Floor Tape, How Do I Love Thee? (Video Edition)

I'm in the middle of summer programming.  It's Math in Your Feet in a lot of ways but also not completely like the program I do in schools.  It's more like a whirlwind of percussive choreography, rhythm, and patterns of all kinds. There's also a lot of math in there as well, just not explicitly. 

My reasoning for this that kids need as much exposure as possible to patterns in multiple, diverse contexts.  These kids I've been working with, for example, are a perfect case in point.  When asked on the first day to find patterns in the room in which we were working, they were at a loss.  In all the groups, color patterns were found first.  Then somebody would notice a sequence of objects, but it didn't repeat.  A potential pattern unit, but not a pattern in itself.  Even the three examples of simple tilings in the room (floor, ceiling and walls) escaped notice, even when I pointed them out. 

Patterns are more than sequences of colors.  They are more than two dimensional shapes.  They are sounds, movements, expressions, order. They are long and short.  They repeat.  They change.  They're everywhere. So, when I say we're not talking about math explicitly I mean we don't need to talk about it because we're doing it.  Calling it 'math' interrupts the flow we've created -- sometimes just doing and experiencing is enough.  This doing time is a chance to get swept up in the creating, to be fully engaged and amazed and delighted in your own abilities.  I believe this because, simply put, that is what I find best about learning something new.

On top of the sheer fun of watching kids engage in new pursuits like percussive dance, one of the reasons I'm enjoying doing the summer version of Math in Your Feet is that I have leeway to experiment with how I deliver the program, engage my young dancers (right now ages eight to eleven) and how I set up the space.

In the videos, below, you can see what I'm trying out right now.  This big grid isn't the normal setup for Math in Your Feet but I was really excited to tape out the space this way.  Normally, when kids start making up their own dance patterns they usually get their own personal square dance spaces taped out in individual groups of two, each pair slightly separated from the other groups. I'll be very interested in how the new set up works out (or doesn't). 

This new set up came about because the floor really lent itself to a large grid format. The girls in the room were hanging out with me before class while I set up and helped me tape out the floor.  Any time I have a chance to let kids help me tape, from preschool to upper elementary, my helpers invariably end up spontaneously exploring their newly taped environment without any prompting.  This is actually my favorite time with kids -- manipulating the floor space with tape and then seeing what they do when they first discover it.  Here's a peek at the space and the only part of their exploration I could capture on video:



Their movement is a natural kid reaction to squares -- Hop Scotch!  But in this second little clip you can see how they started exploring rows as well as columns.



Later, during our class time, when we were talking again about other kinds of patterns they could find, other than the ones we were making with our hands and feet, they noticed that each square of the large blue grid was made up of four smaller tile squares.  Given that on the first day they never even noticed how the floor was designed when I asked them about patterns in the room (before I put down this grid), this was a huge step forward at identifying and describing the structure of their environment.

Speaking of patterns, I've also been sneaking in some Fibonacci numbers as well.   But that's for a future post...  In the mean time, here's my original love note about floor tape and its myriad uses.  And, one of my favorite posts in this blog about how the tape on the floor serves as the 'third teacher' in my Math in Your Feet residencies.

Geometry Discoveries

One of my most enjoyable creative endeavors these days is accompanying my daughter (age six) on her math learning journey.  Sometimes we play games, or work with pattern blocks or Cuisenaire rods.  Sometimes she wants to earn and save money so she can eventually run away with her best friend.  Whatever we do, she learns best through conversation and narrative. 

She also learns math without me.  There are plenty of times when she happens upon something 'by accident' by which I mean: things (books, puzzles, making supplies, marbles, tape...) left around the house, acted upon, forgotten for a while, ultimately to be rediscovered a month or three later and acted upon again, but this time in new ways.

This happens a lot 'round here. 

For instance, we have tangrams in almost every room of our house.  There's a magnetic puzzle book set in the car and approximately six plastic sets on the game shelf, of various colors and all mixed together. I have four sets of magnet tangrams that I got at the NCTM Annual Meeting in Indianapolis this past April.  They have been on the fridge in the kitchen since then with minimal interaction...until recently, and, last I looked, they were all in use in some kind of design or another.

Here's what I found my dear child doing with the set of car tangrams (inside for some reason) over the last few days.

By way of setting the scene, I should tell you that the kid generally initiates and works independently on any project she pleases during her afternoon quiet time, usually with the company of an audio book.  A few days ago during this time she informed me she was "making a math book."  I had observed her tracing tangrams, but was surprised to find that she was doing it in a deliberate way, and that she was also able to clearly describe her discoveries and observations to me. Here is the book, so far.  I am just a scribe here -- these are her words as she dictated them to me, except where noted:

"Four of these triangles that you see here can make a square.  If you pull these triangles apart you can see that they're little triangles.  But you can see on this page that they make a square."  [I see that she has drawn them as individual shapes, which, over the course of her illustration, merge together into her intended shape.]

"This rectangle you see is made up of a parallelogram and two triangles.  Really they're just shapes, but when you put them together they make a rectangle." [It looks like she's numbered the inside angles of the individual shapes.  It also looks like she is again showing the process individual shapes merging into the intended new shape.]

"You see the wheels of this bike as rhombuses but really they're squares turned so their points are facing up and down, and to the side." [She was gesturing this first, and at first she used the word 'flipped' to describe the orientation of the square wheels.  I focused her on the orientation of the corners to describe how the square was turned.]

"The square and the rhombus that you see here, their edges are both the same length.  The difference is a rhombus is a squished square, squished to its side.  The rhombus has two larger angles and two smaller angles than the square.  But the square has the same angles on each corner."  [These are actually tracings of shapes from the pattern blocks set we have.  The ruler markings was her idea for comparing the two shapes.  I supplied some new vocabulary in the form of 'angles' and made some observations about the difference by overlapping the two shapes, in an effort to help her observe and further articulate the difference between the two.]

Writing about all of this made me think to look up more about the van Hiele levels for geometric reasoning.  I need to spend more time with that to analyze how I'm interacting with future discoveries of hers.  I also think I'd like to focus more specifically on flips, turns and slides.  Maybe I'll be super ambitious and have us play around with flips and turns using both 2D and 3D shapes!  

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)

More Than The Sum of It's Parts

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

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

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

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

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

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

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

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

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

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

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."

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. 

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. 

What You Can Learn from A Square

What can you learn from a square?  Well, before you can learn from a square you first have to understand it.  And, to do that, it's best for you to have a chance experience 'squareness' using use all your SENSES.  As Albert Einstein said:

"Learning is experience.  Everything else is just information."

To start, you need to SEE it.  You've probably been looking at squares all your life.  You can correctly identify a square and find examples of it in your environment.  But do you really understand it? 

Possibly.  You might be able to give some facts about a square (number of sides, number of vertices, measurment of angles, etc.) You may even be able to draw one or all four of the lines of symmetry through square.  But if you're a fourth grader being asked to make your body execute a move on the diagonal (opposite corners), it's actually pretty hard for you to do that without a visual reference.  That's where tape comes in. 

So, LOOK AT your taped 2'x2' square on the floor and sit inside it.  Use your fingers to TOUCH and TRACE the parallel sides, the vertices, and the equilateral sides.  TOUCH the directions forward, back, left, right and all the diagonals, and while you do this SAY the words that identify where you're touching. 

By now, it's probably safe to say that you are oriented to your two-dimensional dance space.  It's also likely that you have become inordinately fond of this little piece of property you call "home" and are unwilling to let anyone usurp your territory.  Ah, to be nine again.  No matter, it's all good.

It's also time to count up how many SENSES you've used so far to further your understanding of  'squareness.'  Let's see -- seeing, hearing, and touching.  There's actually one more sense you need to use and it's not smelling or tasting.   It's your VESTIBULAR SYSTEM.  Carla Hannaford in Smart Moves: Why Learning is Not All in Your Head puts it this way:

"...just as important to our development and our lives is the integration of sensory input, which gives us information about gravity and motion, and about our body's muscular movements and position in space -- the vestibular system and proprioception.  These play a surprisingly significant role in our awareness of the world and also...in our ability to understand and learn."

Okay, so now it's time to STAND UP and utilize your body for some high powered learning.  Put your FEET TOGETHER and STAND in the center of your space.  JUMP forward, JUMP center, JUMP back, JUMP center.  SPLIT your feet to the sides of the square.  SPLIT your feet to the diagonals.  TURN your body right, towards the first side.  TURN toward the next side.  TURN toward the third side.  TURN toward the fourth side.  How many times did you have to TURN to get all the way around?  How far, in fractions, did you JUMP on each turn?  How far was each turn in degrees? 

If you JUMP and TURN half way around your square, how far have you gone?  How many jumps will you need to get all the way around?  If you start your movements facing forward, JUMP and TURN 90 degress to the right and then JUMP and TURN 180 degrees to the left, where will you end up?

Are you learning anything new from a square yet?

Teaching Below the Surface: Harnessing the Power of Tape!

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

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

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

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

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

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

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

Floor Tape, How Do I Love Thee? Let Me Count the Ways (Preschool Edition)

A few years ago I went to the Indiana State House in Indianapolis to view "The Hundred Languages of Children," a travelling exhibit about the Reggio Emilia approach to early childhood education.  If you're not familiar with this approach it, among other things, considers the environment (of the classroom, and other spaces) as a 'third teacher'.

Of course, I was drawn to the part of the exhibit that focused on movement and dance as one of the "hundred languages" with which children express themselves.  There was a video that showed the children's first experiences with an old factory space-- a huge room empty except for two rows of large, white columns.  The children were running around and between the columns, peeking around them, and interacting with their friends, all movements and ideas that eventually turned into a formal piece of choreography. 

At the time I was just starting to think about creating a math/dance program for preschoolers and my biggest question was how could I encourage that kind of exploration?  It seemed unlikely I would be able to find an empty factory or other interesting environment and get a bunch of preschoolers there on a weekly basis.  And then it hit me -- I could create an environment out of tape.  I could define three-dimensional space using two-dimensional lines and colors.

By way of explanation, when I say 'floor tape' I am referring to two different products, both of them sticky.  First, there's painters' tape which is blue and low tack so it can come up easily off both hard surfaces and carpet (except when kids poke their pencils into it and it gets perforated, but that's a different story.)  There is also the floor tape that P.E. teachers use, which comes in lots of fabulous colors, the better to design with, my dear. 

So, why am I so passionate about floor tape?  Let's see...

1. Straight Lines, Part 1: A simple straight line taped down a hallway becomes a pathway.  It also divides the space in two, and provides a chance to walk on it or jump over it.  Best of all, one can march (or walk, or skip, or slide, etc) rhythmically down it singing "As I was marching down the street, down the street, down the street..." 
2. Straight Lines, Part 2: When my daughter was three her teachers put down a straight line of tape to help the class 'line up' before leaving the classroom.  A simple, visual learning strategy.  Later in the year I saw pictures of what else the kids had done with the line.  They had used their large blocks to build a wall the length of the tape and then lined up their animals and cars alongside it.  A wonderful example of how a simple alteration of a child's environment can deepen their experience and exploration of the space around them. 
3. Floor tape can define and redefine the space it's in.  Large open spaces encourage a lot of endless running.  The minute you create a large rectangular box on the floor, with corners, you can now have enough of a visual to focus a preschooler's attention to IN (the box), OUT (of the box), AROUND (the sides of the box), CORNERS, and ACROSS, all age-appropriate math terminology.
4. A simple taped perimeter can highlight empty space, as in "Find an empty spot inside the tape and make a shape."
5. Tape two or more parallel lines down a space and see what happens when you sing "Down by the banks of the hankey pankey, when the bullfrogs jump from bank to bankey..."

Ultimately, I would love if every preschool teacher would just put down taped lines in their classrooms and then stand back to observe how the children interact with them.  Start with one straight line and go from there.  Let me know if you want to talk further about this idea --  I'd jump at the chance to see how far we could take this.