the continuation of a dichotomous world view; you know, seeing only us/them, self/other, intellect/emotion, good/evil and not any of the gray area in between.  In particular, one of my main concerns at the time was of the mind/body split.

That's where my former self comes in; it turns out she actually has a lot to offer this discussion.  Here is an excerpt from the introduction of a paper I wrote at the end of a quarter of self-directed study in 1989.  The paper is grandly titled "Connections: Healing the Split within Western Thought" and although I'm pretty sure it wasn't my best work, I find this portion to be particularly interesting. 

(Please excuse my youthful idealism.  And, please keep in mind the first line of the above abstract as you read: "There is mounting research evidence that contests the metaphysical perspective of knowing as mental process detached from the physical world.")

"In a dream I had a couple years ago, I cut off my head and walked around with it under my arm.  But the funny thing was, I could still hear and think, and feel.  I sat it down on a bed and we looked at each other for a while.  Then it was time for me to put the head back on my neck; I tried to keep it there but it flopped around like a little baby's head.  Finally, I got it settled, but then realized that I had to sew it to my neck -- but I hate to sew!  So I just let it sit there and walked around with a bright red line of blood around my neck.  I never did connect my head to my body, until now."

"The dream of severing my head from my body and then being reluctant to reattach it in any permanent way was, I know now, an unconscious image of the dichotomous schema that pervades Western thought.  Polarities such as self/other, us/them, male/female, black/white, mind/body, human/animal, and life/death permeate our mentality and prevent us from seeing the necessary relationships and connections that run between them. [...]

"In the following pages, I touch on the issue of how we have become so disconnected with the world.  And, more importantly, I look at the steps we can take to heal the split to become whole again.  In Part One, I trace briefly the major steps in history that have contributed to the dichotomy of thought that exists in our society today.  In Part Two, I present the foundation of holistic thought, which includes a brief discussion of Gregory Bateson's epistomology -- how we can learn to know the world as it really is.  Part Three investigates the characteristics of creativity and how it can help everyone reach her or his potential in life.  And, finally, Part Four shows how, when combined, Systems Theory, Batesonian epistemology, and creativity create an understanding of how we can, at least in theory, heal the split."

Um.  Okay, I know that was a big bite of thinking I took back then but let's but fast forward to now.  I suppose you could say that in creating a curriculum that integrates math and dance, using concrete movements and patterns executed by the body to illustrate and illuminate the often abstract world of mathematics, I am attempting to 'heal the split.'  I should also say that, at the time, I was acutely aware that I was short on life experience with which to illustrate my ideas.  My twenties were spent searching for a solid tether; when I found step dancing five years after this paper was written I felt a huge relief that I was finally doing something meaningful and real. 

And now?  Now it seems I've come full circle because from where I sit it is clear to me that finding the connection between mind and body has been my life's work all along.  I also like reading about the seeds of my interests in understanding the uses and benefits of creativity outside the realm of artistic process.  But that's for another day. 

(A side note from me as the spouse of a digital archivist -- if I hadn't printed out my papers back in 1989 and only kept my now inaccessible 'floppy discs' there would be no 'former self' to contribute to this blog.  How will you be accessing your digital files twenty years from now?  Just sayin'!)

Sunday, December 26, 2010

Good Words

Another 'map is not the territory' moment... This one hangs in my home studio/office to keep me in line.  Does it relate to your life in any way? 
Artwork by Morag Manzer, Charlottetown, PEI Canada

Tuesday, December 21, 2010

Statement of Purpose: The Nature of Bridges

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

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

Tuesday, December 14, 2010

My New Hat!

You may remember that back in November I had an article accepted for publication in the Teaching Artist Journal (TAJ); the TAJ is a research initiative of the Office of Academic Research, Columbia College Chicago.  Shortly after the article was finalized I was asked to become an Associate Editor of the TAJ.  This is a huge compliment, and a great honor to be included in what is currently the only peer reviewed journal dedicated specifically to the work and thought of teaching artists.

I've subscribed to the TAJ since it's inception, but that was seven years ago now, and in 2003 I had just started thinking about how math and dance (percussive dance in particular) could be brought together.  So, before I receive my first article to shepherd through the peer review process, I thought I had better go back and take a look around past issues and get (re)acquainted with the work that has been done prior to this moment.

What is interesting to me is how much my experience has changed me in the last seven years or so.  As I go through the first four volumes of the TAJ  I realize am looking at these articles with new eyes.  There is so much there that could have been really helpful to me at the time, but I didn't really see it.  Why?  Because I was still new at being a teaching artist.  Because I was in the middle of my own process, slogging away, trying to figure out what a math and dance integration would look like or even if it was a workable idea.  In short, I had to have my own experiences.  I needed more time doing the work of being a teaching artist before reflecting on my place in this profession or even really being able to fully understand what other teaching artists were saying about their own work.

That, in a nutshell, describes my view of how the learning process should be.  Actions first, reflection later.  Concrete to symbolic.  In Math in Your Feet we quite literally jump into dancing from the first moments of the residency.  As children build their understanding of and competency with percussive dance elements, they are able to apply this new understanding towards making connections between math and dance.  By the end of our time together they are usually able to understand their own personal relationship to the world of both dance and math because now they, too, have become creative problem solvers in two great fields of inquiry.  Most kids who complete a Math in Your Feet residency report being proud of their efforts as well as how much more they understand about both math and dance.

Sort of like how I'm feeling right now.

But this is no time to rest on my laurels -- I have seven more years of the TAJ to look through!  I estimate that at the rate of one article a night before bed I may be through them all by some time in early May.  Better get to work!

Sunday, December 12, 2010

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!)

Wednesday, December 8, 2010

What Are They Really Selling?

"Motion Math creates movement-based learning games that give players an intuitive sense of math."

"Motion Math: Move, Play, Learn!"

"Motion Math provides a much-needed experience to bring the body more fully into mathematics learning” – Roy Pea, David Jacks Professor of Learning Sciences, Stanford University

Ummm...this is a hand-held game that involves tilting an iPhone.  If you go to the site and watch the promotional video, you see kids sitting on couches, staring at little screens.  So what if they might get better at fractions?  They most likely already get enough screen time.  And yet, there they are in the video, sitting on the couch, watching a little ball bounce on the screen while their precious brains are wasting away into cyberspace, or wherever brains go when their bodies aren't moving. 
Thus ends my rant.

Monday, December 6, 2010

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."

Sunday, December 5, 2010

Featured NCTM Workshop!

Hey, check this out!  My workshop at the NCTM 2011 Annual Meeting and Exposition is featured in their promotion of hands-on workshops at the conference this coming April.  I see a few there I'd like to attend myself.  Maybe next year I can do one on tape as the ultimate math manipulative?  Big talk, I know, but I'm on a mission to prove my theory.
Will you be there?

Saturday, December 4, 2010

Link: Resources for Integrating Dance with Curriculum

Hey y'all!  Look what I found this morning -- a beautiful and thoughtful blog from a dance specialist in the Seattle Public Schools. 

I really wanted to share because this is the real deal.  I don't know for sure, but I think many of my readers are curious about how dance and/or movement fit together with math, and maybe other subjects as well.  There's a lot to sort through out there in web-world, so I was excited to find this. 

Here's a great link from her blog with a list of resources for integrating dance with curriculum.  You might also like the big picture of her work here.

Friday, December 3, 2010

This Looks Interesting: Math & Movement Program

I'm curious what you think about this Math & Movement program. 

I found it online and it looks interesting and helpful on a couple levels.  Right now, my only clear thought is that it's probably an effective way to get kids moving in classrooms where they normally wouldn't be by helping their teachers become comfortable with using movement as a learning tool.  But, I'm not sure about the program's singular math focus on numaracy (numbers, counting, multiplication, etc.)  There is more than counting in math, and more than counting in movement, too. 

I have other thoughts, but I'm curious about yours.  Even if no one comments on this post, I'll have a follow up discussion with myself, but it'll be more interesting to hear what you think!

Thursday, December 2, 2010

Scary Thought

I recently read an article in the New York Times about the use/overuse of technology in teenagers to the point that their brains never get a chance to rest.  That rest period is crucial to cognitive growth and making connections between ideas, so there's a chance of an entire generation may not be able to access the very human experiences of intuition and instinct, both of which are crucial for creative and divergent thinking. Hmmm...

Tuesday, November 30, 2010

Math & Movement Lesson: Basketball Court Pathways

Ooooh, I just had an idea!  Last year I developed a preschool math/movement program by creating simple pathways through an empty space with different colored tape on the floor, and adding locomotor movements down the different paths.  Within a couple months the kids could follow more complex pathways using combinations of locomotor movements.
Look at all those lines!
I've been thinking recently that what I did with four year olds could be adapted for the K-2 set.  The problem is that putting down tape can take a long time.  However...

Most public schools and sports centers have a gym.  A gym with lines already on the floor.  Basketball court kinds of lines.  Lines that are straight and curved.  (It's hard to make curved lines with tape. Really hard.)  To take advantage of all these lines and all the open space, here's an idea to use with five-to-eight year olds that I came up with that merges an exploration of space with locomotor movements. 

The lesson, below, is definitely in the 'map is not the territory' category.  I've had the idea, I've based it on previous experience, I've mapped it out for you to try, but we won't know how it works until someone tries it out.  That's one of the reasons I am sharing this lesson, because I probably won't have a chance in the near future to try it out with kids and it seems like such an exciting idea!

The lesson is more like a whole unit of activities and you'll need to decide how to break it up into manageable chunks.  Also, since repetition is the key to learning, I encourage you to repeat a lesson until it's clear that everyone understands it physically and cognitively.  In even smaller chunks it could also serve as a movement break when needed in the course of a learning day. 

Finally, this lesson starts out looking a lot like dance, and it will build dance skills.  As you build those skills, the more math you'll be able to explore.  If you try out any aspect of this lesson I'd really love to hear how it went and if you have any suggestions or questions.  And, I'd love to hear from you because I'll have questions for you, too!  Leave a comment here or e-mail me at: malke (dot) rosenfeld (at) earthlink (dot) net! 

Basketball Court Pathways
©2010 Malke Rosenfeld, and
Users of this lesson have permission to share it with others with proper acknowledgement, copyright notice, and website links (as above).  If you want to share this lesson with forums, educational groups, wiki sites, etc. please consider sending me a message to let me know where you put it.  You can e-mail me at:  malke (dot) rosenfeld (at) earthlink (dot) com

After exploring a variety of paths around a basketball court by following the lines, 5 to 8 year olds will:
  • decide on a pathway that has a clear beginning, middle and end;
  • create a pathway that includes both straight and curved lines as well as directional interest and some repetition;
  • decide on two to three locomotor movements  (skip, hop, run, walk, slide, gallop, hop, leap, jump) to use while moving down the pathway and which part of the pathway gets what movement;
  • map out the pathway on paper, including color coding and notating when and where to do their movements.

Children will:
  • Use intentional, meaningful movement to gain experience and competency with spatial relationships, a foundation for mathematics understanding; 
  • Make creative choices about the length, shape, direction and design of the pathway;
  • Express creative choices with appropriate math and dance terminology;
  • Bring their kinesthetic experience to the symbolic realm on the page by creating a simple map of their dance; and, 
  • When appropriate, integrate the concept of scale and coordinate systems when mapping the pathway. 

Locomotor Movements: skip, hop, run, walk, slide, gallop, hop, leap, jump
Other Movements & Attributes: turn, smooth, sharp, slow, quick, big, small, long, short, high, low
Spatial/Directional Terms: left, right, on, around, curve, straight, forward, backward, corner, on, off, double, single, length (time and distance), intersecting lines

  1. Start by playing follow-the-leader around the gym to introduce kids to the different combinations of straight and curved pathway choices.  Start by walking on the lines -- as long as you stay on a line you're playing the 'game' right.  Model the idea of a starting and ending location by saying "We'll start at this corner, where should we finish our path?" and "Now we have finished this path, where should we start the next one?"
  2. As you play this introductory game, start giving kids choices about which locomotor movements to use (skip, hop, run, walk, slide, gallop, hop, leap, jump).  You can stay in the lead or give kids turns taking the lead which will help keep the game fresh.  Spend as long as you like on this, and perhaps even repeat the activity a few times a week for a couple weeks.  You can vary this 'game' by giving different challenges such as:  'How slowly can we move this time?' or 'How smoothly can we move?' or 'When we turn a corner, let's make it a sharp turn!' or 'Let's make our movements big on the straight lines and small on the curved lines.'  Keep it playful!
  3. After you're sure they have the 'follow the lines' concept, put on some music (examples below) and let the kids experiment with the lines to find their own pathways.  At this point it should just be about the path, not the movements. The goal is that eventually every person should have their own unique pathway.  After they've experimented for a couple minutes, have them 'freeze' and reinforce this goal as well as the... 
  4. Rules of the Road: If they cross paths or eventually share part of a pathway with another child, challenge them to be 'good drivers' and share the road.  Also, remind them that they need: a starting point and an ending point, to use at least 1/4 of the gym, and to include repetition (for example, two trips around a circle, or double back down a line).
  5. Let them work for two minutes then gather them in a group and see who wants to share their work.  Ideally, pick a kid who looks like s/he already has a pathway and is able to repeat it.  Get a couple kids to show first then send everyone back out to finalize a pathway they can repeat the same way every time. 
  6. Make sure every kid gets to show his or her pathway before moving on.  Use this time to give feedback; you'll want to make evaluative comments like "The lines you've chosen are all straight lines.  I wonder what it would look like if you added a curved line to your path?" or anything else you've noticed about their work.  Because this is a creative activity, there is no completely wrong answer/path, just decisions to make.  So, try to pose questions that will help the child become conscious of the decisions s/he is making.  When everyone has shared their work, this may be a good time to stop the lesson for the day.  Or, it may be a good time to go directly to the Mapping Activities section and complete Activity #1.
  7. Once everyone has a pathway, take some time away from the paths to review basic locomotor movements by saying, "Who knows what a gallop looks like?  Who would like to show me what a gallop looks like?  That's right, one foot in front of the other!"  Have one child at a time illustrate the different locomotor movements, naming each one as you go.  This is essentially a mini-lesson focusing on locomotor movements where kids get a chance to practice their locomotor movement skills by follow one of the lines on the court instead of a more complicated pathway.  That's a good way to assess where their skills are at.  You can never do too much of this kind of cross-lateral movement, which is why this is good for a movement break as well as a dance/math lesson.
  8. By now, you should have decided on your own pathway too.  The next step is to add locomotor movements to the pathways, so model for them what you are going to do with your path.  The best bet is to have one choice of movement per line and then change to a different movement when the line changes (straight to curved, or after you turn a corner.)
  9. Some final reminders for the pathways: turn all corners sharply, and find smoother movements for moving on the curved lines, which will enhance the attributes of a curve. 

  1. Have kids review their pathways.  Using black marker, pen or pencil, have them draw their pathway as best they can on a piece of unlined paper.
  2. Make a little key of the movements used while traveling the pathway.  Write the moves down (i.e. skip, run, hop) and assign a color to each move.
  3. Redraw the pathway on a second piece of paper, this time using the assigned colors to create each section of the pathway.  An alternative would be to color the existing black-lined map using the assigned colors.   
  4. If you think it would work (7 or 8 year olds) have the kids trade maps and see if they can recreate the other person's pathway.

Remember, the movement itself is furthering spatial understanding and this experience (up through the mapping, above) may be enough for five to eight year olds.  However, if you think your kids are ready, here are some additional suggestions to further the exploration of math concepts:
  1. Have the kids assign a certain number of skips, hops, gallops, etc. to each section of their pathway.  Make sure it can be danced first, and then transfer to the page.
  2. Measure the space and the length of the lines and then create a scale drawing/map of the pathway.
  3. Using the measurements of the space (above), create a scaled-down version of the pathway using an x and y coordinate grid.  The intersection of x and y would be oriented to the center of the space your path runs through.
To further the movement/rhythm concepts (some of which turn out to be math related!) try these suggestions:
  1. Develop beat competency.  Using one of the music selections below, work on moving 'to the beat' while moving on the pathway.
  2. Basic phrasing.  Each line segment in the pathway will have a certain length which can accommodate a certain number of steps.  Kids can figure out how many hops they can do on the line before getting to the corner or the start of the curve and then mark that on their map.  Which brings up another point...
  3. How many small hops on the line?  How many if you do your hops bigger?  An issue of scale, I suppose.  Lots of experimentation and questions (from you and the kids) along with a 'let's try it' kind of attitude can bring out some amazing math connections that none of us know are there yet!  Let me know what you find out!

This music is essentially for background color during the creative work.  Dancing to the beat is a whole other ball of wax, so please just start out using the music as inspiration for the creative work time.  That being said, you can spend some parts of your dancing time just on locomotor movements, and that would be a good time to work on dancing to/with the beat.

Artist/Album/Song -- all on iTunes
Chiwoniso/Rebel Woman/Listen to the Breeze (Modern African)
Vishten/Live/Figeac (Traditional Canadian)
Solas/Sunny Spells/paddy taylor's (Traditional Irish)

Friday, November 26, 2010

On Being A Teaching Artist

My dad reads this blog; he's been following it from the start.  It's something you'd expect from a dad, I suppose, but my father is also an artist.  He grew up with his parents and two older brothers in the back of little grocery store in Chicago in the 1930's.  This little room, where they all lived, was the subject of some of his first paintings.  In the 1950's he went to the Art Institute of Chicago to focus on oil painting, and later he moved to graphic design when that still meant lots of brown paper, dial-a-type, darkrooms, and wax rollers.  Ah, the toys of my childhood!  Now he's put his away his brushes and instead works with fabric, making quilts that are his paintings. 

He recently e-mailed. "I read your blog," he said "and really don't pretend to understand half of it since I base my art on intuition and instinct, allowing the sub-conscious to take over when faced with a visual problem." 

I love his description of his creative process because it is exactly what art is about!  Giving way and letting the mysterious parts of your brain mull something over until one day, the solution seems to come to you out of the blue.  Art and creativity (no matter the form) are about deep thinking with parts of yourself that have no words, just images, feelings, urges, emotions.  Even some writers, I bet, are not thinking entirely in words but possibly visually as well when they imagine the stories and ideas they are trying to put on paper. 

My father probably knows more about his own creative process than he thinks, but he brings up a good point.  He's an artistic person so why doesn't what I have to say here in this blog make sense to him? 

Maybe it's because I am engaging in a second creative pursuit called 'being a teaching artist'.  Not only do I pursue my own artistic and creative visions, but I also focus on how to teach my art in all it's complexities, in a way that I hope makes sense to young learners in academic settings.  I am an interpreter and a guide, using words to make my process clear to others. 

Being a guide to my art form requires me to have perspective on percussive dance as a whole (different styles and traditions, technique, and history) and at the same time be able to articulate to others about the specifics of my creative process as well as my intent as an artist.  For example, clogging is often taught in schools with the focus of teaching a traditional American art form.  Often, traditional artists will tell stories about someones grandfather who passed down a step to his granddaughter, or tales of which step came from whom, or how so-and-so took that step and turned it into something else, or an old square dance that is from a certain part of Kentucky that is still done today.  I did not grow up within a traditional dance and music community. I came to these wonderful traditions as an outsider; those stories are not my stories and  I don't feel like my teaching would be authentic if I brought clogging or step dance to kids that way.  So, I've decided to teach clogging a little differently.  The stories I tell kids through my teaching are more about how I hear the music, how I make choices about what sounds to make with my feet or how I go about making up my steps, and the thrill of taking part in music made by people who are in the same room, playing together.

That is my voice.  The beauty of any and all kinds of art is that there are an infinite number of ways to find a space for yourself and your individual voice.  But if you're a teaching artist you really must step back and reflect about how you use your voice, you must reflect on your own process, because not only are you are teaching about your art you are teaching about yourself as well.  The most important aspect of my job may very well be to ask the questions: Who am I?  What do I believe?  How do I see my art form?  What is my approach?  What is important about my work?  And then, take those answers into the classroom.

Not everyone wants to do this kind of work to make their process visible to others.  I'll admit, it is difficult to switch back and forth between multiple mind-spaces.  The artist part of me is the non-verbal, sensing part that experiences, creates, questions, experiments, listens, responds -- all of this in the moment.  The teaching artist part of me is the interpreter, picking just the right words to frame my work and create lessons that build skill, understanding and connections.  I also have a third role to fill -- the teacher as an artist.  In the end, I have young souls in front of me, many of them unsure of what we're about to do.  I know there is value and relevance in my work in relation their lives, but they don't know it...yet.  Every group of kids I work with is different in their temperament, interest, and school culture.  To really reach them I have to use, as my dad said, "...intuition and instinct, allowing the sub-conscious to take over" when faced with the challenge of real kids in real time.  It seems that what I do in the process of teaching dance is similar to my father's efforts to solve a 'visual problem' and that means he and I have more in common than he thinks. 

As always, I'd love to hear your thoughts!

Wednesday, November 24, 2010

The Right to Move

My daughter (5 years old), upon the occasion visiting a standard fourth grade classroom, remarking on the desks and chairs:

"What's with all this sitting around?"

The teacher's response:

"Well, we try not to do too much of that."

My daughter, proudly, in reply:

"At my kindergarten [half-day program] we only sit around at circle time.  We get to go outside before circle time, and then again after snack..."

I'm not sure if I am rubbing off on her or if this is her own individual expression and sense of entitlement speaking.  In her world, she gets to move, at home and at school.  And what's more, she seems to be cognizant of the fact that she has this freedom, that she is allowed to move and is not tied down to a desk. 

As we work, literally one step at a time, to get kids the opportunities for movement which they need for brain and body growth, as well strong and resilient spirits, I think I will keep this image firmly at the center of my mind: the little girl who believes so firmly that movement is her birthright.

Not an add-on, not an extra, and not something to be earned. A right.

Monday, November 22, 2010

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.

Saturday, November 13, 2010

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!

Thursday, November 11, 2010

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)

Both the dance and the math content are focused on equally; finding connections between the two creates a stronger understanding of both content areas.
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.
Firm grounding in spatial relationships (best learned through the body) is vital to a strong understanding of math concepts. 
Higher order thinking and problem solving skills are strengthened during the process of creating, manipulating, combining, observing, transforming and analyzing foot-based dance patterns.
Teachers consistently report that their students use new math terminology and vocabulary appropriately and with ease in conversations about their work in the program.
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.
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?

Tuesday, November 9, 2010

Tape Chronicles: Math in the Morning

I am a big advocate of supplying children with lots of open ended material and then letting them do what they will.  In my work in schools I use tape and more tape and so there is a lot of extra painters' tape (the low tack kind) hanging around our house. 

We've been getting up kinda extra early since the time change and have had a lot of time on our hands before school.  This morning the kid decided to set up a 'cat store' and, in the process of setting it up, found another interesting use for tape. 

She decided to decorate her 'store' by pulling off long pieces of tape, making them into balls and placing them on the lamp, as shown above.  What intrigued me was the placement of the little tape balls -- it's visually/aesthetically appealing, and quite organized for a little girl whose stuff is usually all over the place. 

I'm tagging this post under "exploring space."

Monday, November 8, 2010

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

Sunday, November 7, 2010

Outside the Box 1: Mundane to Marvelous

The twice yearly time change is a fairly mundane event, and for a news writer it's probably a pretty boring assignment.  On Saturday I was thrilled to read this year's time change reminder in the local paper and I was not surprised that my friend Laura Lane was the author.  This little story is a great example of how one's approach to 'the facts,' or anything else for that matter, is really just a choice of which glasses you decide to put on. 

From the front page of the Herald-Times (Bloomington, IN), Saturday, November 6, 2010:
Reminder: Time to fall back is Sunday
By Laura Lane

Seems like just yesterday that Hoosiers set their clocks ahead an hour anticipating long summer evenings.

Come 2 a.m. Sunday, it's time to set those same clocks back an hour so daylight comes sooner.  Winter is nigh.

Every year on the second Sunday in March, daylight-saving time kicks in.  Then, on the first Sunday in November, it reverts back to standard time.

Don't forget.

And look forward to March 13, 2011, when daylight-saving time returns.
Feel free to send me more examples of thinking 'outside the box.'  Can you guess which is my favorite line in the piece?

Saturday, November 6, 2010

Picture Perfect


A few weeks ago I published a post about focusing on transitions in a moving classroom.  To illustrate the post, I looked around the internet for a picture of a color wheel to show the transitions of colors changing from one into another, but wasn't satisfied with anything I found.

Moments after I published the post, this picture showed up in my inbox! It's from my dancing friend in Minnesota, Julie Young, illustrating the many colors of a northern fall.  She had no idea at the time that she had just sent me the very thing I had been looking for.  Actually, it was much, much better than I had been hoping for.

If a picture is worth a thousand words, I've already said too much.  I think I'll let the beauty of nature, and my friend's creative nature, speak for themselves.

Friday, November 5, 2010

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.

Thursday, November 4, 2010

Teachers: Be There and Be (in a) Square!

Are you going to the NCTM 2011 Annual Meeting in Indianapolis, IN in April? 

I'll be there, so let me know your plans!  My 90 minute hands-on workshop Math in Your Feet: Teaching Geometry through Rhythm and Movement is one of the 650 presentations offered.  I was excited to see that it's been included in their presentation sampling for the 3-5 grade band. 

Come even if you're just curious, but know that teachers can learn to do this too and many before you have successfully implemented Math in Your Feet programming in their own classrooms!  A few years ago I developed a two-part professional development series in association with Clowes Memorial Hall of Butler University and Young Audiences of Indiana.  As part of this process I participated in the Kennedy Center's Seminar, "Artists as Educators: Planning Effective Workshops for Teachers."  This six-hour professional development series presents Math in Your Feet as a sequential program of activities which anyone can teach, even if they don't wish to do much moving themselves. 

My hands-on NCTM workshop will present a portion of the Math in Your Feet program.  You will be engaged in an in-depth investigation of transformations using simple foot-based patterns.  In particular, we'll harness the power of kinesthetic learning for understanding reflection and rotation symmetries in 3-D, a process which I'm sure will bring you some exciting new insights on the subject.  In addition to the math content you will experience learning with and through the arts. 

Hope to see you a square!

The Power of Limits 3: The Lotus Arts Village

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 third 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.  

I've raved before about where I live and how the Lotus World Music and Arts Festival is one of the best things, out of many best things, about our amazing city of Bloomington, IN.   Here's what I found on their blog today, which speaks to this theme of working within one's limits:

Every year, as we devise projects for the Lotus Arts Village, one of our biggest challenges is simply wading through the flood of ideas that evolve into project plans. [...] The urge to “go big” is strong, even though resources are always limited. But the artistic imagination recognizes few boundaries, and the Festival is an opportunity for all of us to dream of new realities … and to stretch ever further to create beauty.
You can read the full post here.  And then you will want to come to Bloomington for next year's festival by buying tickets here!

So far I've been finding a lot of arts-based examples of creative problem solving, but my intent is to try to illustrate non-arts based creativity as well.  Any ideas?

Wednesday, November 3, 2010

The Power of Limits 2: A Circle

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 second 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.  

Here's something I found today in the FAQ section of, a site dedicated to folding circles:
Most paper folding starts with a polygon shape. Origami uses square paper. The square is only part of a circle that has been cut into five pieces and four are discarded. This lacks economy. The circle has infinite diameters; the square has been reduced to two. Having no sides the circle has no limits.
From looking at the examples on this site of what you can do with folded and joined circles, it does seem that there are no limits to a circle. 

It will probably not surprise you to hear that Bradford Hansen-Smith, the creator/instigator of this movement, spent many years as a sculptor.  I love what he is doing with circles.  I feel nothing but pure, shameless joy at finding this beautiful example of the arts and math seamlessly integrated. 

The Power of Limits 1: Thinking Inside the Box

I have spent most of my dance life performing and teaching on a 3'x3' square dance platform.  For perspective's sake I should say that most cloggers, step dancers or tap dancers do not regularly work in such a small space.  For me, working within the confines of my dance board was born out of necessity and eventually influenced the course of my creative life as both an artist and a teacher.

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 post is the first in a series of articles, inspired by his chapter, exploring how limits not only enhance creative problem solving but are actually a requirement of such a process.  Creativity, and all the intense and surprising things that word implies, requires of us resourcefulness, flexibility, ingenuity, and the necessity to think outside the box. 

Which, in my case, meant staying in the box!

The particulars of my situation dictated that I needed to have a portable dance space.  When I was touring and performing with my band Cucanandy, many of the venues we played were not dance friendly, meaning they hosted bands on tiny, often carpeted or tile-over-cement stages in clubs or small auditoriums.  As a dancer whose feet were the percussion section, my dancing contributed to the overall musical experience of our show and the sound of my feet needed to be consistent every time I performed.  It's practically impossible to sound good on cement, plus it's really bad for the body.  So, I bartered dance lessons with a specialty carpenter who created a beautiful wooden dance platform with the capability of producing high end, mid-range and bass tones.  The design of the platform was in itself limited to whether or not it would fit into the back of a Toyota Corolla Hatchback, which just happened to be 3'x3'.

I didn't start dancing until my mid-20's which is another limit I have had to work with in the course of my career.  The reason I tell you this is that, compared to a child's learning process which is quite holistic, an adult learner often approaches new learning self-consciously; self-conscious in ways that both help and hinder.  Having learned percussive dance at a somewhat late age, I remember very clearly not knowing how to dance. 

For this reason, I remember perfectly the day when I realized the creative potential of working within the limits of my dance platform.  I had only been dancing for about four years, two of those years with a professional percussive dance troupe,  and was still quite new to percussive dance. I was listening to a song the band was working on and had no steps in my current repertoire that would work.  I remember looking down at the platform and noticing the outer edges of my space which I normally avoided because I didn't want to fall off.  I remember thinking -- look at all the different directions I can go in.  This insight inspired and generated a whole new set of dance steps and, eventually, the final choreography for the piece.

There is more to the story but suffice it to say that moment eventually led me to creating Math in Your Feet, where students, with a basic vocabulary of percussive dance movements, do creative work within the limits of their own square dance spaces while making meaningful connections to mathematical topics.

See you again soon with another installment of The Power of Limits.  Be you artist, parent, teacher, or friend (or anyone else!) I'd love to hear your thoughts on this topic, so please consider leaving a comment. 

Monday, November 1, 2010

Welcome One and All (and Bring Your Questions!)

I've had a number of new visitors in the last few days, which I'm really excited about.  This blog is still in it's infancy (less than one month old) and I'm glad that the topics here are of interest. 

To everyone, new and returning, WELCOME! 
I'm happy to see evidence of your visits and hope that you will be checking in again. Please consider formally 'following' this blog by clicking the 'Follow' button to the right of this post.

I'm aware that I have a widely focused lens here, including arts integration in general, math and dance/movement integration, kinesthetic learning, creativity and creative problem solving. From my point of view these seemingly disparate topics are all part of the same map.  I will continue creating posts around these themes, but if you have any particular questions or thoughts I am very interested in hearing whatever you'd like to ask or share. 

For example, someone has already asked me about what it is about moving and kinesthetic learning that is so effective in helping kids learn, which I plan to address in the near future.  I have also sketched out a series of posts on the topic of creativity and what Stephen Nachmanovitch calls "the power of limits." 

So, come one come all and bring your questions!  Queries and thoughts gladly received in the comments section of any post or at malke (dot) rosenfeld (at) earthlink (dot) net. 

I look forward to hearing from you!

Sunday, October 31, 2010

More Than Counting: Addendum

I love the web because, well, it's so webby, so interconnected, so like my mind.  My interests are currently taking me to a very interesting space on the Internet where people are having intelligent and interesting conversations about what math is and how to teach math effectively to children. I am enamoured by all these conversations.  I know that I will learn a lot from reading them, and I hope some day soon that this blog will spark some conversations of its own. 

The interesting thing is that in all my Internet ramblings I've not run across many sites on the web that deal with kinesthetic approaches to math education. (I'm really speaking to the issue of math/dance/movement integration, and not at all about the 'math songs with movement' activities out there, and I will save my discussion on this topic for a later post.)  I did run across this post today on math educator Sue Vanhattum's blog Math Mama which has some real meaning in relation to the work I do with kids in Math in Your Feet.  My favorite items on Sue Vanhattum's Top Ten List of Issues in Math Education are:
5. Math is not facts (times tables) and procedures (long division), although those are a part of it; more deeply, math is about concepts, connections, patterns. It can be a game, a language, an art form. Everything is connected, often in surprising and beautiful ways.
This is a perfect addendum to my post from yesterday More Than Counting.  Right now, I can't even describe the pleasure I feel from reading this statement.  I'll save my poetical waxings for another post.

I also loved finding on the list:
3. Games are to math as books are to reading. Let the kids play games (or make up their own games) instead of "doing math", and they might learn more math.
I think you could substitute 'moving' for 'games' and that statement would still work, like this:

Moving is to math as books are to reading. Let the kids dance (or make up their own dances) instead of "doing math", and they might learn more math.
I think that at some point in the not so distant future I might have to revise my statement that I am not a math teacher.  For now, however, I'm enjoying peeking into the minds of some obviously creative and thoughtful educators.

Saturday, October 30, 2010

More Than Counting

Every once in a while I do a Google search for my name or my program's name, Math in Your Feet.  It's instructive and sometimes surprising to find out just how far out in cyber space I am.

Case in point, I recently found an undated conference paper by an associate professor from the Institute of Mathematical Sciences and Physics at the University of the Phillippines Los Baños.  Among other things, the paper makes a case for "the cognitive and aesthetic similarities between mathematics and dance."  Math in Your Feet is cited and described in one of the opening paragraphs.  Never mind the fact that it's just a rehashing of promotional language direct from my website, the rest of the paper makes a pretty good argument for the importance and relevancy of integrating math and dance.

My favorite section of the paper is on pattern recognition (a major connecting theme in my program) and includes a quote from a book called The Math Gene by Keith Devlin, mathematician, NPR's Math Guy, and (among other things) a senior researcher at Stanford University's Center for the Study of Language and Information, who argues:
"mathematics is not about numbers, but about life.  It is about the world in which we live.  It is about ideas, and far from being dull and sterile, as it is often portrayed, is full of creativity.  It is the science of patterns."
Within this one quote are ideas I've been trying to communicate for years to the folks who hear about my program and inevitably reply, "Oh, you mean like counting your steps?"  I always try to find a nice way to say, no, not really, but there's never enough time to explain my reasoning fully.  However, I do have time and a little space here to say mathematics is more than numbers and counting and balancing your checkbook and that a program which teaches math through dance (or dance through math) is about more than counting too.

Mathematics is essentially a language invented to describe, manage and understand the physical world. (And if there are any mathematicians checking in on this blog, feel free to correct me!) That's why connecting math to the real-world helps kids better understand it, because the real world is math.  And, no matter what your opinion is about dance being lumped in with 'things in the real world', please remember that we all move and without a firm grasp on spatial relationships, one of the foundations of a good mathematics education, you will most literally be lost.

That's why even the preschool version of Math in Your Feet has less to do with numbers and more to do with exploring and understanding where you are, where you want to be, and how you're going to get there.  Add to that a chance to develop patterns of movement embedded in time as well as make creative choices while moving and you now have a powerful mathematical experience in real time and real space.  The critical piece (for upper elementary kids, anyhow -- the younger ones just need as much kinesthetic experience with the concepts as their teachers are willing to fit into a school day) is that kids get a chance to bring the math back to the page.  After all, math is a symbolic language, but it is really much more than counting.

I'm sure I'll be revisiting this theme in the future.  But first I have to run to the library to pick up a couple of Keith Devlin's books.


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