VIII. Modelling of Bodies

It really amounts to this. One should seize every opportunity of making use of what is pictorial and tangible. This is all the more necessary because in this way one learns to enter into reality, thereby learning also to form everything in accordance with what is real. It is actually quite arbitrary if I place 3 beans before the child, then add another 3 beans and yet another 3 or maybe 4, and then proceed to teach addition: 3 plus 3 plus 4 equals 10. This is somewhat arbitrary. But it is quite another thing if I have a small pile of beans and do not know to begin with how many there are. This accords with the reality of things in the world. Now I divide the pile. This the child understands immediately. I give one part to one child, another part to a second child and a third part to a third child. So you see, I divide the pile, first showing the child how many beans there are altogether. I begin with the sum and proceed to the parts. I can let the child count the beans because that is just a repetitive process, 1, 2, 3 and so on, up to 12. But now I divide them into 4, into 4 more and still another 4. If I begin with the sum and proceed to the addenda the child will take it in quite easily. It is in accordance with reality. The other way is abstract, one just puts things together, one is intellectualistic. It is also more real if I get the child to the point when he must answer the following question: If I have 12 apples and somebody takes them, goes away and only brings 7 back, how many has he lost? Here one starts with the minuend and goes from the remainder to the subtrahend; one does not subtract, but goes from the remainder, that is to say, from what remains as the result of a living process, to what has been taken away.