I was in my grandson’s Montessori pre-school class the other day, admiring the wisdom and warmth of Maria Montessori’s vision of how a child’s natural curiosity can be used to build a basis for learning. It was grandparent’s day and my wife and I were deeply interested in anything our grandson had to show us from the tadpole growing little legs to the beads used to learn the concept of tens. After the joy of the experience on a crisp and sunny autumn day, the image of the beads remained in the back of my mind.
I kept thinking about how wonderful the visual aspect of the beads translated simple mathematical concepts and how if I had had that same toy to play with as a child, I would not have struggled as much with math. The toy is simple. A single bead is in the first place, in a miniature basket, a beautiful glass bead with a luminescent coloring. On the next square are ten of these beads on a wire, like a small glass caterpillar with ten segments. The beads, aligned in a row, perfectly show the quantity with immediacy.
On the next square of cloth, ten rows of ten beads are aligned on the wires in a grid of 100 beads, a concept that makes the idea of “ten squared” a visual concept that one can pick up and play with, count one side of and the other, count all one hundred beads in the decades like an abacus or rosary, an elemental handling of this abstract idea of mathematics. Finally, the last cloth square is a cube of beads, ten stacks of the ten-square 100 bead squares, wired together to make a gleaming glass cube like a giant glittery grain of salt or sand you can hold in your hand. The effect of holding one thousand beads in one hand is instant, the mass and weight, the size and feel, simply illustrate what it means to “understand” an idea in a concrete way.
I would like to use Madame Montessori’s brilliant visual illustration to conceptualize for you what a trillion of anything looks like. The cube of glass beads in the above math manipulative is the beginning of seeing what we have gotten ourselves into. Until we truly see the depths of our problem, we will never be able to see our way out. The thousand beads of ten, ten by ten stacks, is but one small part of this understanding, but it is the basic building block of my illustration. Consider its size to be approximately 3.5 inches by 3.5 inches by 3.5 inches, a solid, hefty cube of beads.
Now, imagine a thousand of these, which would add up to 1,000,000 beads or 3,500 inches of glass beads, a cube that would stretch 291.666 ft., or just under one football field of glass beads in length, breadth and height. One thousand of these stadium-sized cubes of glass beads would equal a cube of beads 55.23 miles high, wide and deep. That is an hour's drive at fifty five, a little under a thousand of those football fields. Now imagine not ten but 11 of those cubes, stacked up like baby blocks, glittering in the sun of an autumn afternoon. That, my friends, is the legacy this generation is leaving for its grandchildren. It kind of makes me ashamed of the baby boom.