The Math in Your Feet Blog | Constructing an Understanding of Mathematics
Wednesday, October 13, 2010
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 ATyour 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 TOGETHERand STAND in the center of your space. JUMP forward, JUMPcenter, 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?