The Profound Discovery of Numbers in The World
Written by Eden Motto, Second Grade Teacher Minnesota Waldorf School
Numbers govern our world. The beauty and brilliance of nature is comprised of profound numerical patterns. Numbers are a part of our bodies. They are nestled within the delicate structure of the arithmetically spiraling ferns — or as fractals when fern fronds burst from the stalk ever- tinier replications of the entire fern. Number moves through the oscillating waves of sound which creates stunning music that enchants the ear.
Children come into the world understanding numbers innately. How could they not —when these patterns are so intricately interwoven into their bodies. In the early grades children are guided to uncover these mathematical patterns within themselves and the world around them. To see in the simplest yet more profound way that this is the basis of mathematics: a subject full of wonder and majesty.
Ever so slowly the children begin to take these primordial patterns and do as all humans have done before them — try to discover how these patterns work. At first simply with the four processes addition, subtraction, multiplication, and division. Then with deepening understanding these children will go on a true mathematical journey to uncover and discover by doing as the great mathematicians before them did. They will turn to the world and begin to measure and look for the relationships that are found there, pi, the Pythagorean theorem, the parabolic shapes of lamp shade shadows. It is a profound gift to understand number in this way — a gift that they will carry with them throughout their lives lending a deep curiosity, a joyfulness, and sense of awe, as the children discover ever more complex mathematical phenomena that culminates in the waldorf highschool with the mathematics of movement: or calculus. This is a tremendous trajectory that starts with the simple quality of numbers.
The Foundation of The Quality of Number
In Ancient Greece Pythagoras began observing the world around him with wide curious eyes. He understood as did many philosophers and scholars at the time that numbers had personalities, almost human like in nature. Numbers were viewed as acquaintances or even friends. One was singular, and lonely, isolated, but upright. Two introduced a polarity, a contrast, sun and moon, night and day, inside and outside, smooth and jagged. Two was a world of opposites. Three introduced a resolution to the duality. Suddenly there was a middle ground. Two dueling opinions could be mediated by a third. Three held strength. Three was the strength of a triangle, three legs could hold up a stool, three people could be a family, (although there are always many more iterations of family). These qualities of number that were so much a part of the ancient consciousness make up the foundation of what children learn first in the early grades.
Early Grades Curriculum
Children are asked to begin to see the world of numbers as if they were discovering it anew. With deeply curious and discerning eyes they look into the world. Where they find: bunches of two’s within their own bodies, two eyes, two eyebrows, two ears, two cheeks. A few fives crop up! Five fingers on each hand , and five toes on each foot. The lovely 10’s, ten fingers and ten toes; the basis of counting and place value.
(Beyond their vision but humming within them even more devine patterns emerge that will be explored later in the curriculum. The complex pattern of bronchial branches in the lunges forming ever finer fractal- patterns that end in perfectly proportioned clusters of alveoli—little air sacs like grapes).
The children then look beyond the body and into the world. Clovers are clusters of three leaves, tiny clusters of five seeds positioned as five pointed stars are concealed within the apple core -revealing its dicotyledon nature. Lilies boast six perfect petals, spiders scuttle on eight legs. Sea shells curve in geometric and arithmetic spirals that are carefully observed and etched out in middle school geometry. The children find some of these stunning discoveries in first grade, but must wait to truly uncover all of the treasures that number has to offer until later years when the curriculum begins to unfold the complexities of botany, geometry, and human anatomy.