Spiral

In New Zealand, the spiral or koru is the Māori name given to the new, unfurling fern frond. It symbolizes new life, growth, strength, and peace. For me, growth as a person and teacher is a spiral - an unending journey to the center and from the center.

We like to think of education as a simple equation from point A in kindergarten to point B in middle school to point C in high school. Teach this first, then that second. Pacing guides are built around the idea of learning as linear. If we just go back and fix what wasn't learned at point A in the equation, then this child will move to the next step. Sometimes that is true. More often, it is not.

Educating is an art and a science. In much of today's discourse about education, the two are mutually incompatible, but in truth one cannot exist without the other. The act of educating requires balance and symmetry, which is both art and science. Think of education as the Golden Ratio, phi (φ), which mathematically expresses the relationship that the sum of two quantities is to the larger quantity as the larger is to the smaller. It is simple, but its properties have consumed the attention of "some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose" (Livio, Mario (2002). The Golden Ratio: The Story of Phi, The World's Most Astonishing Number. New York: Broadway Books). We cannot deny that educating is a scientific endeavor. It is a simple act built on a highly complex foundation of variables and context. Like scientists, we must test hypotheses and gather data, work to discover the elusive equations that make our students tick, and at all times continue to ask questions.

However, while powerful and seductively convincing at times, science alone is not enough. Science does not set the objectives of a society. It cannot answer the most fundamental questions we ask about ourselves and our purpose. In the end, science must inform art. From Leonardo de Vinci to Salvadore Dali, many artists and architects have proportioned their works to approximate the Golden Ratio - especially in the form of the Golden Rectangle, in which the ratio of the longer side to the shorter is the golden ratio. Some studies of the Acropolis, including the Parthenon, conclude that many of its proportions approximate the Golden Ratio. It is thought that the proportions of the Golden Ratio create a state of perfect beauty. That is the art of educating, creating those fantastic teaching and learning moments we know as perfection in our craft.

Learning is also natural. Using Fibonacci numbers, the Golden Ratio becomes a golden spiral, which many claim to see everywhere in nature - in shells, pine cones, the arrangement of seeds in a sunflower head, even galaxies. Adolf Zeising, a mathematician and philosopher, while studying the natural world, saw the Golden Ratio operating as a universal law "in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical..." (1854, Neue Lehre van den Proportionen des meschlischen Körpers, Leipzig, preface). Learning, taken to an art, understood through science, is also natural with its own universal laws. We often see those laws as simple common sense, and in the pursuit of great art or science, become blinded and forget them. That is when we must stop, reflect, and ground ourselves in what we know at the most basic level, as human beings who strive for beauty and completeness in our lives and in the lives of our children.