Thursday, May 14, 2009

The Meaning of numbers

Rudolf Steiner said "In this way we get the child to enter into life with the ability to grasp a whole, not always to proceed from the lesser to the greater. And this has an extraordinarily strong influence upon the child's whole life of soul. When a child has acquired the habit of adding things together we get a disposition which tends to be desirous and craving. In proceeding from the whole into parts and in treating multiplication similarly, the child has less tendency to acquisitiveness, rather he tends to develop what, in the Platonic sense, the noblest sense of the word, can be called considerateness, moderation; and ones moral likes and dislikes are intimately bound up with the manner in which one has learned to deal with number. At first sight there seems to be no logical connection between the treatment of numbers and moral ideas, moral impulses, so little indeed that one who will only regard things from the intellectual point of view may well laugh when one speaks of it. It may seem to hum absurd."

"It is important to begin with the whole rather than adding with beginning math students. "Do to their musical and rhythmical nature, children experience the world of number in a pedantic way. Thus instead of beginning with addition in a pedantic way, it is better to call on a child and give it some apples or any other suitable objects. Instead of giving it, say, three apples, then four more, and finally another two, and then asking that they all be added together, we begin by giving the child a whole pile of apples, or whatever is convenient. This would be the start of the whole operation. Then we call out two more children and say to the first, "Here you have a heap of apples. Give some to the other two children and keep some for yourself. But each one of you must have the same number of apples." In this way we help the children grasp the idea of sharing by three. We begin with the total amount and lead to the principle of division. The child will respond to and apprehend this process quite naturally. By attuning ourselves to the child's nature, according to our picture of the human being, we do not begin by adding numbers but, but by dividing and subtracting them. Then, retracing our steps and thus reversing the first two processes, we are led to multiplication and addition. Moving from the whole to the part, we follow the original experience of number, which was one of analyzing, having a divisional quality, and not the contemporary method of synthesizing, of putting things together, of adding."

"Steiner suggested that the study of numbers begin with the human being. Each of us is a unit, an indivisible whole; from this we derive the number one. We find the number two expressed by our hands and feet or by our eyes and ears. The number three may be found in the major parts of our bodies: head, truck and limbs. To find the number four we can count our limbs; for five we can refer to the digits on each hand or the toes on each foot."

"According to Steiner, former ages did not develop the numbers by adding one to another, but by dividing the whole into parts. The unit was considered the greatest number, for it contained all of the other numbers. Steiner asserted that by showing children how to derive numbers out of the whole to the parts, we help them develop living concepts."

(above quotes from Rhythms of Learning)

I use Roman Numerals to introduce the concept to very young children as when you write them they make sense. I = one, II = two and so forth. The young child can identify much easier to this concept.

Verse for Introducing Number Qualities:

All together we are class ONE
See, the whole wide world is one
And the brightly shining sun
Sheds its light on everyone.
All alone I stand as one
And my heart shall be a sun.

You and I, we are TWO
And many things together do.
On two feet we walk and stand
With two eyes we view the land.
Two ears to hear what wise men tell
Two hands with which to do things well.

Father, mother and child are THREE
And make one happy family.
As head and heart and limbs so strong
Make one good man who'll do no wrong.

Summer, Autumn, Winter, Spring
FOUR different seasons to us bring.
From East and West, and South and North
The brother winds come blowing forth.
We make FIVE with our head
And our arms and legs outspread.
Now we are most like a star,
Shining brightly from afar.

We find SIX in all that is around
See, sparkling crystals in the ground
The honeycomb made by the bee,
Six-petalled flowers we also see.

The shining rainbow shows us SEVEN
As it stretches down from Heaven,
And the week has seven days
Taking us on different ways.

Wriggling spiders on EIGHT legs crawl
Spinning webs on every wall.
Octopus has eight legs too,
Four times as many legs as you.

NINE is a mystery hidden away
A secret to be revealed one day.

TEN fingers have we on our two hands.
Ten toes, as on two feet we stand.
For ten contains within two fives
Which we'll remember all our lives.


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