On Day Four of the Teacher’s Seminar in 1919, one of the teachers picks up a piece of chalk to demonstrate taking a whole piece of something and showing how it can be divided by being broken. Steiner agrees in concept but advises not to use anything too valuable – like chalk! We don’t want to encourage children to destroy useful things!
Steiner then comments “We proceed from the sum not the addenda.” Start with the whole and then proceed to the parts: this is a key characteristic of Waldorf education.
The discussion moves on to the topic of the temperaments; in the afternoon of the day before, one of the trainees had asked how to consider the four temperaments in arithmetic.
For those of you unfamiliar with the temperaments, Steiner gave a number of lectures about these four basic personality types and how all human beings tend more toward one than the others. This makes the world a more interesting place! And at the same time, our aim as individuals and as teachers is a balance of all four. So Steiner talked a lot with teachers about how to work with the temperaments in a group of children using arithmetic, storytelling and drawing to demonstrate. At home, we can benefit from identifying our own temperament as well as our children’s because it can contribute to us working creatively with our children in healthy, productive ways.
So on Day Four of his Discussions with Teachers, Steiner gives lots of examples to show that:
- Subtraction is suited to melancholics.
- Addition to phlegmatics.
- Multiplication to sanguines.
- Division to cholerics.
Steiner gives little situations such as this, to a sanguine child: “Count out 56 elderberries. Now, look here; here I have 8 elderberries, so now tell me how many times you find 8 elderberries contained in 56.” He wants to bring mathematical concepts to life.
In Waldorf schools and homes all over the world, teachers often introduce math in the early grades by developing a story around four characters who represent the four processes, like king plus and queen minus, or the math gnomes, or math squirrels. Interestingly, the math gnomes that are so prevalent in Waldorf teaching were not Steiner’s idea but were created by a few Waldorf teachers in one of the first American schools years later.
Steiner does advise that we teach all four math processes at once. “By continuing in this way I find it possible to use the four rules of arithmetic to arouse interest among the four temperaments.” Teaching all four at once is important; we can introduce them fairly quickly and then practice them all because they are all related. “They can be assimilated almost simultaneously. You will find that this saves a great deal of time.”
Steiner is big on being efficient and saving time. He really felt that the teacher’s role is to plan in such a way as to teach the most in the least amount of time. He writes more about this in his lectures collected in Soul Economy: Body, Soul, and Spirit in Waldorf Education (lectures given in 1921-1922 which you can read online here); this is one of my favorite Steiner quotes: “The aim of Waldorf education is to arrange all of the teaching so that within the shortest possible time the maximum amount of material can be presented to students by the simplest possible means.”
What is your experience with the temperaments and how do you incorporate them into your math teaching?
The Steiner Cafe is a place to explore and reflect on the lectures that Rudolf Steiner gave at the Teacher’s Seminar in 1919, the very first Waldorf teacher training. Each month here, we ponder one day of the seminar.
To read reflections on previous lectures, check out The Steiner Cafe page.
These lectures are published in three books; the morning lectures in The Foundations of Human Experience; later morning lectures in Practical Advice to Teachers; and afternoon lectures in Discussions with Teachers. We invite you to pick up the books and read along.
If you prefer, you can read online at www.rsarchive.org, or listen at www.rudolfsteineraudio.com. Or, just meet us here each Thursday or Friday at The Steiner Cafe for some lively discussion. Lot’s of options! Hope you’ll join us.