Perfect Reasoning: The Right Brain Initiative (Manifesto)

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!

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!)

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.

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, http://www.mathinyourfeet.blogspot.com/ and http://www.mathinyourfeet.com/
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

LESSON OVERVIEW:
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.

LEARNING GOALS:
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. 

VOCABULARY:
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


MOVEMENT ACTIVITIES:

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. 

MAPPING ACTIVITIES:

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.

EXTENDING THE ACTIVITY:
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!

MUSIC SUGGESTIONS:
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)

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.

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  Wholemovement.com, 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. 

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!