More Than Counting

Every once in a while I do a Google search for my name or my program's name, Math in Your Feet.  It's instructive and sometimes surprising to find out just how far out in cyber space I am.

Case in point, I recently found an undated conference paper by an associate professor from the Institute of Mathematical Sciences and Physics at the University of the Phillippines Los Baños.  Among other things, the paper makes a case for "the cognitive and aesthetic similarities between mathematics and dance."  Math in Your Feet is cited and described in one of the opening paragraphs.  Never mind the fact that it's just a rehashing of promotional language direct from my website, the rest of the paper makes a pretty good argument for the importance and relevancy of integrating math and dance.

My favorite section of the paper is on pattern recognition (a major connecting theme in my program) and includes a quote from a book called The Math Gene by Keith Devlin, mathematician, NPR's Math Guy, and (among other things) a senior researcher at Stanford University's Center for the Study of Language and Information, who argues:

"mathematics is not about numbers, but about life.  It is about the world in which we live.  It is about ideas, and far from being dull and sterile, as it is often portrayed, is full of creativity.  It is the science of patterns."

Within this one quote are ideas I've been trying to communicate for years to the folks who hear about my program and inevitably reply, "Oh, you mean like counting your steps?"  I always try to find a nice way to say, no, not really, but there's never enough time to explain my reasoning fully.  However, I do have time and a little space here to say mathematics is more than numbers and counting and balancing your checkbook and that a program which teaches math through dance (or dance through math) is about more than counting too.

Mathematics is essentially a language invented to describe, manage and understand the physical world. (And if there are any mathematicians checking in on this blog, feel free to correct me!) That's why connecting math to the real-world helps kids better understand it, because the real world is math.  And, no matter what your opinion is about dance being lumped in with 'things in the real world', please remember that we all move and without a firm grasp on spatial relationships, one of the foundations of a good mathematics education, you will most literally be lost.

That's why even the preschool version of Math in Your Feet has less to do with numbers and more to do with exploring and understanding where you are, where you want to be, and how you're going to get there.  Add to that a chance to develop patterns of movement embedded in time as well as make creative choices while moving and you now have a powerful mathematical experience in real time and real space.  The critical piece (for upper elementary kids, anyhow -- the younger ones just need as much kinesthetic experience with the concepts as their teachers are willing to fit into a school day) is that kids get a chance to bring the math back to the page.  After all, math is a symbolic language, but it is really much more than counting.

I'm sure I'll be revisiting this theme in the future.  But first I have to run to the library to pick up a couple of Keith Devlin's books.

Preschool Tape, Part 2

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.