Waldorf Math through Plato and Dodecahedrons

By Heather Collis-Puro, Handwork Teacher

At Waldorf School at Moraine Farm, beautiful geometric drawings are often what come to mind when we think about math in sixth grade.   Many of us have purchased the notecards that Mr. Yoors’ (sixth grade) class sold at the Holiday Fair last year.  I have a hard time using them!  Working with accuracy and patience to create these incredible forms is just developing in the 12-year-old, and understanding symmetry gives a basis for grasping further mathematical concepts like algebraic equations that are taught later in middle school.  In handwork, the students work with symmetry and geometry starting with knitting in first grade, creating simple animals from knitted squares and rectangles.  In sixth grade the students make dolls, using the mathematical concepts of the Golden Ratio in order to create a symmetrical pattern for the body of the doll.  Creating a doll by hand takes accuracy and skill, and the students spend the year honing their ability to be precise.  Often the students will take a break from regular project work to take up some other craft around a holiday or vacation, and this year, the sixth graders created these star lanterns at the new year.

Winter 2016 749These lanterns are made in the form of a dodecahedron. The dodecahedron form is one of five platonic solids, each solid assigned by Plato to represent the one of elements and the universe.  Plato’s theory was a bit premature, only a first step to understanding the chaotic world of earth, air, fire and water.   Although we are not learning about these shapes in order to further our understanding about science, we are stretching the students’ imagination: we are taking a shape from an idea, to a two dimensional form and then into a three dimensional solid. This imaginative capacity is an important skill to develop.  Therefore, the lantern-making process supports further learning in math, bringing concepts into real experiences for the students.

Winter 2016 751In order to create these lanterns, each student used a compass to create a pentagon inside a circle.  This rendering was used as a template for cutting, folding and gluing 12 pentagons to create a dodecahedron.  When a light is placed inside, a precise star is revealed to us.  Is it no wonder that Plato considered the dodecahedron to be a representation of the universe?

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