QUESTIONS AND
ANSWERS
[The questions were handed in to Dr. Steiner in
writing.]
20th August,
1924
The first
question is as follows:
What
is the real difference between multiplication and division in this
method of teaching? Or should there be no difference at all in the
first school year
The
question probably arises from my statement that in multiplication the
so-called multiplicand (one factor) and the product are given, and
the other factor has to be found. Of course this really gives what is
usually regarded as division. If we do not keep too strictly to
words, then on the same basis we can consider division, as
follows:
We can
say: if a whole is divided in a certain way, what is the amount of
the part? And you have only another conception of the same thing as
in the question: By what must a number be multiplied in order to get
a certain other number?
Thus, if
our question refers to dividing into parts, we have to do with a
division: but if we regard it from the standpoint of “how many
times ...” then we are dealing with a multiplication. And it is
precisely the inner relationship in thought which exists between
multiplication and division which here appears most clearly.
But quite
early on it should be pointed out to the child that it is possible to
think of division in two ways. One is that which I have just
indicated; here we examine how large each part is if we separate a
whole into a definite number of parts. Here I proceed from the whole
to find the part: that is one kind of division. In the other kind of
division I start from the part, and find out how often the part is
contained in the whole: then the division is not a separation into
parts, but a measurement. The child should be taught this difference
between separation into parts and measurement as soon as possible,
but without using pedantic terminology. Then division and
multiplication will soon cease to be something in the nature of
merely formal calculation, as it very often is, and will become
connected with life.
So in the
first school years it is really only in the method of expression that
you can make a difference between multiplication and division; but
you must be sure to point out that this difference is fundamentally
much smaller than the difference between subtraction and addition. It
is very important that the child should learn such things.
Thus we
cannot say that no difference at all should be made between
multiplication and division in the first school years, but it should
be done in the way I have just indicated. [An * was
noted in the text, but no footnote was on this page! –
e.Ed.]
At
what age and in what manner should we make the transition from the
concrete to the abstract in Arithmetic?
At first
one should endeavour to keep entirely to the concrete in Arithmetic,
and above all avoid abstractions before the child comes to the
turning point of the ninth and tenth years. Up to this time keep to
the concrete as far as ever possible, by connecting everything
directly with life.
When we
have done that for two or two-and-a-half years and have really seen
to it that calculations are not made with abstract numbers, but with
concrete facts presented in the form of sums, then we shall see that
the transition from the concrete to the abstract in Arithmetic is
extraordinarily easy. For in this method of dealing with
numbers they become so alive in the child that one can easily pass on
to the abstract treatment of addition, subtraction, and so on.
It will
be a question, then, of postponing the transition from the concrete
to the abstract, as far as possible, until the time between the ninth
and tenth years of which I have spoken.
One thing
that can help you in this transition from the abstract to the
concrete is just that kind of Arithmetic which one uses most in real
life, namely the spending of money; and here you are more favourably
placed than we are on the Continent, for there we have the decimal
system for everything. Here, with your money, you still have a more
pleasing system than this. I hope you find it so, because then you
have a right and healthy feeling for it. The soundest, most healthy
basis for a money system is that it should be as concrete as
possible. Here you still count according to the twelve and twenty
system which we have already “outgrown,” as they say, on
the Continent. I expect you already have the decimal system for
measurements? (The answer was given that we do not use it for
everyday purposes, but only in science.) Well, here too, you have the
pleasanter system of measures! These are things which really keep
everything to the concrete. Only in notation do you have the decimal
system.
What is
the basis of this decimal system? It is based on the fact that
originally we really had a natural measurement. I have told you that
number is not formed by the head, but by the whole body. The head
only reflects number, and it is natural that we should actually have
ten, or twenty at the highest, as numbers. Now we have the number ten
in particular, because we have ten fingers. The only numbers we write
are from one to ten: after that we begin once more to treat the
numbers themselves as concrete things.
Let us
just write, for example: 2 donkeys. Here the donkey is the concrete
thing, and 2 is the number. I might just as well say: 2 dogs. But if
you write 20, that is nothing more than 2 times 10. Here the 10 is
treated as a concrete thing. And so our system of numeration rests
upon the fact that when the thing becomes too involved, and we no
longer see it clearly, then we begin to treat the number itself as
something concrete, and then make it abstract again. We should make
no progress in calculation unless we treated the number I itself, no
matter what it is, as a concrete thing, and afterwards made it
abstract. 100 is really only 10 times 10. Now, whether I have 10
times 10, and treat it as 100, or whether I have 10 times 10 dogs, it
is really the same. In the one case the dogs, and in the other the 10
is the concrete thing. The real secret of calculation is that the
number itself is treated as something concrete. And if you think this
out you will find that a transition also takes place in life itself.
We speak of 2 twelves — 2 dozen — in exactly the same way
as we speak of 2 tens, only we have no alternative like
“dozen” for the ten because the decimal system has been
conceived under the influence of abstraction. All other systems still
have much more concrete conceptions of a quantity: a dozen: a
shilling. How much is a shilling? Here, in England, a shilling is 12
pennies. But in my childhood we had a “shilling” which
was divided into 30 units, but not monetary units. In the
village in I which I lived for a long time, there were houses along
the village street on both sides of the way. There were walnut trees
everywhere in front of the houses, and in the autumn the boys knocked
down the nuts and stored them for the winter. And when they came to
school they would boast about it. One would say: “I've got five
shillings already,” and another: “I have ten shillings of
nuts.” They were speaking of concrete things. A shilling always
meant 30 nuts. The farmers' only concern was to gather the nuts
early, before all the trees were already stripped! “A
nut-shilling” we used to say: that was a unit. To sell these
nuts was a right: it was done quite openly.
And so,
by using these numbers with concrete things — one dozen,
two dozen, one pair, two pair, etc., the
transition from the concrete to the abstract can be made. We do not
say: “four gloves,” but: “Two pairs of
gloves;” not: “Four shoes,” but “two pairs of
shoes.” Using this method we can make the transition from
concrete to abstract as a gradual preparation for the time between
the ninth and tenth years when abstract number as such can be
presented. [It should be noted that before this
transition from the concrete to the abstract dealt with above,
a rhythmic approach is
used in the teaching of the rudiments of number, e.g. the tables, in
the lower classes.]
When
and how should drawing be taught?
With
regard to the teaching of drawing, it is really a question of viewing
the matter artistically. You must remember that drawing is a sort of
untruth. What does drawing mean? It means representing something by
lines, but in the real world there is no such thing as a line. In the
real world there is, for example, the sea. It is represented by
colour (green); above it is the sky, also represented by colour
(blue). If these colours are brought together you have the sea below
and
the sky
above (see sketch). The line forms itself at the boundary between the
two colours. To say that here (horizontal line) the sky is bounded by
the sea, is really a very abstract statement. So from the artistic
point of view one feels that the reality should be represented in
colour, or else, if you like, in light and shade. What is actually
there when I draw a face? Does such a thing as this really exist?
(The outline of a face
is drawn.)
Is there anything of that sort? Nothing of the kind exists at all.
What does exist is this: (see shaded drawing). There are certain
surfaces in light and shade, and out of these a face appears. To
bring lines into it, and form a face from them, is really an untruth:
there is no such thing as this.
An
artistic feeling will prompt you to work out what is really there out
of black and white or colour. Lines will then appear of themselves.
Only when one traces the boundaries which arise in the light and
shade or in the colour do the “drawing lines” appear.
Therefore
instruction in drawing must, in any case, not start from drawing
itself but from painting, working in colour or in light and shade.
And the teaching of drawing, as such, is only of real value when it
is carried out in full awareness that it gives us nothing real. A
terrible amount of mischief has been wrought in our whole method of
thinking by the importance attached to drawing. From this has arisen
all that we find in optics, for example, where people are eternally
drawing lines which are supposed to be rays of light. Where can we
really find these rays of light? They are nowhere to be found. What
you have in reality is pictures. You make a hole in a wall; the sun
shines through it and on a screen an image is formed. The rays can
perhaps be seen, if at all, in the particles of dust in the room
— and the dustier the room, the more you can see of them. But
what is usually drawn as lines in this connection is only imagined.
Everything, really, that is drawn, has been thought out. And it is
only when you begin to teach the child something like perspective, in
which you already have to do with the abstract method of explanation
that you can begin to represent aligning and sighting by lines.
But the
worst thing you can do is to teach the child to draw a horse
or a dog with lines. He should take a paint brush and make a painting
of the dog, but never a drawing. The outline of the dog does not
exist at all: where is it? It is, of course, produced of itself if we
put on paper what is really there.
We are
now finding that there are not only children but also teachers who
would like to join our school. There may well be many teachers in the
outer world who would be glad to teach in the Waldorf School, because
they would like it better there. I have had really quite a number of
people coming to me recently and describing the manner in which they
have been prepared for the teaching profession in the training
colleges. One gets a slight shock in the case of the teachers of
History, Languages, etc., but worst of all are the Drawing teachers,
for they are carrying on a craft which has no connection whatever
with artistic feeling: such feeling simply does not exist.
And the
result is (I am mentioning no names, so I can speak freely) that one
can scarcely converse with the Drawing teachers: they are such
dried-up, such terribly “un-human” people. They have no
idea at all of reality. By taking up drawing as a profession they
have lost touch with all reality. It is terrible to try to talk to
them, quite apart from the fact that they want to teach drawing in
the Waldorf School, where we have not introduced drawing at all. But
the mentality of these people who carry on the unreal craft of
drawing is also quite remarkable. And they have no moisture on the
tongue — their tongues are quite dry. It is tragic to see what
these drawing teachers gradually turn into, simply because of having
to do something which is completely unreal.
I will
therefore answer this question by saying that where-ever possible you
should start from painting and not from drawing. That is the
important thing.
I will
explain this matter more clearly, so that there shall be no
misunderstanding. You might otherwise think I had something personal
against drawing teachers. I would like to put it thus: here is a
group of children. I show them that the sun is shining in from this
side. The sun falls upon something and makes all kinds of light, (see
sketch). Light is shed upon everything. I can see bright patches. It
is because the sun is shining in that I can see the bright patches
everywhere. But above them I see no bright patches, only darkness
(blue). But I also see darkness here, below the bright patches: there
will perhaps be just a little light here. Then I look at something
which, when the light falls on it in this way, looks greenish in
colour. Here, where the light falls, it is whitish, but then, before
the really black shadow occurs, I see a greenish colour; and here,
under the black shadow, it is also greenish, and there are other
curious things to be seen in between the two. Here the light does not
go right in.
You see,
I have spoken of light and shadow, and of how there is something here
on which the light does not impinge: and lo, I have made a tree! I
have only spoken about light and colour, and I have made a tree. We
cannot really paint the tree: we can only bring in light and shade,
and green, or,
a little
yellow, if you like, if the fruit happens to be lovely apples. But we
must speak of colour and light and shade; and so indeed we shall be
speaking only of what is really there — colour, light and
shade. Drawing should only be done in Geometry and all that is
connected with that. There we have to do with lines, something which
is worked out in thought. But realities, concrete realities must not
be drawn with a pen; a tree, for example, must be evolved out of
light and shade and out of the colours, for this is the reality of
life itself. [The sketch was made on the blackboard
with coloured chalks but it has only been possible to reproduce it in
black and white.]
It would
be barbarous if an orthodox drawing teacher came and had this tree,
which we have drawn here in shaded colours, copied in lines. In
reality there are just light patches and dark patches. Nature does
that. If lines were drawn here, it would be an untruth.
Should
the direct method, without translation, be used, even for Latin and
Greek?
In this
respect a special exception must be made with regard to Latin and
Greek. It is not necessary to connect these directly with practical
life, for they are no longer alive, and we have them with us only as
dead languages. Now Greek and Latin (for Greek should actually
precede Latin in teaching) can only be taught when the children are
somewhat older, and therefore the translation method for these
languages is, in a certain way, fully justified.
There is
no question of our having to converse in Latin and Greek, but our aim
is to understand the ancient authors. We use these languages first
and foremost for the purposes of translation. And thus it is that we
do not use the same methods for the teaching of Latin and Greek as
those which we employ with all living languages.
Now once
more comes the question that is put to me whenever I am anywhere in
England where education is being discussed:
How
should instruction in Gymnastics be carried out, and should Sports be
taught in an English school, hockey and cricket, for example, and if
so in what way?
It is
emphatically not the aim of the Waldorf School Method to suppress
these things. They have their place simply because they play a great
part in English life, and the child should grow up into life. Only
please do not fall a prey to the illusion that there is any other
meaning in it than this, namely, that we ought not to make the child
a stranger to his world. To believe that sport is of tremendous value
in development is an error. It is not of great value in development.
Its only value is that it is a fashion dear to the English people,
and we must not make the child a stranger to the world by excluding
him from all popular usages. You like sport in England, so the child
should be introduced to sport. One should not meet with philistine
opposition what may possibly be philistine itself.
With regard to “how it should really be taught,”
there is very little indeed to be said. For in these things it is
really more or less so that someone does them first, and then the
child imitates him. And to devise special artificial methods here
would be something scarcely appropriate to the subject.
In
Drill or Gymnastics one simply learns from anatomy and physiology in
what position any limb of the organism must be placed in order that
it may serve the agility of the body. It is a question of really
having a sense for what renders the organism skilled, light and
supple; and when one has this sense, one has then simply to
demonstrate. Suppose you have a horizontal bar: it is customary to
perform all kinds of exercises on the bar except the most valuable
one of all, which consists in hanging on to the bar, hooked on, like
this ... then swinging sideways, and then grasping the bar further
up, then swinging back, then grasping the bar again. There is no
jumping but you hang from the bar, fly through the air, make the
various movements, grasp the bar thus, and thus, and so an
alternation in the shape and position of the muscles of the arms is
produced which actually has a healthy effect upon the whole
body.
You
must study which inner movements of the muscles have a healthy effect
on the organism, so that you will know what movements to teach. Then
you have only to do the exercises in front of the children, for the
method consists simply in this preliminary demonstration.
[A method of Gymnastic
teaching on the lines indicated above was subsequently worked out by
Fritz Graf Bothmer, teacher of Gymnastic s at the Waldorf School,
Stuttgart.]
How
should religious instruction be given at the different ages?
As
I always speak from the standpoint of practical life, I have to say
that the Waldorf School Method is a method of education and is not
meant to bring into the school a philosophy of life or anything
sectarian. Therefore I can only speak of what lives within the
Waldorf School principle itself.
It
was comparatively easyfor us in
Württemberg, where the laws of education were
still quite liberal: when the Waldorf School was established we were
really shown great consideration by the authorities. It was even
possible for me to insist that I myself should appoint the teachers
without regard to their having passed any State examination or not. I
do not mean that everyone who has passed a State examination is
unsuitable as a teacher! I would not say that. But still, I could see
nothing in a State examination that would necessarily qualify a
person to become a teacher in the Waldorf School.
And
in this respect things have really always gone quite well. But one
thing was necessary when we were establishing the school, and that
was for us definitely to take this standpoint: We have a
“Method-School”; we do not interfere with social life as
it is at present, but through Anthroposophy we find the best method
of teaching, and the School is purely a
“Method-School.”
Therefore
I arranged, from the outset, that religious instruction should not be
included in our school syllabus, but that Catholic religious teaching
should be delegated to the Catholic priest, and the Protestant
teaching to the pastor and so on.
In
the first few years most of our scholars came from a factory (the
Waldorf-Astoria Cigarette Factory), and amongst them we had many
“dissenting” children, children whose parents were of no
religion. But our educational conscience of course demanded that a
certain kind of religious instruction should be given them also. We
therefore arranged a “free religious teaching” for these
children, and for this we have a special method.
In
these “free Religion lessons” we first of all teach
gratitude in the contemplation of everything in Nature. Whereas in
the telling of legends and myths we simply relate what things do
— stones, plants and so on — here in the Religion lessons
we lead the child to perceive the Divine in all things. So we begin
with a kind of “religious naturalism,” shall I say, in a
form suited to the children.
Again, the child cannot be brought to an understanding of the Gospels
before the time between the ninth and tenth years of which I have
spoken. Only then can we proceed to a consideration of the Gospels in
the Religion lessons, going on later to the Old Testament. Up to this
time we can only introduce to the children a kind of Nature-religion
in its general aspect, and for this we have our own method. Then we
should go on to the Gospels but not before the ninth or tenth year,
and only much later, between the twelfth and thirteenth years, we
should proceed to the Old Testament. [This paragraph can easily be misunderstood
unless two other aspects of the education are borne in mind. Firstly:
Here Dr. Steiner is only speaking of the content of the actual
Religion lessons. In the class teaching all children are introduced
to the stories of the Old Testament. Secondly, quite apart from the
Religion lessons the Festivals of the year are celebrated with all
children in a Rudolf Steiner School, in forms adapted to their ages.
Christmas takes a very special place, and is prepared for all through
Advent by carol singing, the daily opening of a star-window in the
“Advent Calendar,” and the lighting of candles on the
Advent wreath hung in the classroom. At the end of the Christmas term
the teachers perform traditional Nativity Plays as their gift to the
children. All this is in the nature of an experience for the children, inspired by feeling and the
Christmas mood. Later, in the Religion lessons, on the basis of this
experience, they can be brought to a more conscious knowledge and
understanding of the Gospels.]
This then is how you should think of the free Religion
lessons. We are not concerned with the Catholic and Protestant
instruction: we must leave that to the Catholic and Protestant
pastors. Also every Sunday we have a special form of service for
those who attend the free Religion lessons. A service is performed
and forms of worship are provided for children of different ages.
What is done at these services has shown its results in practical
life during the course of the years; it contributes in a very special
way to the deepening of religious feeling, and awakens a mood of
great devotion in the hearts of the children.
We
allow the parents to attend these services, and it has become evident
that this free religious teaching truly brings new life to
Christianity And there is real Christianity in the Waldorf School,
because through this naturalistic religion during the early years the
children are gradually led to an understanding of the Christ Mystery,
when they reach the higher classes.
Our
free Religion classes have, indeed, gradually become full to
overflowing. We have all kinds of children coming into them from the
Protestant pastor or the Catholic priest, but we make no propaganda
for it. It is difficult enough for us to find sufficient Religion
teachers, and therefore we are not particularly pleased when too many
children come; neither do we wish the school to acquire the
reputation of being an Anthroposophical School of a sectarian kind.
We do not want that at all. Only our educational conscience has
constrained us to introduce this free Religion teaching. But children
turn away from the Catholic and Protestant teaching and more and more
come over to us and want to have the free Religion teaching: they
like it better. It is not our fault that they run away from their
other teachers: but as I have said, the principle of the whole thing
was that religious instruction should be given, to begin with, by the
various pastors. When you ask, then, what kind of religious teaching
we have, I can only speak of what our own free Religion teaching is,
as I have just described it.
Should
French and German be taught from the beginning, in an English School?
If the children come to a Kindergarten Class at five or six years
old, ought they, too, to have language lessons?
As to
whether French and German should be taught from the beginning in an
English School, I should first like to say that I think this must be
settled entirely on grounds of expediency. If you simply find that
life is making it necessary to teach these languages, you must teach
them. We have introduced French and English into the Waldorf School,
because with French there is much to be learnt from the inner quality
of the language, not found elsewhere, namely, a certain feeling for
rhetoric which it is very good to acquire: and English is taught
because it is a universal world language, and will become so more and
more.
Now, I
should not wish to decide categorically whether French and German
should be taught in an English School, but you must be guided by the
circumstances of life. It is not at all so important which language
is chosen as that foreign languages are actually taught in the
school.
And if
children of four or five years do already come to school (which
should not really be the case) it would then be good to do languages
with them also. It would be right for this age. Some kind of language
teaching can be given even before the age of the change of teeth, but
it should only be taught as a proper lesson after this change. If you
have a Kindergarten Class for the little children, it would be quite
right to include the teaching of languages but all other school
subjects should as far as possible be postponed until after the
change of teeth.
I should
like to express, in conclusion, what you will readily appreciate,
namely, that I am deeply gratified that you are taking such an active
interest in making the Waldorf School Method fruitful here in
England, and that you are working with such energy for the
establishment of a school here, on our Anthroposophical lines. And I
should like to express the hope that you may succeed in making use of
what you were able to learn from our Training Courses in Stuttgart,
from what you have heard at various other Courses which have been
held in England, and, finally, from what I have been able to give you
here in a more aphoristic way, in order to establish a really good
school here on Anthroposophical lines. You must remember how much
depends upon the success of the very first attempt. If it does not
succeed, very much is lost, for all else will be judged by the first
attempt. And indeed, very much depends on how your first project is
launched: from it the world must take notice that the matter is
neither something which is steeped in abstract, dilettante plans of
school reform, nor anything amateur but something which arises out of
a conception of the real being of man, and which is now to be brought
to bear on the art of education. And it is indeed the very
civilisation of today, which is now moving through such critical
times, that calls us to undertake this task, along with many other
things.
In
conclusion I should like to give you my right good thoughts on your
path — the path which is to lead to the founding of a school
here on Anthroposophical lines.
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