Introducing the Tape Chronicles Project

It's really no secret I love tape. I should have bought stock in it long ago.  In my mind, tape is the ultimate open-ended, the world is your oyster, creative, hands-on learning and making supply.  I mean, just look at how versatile it is:

You can change an environment in an instant!  Need kids to be able to visualize diagonals while creating foot-based percussive patterns? Voila!

Are you six and want to visualize a trajectory to the moon?  Tape's for you!

Even clear packing tape can be harnessed in the pursuit of art making and invention:

Check out the endless ways tape can be employed in the interest of math, art, kinesthetic exploration, invention and education -- and then consider submitting some examples of your own!  The Tape Chronicles are housed over at the Math in Your Feet website.  Hope to hear from you!

Making Math: Big Dreams of Building

We are going to build a cottage.  That we can live in.

We are building it out of straws and pipe cleaners.  We started with one cube and attached another to it.  You should have seen the kid's jaw drop -- it was like magic.  And, did you know that after the first cube you don't need to make a complete cube ever again?

I quickly figured out my methods, but it was hard for my six year old to keep up with the precision.  To attach the straws use half a pipe cleaner folded at each end, then bend it into a 90 degree angle and slide the straws on. 

Unless of course you are attaching your cubes together.  In that case you make one folded end for the open straw, and slide an unfolded end into the attachment point. 

But that's just what I discovered and, honestly, half the fun was in trying to figure it out!  I suspect there are a lot of right ways to go about doing something like this.  If you decide to try building like this I'd love to see pictures of what you make!

In the end, the kid and I worked as a team for a while and then she left to rehearse her show which opens with the song "The Moral of the Soggy Hat" (an original number).  I imagine this building activity continuing mostly on mama power, but that's because I have ulterior motives.

I get to do a ten-day version of Math in Your Feet this summer for some inner-city programs for kids ages 6-12.  In addition to rhythm and pattern in the feet and hands, we'll be exploring what else you can do with a pattern unit, which includes building!  I can imagine, over two weeks, the older kids will have built something really cool.  And if they get really good at it, I might suggest trying to construct something out of tetrahedral units just for fun!  But I think I should try it out first, just to get a sense of what the pitfalls might be. 

As for my girl?  She's all for building something she can live in, even if it's made from drinking straws. "But Mama,"  she said, "Will I have any privacy?"

Marshmallow Math: Solids & Sculpture

Given my daughter's resistance to formal lessons, it really was the perfect storm.  A supervised math activity of new concepts thinly disguised as 'something to do while mama makes dinner'?  Yes, please!

It came about as a sort of semi-premeditated accident: It was time to get dinner ready and there was a lot of prep work to it.  I had the mini-marshmallows and toothpicks at the ready, as well as buy-in from the kid who had seen this post of the amazing, huge, Serpinski-esqe giant tetrahedron built by the kids at Almost Unschoolers the day before.

I laid out some newspapers on the kitchen floor and poured the marshmallows into one bowl, the toothpicks into another.  Completely off the cuff I said, "Here's how you can make a square base, and then build up from there."  I built about one half of a cube and then said, "I really want to make tetrahedrons, but I don't have time now.  See what you can do."

The kid jumped in enthusiastically.  She started by making one cube, no problem. She added on another cube, then two more to make a four-cube base.  She built it up a level, and up a level again. 

"I'm an artist!  I'm making a sculpture!  Let's put these piece under glass, like in a museum. It's marshmallow art."  Despite this enthusiastic chatter she was actually a little worried that the kids at Almost Unschoolers would be mad at her for copying their work. This led to some conversation about copying vs. learning the basics so you have the skills to express your own personal vision, and then, thankfully, our attention was diverted. 

The tower/sculpture of cube units started to lean. 

These marshmallows are tricky!  The kids at Almost Unschoolers made it look easy, but it's not!  There are all sorts of structural problem solving challenges to overcome. I suggested turning her 'sculpture' on its side (pictured below) so it would be a little more sturdy.  We counted how many cube units made the structure.

When she was done, thinking toward my goal of tetrahedrons, I casually mentioned she might try a triangle base.  After some experimentation she started making this:

It has an interesting twisting quality to it and is my personal favorite of all her 'marshmallow art' pieces.

By this time, dinner was in the oven and I had time to experiment myself.   I made a tetrahedron, then attempted a larger one using four tetrahedral units.  It was a pretty strong structure, but only after I figured out that if you're going to connect the tetrahedral unit patterns, you need to share the same marshmallow where the vertices make contact.  (An aside: Spell check said that is was 'vertexes' instead of 'vertices'.  What do you think?)

She worked on another sculpture and then...lo!  The girl created a tetrahedron of her own, then played around and discovered, on her own, how to create an octahedron!

The picture below shows all of today's creations. The 'sculptures' which she created first, are in the back row.  The geometric/platonic solids, created at the end, are in the front.  What's interesting to me, in terms of my daughter's learning process, is that it is more apparent than ever that she really wants to explore and discover new things on her own first and then, when she's had her fill, she comes more easily and willingly toward 'the point' of the lesson. 

Whatever you call this afternoon's explorations it was a fun, full hour of inquiry.  It was also the first time, except for origami, that I've willingly pushed us into 3D math.  I'm learning right along with her, and it's an amazing journey.

Math & Making Moment: Sewing Edition

My daughter, who is six years old, loves to sew and has taught herself most of what she knows.  She is, however, so fiercely independent in her learning that it has been quite difficult to give her new information or coaching when it's clear she needs it to move forward.  Today, however, we had a breakthrough!

This morning she mentioned wanting to sew a new dress for her stuffed kitty Hazelnut.  She's done this before and the dresses always end up too small.  I figured out recently that she would measure the fabric around the cat, and cut the fabric to size without leaving room for what they call  the 'seam allowance'.  I casually mentioned to her that professional seamstresses measure the subject first and then add an inch to that measurement for hems and such before they cut the fabric.  If she wanted to use my tape measure I'd be happy to show her.

She was all for it! We measured Hazelnut from neck to toe and added an inch.  While we measured I realized the tape measure was like a number line.  I said, "The end is zero and you put it where you want to start measuring."  After measuring the whole length of the dress she informed me it was actually to be in two pieces, so we measured again, this time from neck to waist, and waist to toe.  All of this got written down, which was her idea. 

So we covered the length of the garment, but not the width.  To do that she measured around the kitty and added an inch, and wrote that down. 

The finished outfit, made from Papa's old

pajamas, and a new beaded necklace to go

with it!

I left her alone to cut the fabric and went off to do other things.  I came back about 10 minutes later to find that she really hadn't made the leap from measuring the doll to measuring the fabric.   This was a great opportunity to walk her through the concepts of length and width again.  When the pieces were cut to the right size, the finished product went together easily!

So, what did we cover?  Basic measurement and computation and length and width in two different contexts (the cat and the fabric needed to fit the cat).  Also, a little writing practice as well as some new information about how to abbreviate words ('inch' = 'in').   She happily pinned the hem, sewed it up and sewed the whole thing together without any more help from me.  I'll be interested to see how she extends, applies or connects this new information in the future. 

Learning Environments: Video Games vs. Making Stuff

It is with very mixed feelings that I have been reading about efforts to create learning environments within the context of video games.  I'm not against using video games as educational tools, necessarily, but I still have this thought in the back of my head:

Why do we need to give kids more screen time then they already have when there are so many more fabulous things they could be doing, like making stuff?

Keith Devlin gave a really worthwhile presentation at the NCTM annual meeting in Indy back in April about the potential of video games in mathematics education and has a new book out on the subject.  He's all for it because gaming is a lifestyle for many kids already -- why not meet kids where they're at with what already motivates them?   His argument (as expressed here) is that well-designed video games "can help develop mathematical thinking, but they are a lot more difficult to design than a simple skills-tester." 

Essentially this means game developers need to think well beyond the basic number skills, factual recall, and symbolic systems that most people think of as 'math' and instead create a game context that engages kids in mathematical thinking and problem solving.  Developing a game like this, Keith says, is unfortunately a huge task with little return on investment and so, until someone comes up with the money, we are relegated to a host of math-fact recall games like this one. 

So, kids like video games, that much is clear.  But, well designed or not, how much more screen time does a kid need??  I read somewhere that many/most kids spend as much time gaming as they do in school (that may have been from Keith Devlin's NCTM talk, actually). My biggest concern, given my commitment to getting kids away from their desks and physically engaged in a thinking/solving/creating process, is that the 'We' with a capital W continue to ignore evidence (and more evidence and a really good argument presenting evidence) that not only do kids need to move more but that...

...real, true comprehension of subject matter and thinking is something that happens in concert between the learner's body, brain, mind, heart and soul.

I recently found something that speaks to all these parts of us called the Tinkering School:

"The Tinkering School offers an exploratory curriculum designed to help kids – ages 8 to 17 – learn how to build things. By providing a collaborative environment in which to explore basic and advanced building techniques and principles, we strive to create a school where we all learn by fooling around. All activities are hands-on, supervised, and at least partly improvisational. Grand schemes, wild ideas, crazy notions, and intuitive leaps of imagination are, of course, encouraged and fertilized."

Gever Tully, who started the Tinkering School, has just described my ideal learning environment for all kids!  A guide, some materials, a few questions, a lot of play, some answers, and then more questions.  So I was thrilled to find his post which approached the issue of video games from my perspective -- as someone who makes things and thinks all kids can benefit from such activity.  Here's what he wrote:

Video games and kids – it’s a complicated issue. On the one hand, I was inspired by games on the Apple II to learn how to program, arguably a seminal period in my life, on the other hand games can clearly seduce the distractible child away from even their own projects. However, I occasionally find these moments where games inspire us to actions we might not otherwise take. Jane McGonigal makes the point that in games we can do the things and be the people we imagine ourselves to be. It seems true, to some extent, but I wonder if habitually playing games slowly changes our definition of success to match the accomplishments programmed into the games (and I appreciate Jane’s work mapping game mechanics onto real life to combat this).  The moment in question today came from Erik’s blog today. His blog offers a plethora of details about everything from zero-carbon houses to Sudbury schools, but I was charmed by this recent entry where he says:

Minecraft and the Tinkering School (it’s a camp) have me inspired to use power tools and knives more with the kids.

Consider that for a moment. The experience of constructing a virtual world inspired him to introduce his children to real tools. Perhaps Jane is right.

In the end, I have no answers and no final opinion, just the hope that we can all maintain perspective about the rush to use video games in education just because kids 'like' to play them.  For now, at least, kids still have bodies that need to move and are well worth harnessing in the pursuit of learning.  We also need to find many more opportunities to help kids be in charge of their own learning.  Certainly, one feels in charge in a gaming environment but, as Gever says, success comes within the confines of the programmed game structure.  Real life is much more open ended and complicated and for these reasons there's nothing more empowering than mastering the unpredictability of life by learning to make your own stuff.

Yoda Says Do (Embodied Aphorisms)

I wrote recently about a phrase that popped into my head one morning.   I was thinking about how to explain my five year old on her best days.  The words that popped up into my head were "fearlessly creative."  And then I thought, what does that mean? 

Well, the most important thing that it means is that when you are fearlessly creative you DO no matter what.  The doing doesn't have to be Art with a capital A, but a lot of times it has to do with making something.  So, you just DO.  Even if doesn't turn out exactly the way you planned.  Even if it's not perfect (whatever that is).  Even if it amounts to nothing.  Even if it just leads you to the next question or the next idea. 

In the process of mulling over this idea, a classic aphorism popped into my head:

You never know until you try.

And then I wondered what other words of wisdom speak to the doing, so I asked my Facebook friends and here's what they came up with:

Practice makes permanent.
Nothing ventured nothing gained.
All work and no play makes Jack a dull boy.
If at first you don't succeed, try, try again.
Genius is 1% inspiration and 99% perspiration.
Failure is always an option. (Myth Busters)
"Play your own special music, play your own special song; play your own kind of music, even if nobody plays along..."  (Mama Cass)
Do, or not do.  There is no try. (Yoda)
Just do it. (Nike)

When I look at this list I see Math in Your Feet.  And, I think the program embodies almost every saying there:

Practice makes permanent.  Kids practice and practice and practice.  It's part of the process.  And then, lo!  They remember and they understand! 

Nothing ventured nothing gained.  You just gotta get going.  Move your feet.  Even though getting started is sometimes the hardest bit.  The journey of a thousand miles begins with one step.  Literally.

All work and no play makes Jack a dull boy.  Kids play with math for possibly the first time in their lives. 

If at first you don't succeed, try, try again.  Trying is like practice, you just do it and see how much further you can get with each try.  If it's not working, then try something else!

Genius is 1% inspiration and 99% perspiration.  Yes, we perspire in Math in Your Feet.  I would expect nothing less!

Failure is always an option.  You know, I don't really require the kids to be good dancers, or even good at math.  I just require they be present and put in the effort.  Plus, in my experience, I've learned more from failure than from doing something exactly right.

I'm thinking I might make these aphorisms part of the residency reflection and wrap up.  Wouldn't that be cool?  "Okay kids, have you ever heard the saying 'If at first you don't succeed, try, try again'?  Yes?  Well, give me one example of how it relates to your experience in Math in Your Feet this week."

We'll create a whole new assessment trend:  Aphoristic Assessment.  It's at least worth a try.  I'll let you know how it goes!

Family Math Night Fun!

I did a family math night at Christel House Academy in Indianapolis this week and we had a blast!!  This math night extends the dance residency's themes so that anyone can participate from 10 months to 100 years old.  The same principles that run through my residency program show up in the family night as well:

Making is fun.

Patterns are fun.

Choice is fun.

Art is fun.

Dance is fun.

Math is fun.

Challenge is fun.
Learning is fun.

Glue, tape and paper are fun.

The more colorful the better.

The more choice the better.

The following pictures don't represent every activity in the night, but you can probably tell by the focused hands that everyone was engaged in what they were doing.  Fun!

The Math in Your Feet Family Math Night is called "Pizza, Patterns & Problem Solving."  The key ingredients to this night are MAKING and CHOICE.  Sure, everyone is designing a paper pizza that illustrates turn symmetry, but every pizza is different.  



I made up this name pattern activity based on the frequency of vowels and consonants in one's name, but I'm sure it's not an original idea.  It's fun to watch kids discover the larger pattern that emerges from repeating their name pattern over and over. 

This family night is an extension of the Math in Your Feet residency topics.  For example, in the dance residency, kids use flips, slides and turns to transform their dance patterns.  Here they do the same thing with tangram puzzle pieces as they work to make the shadow shapes.  

  

This is a night for the entire family, so there are little babies all the way up to grandparents making and solving next to each other.  It's quite amazing to see the generations working together, all in one room.  I am always heartened to see the adults trying new things.

Mirror symmetry.



Patterns in the feet.







A List

Mathematical aesthetics. 
I had heard about the beauty of mathematics, but I never really understood what that meant.  Now, I think I'm 'getting it'; not with numbers, but definitely on a visual level.  Sue VanHattum from Math Mama Writes posted this video called Doodling in Math Class: Infinity Elephants.  When I watched it something just clicked for me. 

More pictures of tape in action.
I've got this idea in my head to find as many examples of tape being put on the floor (or wherever) to further a child's learning, or to change an environment to promote exploration of space.  Send me yours!

Heading toward the front left diagonal!

Find new music and dance to it. 
Always on the look out for a great tune.

Gestures and embodied cognition in mathematics learning. 
After reading research findings about this, I've been more aware of how people move their hands while talking, especially when they're trying to describe a procedure or a design.  A friend was describing a plaid shirt in her closet; her hands moved across the front of her body horizontally and vertically while she said the word 'plaid'.   

Clear the mind.
Find new music and dance to it.  Better yet, I'm teaching kids next week!  There's nothing like a class of moving fifth graders to keep one in the present moment.

Building an icosahedron by folding paper plates. 

How many paper plates will it take?  I've made a two-frequency tetrahedron so far, which is four plates.  The reason I'm interested is that I've read that Labanotation (a method for notating dance movements and choreography) was created by visualizing the human body inside an icosahedron. 

This is actually an open icosahedron
from http://www.wholemovement.com/

Van Hiele Levels of Geometric Reasoning. 
Is this useful to me as a dance teacher teaching math?  I teach a lot of geometry.  I think the kinds of questioning employed that are intended to help move children from level 0 to level 2 might be helpful.  Need to look into it more.
 
Learn how to teach math with Cuisenaire Rods using daughter as guinea pig.  

I wish my math education had consisted of these, but I can re-learn math as I teach my own daughter.  These unit blocks are great for developing a real sense of what numbers mean, but when when you grow tired of that focus, you can use them in other ways!  I drew a line of symmetry and made up a game where one person puts down a rod, and the other person 'reflects' it on the other side of the line.  In this case my daughter led and I followed, but you could take turns in any number of ways.  Maria Droujkova from Natural Math posted some very interesting, videos of kids using these rods.

Making Things

Curried red lentil soup with sweet potatoes and greens.

I know a lot of people who make things -- dinner, for example.  I know people who grow their own food, make their own music, build their own rock walls, design and build their own houses, decorate their homes with their own artwork, sew their own quilts, and bake their own bread, all as a matter of course.  I know people who knit their own socks!

Then again, when I go into schools, I meet legions of children who never even considered the possibility that they could make something, let alone their own percussive dance patterns.  Here the thing, though -- most kids, even if they don't regularly engage in making things, get excited when it's their turn to make their own dance patterns in class.  It's amazing and energizing to watch, honestly.  It's like I'm giving them permission to take their rightful place in the human race.

I have been reading back issues of the Teaching Artist Journal and finding common themes emerging in what I read.  One of the things that comes forward is that many Teaching Artists (like myself) teach with less of a focus on the technical aspects of their art and put more emphasis on helping their students make things within the structure of an artistic practice and process.  When a Teaching Artist takes their art into the classroom (or community center, or after-school program, or a nursing home, or wherever people are)  they work with people who may have never taken a dance class or made music or used paint in a meaningful way in their entire lives.  They usually have limited amounts of time to work with a group of students and so they become masters at helping people make personally relevant art with a limited vocabulary of skills.  

This is what I do in Math in Your Feet.  In an upcoming article to be published in April 2011 in the Teaching Artist Journal, I go into detail about a teaching tool I created which I call 'Jump Patterns.'  Essentially, Jump Patterns are to percussive dance what creative movement is to ballet or modern dance.  Jump Patterns reflect the elements of percussive dance and allow children to be creative and successful in this particular dance style, but without great need for technical development. 



Don't get me wrong, skill development is important, but sometimes a focus on technical issues creates a huge obstacle to experiencing the incredible joy and importance of just making...things.  Art.  Ideas.  Music.  Shoes out of paper plates.  Even having this particular discussion is part of the cultural baggage we carry, a particular mindset that gets activated and reactivated whenever we think of art solely as something to be 'good' at  instead of an opportunity to make things.  And that's a pity, because I believe that making things is one of the most meaningful activities in which a person can engage. 

An 'old fashioned dress' the creation
of which was facilitated by safety pins and
some adult modeling.

Right about now you might be asking yourself, 'Just how can someone make something without skills?'  The answer is facilitated making.  Kids are like everyone else, you do have to give them something to work with before they can begin to create.  But, in the end, all you really have to do is help kids explore the medium, find a way for them to  investigate the processes of the art form, help them formulate some questions or just wait until one is asked, and, when it's time, add instruction on specific skills when the student is ready for them.

Here are some examples of what I mean by facilitated making:

Example I:  In Math in Your Feet, Jump Patterns are the tool that facilitate the making of foot-based dance patterns.  Once a kid learns three of the four elements of percussive dance (leaving out the most technical aspect, parts of the feet) they are then ready to experiment and create their work.  They become participants in the traditional aesthetic -- everyone has something to offer, everyone has their own style or take on the dance, everyone is welcome.  Not everyone is good but, more importantly, everyone participates.  Without participation there is no form.

Example II: A Teaching Artist friend of mine works with kids who, more often that not, have no formal music training.  When he sets up digital recording studios in their schools they are able to get immediate feedback on their own ideas and find ways to evaluate and adjust their ideas to make real, and often interesting, music and lyrics in a collaborative way with their friends.  He spends parts of each class talking about the science of sound or new techniques for using the equipment but mostly the kids experiment on their own and come to him if they have questions.  In this case, the facilitation is the TA's approach to using the equipment with his students. 

Mermaid's Tail

Example III: My daughter, who is five, has always had many ideas and many of them get expressed through her art supplies.  When she was two, she wanted paper cut into shapes so she could make something with them.  She had an idea but still did not yet have the skill to cut the paper the way she wanted.  Did I say, "Sorry darlin'.  You'll have to wait until your hand muscles are stronger and more coordinated before you can get that idea out of your head"?  Nope.  I cut the shapes for her and she did the rest.  Did it change the fact that it was her artwork?  Nope.  A few years later, when she was a few months shy of her fourth birthday, she had an idea for a mermaid's tail.  By then, facilitating her making process simply consisted of making sure the tape was secure so all those little pieces stayed together.

Making things is not rocket science...well, unless you're trying to build a rocket.  But what comes before that rocket?   All the times when kids get a chance to ask questions, experiment with materials, find their own answers and get some help and guidance from adults along the way.  We can sometimes get wrapped up in giving kids what we think they need to learn, but it's in the doing where the meaning is made.