I had been watching her play with the kinetic sand for several minutes. She was carefully forming it into a small, smooth dome, then using a wooden knife to cut it first in half, then into quarters before re-forming it into a single dome to do it all over again. She must have done it a half dozen times or more.
She said, "Look, Teacher Tom."
I had already been watching, so I said, "I'm looking at your sand."
"It's a muffin."
"I'm looking at your muffin."
"Now watch," she commanded as she picked up a wooden knife. "It's just one muffin, right?"
"Yes, I see one muffin."
She then cut it in half. "Now I have two pieces."
"It's true," answered, "There are two pieces."
"But I only cut it once!" she said it with exaggeratedly raised eyebrows, selling the feeling of wonder that she must have felt a few moments ago when she discovered this mathematical principle. "Now watch!" She carefully placed the knife perpendicular to her previous cut and did it again, cutting it into quarters.
She looked at me with a smile that asked, Mind blown?
I said, "Now you have four pieces."
"Except," she replied, shaking her head while directing my attention to the sand with her open palms, "I only cut it two times!" As she gathered the sand back into a single muffin, she asked, "Want to see it again?"
Mathematics is something that gives human beings great pleasure. Of course, I was tempted to fill the air with concepts like "whole," "half," and "fourth." Of course, I imagined myself helping her take it a step farther, introducing "thirds" or "eighths" or whatever. But it was easy to stop myself because over the course of my education, the way I'd been taught math caused me to slowly lose my enthusiasm for it. For most of my life I'd believed that it was the subject matter, but the longer I've been teaching preschoolers, the more I've come to understand that my classroom aversion to math is a result not of math being hard, but of how it was taught to me: a dry process of drilling, rote, and formula.
I still don't know how to "teach" math without ruining it, but when it happens like this, when it's principles are simply discovered by a child, it's so beautiful that I just know the other way is wrong.
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4 comments:
Math is an art form. Some people have the math "gift" but most others just see it for it's computational purposes in life. Maybe she is one of the gifted math people that will want to play with math in all it's artsy glory.
This is AWESOME. Not only that it happened for her, but that you got to experience it with her. Wow. Great. it's those tiny, quiet moments that are breathtaking. As well as those louder moments when a child teaches herself to jump over the arm of a chair on one hand (maybe that's too hard to describe, but it's breathtaking, too).
I took a course on the History of Math in college. You might like to find a book on it (my books are packed, so I cannot find a title to suggest), but I really thought it should have been studied in Jr. High and more kids would have loved/appreciated/been able to withstand math.
This was beautiful! I can picture her amazement :). So wonderful to witness the joy of new discoveries!
I love the awe and curiosity of the child you've described. It's so interesting how children can be focused on one task so much when they're enjoying it while gaining new knowledge and understanding.
Children are tactile learners, yet they are capable of understanding abstract concepts if given the chance to explore their curiosities and learn through the process of inquiry and investigation.
I'm glad you allowed her to make her own discoveries through sensory play.
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