Waldorf schools are often fond of speaking about how we are different, and math is no exception. We do approach math differently than traditional schools, but we do many things the same. As Yogi Berra might have said, ”Math is, after all, math.” In grades one through eight at the Waldorf School of Atlanta, a child will learn the same math skills that s/he would learn at other area schools. The primary difference is in how it will be learned.
Movement and Rhythm
At some time in our lives, we have all wrestled with the multiplication tables. How were we to learn such a long list of dry facts? At our school, we first teach math facts by “getting them into children’s bodies.” In the younger grades, the children will spend some time each day clapping and stamping different number patterns. First graders may walk in a circle like an old man and count extra loud when his cane lands: 1-2-3-4-5-6-7-8-9-10-11-12. This lays the foundation for learning the multiples of three for multiplication and division. Better still, it gives a child a feeling for three, a relationship that exists in her body and not just as a symbol on a page.
Another exercise that comes later is to have four children walk geometrical figures that are all joined at a central point. A child walks each figure repeatedly counting each time she comes to a corner. The children take note of the “friendly numbers” where they meet in the middle. For example, 15 is a friendly number for the triangle and the pentagon because both of the children walking those figures will meet in the middle when they say “15”. There is quite a bit of excitement when the children reach 60, the first number friendly to all of the figures. This exercise lays the foundation for a meaningful relationship to the concept of a common factor that is needed for working with fractions.
Story and Image
During the elementary school years, we strive to educate children through images. There is a twofold purpose to this. First, children love to live into stories and pictures. They develop an active relationship with material when it is presented in this way. Second graders often hear a story of gnomes who are digging gems from a mountain. When the gnomes get ten gems, they put them in a bag. Ten bags are too hard to carry, so they put those in a cart (100 gems). Ten cart loads go into a wagon (1,000 gems). Thus the children are introduced to the concept of place value.
The process of creating exact mental images is a thinking skill in and of itself. The stronger and sharper images a child can create, the sharper is his thinking. In eighth grade, we study the Platonic solids – a series of “perfect” solids described by Plato in his dialogue “Timaeus.” When we introduce each figure, it is described by a story (e.g. an ant walking around a cube or a series of ropes in a zero gravity room) to lead them through creating a picture of a three dimensional geometrical solid in their minds. Ideally, the first time a child “looks at” these figures, she sees a picture she created internally.
Meeting the Developing Child
The benefits of math as a learning tool are well known. Since the time of the Ancient Greeks, math has been the accepted method for developing logical and abstract thinking. In Waldorf schools, we pick the topics for our curriculum not only because children are intellectually ready for them but also because it meets a developmental need. In fourth grade, for example, a child separates from the unity of the world and often feels the loneliness of emerging individuality. We see this reflected in the introduction of fractions, where a whole number falls into many pieces. The work with fractions helps to support the child through this life transition.
Seventh grade can often be a tumultuous time for children due to physical changes in their bodies combined with drastic emotional swings. For this reason, we take up the study of algebra
in seventh grade. The process of unraveling difficulties using a clear, steady process of maintaining balance (i.e. balancing equations) is a balm to the young adolescent soul. These are some of the ways that our curriculum works with math and strives to make it more than a collection of skills. Perhaps you will have a chance to observe some of these activities in our classrooms this Grandparent’s Day.
Faculty Chair & Math Instructor
Originally printed in March 2012 Garden Breeze of the Waldorf School of Atlanta