Quality of Numbers

Some thoughts on the QUALITY OF NUMBERS
from Rhythms of Learning, "Teaching Arithmetic" a lecture Rudolf Steiner gave in Torquay, August 16, 1924.

"'Look, here is your right hand but you have another hand too, your left hand...For when this hand moves and the other hand moves as the same time, then they can take hold of each other, they can come together. That is different from when you simply move alone. In that you walk alone you are a unit. But the one hand can touch the other hand. This is not longer a unit, this is a duality, a two. See, you are one, but you have two hands.' Then you show it like this (roman numberals) 'I I'."

"...in truth a person is permeated with soul and spirit in the whole body. The head is the traveller that sits back restfully inside and does nothing, while the body, every part of it, is the chauffeur who has to do everything...it is important to pass on and not merely take counting by adding one thing to another; indeed this is the least important aspect of counting and you should teach the child as follows: 'This is something that is ONE. Now you divide it like this, and you have something that is TWO. It is not two ONEs put together but the two come out of the ONE.' And so on with three and four. Thus you can awaken the thought that the ONE is really a comprehensive thing that contains within itself the TWO, the THREE, the FOUR, and if you learn to count in this way, then the child will have concepts that are living and thereby come to experience something of what it is to be inwardly permeated with the element of number (and not a mere abstraction)."

From The Tasks and Content of the Steiner-Waldorf Curriculum, "Arithmetic and Mathematics”

"Motivation should be awakened through pictorial description of number qualities. The [will activity and soul activity] dual aspect is important: on the one hand it educates the bodily senses through experience of movement, unfolding of movement possibilities (both course and fine), and co-ordination exercises. On the other hand internalizing of the expressed activities [through calculation]. Here the main medium for achieving this is the use of pictures. Through pictures, children can grasp internally what is intended. Pure symbolic, logical representation can never achieve this. In order to be able to handle quantitative numbers freely, an inner numerical space needs to be created..."