The Map is Not the Territory

There was a bright, blue sky up above, and at ground level there was frozen fog.  The result was a morning delicately dressed in sparkles.  Perfect for a walk.

Down the driveway.  Pick a piece of lavender, covered with millions of tiny ice crystals.  Which way do you want to turn, left or right?  Next intersection, right or left? 

We walked through the fog, already burning off.  We could feel the sparkles entering our lungs with each breath.

Busy road and cars zooming.  Three choices, right, left, or straight ahead.  "Mama, I used to be afraid of those trees, but I'm not any more."  We pick tiny pine cones off the tips of the branches. 

Next crossroads, "Mama, that's University Street down there, let's go there."  Thinly frozen puddles alongside thinly disguised reading practice: "What does that P stand for, do you think?  The one with the red circle and the cross over it?  What does the rest of the sign say?" I ask.

Right turn down University and an old dog barking at us across the lawn.  "Mama, I used to be afraid of dogs, but now I just don't like their licking."

Find two sticks, clap them together and then we're marching.  Left turn.  Right turn. Rose street!  Find the stone pig, march on home.  "I wanna make a map!" the girl says.



She wanted red and blue like the roads in the atlas.  We recalled which way we turned, what we saw, remembered the crossroads, one block at a time.  All of a sudden, she notices corners and the geometry of the street layout.  "I always thought the blocks went in a circle.  I didn't know they were squares."  The things she loves go on the map (friends' house, stone pig) as well as the things that 'used to' frighten her.  Her long battle with anxiety has its landmarks as well.

It may not be to scale, but when we go out again this afternoon to follow our map, the issue of scale might come up.  I'm also pretty sure we didn't get all the streets on there especially at the end of our route, but next time we'll bring paper and make some notes as we walk.

Mapping the familiar twists and turns and landmarks of our neighborhood -- bodies first, memories second, paper and pencils third.  I marvel at the human brain inside my six year old daughter's head that is so driven toward representation of her experiences and activities; driven toward it even though she is still just learning to decode print and write using 'the rules' .

She makes maps of other kinds, too.  Sewing "patterns", also not to scale, but clearly a sequence of steps mapped out:

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)