I was at a Waldorf School curriculum presentation last night. They place a lot of attention on teaching according to a child’s developmental stage. There is good scientific evidence supporting the idea that during the first seven years of life, children are wired to survive and make choices based on imitation of those around them. Hello mirror, there you are…. again.
It is a tough job being transparent to the all seeing of a child. What this means for me is working on walking the talk with the kids. Pausing and looking more at what I do, and the genuine affect it has on my children. It is scary the power we have in molding these little people.
My dear friend, and date for the Waldorf night, saw this clearly. She is afraid to put the following quote on her fridge: “Am I worthy of imitation?” And frankly, so am I. Google “am i worthy of imitation” and you get umpteen references to the bible. From what I’ve been told though, nothing associated with God is easy.
Waldorf Education does not teach math in isolation of other subjects. It is part of a holistic learning approach, which connects the child’s inner self (that Waldorf’s founder Rudolph Steiner refers to as “will”) and body through muscle-memory exercises. Waldorf Math is really a kinesthetic or whole body learning experience for the Class 1 child. Math is also closely related and taught with music, furthering the important connecting between a child’s body, and their understanding of numbers. As an adult I know that the most lasting memories for me are always those with more than one sense being used. I still remember vividly walking by a jam factory near my house when I was a child on the way to school, and counting the metal fence rungs while breathing in the aromas.
By moving to math in the early grades, even before reading and writing, the child develops a proficiency much like a musician memorizing their scales. It is a slow and unhurried approach that does not push the child to count or read too early, which has been found to taint a child’s passion to learn. Once a child is moving to math, he or she may begin to use beans or glass beads to better understand the relationships that additions and subtractions make with the whole. Imaginative math fairy tales are told, where the children get to participate by solving the same word problems the main characters do. This allows for a real “living” math to develop within the children. When children begin writing, they begin with roman numerals and integrate this lesson within their form drawing block. Roman numerals have much easier forms and more straight lines than our common curvy numerals.
Waldorf starts off the introduction to math by asking a seemingly simple question, “What is the largest number in the universe?”. My son (aged 5) came home from school and asked me the same question. I answered “Well, erhmmm, it’s infinity.”. He said “No, one is the biggest because I am one.”. Other responses discussed in class are “One is the biggest because without it there isn’t any 2, or 3, or even a million.” “One is the biggest because everything there is is in one Universe.” “One is the biggest because it can be any number it wants.” All sorts of philosophical and mathematical truths become evident through just this “one” discussion. This gets them thinking in a whole new way about numbers, and how they relate to us and the world. Eventually the children arrive at “I am one!”, they see how their bodies are shaped like the number one, they relate themselves to the vastness of the Universe, and realize at that point that they are co-creators.
Each number, 1-12, is a discussion involved in this deep intensity of imagination. Waldorf begins with Roman numerals and incorporate geometry into the discussion of each number, scribing freehand the relative polygons and stars. The children work to master each of the stars, crossing the vertical midline over and over again as they practice on large sheets of paper. Eventually, a particular star will stand out as the class favorite which tells the Class Teacher an immeasurable amount about the class itself. All of this happens in 1st grade.
So from the start, children are aware of the significance of numbers and enter very deeply into them. When they have the imaginations of the numbers, they use their will to execute stars and polygons. They move their bodies through the math facts of all four processes (+ – / x) each day, and create personalities for each math function. There is Tessa Times, Mickey Minus, Penelope Plus and David Divide. Each character is known by how they appear and act, for example, David Divide has a sword and always chops things up, sometimes in half or more. Children take part in music classes involving flute, voice, and lyre to illustrate the beauty of the voice of numbers. They use manipulatives (e.g. bean bags, chesnuts) to work through exciting math tales and classroom conundrums.
This multi-faceted learning approach continues into Class 2. Here is a Class 2 report summary of a math block lesson:
Column algorithms vertical addition 1, 10,100. By using the image of the chipmunks and their holes, rooms and chambers to store and count the nuts, the children understood well by the end of this block. We practised many sums and wrote some in our books. We worked the times tables in many different ways, always with rhythm: sticks, walking clapping bean bag throwing etc. We reviewed the 2 and learnt the 4, 8, and 11 times table. In circle we are doing lots of mid line work, expansion contraction, throwing and catching, and recently juggling! We have been walking squares, stars, and some eurythmy.
A genuine love of math can only be enhanced by a practical approach in the mid to later grades In the third grade curriculum, fractions are learned through cooking and building. At this stage, there is the introduction of the orchestral stringed instruments at that same time, which also leverages many math basics. Math is the key to participating in the music lessons. Math is everywhere. The sixth grader gets to experience this by working with the Fibonacci sequence and Euclidean to Platonic geometries. Waldorf Education seeks to help students develop and integrate math, music, building, movement, storytelling, and more all at once.