First we folded a piece of paper into fourths and I drew five sections (middle for equal). We started with equal and I told him about how he and Elie love to go on the teeter-totter and what does it look like if they got it balanced so it didn't go up or down. Then I drew a picture and he copied and then I said, ah in the picture, you're both in the same place - you're Equal! And then I drew the equal sign and said it's like the top and bottom of the teeter totter when it's perfectly balanced.
We did a similar format for each of the Processes. The picture ideas are from Jarman's "Teaching Mathematics in Rudolf Steiner Schools" except the plus which is from Schuberth's "Teaching Mathematics in First and Second Grades in Waldorf Schools".
So Plus is a man holding out his two hands to collect things (we drew flowers); Minus is a man giving something (we drew a tack based on our example from last week - also note that I spoke of division as giving versus taking away - Waldorf stresses the moral benefit thinking this way, which I agree with); Divide is a man with one hand on top and bottom of a plate of muffins to share. Multiplication is a sower of corn with arms and legs outstretched - we drew the seeds on the left and the fully grown corn on the right.
Next we went back to our work from last week to add the symbols to our equations:
Yoav had so much fun with this. He kept saying how much fun it was. I'm curious to see how well the ideas will stick. I think we'll do one more day with the pictorial computations and then move to straight equations.
For many Waldorf people, this might seem quite contrary to the "standard" Waldorf treatment of the Four Processes. Jarman and Schuberth are both against the overly pictorial introduction of the Four Processes. I can see the benefits both ways but Jarman's explanations in particular really made me decide to go with this particular method.
About the different methodologies, Jarman says (in his book, "Teaching Mathematics in Rudolf Steiner Schools for Classes 1-8":
Whist it is of great value to introduce any educational subject to children by means of pictorial presentation - and each topic within that subject, too - there is a danger in adopting a similar attitude to the development of the subject or topic irrespective of its nature. When teaching reading and writing, or history, or art, the pictorial element always needs to be present. Mathematics teaching, though , is quite different in this respect. Human feelings and thought pictures nurture the essence of literature and history, but mathematics is essentially a will subject. The will has to be brought into thinking. While the introduction to mathematical topics does require the pictorial element - only in contemplating the pictorial is a growing human being left free, for pictures do not compel - this needs to give way to a musical element in the development of such topics. To use Rudolf Steiner's terminology, whilst literature and history rely on Imagination, mathematics relies on Inspiration. Mathematical progress depends upon overcoming and freeing oneself from the pictorial and living in sense-free concepts. This is why all pictures used in introducing mathematical topics need to be precise. Teachers who like to bring fairies and gnomes into Class I arithmetic need to be aware of the dangers indicated above.