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The Hidden Beauty of Division

Leigh Ebrom

by Jan Reed, Elementary Guide and Parent

A six-year-old student carefully watches as an older friend sets up his work spot for a big work. First, he unrolls a rug. Next, he gently slides a long tray of tubes and beads to the edge of the shelf and carefully balances the weight of the work between his hands. Slowly he makes his way to the rug.

montessori test tube division.jpg

As I watch, I can just barely hear the low tap of the beads rattling in plastic tubes. Rows of these tubes rap out a tune- perhaps warning us of the possibility of a large spill- 700 beads to be exact.  Finally, the student arrives at his workspace where he strategically plants the tray to the top of the mat. Back to the shelf the child goes to get a wooden board. 

The six-year-old moves a bit closer.

Her curiosity draws her as the older child continues to move with purpose.

Checking his paper to see what numerical challenge awaits him, the child begins setting out little cups, filling each with tiny beads- building the dividend by putting beads into colored cups. Each cup represents a place—thousands, hundreds, tens and units.

By the time the child is ready to set out colored skittles (small tiles also representing a quantity) on the board to represent the divisor, the younger child is sitting next to her friend. The older child places the skittles out on the board, and the younger child watches with interest.

It is silent.

The student begins dividing by laying out the beads, exchanging when needed, one place value at a time. When he has completed laying out the work, exchanging and dividing, the student records his work on his paper. He has calculated the answer to his division problem.

The student turns back to his work, returning beads to their identified tubes so that he might begin again with the next challenge.

With a graceful swipe of his hand, the older child cleans up the beads from the board replacing them back into the tube without touching them. Magic. Finally the silence is broken. “How do you vacuum the beads up without spilling them?” asks the young girl. The older child demonstrates, answering the younger child’s question.

With one material so many things happen.

The material entices the child into using it:  perhaps with its name “test tube division” perhaps with its colors and design; or perhaps with the orderly keeping of the little pieces.

The material builds confidence and concentration with patterns and handwork. The child learns to manipulate small beads with a small tube. He works to balance a large tray and carry all 700 beads across a busy room.

And finally it’s the discovery- I get it. The child notices the patterns in the material—the diagonals, the colors, the way that units flow into tens that flow into hundreds and that build thousands.

In the end, it is the child who owns the algorithm. It is not memorized but discovered.

I love this work because every year I witness the beauty of a three-year cycle though this material. The confident older child magically luring the younger child in. In where? Into our community. Into learning.

If you're interested in learning more about Montessori education and Stepping Stones, please contact us.