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)

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

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

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

Stay with me here...

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

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

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

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

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

The author goes on to say,

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

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

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

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

More Than One Right Answer

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

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

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

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

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

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

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

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

YES!

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?

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.