The Rudolf Steiner Archive

Speech exercise.

Deprive me not of what, when I give it to you freely, pleases you.

Rudolf Steiner: This sentence is constructed chiefly to show the break in the sense, so that it runs as follows: First the phrase “Deprive me not of what,” and then the phrase “pleases you,” but the latter is interrupted by the other phrase, “when I give it to you freely.” This must be expressed by the way you say it. You must notice that the emphasis you dropped on the word “what” you pick up again at “pleases you.”

Rateless ration
roosted roomily
reason wretched
ruined Roland
royalty roster

Name neat Norman on nimble moody mules

Piffling fifer
prefacing feather
phlegma fluting
fairground piercing

Weekly verse from The Calendar of the Soul:

I feel a strange power bearing fruit,
Gaining strength, bestowing me on myself,
I sense the seed ripening
And presentiment weaving, full of Light,
Within me on my selfhood’s power.¹

RUDOLF STEINER: Now we arrive at the difficult task before us today. Yesterday I asked you to consider how you would prepare the lessons in order to teach the children about the lower and higher plants, making use of some sort of illustration or example. I have shown you how this can be done in the case of animals—with a cuttlefish, a mouse, a horse, and a person—and your botany lessons must be prepared in the same spirit. But let me first say that the correct procedure is to study the animal world before coming to terms with the natural conditions of the plants. In the efforts necessary to characterize the form of your botany lessons—finding whatever examples you can from one plant or another—you will become clear why the animal period must come first.

Perhaps it would be a good idea if we first ask who has already given botany lessons. That person could speak first and the others can follow.

Comment: The plant has something like an instinctive longing for the Sun. The blossoms turn toward the Sun even before it has risen. Point out the difference between the life of desire in animals and people, and the pure effort of the plant to turn toward the Sun. Then give the children a clear idea of how the plant exists between Sun and Earth. At every opportunity mention the relation of the plant to its surroundings, especially the contrast between plants and human beings, and plants and animals. Talk about the outbreathing and in-breathing of the plant. Allow the children to experience how “bad” air is the very thing used by the plant, through the power of the Sun, to build up again what later serves as food for people. When speaking of human dependence on food you can point to the importance of a good harvest, and so on. With regard to the process of growth it should be made clear that each plant, even the leaf, grows only at the base and not at the tip. The actual process of growth is always concealed.

RUDOLF STEINER: What does it actually mean that a leaf only grows at the base? This is also true of our fingernails, and if you take other parts of the human being, the skin, the surfaces of the hands, and the deeper layers, the same thing applies. What actually constitutes growth?

Comment: Growth occurs when dead matter is “pushed out” of what is living.

RUDOLF STEINER: Yes, that’s right. All growth is life being pushed out from inside, and the dying and gradual peeling off of the outside. That is why nothing can ever grow on the outside. There must always be a pushing of substance from within outward, and then a scaling off from the surface. That is the universal law of growth—that is, the connection between growth and matter.

RUDOLF STEINER: Much of what you have said is good, but it would also be good in the course of your description to acquaint your students with the different parts of a single plant, because you will continually have to speak about the parts of the plant—leaf, blossom, and so on. It would therefore be good for the pupil to get to know certain parts of a plant, always following the principle that you have rightly chosen—that is, the study of the plant in relation to Sun and Earth. That will bring some life to your study of the plants; from there you should build the bridge to human beings. You have not yet succeeded in making this connection, because everything you said was more or less utilitarian—how plants are useful to people, for example—and other external comparisons.

There is something else that must be worked out before these lessons can be of real value to the children; after you have made clear the connection between animal and human being, you must also try to show the connection between plant and human being. Most of the children are in their eleventh year when we begin this subject, and at this point the time is ripe to consider what the children have already learned—or rather, we must keep in mind that the children have already learned things in a certain way, which they must now put to good use. Then too you must not forget to give the children the kind of image of the plant’s actual form that they can understand.

Comment: The germinating process should be demonstrated to the children—for example, in the bean. First the bean as a seed and then an embryo in its different stages. We could show the children how the plant changes through the various seasons of the year.

RUDOLF STEINER: This should not really be given to your students until they are fifteen or sixteen years old. If you did take it earlier you would see for yourself that the children who are still in the lower grades cannot yet fully understand the germinating process. It would be premature to develop this germinating process with younger children—your example of the bean and so on. That is foreign to the child’s inner nature.

I only meant to point out to the children the similarity between the young plant and the young animal, and the differences as well. The animal is cared for by its mother, and the plant comes into the world alone. My idea was to treat the subject in a way that would appeal more to the feelings.

RUDOLF STEINER: Even so, this kind of presentation is not suitable for children; you would find that they could not understand it.

Question: Can one compare the different parts of the plant with a human being? The root with the head, for example?

RUDOLF STEINER: As Mr. T. correctly described, you must give plants their place in nature as a whole—Sun, Earth, and so on—and always remember to speak of them in relation to the universe. Then when you give the proper form to your lesson you will find that the children meet what you present with a certain understanding.

Someone described how plants and human beings can be compared—a tree with a person, for example: human trunk = tree trunk; arms and fingers = branches and twigs; head = root. When a person eats, the food goes from above downward, whereas in a tree the nourishment goes from below upward. There is also a difference: whereas people and animals can move around freely and feel pleasure and pain, plants cannot do this. Each type of plant corresponds to some human characteristic, but only externally. An oak is proud, while lichens and mosses are modest and retiring.

RUDOLF STEINER: There is much in what you say, but no one has tried to give the children an understanding of the plant itself in its various forms. What would it be like if, for example, you perhaps ask, “Haven’t you ever been for a walk during the summer and seen flowers growing in the fields, and parts of them fly away when you blow on them? They have little ‘fans’ that fly away. And you have probably seen these same flowers a little earlier, when summer was not quite so near; then you saw only the yellow leaf shapes at the top of the stem; and even earlier, in the spring, there were only green leaves with sharp jagged edges. But remember, what we see at these three different times is all exactly the same plant! Except that, to begin with, it is mainly a green leaf; later on it is mainly blossom; and still later it is primarily fruit. Those are only the fruits that fly around. And the whole is a dandelion! First it has leaves—green ones; then it presents its blossoms, and after that, it gets its fruit.

“How does all this happen? How does it happen that this dandelion, which you all know, shows itself at one time with nothing but green leaves, another time with flowers, and later with tiny fruits?

“This is how it comes about. When the green leaves grow out of the earth it is not yet the hot part of the year. Warmth does not yet have as much effect. But what is around the green leaves? You know what it is. It is something you only notice when the wind passes by, but it is always there, around you: the air. You know about that because we have already talked about it. It is mainly the air that makes the green leaves sprout, and then, when the air has more warmth in it, when it is hotter, the leaves no longer remain as leaves; the leaves at the top of the stem turn into flowers. But the warmth does not just go to the plant; it also goes down into the earth and then back again. I’m sure that at one time or another you have seen a little piece of tin lying on the ground, and have noticed that the tin first receives the warmth from the Sun and then radiates it out again. That is really what every object does. And so it is also with warmth. When it is streaming downward, before the soil itself has become very warm, it forms the blossom. And when the warmth radiates back again from the earth up to the plant, it is working more to form the fruit. And so the fruit must wait until the autumn.”

This is how you should introduce the organs of the plant, at the same time relating these organs to the conditions of air and heat. You can now go further, and try to elaborate the thoughts that were touched on when we began today, showing the plants in relation to the outer elements. In this way you can also connect morphology, the aspect of the plant’s form, with the external world. Try this.

Someone spoke about plant-teaching.

RUDOLF STEINER: Some of the thoughts you have expressed are excellent, but your primary goal must be to give the children a comprehensive picture of the plant world as a whole: first the lower plants, then those in between, and finally the higher plants. Cut out all the scientific facts and give them a pictorial survey, because this can be tremendously significant in your teaching, and such a method can very well be worked out concerning the plant world.

Several teachers spoke at length on this subject. One of them remarked that “the root serves to feed the plant.”

RUDOLF STEINER: You should avoid the term serves. It’s not that the root “serves” the plant, but that the root is related to the watery life of earth, with the life of juices. It is however not what the plant draws out of the ground that makes up its main nourishment, but rather the carbon from the air.

Children cannot have a direct perception of a metamorphosis theory, but they can understand the relationship between water and root, air and leaves, warmth and blossoms.

It is not good to speak about the plants’ fertilization process too soon—at any rate, not at the age when you begin to teach botany—because children do not yet have a real understanding of the fertilization process. You can describe it, but you’ll find that they do not understand it inwardly.

Related to this is the fact that fertilization in plants does not play as prominent a part as generally assumed in our modernday, abstract, scientific age. You should read Goethe’s beautiful essays, written in the 1820s, where he speaks of pollination and so on. There he defends the theory of metamorphosis over the actual process of fertilization, and strongly protests the way people consider it so terribly important to describe a meadow as a perpetual, continuous “bridal bed!” Goethe strongly disapproved of giving such a prominent place to this process in plants. Metamorphosis was far more important to him than the matter of fertilization. In our present age it is impossible to share Goethe’s belief that fertilization is of secondary importance, and that the plant grows primarily on its own through metamorphosis; even though, according to modern advanced knowledge, you must accept the importance of the fertilization process, it still remains true, however, that we are doing the wrong thing when we give it the prominence that is customary today. We must allow it to retire more into the background, and in its place we must talk about the relationship between the plant and the surrounding world. It is far more important to describe the way air, heat, light, and water work on the plant, than to dwell on the abstract fertilization process, which is so prominent today. I want to really emphasize this; and because this is a very serious matter and particularly important, I would like you to cross this Rubicon, to delve further into the matter, so that you find the proper method of dealing with plants and the right way to teach children about them.

Please note that it is easy enough to ask what similarities there are between animal and humankind; you will discover this from many and diverse aspects. But when you look for similarities between plants and humankind, this external method of comparison quickly falls apart. But let’s ask ourselves: Are we perhaps on the wrong path in looking for relationships of this kind at all?

Mr. R. came closest to where we should begin, but he only touched on it, and he did not work it out any further.

We can now begin with something you yourselves know, but you cannot teach this to a young child. Before we meet again, however, perhaps you can think about how to clothe, in language suited to children, things you know very well yourselves in a more theoretical way.

We cannot just take human beings as we see them in life and compare them with the plant; nevertheless there are certain resemblances. Yesterday I tried to draw the human trunk as a kind of imperfect sphere.² The other part that belongs to it—which you would get if you completed the sphere—indeed has a certain likeness to the plant when you consider the mutual relationship between plants and human beings. You could even go further and say that if you were to “stuff ” a person (forgive the comparison—you will find the right way of changing it for children) especially in relation to the middle senses, the sense of warmth, the sense of sight, the sense of taste, the sense of smell, then you would get all kinds of plant forms.³ If you simply “stuffed” some soft substance into the human being, it would assume plant forms. The plant world, in a certain sense, is a kind of “negative” of the human being; it is the complement.

In other words, when you fall asleep everything related to your soul passes out of your body; these soul elements (the I and the actual soul) reenter your body when you awaken. You cannot very well compare the plant world with the body that remains lying in your bed; but you can truthfully compare it with the soul itself, which passes in and out. And when you walk through fields or meadows and see plants in all the brightness and radiance of their blossoms, you can certainly ask yourselves: What temperament is revealed here? It is a fiery temperament! The exuberant forces that come to meet you from flowers can be compared to qualities of soul. Or perhaps you walk through the woods and see mushrooms or fungi and ask: What temperament is revealed here? Why are they not growing in the sunlight? These are the phlegmatics, these mushrooms and fungi.

So you see, when you begin to consider the human element of soul, you find relationships with the plant world everywhere, and you must try to work out and develop these things further. You could compare the animal world to the human body, but the plant world can be compared more to the soul, to the part of a human being that enters and “fills out” a person when awaking in the morning. If we could “cast” these soul forms we would have the forms of the plants before us. Moreover, if you could succeed in preserving a person like a mummy, leaving spaces empty by removing all the paths of the blood vessels and nerves, and pouring into these spaces some very soft substance, then you would get all kinds of forms from these hollow shapes in the human body.

The plant world is related to human beings as I have just shown, and you must try to make it clear to the children that the roots are more closely related to human thoughts, and the flowers more related to feelings—even to passions and emotions. And so it happens that the most perfect plants—the higher, flowering plants—have the least animal nature within them; the mushrooms and the lowest types of plant are most closely akin to animals, and it is particularly these plants that can be compared least to the human soul.

You can now develop this idea of beginning with the soul element and looking for the characteristics of the plants, and you can extend it to all the varieties of the plant world. You can characterize the plants by saying that some develop more of the fruit nature—the mushrooms, for example—and others more of the leaf nature, such as ferns and the lower plants, and the palms, too, with their gigantic leaves. These organs, however, are developed differently. A cactus is a cactus because of the rampant growth of its leaves; its blossom and fruit are merely interspersed among the luxuriant leaves.

Try now to translate the thought I indicated to you into language suited for children. Exert your fantasy so that by next time you can give us a vivid description of the plant world all over the Earth, showing it as something that shoots forth into herb and flower, like the soul of the Earth, the visible soul, the soul made manifest.

Then try to bring some fruitful thoughts about how to distinguish between annuals and perennials, or between the flora of western, central, and eastern European countries. Another fruitful thought that you could come to is about how the whole Earth is actually asleep in summer and awake in winter.

You see, when you work in this way you awaken in the child a real feeling for intimacy of soul and for the truth of the spirit. Later, when the children are grown, they will much more easily understand how senseless it is to believe that human existence, as far as the soul is concerned, ceases every evening and begins again each morning. Thus they will see, when you have shown them, that the relationship between the human body and soul can be compared to the interrelationship between the human world and the plant world. How then does the Earth affect the plant? Just as the human body works, so when you come to the plant world you have to compare the human body with the Earth—and with something else, as you will discover for yourselves.

I only wanted to give you certain suggestions so that you, yourselves, using all your best powers of invention, can discover even more before next time. You will then see that you greatly benefit the children when you do not give them external comparisons, but those belonging to the inner life.

• 1. Verse for August 25–31 (twenty-first week); see Rudolf Steiner, The Calendar of the Soul, Anthroposophic Press, Hudson, NY, 1988.
• 2. See Practical Advice to Teachers, lecture 7.
• 3. See The Foundations of Human Experience, lecture 8.

Speech Exercises:

Children chiding
Chaffinch chirping
Choking chimneys
Cheerfully chattering

Children chiding and fetching
Chaffinch chirping switching
Choking chimneys hitching
Cheerfully chattering twitching

Beach children chiding and fetching
Reach chaffinch chirping switching
Birches choking chimneys hitching
Perches cheerfully chattering twitching

RUDOLF STEINER: The “ch” should be sounded in a thoroughly active way, like a gymnastic exercise.¹

The following is a piece in which you have to pay attention both to the form and the content.

From “Galgenlieder” by Christian Morgenstern:

The Does’ Prayer

The does, as the hour grows late,
Med-it-ate;
Med-it-nine;
Med-i-ten;
Med-eleven;
Med-twelve;
Mednight!
The does, as the hour grows late,
Meditate,
They fold their little toesies,
the doesies.²

RUDOLF STEINER: Now we will continue our talk about the plant world.

Various contributions were offered by those present.

RUDOLF STEINER: Later there will be students in the school who will study the plant kingdom on a more scientific basis, in which case they would learn to distinguish mosses, lichens, algae, monocotyledons, dicotyledons, and so on. All children, who in their youth learn to know plants according to scientific principles, should first learn about them as we have described—that is, by comparing them with soul qualities. Later they can study the plant system more scientifically. It makes a difference whether we try first to describe the plants and then later study them scientifically, or vice versa. You can do much harm by teaching scientific botany first, instead of first presenting ideas that relate to the feeling life, as I have tried to show you. In the latter case the children can tackle the study of scientific botanical systems with a truly human understanding.

The plant realm is the soul world of the Earth made visible. The carnation is a flirt. The sunflower an old peasant. The sunflower’s shining face is like a jolly old country rustic. Plants with very big leaves would express, in terms of soul life, lack of success in a job, taking a long time with everything, clumsiness, and especially an inability to finish anything; we think that someone has finished, but the person is still at it. Look for the soul element in the plant forms!

When summer approaches, or even earlier, sleep spreads over the Earth; this sleep becomes heavier and heavier, but it only spreads out spatially, and in autumn passes away again. The plants are no longer there, and sleep no longer spreads over the Earth. The feelings, passions, and emotions of people pass with them into sleep, but once they are there, those feelings have the appearance of plants. What we have invisible within the soul, our hidden qualities—flirtatiousness, for example—become visible in plants. We don’t see this in a person who is awake, but it can be observed clairvoyantly in people who are sleeping. Flirtation, for example, looks like a carnation. A flirt continually produces carnations from the nose! A tedious, boring person produces gigantic leaves from the whole body, if you could see them.

When we express the thought that the Earth sleeps, we must go further: the plant world grows in the summer. Earth sleeps in the summer and is awake during winter. The plant world is the Earth’s soul. Human soul life ceases during sleep, but when the Earth goes to sleep its soul life actually begins. But the human soul does not express itself in a sleeping person. How are we going to get over this difficulty with children?

One of the teachers suggested that plants could be considered the Earth’s dreams.

RUDOLF STEINER: But plants during high summer are not the Earth’s dreams, because the Earth is in a deep sleep in the summer. It is only how the plant world appears during spring and autumn that you can call dreams. Only when the flowers are first beginning to sprout—when the March violet, for example, is still green, before flowers appear, and again when leaves are falling—that the plant world can be compared to dreams. With this in mind, try to make the transition to a real understanding of the plant.

For example, you can begin by saying, “Look at this buttercup,” or any plant we can dig out of the soil, showing the root below, the stalk, leaves, blossoms, and then the stamens and pistil, from which the fruit will develop. Let the child look at a plant like this. Then show a tree and say, “Imagine this tree next to the plant. What can you tell me about the tree? Yes, it also has roots below of course; but instead of a stalk, it has a trunk. Then it spreads its branches, and it’s as if the real plants grew on these branches, because many leaves and flowers can be found there; it’s as if little plants were growing on the branches above. So, we could actually look at a meadow this way: We see yellow buttercups growing all over the meadow; it is covered with individual plants with their roots in the Earth, and they cover the whole meadow. But when we look at the tree, it’s as if someone had taken the meadow, lifted it up, and rounded it into an arch; only then do we find many flowers growing very high all over it. The trunk is a bit of the Earth itself. So we may say that the tree is the same as the meadow where the flowers grow.

“Now we go from the tree to the dandelion or daisy. Here there is a root-like form in the soil, and from it grows something like a stalk and leaves, but at the top there is a little basket of flowers, tiny little blossoms close together. It’s as though the dandelion made a little basket up there with nothing in it but little flowers, perfect flowers that can be found in the dandelion-head. So we have the tree, the little ‘basket-bloomers,’ and the ordinary plant, a plant with a stalk. In the tree it’s as though the plants were only high up on the branches; in the compound flowers the blossom is at the top of the plant, except that these are not petals, but countless fully-developed flowers.

“Now imagine that the plant kept everything down in the Earth; suppose it wanted to develop roots, but that it was unsuccessful—or perhaps leaves, but could not do this either; imagine that the only thing to unfold above ground were what one usually finds in the blossom; you would then have a mushroom. At least, if the roots down below fail and only leaves come up, you would then have ferns. So you find all kinds of different forms, but they are all plants.”

Show the children the buttercup, how it spreads its little roots, how it has its five yellow-fringed petals, then show them the tree, where the “plant” only grows on it, then the composite flowers, the mushroom, and the fern; do not do this in a very scientific way, but so that the children get to know the form in general.

Then you can say, “Why do you think the mushroom remained a mushroom, and why did the tree become a tree? Let’s compare the mushroom with the tree. What is the difference between them? Take the tree. Isn’t it as though the Earth had pushed itself out with all its might—as though the inner being of the tree had forced its way up into the outside world in order to develop its blossoms and fruits away from the Earth? But in the mushroom the Earth has kept within itself what usually grows up out of it, and only the uppermost parts of the plant appear in the form of mushrooms. In the mushroom the ‘tree’ is below the soil and only exists as forces. In the mushroom itself we find something similar to the tree’s outermost part. When lots and lots of mushrooms are spread over the Earth, it is as though you had a tree growing down below them, inside the Earth. And when we look at a tree it is as though the Earth had forced itself up, turning itself inside out, as it were, bringing its inner self into the outer world.”

Now you are coming nearer to the reality: “When you see mushrooms growing you know that the Earth is holding something within itself that, in the case of a growing tree, it pushes up outside itself. So in producing mushrooms the Earth keeps the force of the growing tree within itself. But when the Earth lets the trees grow it turns the growing-force of the tree outward.” Now here you have something not found within the Earth during summer, because it rises out of the Earth then and when winter comes it goes down into the Earth again. “During summer the Earth, through the force of the tree, sends its own force up into the blossoms, causing them to unfold, and in winter it draws this force back again into itself. Now let us think of this force, which during the summer circles up in the trees—a force so small and delicate in the violet but so powerful in the tree. Where can it be found in winter? It is under the surface of the Earth. What happens during the depth of winter to all these plants—the trees, the composite flowers, and all the others? They unfold right under the Earth’s surface; they are there within the Earth and develop the Earth’s soul life. This was known to the people of ancient times, and that was why they placed Christmas—the time when we look for soul life—not in the summer, but during winter.

“Just as a person’s soul life passes out of the body when falling asleep, and again turns inward when a person wakens, so it is also for the Earth. During summer while asleep it sends its sap-bearing force out, and during winter takes it back again when it awakens—that is, it gathers all its various forces into itself. Just think, children, our Earth feels and experiences everything that happens within it; what you see all the summer long in flowers and leaves, the abundance of growth and blossom, in the daisies, the roses, or the carnations—this all dwells under the Earth during winter, and there it has feelings like you have, and can be angry or happy like you.”

In this way you gradually form a view of life lived under the Earth during winter. That is the truth. And it is good to tell the children these things. This is something that even materialists could not argue with or consider an extravagant flight of fancy. But now you can continue from this and consider the whole plant. The children are led away from a subjective attitude toward plants, and they are shown what drives the sap over the Earth during summer heat and draws it back again into itself in winter; they come to see the ebb and flow in plant life. In this way you find the Earth’s real soul life mirrored in plants. Beneath the Earth ferns, mosses, and fungi unfold all that they fail to develop as growing plants, but this all remains etheric substance and does not become physical. When this etheric plant appears above the Earth’s surface, the external forces work on it and transform it into the rudiments of leaves we find in fungi, mosses, and ferns. But under a patch of moss or mushrooms there is something like a gigantic tree, and if the Earth cannot absorb it, cannot keep it within itself, then it pushes up into the outer world.

The tree is a little piece of the Earth itself. But what remains underground in mushrooms and ferns is now raised out of the Earth, so that if the tree were slowly pushed down into the Earth everything would be different, and if it were to be thus submerged then ferns, mosses, and mushrooms would appear; for the tree it would be a kind of winter. But the tree withdraws from this experience of winter. It is the nature of a tree to avoid the experience of winter to some extent, but if I could take hold of a fern or a mushroom by the head and draw it further and further out of the Earth so that the etheric element in it reached the air, then I would draw out a whole tree, and what would otherwise become a mushroom would now turn into a tree. Annual plants are midway between these two. A composite flower is merely another form of what happens in a tree. If I could press a composite flower down into the Earth it would bear only single blossoms. A composite flower could almost be called a tree that has shot up too quickly.

And so we can also find a wish, a desire, living in the Earth. The Earth feels compelled to let this wish sink into sleep. The Earth puts it to sleep in summer, and then the wish rises as a plant. It is not visible above the Earth until it appears as a water-lily. Down below it lives as a wish in the Earth, and then up above it becomes a plant.

The plant world is the Earth’s soul world made visible, and this is why we can compare it with human beings. But you should not merely make comparisons; you must also teach the children about the actual forms of the plants. Starting with a general comparison you can then lead to the single plant species.

Light sleep can be compared with ordinary plants, a kind of waking during sleep with mushrooms (where there are very many mushrooms, the Earth is awake during the summer), and you can compare really sound deep sleep with the trees.

From this you see that the Earth does not sleep as people do, but in one part it is more asleep and in another more awake; here more asleep, there more awake. People, in their eyes and other sense organs, also have sleeping, waking, and, dreaming side by side, all at the same time.

Now here is your task for tomorrow. Please make out a table; on the left place a list of the human soul characteristics, from thoughts down through all the emotions of the soul—feelings of pleasure and displeasure, actively violent emotions, anger, grief, and so on, right down to the will; certain specific plant forms can be compared with the human soul realm. On the right you can then fill in the corresponding plant species, so that in the table you have the thought plants above, the will plants below, and all the others in between.

Rudolf Steiner then gave a graphic explanation of the Pythagorean theorem and referred to an article by Dr. Ernst Müller in Ostwald’s magazine for natural philosophy, Annalen der Naturphilosophie, entitled “Some Observations on a Theory of Knowledge underlying the Pythagorean theorem.”

In the drawing, the red parts of the two smaller squares already lie within the square on the hypotenuse. By moving the blue and the green triangles in the direction of the arrows, the remaining parts of the two smaller squares will cover those parts of the square on the hypotenuse still uncovered.

You should cut out the whole thing in cardboard and then you can see it clearly.³

• 1. The original German exercise (which appears in the appendix) uses the “pf ” sound; the “ch” sound has been substituted in the English version.
• 2. Max Knight, trans., University of California Press, Berkeley, 1964.
• 3. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. For another brief discussion of the Pythagorean theorem in teaching see Rudolf Steiner, The Kingdom of Childhood: Introductory Talks on Waldorf Education, Anthroposophic Press, Hudson, NY, 1995, pp. 85–90.

RUDOLF STEINER: In the speech exercises that we will take now, the principal purpose is to make the speech organs more flexible.

Curtsey Betsy jets cleric
lastly light sceptic

One should acquire the habit of letting the tongue say it on its own, so to speak.

Tu-whit twinkle ‘twas
twice twigged tweaker
to twenty twangy twirlings
the zinnia crisper
zither zooming shambles
this smartened smacking
smuggler sneezing
snoring snatching.

Both these exercises are really perfect only when they are said from memory.

From “We Found a Path” (by Christian Morgenstern):

Those who don’t know the goal
can’t find the way,
they will trot the same circle
all their lives long,
and return in the end
whence they began,
their piece of mind
more disturbed than before.

RUDOLF STEINER: Now we will proceed to the task that we have been gnawing at for so long.

Someone presented a list of the human soul moods and the soul moods of plants that could be said to correspond to them.

RUDOLF STEINER: All these things that have been presented are reminiscent of when phrenology was in vogue, when people classified human soul qualities according to their fantasies, and then searched the head for all kinds of bumps that were then associated with these qualities. But things are not like that, although the human head can certainly be said to express human soul nature. It is true that if a person has a very prominent forehead, it may indicate a philosopher. If a person has a very receding forehead and is at the same time talented, such a person may become an artist. You cannot say that the artist is located in a particular part of the head, but through your feelings you can differentiate between one or another form. You should consider the soul in this way. The more intellectual element drives into the forehead, and the more artistic element allows the forehead to recede. The same thing is also true in the study of plants. I mean your research should not be so external, but rather you should enter more deeply into the inner nature of plants and describe conditions as they actually are.

Some remarks were added.

RUDOLF STEINER: When you confine yourself too much to the senses, your viewpoint will not be quite correct. The senses come into consideration insofar as each sense contributes to the inner life of human beings, whatever can be perceived by a particular sense. For example, we owe several soul experiences to the sense of sight. We owe different soul experiences to other senses. Thus we can retrace our soul experiences to these various senses. In this way the senses are associated with our soul nature. But we should not assert unconditionally that plants express the senses of the Earth, because that is not true.

Someone cited samples from the writings of Emil Schlegel, a homeopathic doctor from Tübingen.

RUDOLF STEINER: Schlegel’s comparisons are also too external. He returns to what can be found in the mystics—Jacob Boehme and others—to the so-called “signatures.” Mystics in the Middle Ages were aware of certain relationships to the soul world that led them into deeper aspects of medicine. You find, for example, that a definite group of plants is associated with a quality of soul; mushrooms and fungi are associated with the quality that enables a person to reflect, to ponder something, the kind of inner life that lies so deeply in the soul that it does not demand much of the outer world for its experience, but “pumps,” as it were, everything out of itself. You will also find that this soul quality, most characteristic of mushrooms, is very intimately associated with illnesses of a headache nature; in this way you discover the connection between mushrooms and illnesses that cause headaches. Please note that you cannot make such comparisons when teaching about animals.

There are, as yet, no proper classifications of plants, but by means of these relationships between human soul qualities and groups of plants you must try to bring some kind of classification into the life of plants. We will now attempt to classify the plant kingdom.

You must first distinguish what are properly seen as the different parts of the plant—that is, root, stem (which may develop into a trunk), leaves, blossoms, and fruits. All the plants in the world can be divided into groups or families. In one family the root is more developed; the rest of the plant is stunted. In another the leaves are more developed, and in others the blossoms; indeed, these last are almost entirely blossom. Such things must be considered in relation to each other. Thus we can classify plants by seeing which system of organs predominates, root, trunk, leaves, and so on, since this is one way that plants vary. Now, when you recognize that everything with the nature of a blossom belongs to a certain soul quality, you must also assign other organic parts of the plant to other soul qualities. Thus, whether you associate single parts of the plant with qualities of soul or think of the whole plant kingdom together in this sense, it is the same thing. The whole plant kingdom is really a single plant.

Now what are the actual facts about the sleeping and waking of the Earth? At the present time [September] the Earth is asleep for us, but it is awake on the opposite side of the Earth. The Earth carries sleep from one side to the other. The plant world, of course, takes part in this change, and in this way you get another classification according to the spatial distribution of sleeping and waking on the earth—that is, according to summer and winter. Our vegetation is not the same as that on the opposite side of the Earth.

For plant life, everything is related with the leaves, for every part of a plant is a transformed leaf.

Someone compared groups of plants with temperaments.

RUDOLF STEINER: No, you are on the wrong track when you relate the plant world directly to the temperaments.

We might say to the children, “Look children, you were not always as big as you are now.¹ You have learned to do a great many things that you couldn’t do before. When your life began you were small and awkward, and you couldn’t take care of yourselves. When you were very small you couldn’t even talk. You could not walk either. There were many things you could not do that you can do now. Let’s all think back and remember the qualities you had when you were very young children. Can you remember what you were like then and what kinds of things you did? Can you remember this?” Continue to ask until they all see what you mean and say “No.” “So none of you know anything about what you did when you were toddlers?

“Yes, dear children, and isn’t there something else that happens in your lives that you can’t remember, and things that you do that you can’t remember afterward?” The children think it over. Perhaps someone among them will find the answer, otherwise you must help them with it. One of them might answer, “While I was asleep.” “Yes, the very same thing happens when you are very young that happens when you go to bed and sleep. You are ‘asleep’ when you are a tiny baby, and you are asleep when you are in bed.

“Now we will go out into nature and look for something there that is asleep just like you were when you were very young. Naturally you could not think of this yourselves, but there are those who know, and they can tell you that all the fungi and mushrooms that you find in the woods are fast asleep, just as you were when you were babies. Fungi and mushrooms are the sleeping souls of childhood.

“Then came the time when you learned to walk and to speak. You know from watching your little brothers and sisters that little children first have to learn to speak and walk, or you can say walk and then speak. That was something new for you, and you could not do that when you began your life; you learned something fresh, and you could do many more things after you learned to walk and speak.

“Now we will go out into nature again and search for something that can do more than mushrooms and fungi. These are the algae,” and I now show the children some examples of algae, “and the mosses,” and I show them some mosses. “There is something in algae and mosses that can do much more than what is in the fungi.”

Then I show the children a fern and say, “Look, the fern can do even more than the mosses. The fern can do so much that you have to say it looks as if it already had leaves. There is something of the nature of a leaf.

“Now you do not remember what you did when you learned to speak and walk. You were still half asleep then. But if you watch your brothers and sisters or other little children you know that, when they grow a little older, they do not sleep as long as when they were first born. Then came the time when your mind woke up, and you can return to that time as your earliest memory. Just think! That time in your mind compares with the ferns. But ever since then you can remember more and more of what happened in your mind. Now let’s get a clear picture of how you came to say ‘I.’ That was about the time to which your memory is able to return. But the I came gradually. At first you always said ‘Jack wants.. .’ when you meant yourself.”

Now have a child speak about a memory from childhood. Then you say to the child, “You see, when you were little it was really as though everything in your mind was asleep; it was really night then, but now your mind is awake. It is much more awake now, otherwise you would be no wiser than you used to be. But you are still partly asleep; not everything in you is awake yet; much is still sleeping. Only a part of you has awakened. What went on in your mind when you were four or five years old was something like the plants I am going to show you now.”

We should now show the children some plants from the family of the gymnospernms—that is, conifers, which are more perfectly formed than the ferns—and then you will say to the children, “A little later in your life, when you were six or seven years old, you were able to go to school, and all the joys that school brought blossomed in your heart.” When you show a plant from the family of the ferns, the gymnosperms, you go on to explain, “You see there are still no flowers. That was how your mind was before you came to school.

“Then, when you came to school, something entered your mind that could be compared to a flowering plant. But you had only learned a little when you were eight or nine years old. Now you are very smart; you are already eleven years old and have learned a great many things.

“Now look; here is a plant that has leaves with simple parallel veins

and here is another with more complicated leaves with a network of veins. When you look at the blossoms that belong to the simple leaves, they are not the same as those on the plants with the other kind of leaf, where the blossoms and everything else are more complicated than in those with the simpler leaves.”

Now you show the children, for example, an autumn crocus, a monocotyledon; in these plants everything is simple, and you can compare them to children between seven and nine. Then you can continue by showing the children plants with simple blossoms, ones that do not yet have real petals. You can then say, “You have plants here in which the green sepals and the colored petals are indistinguishable, in which the little leaves under the blossom cannot be distinguished from those above. This is you! This is what you are like now.

“But soon you will be even older, and when you are twelve, thirteen, or fourteen you will be able to compare yourselves with plants that have calyx and corolla; your mind will grow so much that you’ll be able to distinguish between the green leaves we call the calyx and the colored leaves called petals. But first you must reach that stage!” And so you can divide the plants into those with a simple perianth—compared to the elevenyear- old children—and plants with a double perianth—those of thirteen to fourteen years.² “So children, this is another stage you have to reach.”

Now you can show the children two or three examples of mosses, ferns, gymnosperms, monocotyledons, and dicotyledons, and it would be a fine thing at this point to awaken their memory of earlier years. Have one of them speak of something remembered about little four-year-old Billy, and then show your ferns; have another child recall a memory of seven-year-old Fred, and then show the corresponding plant for that age; and yet another one could tell a story about eleven-year-old Ernie, and here you must show the other kind of plant. You must awaken the faculty of recalling the various qualities of a growing child and then carry over to the plant world these thoughts about the whole development of the growing soul. Make use of what I said yesterday about a tree, and in this way you will get a parallel between soul qualities and the corresponding plants.

There is an underlying principle here. You will not find parallels accidentally according to whatever plants you happen to pick. There is principle and form in this method, which is necessary. You can cover the whole plant kingdom in this way, with the exception of what happens in the plant when the blossom produces fruit. You point out to the child that the higher plants produce fruits from their blossoms. “This, dear children, can only be compared to what happens in your own soul life after you leave school.” Everything in the growth of the plant, up to the blossom, can be compared only with what happens in the child until puberty. The process of fertilization must be omitted for children. You cannot include it.

Then I continue, “You see, dear children, when you were very small you really only had something like a sleeping soul within you.” In some way remind the children, “Now try to remember, what was your main pleasure when you were a little child? You have forgotten now because, in a way, you were really asleep at that time, but you can see it in little Anne or Mary, in your little baby sister. What is her greatest joy? Certainly her milk bottle! A tiny child’s greatest joy is the milk bottle. And then came the time when your brothers and sisters were a little older, and the bottle was no longer their only joy, but instead they loved to be allowed to play. Now remember, first I showed you fungi, algae, mosses; almost everything they have, they get from the soil. We must go into the woods if we want to get to know them. They grow where it is damp and shady, they do not venture out into the sunlight. That’s what you were like before you ‘ventured out’ to play; you were content with sucking milk from a bottle. In the rest of the plant world you find leaves and flowers that develop when the plants no longer have only what they get from the soil and from the shady woods, but instead come out into the sun, to the air and light. These are the qualities of soul that thrive in light and air.” In this way you show the child the difference between what lives under the Earth’s surface on the one hand (as mushrooms and roots do, which need the watery element, soil, and shade), and on the other hand, what needs air and light (as blossoms and leaves do). “That is why plants that bear flowers and leaves (because they love air and light) are the so-called higher plants, just as you, when you are five or six years old, have reached a higher stage than when you were a baby.”

By directing the children’s thoughts more and more—at one time toward qualities of mind and soul that develop in childhood, and then toward the plants—you will be able to classify them all, based on this comparison. You can put it this way:

Pleasures of infancy (babies): Mushrooms and Fungi
Pleasures of early childhood (the awakening life of feeling, both sorrows and joys): Algae, Mosses
Experiences at the awakening of consciousness of self: Ferns
Experiences of fifth and sixth year, up to school age: Gymnosperms, Conifers
First school experiences, seventh, eighth, ninth, tenth and eleventh year: Parallel-veined plants, Monocotyledons; Plants with simple perianth
Experiences of the eleven-year-old: Simple dicotyledons
School experiences from twelfth to fifteenth year: Net-veined plants, Dicotyledons; Plants with green calyx and colored petals

“You are not smart enough yet for these last experiences (the plants with a green calyx and colored blossoms), and you won’t know anything about them until you are thirteen or fourteen years old.

“Just think; how lovely! One day you will have such rich thoughts and feelings, you will be like the rose with colored petals and green sepals. This will all come later, and you can look forward to it with great pleasure. It is lovely to be able to rejoice over what is coming in the future.” The important thing is that you arouse within children’s hearts a joyful anticipation of what the future will bring them.

Thus, all the successive soul qualities before puberty can be compared with the plant kingdom. After that the comparison goes no further because at this point the children develop the astral body, which plants do not possess. But when the plant forces itself into fertilization beyond its nature, it can be compared with soul qualities of the sixteenth to seventeenth year. There is no need to call attention to the process of fertilization, but you should speak of the process of growth, because that agrees with reality. The children would not understand the process of fertilization, but they would understand the process of growth, because it can be compared with the process of growth in the mind and soul. Just as a child’s soul is different at various ages, so also the plants are different because they progress from the mushroom to the buttercup, which is usually included among the most highly developed plants, the Ranunculuses. It is indeed true that, when the golden buttercups appear during spring in lush meadows, we are reminded of the soul life and soul mood of fourteen-and fifteen-year-old boys and girls.

If at some time a botanist should go to work along these lines in a thoroughly systematic way, a plant system would be found that corresponds to fact, but you can actually show the children the whole external plant world as a picture of a developing child’s soul. Much can be done in this way. You should not differentiate in the individualized way practised by the old phrenologists, but you should have one clear viewpoint that can be carried right through your teaching. Then you will find that it is not quite correct to merely take everything with a root nature and relate it to thought. Spirit in the head is still asleep in a child. Thus, thinking in general should not be related to what has root nature, but a child’s way of thinking, which is still asleep. In the mushroom, therefore, as well as in the child, you get a picture of childlike thinking, still asleep, that points us toward the root element in plants.

Rudolf Steiner then gave the following assignments:

1. To comprehensively work out the natural history of plants as discussed up to this point;

2. The geographical treatment of the region of the lower Rhine, from the Lahn onward, “in the way I showed you today when speaking of lessons in geography”: mountains, rivers, towns, civilization, and economics.³

3. Do the same for the basin of the Mississippi.

4. What is the best way to teach the measurement of areas and perimeters?

• 1. According to the Waldorf curriculum, the children are around eleven years old when they are taught about the plant kingdom.
• 2. The perianth is the envelope of a flower, particularly one in which the calyx and corolla are combined so that they are indistinguishable from one another; these include such flowers as tulips, orchids, and so on. The perianth is single when it has one verticil, and double when it has both calyx and corolla.
• 3. See Practical Advice to Teachers, lecture 11.

Speech Exercises:

Curtsey cressets Betsy jets cleric
lastly plotless light skeptic

RUDOLF STEINER: You will only get the words right when you can reel them off by heart. Be conscious of every syllable you speak!

Narrow wren
mirror royal
gearing grizzled
noting nippers
fender coughing

Some of the teachers, as requested, gave a comprehensive survey of the natural history of plants as discussed in yesterday’s discussion.

RUDOLF STEINER: Give as many examples as possible! Ideas about metamorphosis and germination cannot really be understood by children under the age of fourteen, and certainly not by children of nine to eleven. Related to this is something else of great importance that needs to be said. You must have followed the recent discussions from every side about so-called “sex education” for children. Every possible perspective, for and against, has been presented.

The subject essentially breaks down into three questions. First, we consider who should present such sex education. Those who think seriously about their great responsibility as teachers in the school soon realize the extraordinary difficulty of such an undertaking. I doubt if any of you would really welcome the job of providing sex education to young teenagers between twelve and fourteen. The second question concerns how this teaching should be given. This is not an easy question either. The third question is about its place in education. Where should you introduce it? In natural history lessons perhaps?

If teaching were based on true educational principles this task would fall very naturally into place. If in your teaching you explain the process of growth to the children in relation to light, air, water, earth, and so on, the children will absorb such ideas so that you can proceed gradually to the process of fertilization in plants, and then in animals and human beings. But you must look comprehensively at this matter and show how plants come into existence through light, water, earth, and so on; in short, for the complicated process of growth and fertilization you must prepare ideas that will provide children with a foundation in imaginative thinking. The fact that there has been so much chatter about sex education proves that there is something wrong with teaching methods of today; it should certainly be possible in the early school years to prepare for later sex education. For instance, by explaining the process of growth in connection with light, air, water, and so on, the teacher could foster the pure and chaste views necessary for sex education later on.

In map drawing you should color the mountains brown and rivers blue. Rivers should always be drawn as they flow, from source to mouth, never from mouth to source. Make one map for the soil and ground nature—coal, iron, gold, or silver, and draw another map for towns, industries, and so on. I ask you to note the importance of choosing some particular part of the world as a subject for your lessons, and then as you continue, you should refer back to this area again and again. The way that your subject is presented is also very important; try to live directly into your subject so that the children always get the feeling that you are describing something in which you are actually involved. When you describe an industry they should feel that you are working there, and the same is true when you describe a mine, and so on. Make it as lively as possible! The more life there is in your descriptions, the better the children will work with you.

Someone calculated the measurement of areas, beginning with the square and proceeding to the rectangle, parallelogram, trapezium, and triangle.

RUDOLF STEINER: It is difficult to explain to a child what an angle actually is. Can you make up a method for doing this? Perhaps you remember how difficult it was for you to be clear about it—aside from the fact that there may be some of you who do not yet know what an angle really is.

You can explain to the children what a larger or smaller angle is by drawing angles, first with longer arms and then with shorter arms. Now which angle is the larger? They are exactly the same size!

Then have two of the children walk from a certain point simultaneously, two times, and show them that the first time they walked they made a larger angle, and the second time a smaller one. When they walked making the smaller angle their paths were closer together, with the larger angle further apart. This can also be shown with an elbow movement.

It’s good to arrive at a view of larger and smaller angles before beginning to measure angles in degrees.

The transformation of a parallelogram into a square was spoken about, to show that the area, in both cases, is base multiplied by height.

RUDOLF STEINER: Yes, it can be done like that. But if by tomorrow you would consider the whole subject on a somewhat different basis, perhaps you will find it beneficial to introduce the children to a clear concept of area as such first, and then the size of the area. The children know the shape of a square, and now you want to show it to them as a surface that could be larger or smaller.

Second, figure out for tomorrow how you would give the children arithmetical problems to solve without writing down any figures—in other words, what we could call mental arithmetic. You could, for example, give the children this problem to do: A messenger starts from a certain place and walks so many miles per hour; another messenger begins much later; the second messenger does not walk but rides a bicycle at a certain number of miles per hour. When did the cyclist pass the messenger on foot?

The object of these problems is to develop in children a certain presence of mind in comprehending a situation and evaluating it as a whole.

Speech Exercises:

Clip plop pluck cluck
clinked clapper richly
knotted trappings
rosily tripled

RUDOLF STEINER: Memorize this before you practice it!

An attempt was made to illustrate the concept of a surface area for nine-year-old children; have the children cut out squares to measure from larger squares and copy them.

RUDOLF STEINER: It is certainly good to make it clear to children that, if the length of one side of a square is 3 feet, the area of the surface is 9 square feet, but this limits us to an area of thought where a whole is built from its parts, and this will not help children to gain a true concept of what a surface area really is. What I meant was: What is the right way to proceed, and at what age, in order to actually discover what a surface really is, and that it is obtained by multiplying length by breadth. How can you manage to awaken this concept of a surface in the child? This depends on when you begin teaching children about surface areas. It doesn’t make sense to teach them about surface areas until after you teach them some algebra. The answer, therefore, is to wait for lessons on surface areas until after we deal with algebra.

Now comes another question: How do you make the transition from ordinary problems with figures to problems with letters—that is, algebra? I will give you a suggestion about how to begin, and then you can work it out for yourselves. Before you move on to algebra you must have already worked on interest with the children; interest is principal multiplied by rate percent multiplied by time, divided by 100.

Interest = Principal × Rate × Time

To arrive at this formula, begin with ordinary numbers, and children understand principal, rate percent, time, and so on, relatively easily. So you will try to make this process clear and assure yourself that most of the children have understood it; from there you should move on to the formula, and always make sure that you work according to rule.

\(P\) = principal; \(R\) = rate; \(T\) = time; and \(I\) = interest. What I gave you is a formula I view merely as a basic formula, and with this formula I have taken the first step in moving to algebra. When the children have this formula they merely need to substitute figures for the letters, and then they will always get the right answer.

Now if you have the following formula derived from the first:

you can see that you can change about the 3 letters \(P\), \(R\), \(T\), however you wish, so that the following are also possibilities:

In this way we have taught the children how to work with\(\) interest, and now we can go on to algebra. You can simply say, “We have learned that a sum of \(25\) was equal to \(8\), then \(7\) and \(5\), and another \(5\): that is, \(25 = 8 + 7 + 5 + 5\).” The children will already have understood. Now after you have explained this, you can say, “Here, instead of 25 you could have a different number, and, instead of \(8\), \(7\), \(5\), \(5\) you could have other numbers; in fact, you could tell them that any number could be there. You could have \(s\), for example, as a total, and then you could have \(a + b + c + c\); but if c represents the first \(5\), then \(c\) must also represent the second 5. Just as I put P in place of principal, so in the same place I put the lettecr .

After having shown in a concrete example the transition from number to letter you can now explain the concept of multiplication, and out of this concrete \(g × g\) you can develop \(a × a\), or from \(a × 2\) you can evolve \(a × b\), and so on. This then would be the way to progress from the numbers in arithmetic to algebra with its letters, and from algebra to the calculation of surface areas; \(a × a = a^2\).

Now here is your task for tomorrow. Try to find a truly enlightened way to present to children of ten and eleven the concept of interest and everything associated with it, as well as inverse calculations of rate, time, and principal; then from there demonstrate how to deal with discount—how to teach a child the discounting of bills and the cost of packing and conveyancing, and then continue on to bills of exchange and how to figure them out. That belongs to the twelfth and thirteenth year, and if it is taught at this time it will be retained for the rest of life; otherwise it is always forgotten again. It is possible to deal with it in a simpler form, but it should be done at this age. Anyone who can do this properly has mastered the fundamental method of all computation. Compound interest is not involved at this time. You should therefore go over algebra in an organic way until multiplication, and then continue on to surface area calculation.

Now let’s proceed to the other questions from yesterday, because here it is important also that you should engender presence of mind in the children by assigning them problems.

Someone proposed setting up a little stall with fruit, vegetables, potatoes, and so on, so that the children would have to buy and sell, pay for their purchases, and actually figure out everything for themselves.

RUDOLF STEINER: This idea of buying and selling is very good for the second grade. Also, you should insist that those who have been assigned a problem should really work it out for themselves; you must not allow anyone else do it for them. Keep their interest awake and alive at every point!

Mental arithmetic was discussed.

RUDOLF STEINER related how Gauss¹ as a boy of six arrived at the following solution to a problem he had to do: all of the numbers from 1 to 100 had to be added together. Gauss thought about the problem and concluded it would be a simpler and easier to get a quick answer by taking the same numbers twice, arranging them in the first row in the usual order from left to right—1, 2, 3, 4, 5... up to 100, and beneath that a second row in the reverse order—100, 99, 98, 97, 96 ... and so on to 1; thus 100 was under the 1, 99 under the 2, 98 under the 3, and so on. Then each of these 2 numbers would in every case add up to the whole. This sum would then have to be taken 100 times, which makes 10,100; then, because you have added each of the numbers from 1 to 100 twice (once forward and once backward) this sum would then be halved, and the answer is 5,050. In this way Gauss, to the great astonishment of his teacher, solved the problem in his head.

RUDOLF STEINER: You can use your imagination in making up arithmetical problems, and you can engender presence of mind through problems that deal with movement. With yesterday's example you can progress to practical life by saying, “I sent an express messenger with a letter. Because of certain circumstances the letter was no longer valid. So I sent another messenger. How quickly must the second messenger travel to arrive before the letter had caused any harm? The children should be able to figure this out at least approximately, which is good for them.

One of the teachers spoke of errors in calculation.

RUDOLF STEINER: These kinds of errors in calculations are usual. It is very common to figure the errors into the whole. There is one such mistake made these days that will at sometime or another have to be corrected. When Copernicus formulated his “Copernican system” he proposed three laws. If all three were to be used to describe the Earth’s course through space we would get a very different movement from what is now accepted by astronomers and taught in schools. This elliptic movement would only be possible if the third law were disregarded. When the astronomer uses the telescope, these things do not add up. Because of this, corrections are inserted into the calculations; through the use of Bessel's equations, corrections are introduced every year to account for what does not accord with reality.² In Bessel’s corrections there is the third law of Copernicus.

Your method must never be simply to occupy the children with examples you figure out for them, but you should give them practical examples from real life; you must let everything lead into practical life. In this way you can always demonstrate how what you begin with is fructified by what follows and vice versa.

How would you resolve all these problems? (the flow of fluids slowly through small holes, quickly through large holes; rates of circular motion in machines with wheels of different sizes, and so on.)

The best way would be to proceed at this point to the explanation of what a clock is in its various forms—pendulumclocks, watches, and so on.

These are your tasks for tomorrow:

1. Some historical subject related to the history of civilization to be worked out on the lines of the example.

2. The treatment of some subject taken from nature—sunrise and sunset, seasons of the year and so on—whatever may suggest itself to you, something out of the great universe. The point is to show your method of teaching.

3. The principles of music for the first school year.

4. What form would you give to teaching the poetry of other languages? How would you give the children a feeling for what is poetic in other tongues?

5. How can you provide children with an idea of the ellipse, hyperbola, circle, and lemniscate; also the concept of geometrical locus? The children must be taught all this just before they leave our school at fourteen.

• 1. Carl Friedrich Gauss (1777–1855), German mathematician and astronomer. He demonstrated that a circle can be divided into seventeen equal arcs through elementary geometry and developed a new technique for calculating the orbits of asteroids. He is also the originator of the Gaussian error curve in statistics and is considered the founder of the mathematical theory of electricity, from which derives the gaussmeter.
• 2. Friedrich Wilhelm Bessel (1784–1846), German astronomer; he calculated the orbit of Halley’s comet in 1804 and made the first “authenticated” calculation of a star’s distance from Earth. He also calculated the elliptical nature of Earth’s orbit.

The principles were developed for teaching music to the first and second grades.

RUDOLF STEINER: Children should be allowed to hear an instrument, to hear music objectively, apart from themselves. This is important. It should be a matter of principle that well before the ninth year the children should learn to play solo instruments, and the piano can be added later for those for whom it is considered advisable. What matters most is that we make a right beginning in this sphere.

Further remark on the concept of interest, proceeding to algebra:

If \(A =\) amount, \(P =\) principal, \(I =\) interest, \(R =\) rate of interest, \(T =\) time, then \(A = P + I\).

Since

$$I = \frac{PRT}{100}$$

then

$$A = P + \frac{PRT}{100}$$

RUDOLF STEINER: It would never be possible to describe capital in this way these days; this formula only has real value if \(T\) equals a year or less, because in reality two cases are given: Either you remove the interest each year, in which case the same initial capital always remains, or else you leave the interest with the capital, in which case you need to figure according to compound interest. If you omit \(T\)—that is, if you figure it for only one year, then it is an actual thing; it is essential to present realities to the children. Do not fail to observe that the transition to algebra as we have spoken of it, is really carried out—first from addition to multiplication, and then from subtraction to division. This must be adhered to strictly.

RUDOLF STEINER explained the transition from arithmetic to algebra with the following example: First you write down a number of figures in which all the addenda are different:

Some of the addenda could also be equal:

Or all the addenda could be the same:

If you proceed, as described in our previous discussion, to replace numbers with letters, then you could have the equation:

\(S_1 = a + a + a\); that is, three \(a\)’s, or three times \(a = 3a\).

then

then

\(S_3 = a + a + a + a + a + a + a\); or seven times \(a = 7a\)

and so on. I can keep doing this; I could do it \(9\) times, \(21\) times, \(25\) times, I can do it \(n\) times:

\(S_n = a + a + a ... n\) times \(= na\)

Thus, I get the factor by varying the number of the addenda, while the addendum itself is the other factor. In this way multiplication can easily be developed and understood from addition, and you thus make the transition from actual numbers to algebraic quantities:

\(a × a = a2\), \(a × a × a = a3\).

In the same way you can derive division from subtraction. If we take b away from a very large number a, we get the remainder \(r\):

\(r = a – b\)

If we take b away again, we get the remainder:

\(r_2 = a – b – b = a – 2b\)

If b is taken away a third time we obtain:

\(r_3 = a – b – b – b = a – 3b\) and so on.

We could continue until there is nothing left of number \(a\): suppose this happens after subtracting \(b\) \(n\) times:

\(r_n = a – b – b – b ... n\) times \(= – nb\) When there is nothing left—that is, when the last remainder is \(0\), then:

\(0 = a – nb\)

So a is now completely divided up, because nothing remains:

\(a = nb\)

I have taken b away n times, I have divided \(a\) into nothing but \(bs\), \(a/b = n\), so the \(a\) is completely used up. I have discovered that I can do this \(n\) times, and in so doing I have gone from subtraction to division.

Thus we can say: multiplication is a special case of addition, and division is a special case of subtraction, except that you add to it or take away from it, not just once, but repeatedly, as the case may be.

Negative and imaginary numbers were discussed.

RUDOLF STEINER: A negative number is a subtrahend [the number subtracted] for which there is no minuend [the number from which it is subtracted]; it is a demand that something be done: there being nothing to do it with, thus it cannot be done. Eugen Dühring rejected imaginary numbers as nonsense and spoke of Gauss’s definition of “the imaginary” as completely stupid, unrealistic, farfetched nonsense.¹

From addition, therefore, you develop multiplication, and from multiplication, rise to a higher power. And then from subtraction you develop division, and from division, find roots.

addition—subtraction
multiplication—division
raising to a higher power—finding roots

You should not proceed to raising to a higher power and finding roots until after you have begun algebra (between the eleventh and twelfth years), because, with roots, raising to a power of an algebraic equation of more than one term (polynomial) plays a role. In this connection you should also deal with figuring gross, net, taxes, and packing charges.

A question about the use of formulas.

RUDOLF STEINER: The question is whether you should avoid the habitual use of formulas, but go through the thought processes again and again (a good opportunity for practicing speech), or whether it might be even better to go ahead and use the formula itself. If you can succeed, tactfully, in making the formula fully understood, then it can be very useful to use it as a speech exercise—to a certain extent.

But from a certain age on, it is also good to make the formula into something felt by the children, make it into something that has inner life, so that, for example, when the \(T\) increases in the formula \(I = PRT/100\), it gives the children a feeling of the whole thing growing.

In effect, this is what I wanted to say at this point—that you should use the actual numbers for problems of this kind—for example, in interest and percentages—in order to make the transition to algebra, and in doing so, develop multiplication, division, raising powers, and roots. These are things that certainly must be done with the children.

Now I would like to ask a question: Do you consider it good to deal with raising to a higher power and finding roots before you have done algebra, or would you do it later?

Comment about raising to a higher power first and finding roots after.

RUDOLF STEINER: Your plan then would be (and should continue to be) to start with algebra as soon as possible after the eleventh or twelfth year, and only after that proceed to raising to a higher power and finding roots. After teaching the children algebra, you can show them in a very quick and simple way how to square, cube, raise to a higher power, and extract the root, whereas before they know algebra you would have to spend a terribly long time on it. You can teach easily and economically if you take algebra first.

A historical survey for the older children (eleven to fourteen years) was presented concerning the founding and development of towns, referring to the existence of a “Germany” at the time of the invasion of the Magyars.

RUDOLF STEINER: You must be very careful not to allow muddled concepts to arise unconsciously. At the time of Henry, the so-called “townbuilder,” there was of course no “Germany.” You would have to express what you mean by saying “towns on the Rhine” or “towns on the Danube” in the districts that later became “German.”²

Before the tenth century the Magyars are not involved at all, but there were invasions of Huns, Avars, and so on. But after the tenth century you can certainly speak of “Germany.” When the children reach the higher grades (the seventh and eighth grades) I would try to give them a concept of chronology; if you just say ninth or tenth century, you do not give a sufficiently real picture. How then would you manage to awaken in the children a concrete view of time?

You could explain it to them like this: “if you are now of such and such an age, how old are your mother and father? Then, how old are your grandfather and grandmother?” And so you evoke a picture of the whole succession of generations, and you can make it clear to the children that a series of three generations makes up about 100 years, so that in 100 years there would be three generations. A century ago the great grandparents were children. But if you go back nine centuries, there have not been three generations, but \(9\ x\ 3 = 27\) generations. You can say to the child: “Now imagine you are holding your father’s hand, and he’s holding your grandfather’s hand, and he is, in turn, holding your great-grandfather’s hand, and so on. If they were now all standing together side by side, which would be Henry I, which number in the row would have stood face to face with the Magyars around the year 926? It would be the twenty-seventh in the row.” I would demonstrate this very clearly in a pictorial way. After giving the children this concrete image of how long ago it was, I would present a graphic description of the migrations of the Magyars. I would tell them about the Magyars’ invasion of Europe at that time, how they broke in with such ferocity that everyone had to flee before them, even the little children in their cradles, who had to be carried up to the mountaintops, and how then the onrushing Magyars burned the villages and forests. Give them a vivid picture of this Magyar onset.

It was then described how Henry, knowing he had been able to resist the Magyars in fortified Goslar, resolved to build fortified towns, and in this way it come about that numerous towns were founded.

RUDOLF STEINER: Here again, could you not present this more in connection with the whole history of civilization? It is only a garbled historical legend to say that Henry founded these towns. All these tenth century towns were built on their original foundations—that is, the markets—before then. But what helped them to expand was the migration of the neighboring people into the towns in order to defend themselves more easily against the Magyars’ assaults, and for this reason they fortified these places. The main reasons for building these towns were more economic in nature. Henry had very little part in all this.

I ask you to be truly graphic in your descriptions, to make everything really alive, so that the children get vivid pictures in their minds, and the whole course of events stands out clearly before them. You must stimulate their imagination and use methods such as those I mentioned when I showed you how to make time more real. Nothing is actually gained by knowing the year that something occurred—for example, the battle of Zama; but by using the imagination, by knowing that, if they held hands with all the generations back to Charles the Great, the time of their thirtieth ancestor, the children would get a truly graphic, concrete idea of time. This point of time then grows much closer to you—it really does—when you know that Charles the Great is there with your thirtieth ancestor.

Question: Wouldn’t it also be good when presenting historical descriptions to dwell on the difference in thought and feeling of the people of those times?

RUDOLF STEINER: Yes. I have always pointed this out in my lectures and elsewhere. Most of all, when speaking of the great change that occurred around the fifteenth century, you should make it very clear that there was a great difference between the perception, feeling, and thought of people before and after this time. Lamprecht too (whom I do not however especially recommend) is careful to describe a completely different kind of thinking, perceiving, and feeling in people before this time.³ The documents concerning this point have not yet been consulted at all.

In studying the books written on cultural history you must, above all, develop a certain perceptive faculty; with this you can properly assess all the different things related by historians, whether commonplace or of greater importance, and so gain a truer picture of human history.

Rudolf Steiner recommended for the teachers’ library Buckle’s History of Civilization in England and Lecky’s History of Rationalism in Europe.

RUDOLF STEINER: From these books you can learn the proper methods of studying the history of human progress. With Lamprecht only his earlier work would be suitable, but even much of this is distorted and subjective. If you have not acquired this instinct for the real forces at work in history, you will be in danger of falling into the stupidity and amateurism of a “Wildenbruch” for example;⁴ he imagined that the stories of emperors and kings and the family brawls between Louis the Pious and his sons were important events in human history.

Gustav Freytag’s Stories from Ancient German History are very good;⁵ but you must beware of being influenced too much by this rather smug type of history book (written for the unsophisticated). The time has come now when we must get out of a kind of thinking and feeling that belonged to the middle of the nineteenth century.

Mention was made of Houston Stuart Chamberlain’s Foundations of the Nineteenth Century.⁶

RUDOLF STEINER: With regard to Chamberlain also you must try to develop the correct instinct. For one part of clever writing you get three parts of bad, unwholesome stuff. He has some very good things to say, but you must read it all yourselves and form your own judgements. The historical accounts of Buckle and Lecky are better.⁷ Chamberlain is more one of these “gentlemen in a dinner jacket.” He is rather a vain person and cannot be accepted as an authority, although many of his observations are correct. And the way he ended up was not particularly nice—I mean his lawsuit with the “Frankfurter Zeitung.”

Kautsky’s writings were mentioned.⁸

RUDOLF STEINER: Well yes, but as a rule you must assume that the opposite of what he says is true! From modern socialists you can get good material in the way of facts, as long as you do not allow yourselves to be deceived by the theories that color all their descriptions. Mehring too presents us with rather a peculiar picture;⁹ because at first, when he was himself a progressive Liberal, he inveighed against the Social Democrats in his book on Social Democracy; but later when he had gone over to the Social Democrats he said exactly the same things about the Liberals!

An introduction was presented on the fundamental ideas in mathematical geography for twelve-year-old children, with observations on the sunrise and the ecliptic.

RUDOLF STEINER: After taking the children out for observations, it would be very good to let them draw what they had observed; you would have to make sure there is a certain parallel between the drawing and what the children saw outside. It is advisable not to have them do too much line drawing. It is very important to teach these things, but if you include too much you will reach the point where the children can no longer understand what you are saying. You can relate it also to geography and geometry.

When you have developed the idea of the ecliptic and of the coordinates, that is about as far as you should go.

Someone else developed the same theme—that is, sunrise and sunset—for the younger children, and tried to explain the path of the Sun and planets in a diagrammatic drawing.

RUDOLF STEINER: This viewpoint will gradually lose more and more of its meaning, because what has been said until now about these movements is not quite correct. In reality it is a case of a movement like this (lemniscatory screw-movement):

Here, for example, [in position 1] we have the Sun; here are Saturn, Jupiter, Mars, and here are Venus, Mercury, and Earth. Now they all move in the direction indicated [spiral line], moving ahead one behind the other, so that when the Sun has progressed to the second position we have Saturn, Jupiter, and Mars here, and we have Venus, Mercury, and Earth over there. Now the Sun continues to revolve and progresses to here [position 3]. This creates the illusion that Earth revolves round the Sun. The truth is that the Sun goes ahead, and the Earth creeps continually after it.

The ancient Egyptian civilization was described.

RUDOLF STEINER: It is most important to explain to the children that Egyptian art was based on a completely different method of representing nature. The ancient Egyptians lacked the power of seeing things in perspective. They painted the face from the side and the body from the front. You may certainly explain this to the children, especially the Egyptian concept of painting. Then you must point out how Egyptian drawing and painting was related to their view of natural history—how, for example, they portrayed men with animal heads and so on.

In ancient times the habit of comparing people with the animals was very common. You could then point out to the children what is present in seed form, as it were, within every human face, which children can still see to a certain extent.¹⁰ The Egyptians still perceived this affinity of the human physiognomy with animals; they were still at this childlike stage of perception.

Question: What should one really tell children about the building of the Egyptian pyramids?

RUDOLF STEINER: It is of course extraordinarily important for children too that you should gradually try to present them with what is true rather than what is false. In reality the pyramids were places of initiation, and this is where you reach the point of giving the children an idea of the higher Egyptian education, which was initiation at the same time. You must tell them something about what happened within the pyramids. Religious services were conducted there, just as today they are conducted in churches, except that their services led to knowledge of the universe. Ancient Egyptians learned through being shown, in solemn ritual, what comes about in the universe and in human evolution. Religious exercises and instruction were the same; it was really such that instruction and religious services were the very same thing.

Someone described the work of the Egyptians on the pyramids and obelisks, and said that several millions of people must have been needed to transport the gigantic blocks of stone, to shape them, and to set them in place. We must ask ourselves how it was possible at all, with the technical means available at that time, to move these great heavy blocks of limestone and granite and to set them in place.

RUDOLF STEINER: Yes, but you only give the children a true picture when you tell them: If people were to do this work with the physical strength of the present day, two and a half times as many people would be necessary. The fact is that the Egyptians had two and a half times the physical strength that people have today; this is true, at least, of those who worked on the pyramids and so on. There were also, of course, those who were not so strong.

Question: Would it be good to include Egyptian mythology?

RUDOLF STEINER: Unless you can present Egyptian mythology in its true form, it should be omitted. But in the Waldorf school, if you want to go into this subject at all, it would be a very good plan to introduce the children to the ideas of Egyptian mythology that are true, and are well known to you.¹¹

• 1. Karl Eugen Dühring (1833–1921), German positivist philosopher and economist. Wrote Kapital und Arbeit (Capital and Labor), and Logik und Wissenschaftstheorie (Logic and Epistemological Theory).
• 2. This could as well apply to speaking of “America” in regard to events and places prior to the time of Columbus and the European settlers.
• 3. Karl Gottfried Lamprecht (1856–1915), historian who developed the theory that history is social-psychological rather than political.
• 4. Ernst von Wildenbruch (1845–1909), German writer, author of Spartacus.
• 5. Gustav Freytag (1816–1895), German writer, promoter of German liberalism and the middle class. His books included a series of six historical novels.
• 6. Houston Stuart Chamberlain (1855–1927), British publicist, naturalized German citizen. Wrote on the superiority of the Western Aryan race.
• 7. Probably refers to Henry Thomas Buckle (1821–1862), English historian, who wrote the incomplete History of Civilization in England. William Edward Hartpole Lecky 1838–1903), Irish historian who wrote on modern European history.
• 8. Karl Johann Kautsky (1854–1938), German Marxist theorist, journalist, and secretary to Friedrich Engels in London, he opposed Bolshevism and the Russian revolution.
• 9. Franz Mehring (1846–1919), German Socialist historian and journalist.
• 10. See The Foundations of Human Experience, lecture 9.
• 11. See Rudolf Steiner, Egyptian Myths and Mysteries, Anthroposophic Press, Hudson, NY, 1990.

Speech Exercises:

Slinging slanging a swindler
the wounding fooled a victor vexed
The wounding fooled a swindler
slinging slanging vexed

March smarten ten
clap rigging rockets
Crackling plopping lynxes
fling from forward forth

Crackling plopping lynxes
fling from forward forth
March smarten ten
clap rigging rockets

RUDOLF STEINER: With this exercise you should share the recitation, like a relay race, coming in quickly one after the other. One begins, points to another to carry on, and so on.

Someone spoke about the ellipse, the hyperbola, the circle, the lemniscate, and the conception of geometrical loci. At the same time he mentioned how the lemniscate (Cassini curve) can take on the form III, in the diagram, where the one branch of the curve leaves space and enters space again as the other branch.

RUDOLF STEINER: This has an inner organic correlate. The two parts have the same relation to each other as the pineal gland to the heart. The one branch is situated in the head—the pineal gland, the other lies in the breast—the heart. Only the pineal gland is more weakly developed, the heart is stronger.

Someone spoke on a historical theme—the migrations of various peoples.

RUDOLF STEINER: The causes assigned to such migrations very often depend on the explanations of historical facts. As to the actual migrations—for example, the march of the Goths—at the root of the matter, you will find that the Romans had the money and the Germanic peoples had none, and at every frontier there was a tendency among the Germanic peoples to try to acquire Roman money one way or another. Because of this, they became mercenaries and the like. Whole legions of the Germanic peoples entered into Roman hire. The migration of the people was an economic matter. This was the only thing that made the spread of Christianity possible, but the migrations as such began, nevertheless, with the avarice of the Germanic peoples who wanted to acquire Roman money. The Romans of course were also impoverished by this. This was already the case as early as the march of the Cimbri. The Cimbri were told that the Romans had money, whereas they themselves were poor. This had a powerful effect on the Cimbri. “We want gold,” they cried, “Roman gold!”

There are still various race strata—even Celtic traces. Today there are definite echoes of the Celtic language—for example, at the sources of the Danube, Brig and Breg, Brigach, and Brege, and wherever you find the suffix ach in the place names such as Unterach, Dornach, and so on. Ach comes from a word meaning a “small stream” (related to aqua), and points to a Celtic origin. “Ill,” too, and other syllables remind us of the old Celtic language. The Germanic language subsequently overlaid the Celtic.

[Rudolf Steiner referred to the contrast between Arians and Athanasians.¹]

There is something connected with the history of these migrations that is very important to explain to the children—that is, that it was very different for the migrating peoples to come into districts that were already fully developed agriculturally. In the case of the Germanic peoples, such as the Goths in Spain and Italy, they found that all the land was being cultivated already. The Goths and other ethnic groups arrived but soon disappeared. They became absorbed by the other nations who were there before them. The Franks, on the other hand, preferred to go to the West, and arrived in districts not yet fully claimed for agriculture, and they continued to exist as Franks. Nothing remained of the Goths who settled where the land was all already owned. The Franks were able to preserve their nationality because they had migrated into untilled areas. That is a very important historical law. You can refer to this law again later in relation to the configuration of North America. There, it is true that the Red Indians were almost exterminated, but it was also true, nevertheless, that people could migrate into uncultivated districts.

It is also important to explain the difference between such things as, for example, the France of Charles the Great and the state of a later time. If you are unaware of this difference, you cannot cross the Rubicon of the fifteenth century. The empire of Charles the Great was not yet a state. How was it for the Merovingians? Initially they were no more than large-scale landowners. The only thing that mattered to them was civil law. As time passed, this product of the old Germanic conditions of ownership became the Roman idea of “rights,” whereby those who were merely administrators gradually acquired power. And so, by degrees, property went to the administrative authorities, the public officials, and the state arose only when these authorities became the ruling power later. The state, therefore, originated through the claims of the administration. The “count nobility” arose as the antithesis of “prince nobility.” The word Graf (count) has the same origin as “graphologist” or “scribe.” It is derived from graphein, to write. The “count” is the Roman scribe, the administrator, whereas the “prince nobility,” originally the warrior nobility, is still associated with bravery, heroism, and similar qualities. The prince (Fürst) is “first,” the foremost one. And so this transition from Fürst to Graf (prince to count) marked the rise of the concept of “state.” This can of course be made very clear by using examples such as these.

Someone described how he would introduce the spread of Christianity among the Germanic peoples.

RUDOLF STEINER: Arian Christianity, expressed in practical life, is very similar to later Protestantism, except that it was less abstract and more concrete. During the first and second centuries the Mithras cult was very widespread among Roman soldiers on the Rhine and the Danube, especially among the officers. In what is now Alsace and elsewhere, Thor, Wotan, and Saxnot were worshipped as the three principal gods of the ancient Germanic people, and the old Germanic religious rites and ceremonies were used.²

We could describe many scenes that demonstrate how the little churches were built in Alsace and the Black Forest by the Roman clerics. “We want to do this or that for Odin” sang the men. The women sang, “Christ came for those who do nothing by themselves.” This trick was actually used to spread Christianity—that by doing nothing one could achieve salvation.

Eiche (the oak), in the old Germanic cult-language, designates the priest of Donar. During the time of Boniface it was still considered very important that the formulas were still known. Boniface knew how to gain possession of some of these formulas; he knew the magic word, but the priest of Donar no longer knew it. Boniface, through his higher power, felled the priest of Donar—the “Donar-oak”—by means of his “axe,” the magic word. The priest died of grief; he perished through the “fire from Heaven.” These are images of imagination. Several generations later this was all transformed into the well-known picture.

You must learn to “read” pictures of this kind, and thus through learning to teach, and through teaching to learn.

Boniface romanized Germanic Christianity. Charles the Great’s biography was written by Eginhard, and Eginhard is a flatterer.

Music teaching was spoken about.

RUDOLF STEINER: Those who are less advanced in music should at least be present when you teach the more advanced students, even if they do not take part and merely listen. You can always separate them later as a last resort. There will be many other subjects in which the situation will be just as bad, in which it will be impossible for the more advanced students to work with those who are backward. This will not happen as often if we keep trying to find the right methods. But due to a variety of circumstances, such things are not obvious now. When you really teach according to our principles you will discover that the difficulties, usually unnoticed, will appear not only in music lessons, but in other subjects as well—for example, in drawing and painting. You will find it very difficult to help some of the children in artistic work, and also in the plastic arts, in modeling.

Here, too, you should try not to be too quick to separate the children, but try to wait until they can no longer work together.

,em>Someone spoke about teaching poetry in French and English [foreign language] lessons.

RUDOLF STEINER: We must stay strictly with speaking a certain amount of English and French with the children right from the beginning—not according to old-fashioned methods, but so that they learn to appreciate both languages and get a feeling for the right expressions in each.

When a student in the second, third, or fourth grade breaks down over recitation, you must help in a kind and gentle way, so that the child trusts you and doesn’t lose courage. The child’s good will must also be aroused for such tasks.

The lyric-epic element in poetry is suitable for children between twelve and fifteen years of age, for example, ballads or outstanding passages from historical writings, good prose extracts, and selected scenes from plays.

Then in the fourth grade we begin Latin, and in the sixth grade Greek for those who want it, and in this way they can get a three-year course. If we could enlarge the school we would begin Latin and Greek together. We shall have to see how we can manage to relieve children who are learning Latin and Greek of some of their German. This can be done very easily, because much of the grammar can be dealt with in Latin and Greek, which would otherwise come into the German lessons. There can also be various other ways.

C was pronounced “K” in old Latin; and in medieval Latin, which was a spoken language, it was C as in “cease.” The ancient Romans had many dialects in their empire. We can call Cicero “Sisero” because in the Middle Ages it was still pronounced like that. We can’t speak of what is “right” in pronunciation because it is something quite conventional. The method of teaching classical languages can be similarly constructed; here, however, with the exception of what I referred to this morning,³ it is usually possible to use the normal contemporary curricula, because they originated in the best educational periods of the Middle Ages, and they still contain much that has pedagogical value for teaching Latin and Greek. Today’s curricula still copy from the old, which makes good sense.

You should avoid one thing, however: the use of the little doggerel verses composed for memorizing the rules of grammar. To the people of today they seem rather childish, and when they are translated into German they are just too clumsy. You must try to avoid these, but otherwise such methods are not at all bad.

Sculpting should begin before the ninth year. With sculpture too, you should work from the forms—spheres first, then other forms, and so on.

Someone asked whether reports should be provided.

RUDOLF STEINER: As long as children remain in the same school, what is the purpose of writing reports? Provide them when they leave school. Constant reports are not vitally important to education. Remarks about various individual subjects could be given freely and without any specific form.

Necessary communication with the parents is in some cases also a kind of grading, but that cannot be entirely avoided. It may also prove necessary, for example, for a pupil to stay in the same grade and repeat the year’s work (something we should naturally handle somewhat differently than is usual); this may be necessary occasionally, but in our way of teaching it should be avoided whenever possible. Let’s make it our practice to correct our students so that they are really helped by the correction.

In arithmetic, for example, if we do not stress what the child cannot do, but instead work with the student so that in the end the child can do it—following the opposite of the principle used until now—then “being unable” to do something will not play the large role it now does. Thus in our whole teaching, the passion for passing judgment that teachers acquire by marking grades for the children every day in a notebook should be transformed into an effort to help the children over and over, every moment. Do away with all your grades and placements. If there is something that the student cannot do, the teachers should give themselves the bad mark as well as the pupil, because they have not yet succeeded in teaching the student how to do it.

Reports have a place, as I have said, as communication with the parents and to meet the demand of the outside world; in this sense we must follow the usual custom. I don’t need to enlarge on this, but in school we must make it felt that reports are very insignificant to us. We must spread this feeling throughout the school so that it becomes a kind of moral atmosphere.

You now have a picture of the school, because we have been through the whole range of subjects, with one exception; we still have to speak about how to incorporate technical subjects into school. We have not spoken of this yet, merely because there was no one there to do the work. I refer to needlework, which must still be included in some way. This must be considered, but until now there was no one who could do it. Of course it will also be necessary to consider the practical organization of the school; I must speak with you about who should teach the various classes, whether certain lessons should be given in the morning or afternoon, and so on. This must be discussed before we begin teaching. Tomorrow will be the opening festival, and then we will find time, either tomorrow or the day after, to discuss what remains concerning the practical distribution of work. We will have a final conference for this purpose where those most intimately concerned will be present. I shall then also have more to say about the opening ceremony.

• 1. Athanasian refers to the doctrine of Saint Athanasius, or Athanasius the Great (c. 293–373), who was a Greek theologian and prelate in Egypt. Throughout his life he opposed Arianism and became known as the “Father of Orthodoxy.” He was exiled three times by Roman emperors for his stand; he wrote Four Orations against the Arians but not the Athanasian Creed (written after the fifth century), which espouses his teachings on the Trinity. The Arian doctrine, on the other hand, has to do with Arius (c. 250–336), also a Greek ecclesiastic in Alexandria, who taught a Neoplatonic doctrine that God is alone and unknowable, the creator of every being, including the Christ. Emperor Constantine I formed the Council of Nicaea in 325 to declare Arianism a heresy.
• 2. This is a reference to Steiner’s lectures on the history of the Middle Ages, given in the Workers’ College in Berlin between October 18 and December 20, 1904 Geschichte des Mittelalters bis zu den großen Erfindungen und Entdeckungen (GA 51).
• 3. See morning lecture pp. 189–190.

My dear friends, it would still be possible, of course, to present many more details from the field of general pedagogy. However, since we are always forced in such cases to conclude prematurely, we will use the remaining time this morning to take our general discussions of education over into an outline of instructional goals for the individual grades. In our general pedagogical studies, we have been trying to acquire the right point of view for dividing up the subject matter with regard to the development of the growing human being. We must always remember the necessity of consolidating our instruction in the way that I demonstrated. For example, we can proceed from mineralogy to geography or use ethnological characteristics to link history and geography when we deal with cultural history in a spiritual way. Bearing in mind this possibility of proceeding from one subject to another, let’s go through the subject matter we want to present to our young charges and divide it into individual categories.

The first thing we need to consider when we welcome children into the first grade is to find appropriate stories to tell them and for them to tell back to us. In the telling and retelling of fairy tales, legends, and accounts of outer realities, we are cultivating the children’s speech, forming a bridge between the local dialect and educated conversational speech. By making sure the children speak correctly, we are also laying a foundation for correct writing.

Parallel to such telling and retelling, we introduce the children to a certain visual language of forms. We have them draw simple round and angular shapes simply for the sake of the forms. As already mentioned, we do not do this for the sake of imitating some external object, but simply for the sake of the forms themselves. Also, we do not hesitate to link this drawing to simple painting, placing the colors next to each other so that the children get a feeling for what it means to place red next to green, next to yellow, and so on.

On the basis of what we achieve through this, we will be able to introduce the children to writing in the way that we have already considered from the perspective of educational theory. The natural way to go about it would be to make a gradual transition from form drawing to the Latin alphabet. Whenever we are in a position to introduce the Latin alphabet first, we should certainly do so, and then proceed from the Latin alphabet to German script. After the children have learned to read and write simple handwritten words, we make the transition to printed letters, taking the Latin alphabet first, of course, and following it up with the German.¹

If we proceed rationally, we will get far enough in the first grade so that the children will be able to write simple things that we say to them or that they compose themselves. If we stick to simple things, the children will also be able to read them. Of course we don’t need to aim at having the children achieve any degree of accomplishment in this first year. It would be completely wrong to expect that. The point is simply that, during the first grade, we should get the children to the point where they no longer confront the printed word as a total unknown, so to speak, and are able to take the initiative to write some simple things. This should be our goal with regard to language instruction, if I may put it like that.

We will be helped in this by what we are going to consider next—namely the elasticity and adaptability that the children’s speech organs can gain from instruction in singing. Without our making a special point of it, they will develop a greater sensitivity to long and short vowels, voiced or voiceless sounds, and so on. Even though this may not be our intention in teaching music, the children will be introduced nonetheless to an auditory understanding of what the instrument of the voice produces in music—in a simple way at first, so that they can get ... well, of course it’s impossible to get an overview of sounds, so I would actually have to invent a word and say: so that they can get an “overhearing” of it. By “overhearing” I mean that they really experience inwardly the single thing among the many, so that they are not overwhelmed by things as they perceive them.

In addition to this we must add something that can stimulate the children’s thinking when we tell them about things that are close at hand, things that will later appear in a more structured form in geography and science. We explain such things and introduce them to the children’s understanding by relating them to things that are already familiar—to familiar animals, plants, and soil formations, or to local mountains, creeks, or meadows. Schools call this “local history,” but the purpose is to bring about a certain awakening in the children with regard to their surroundings; a soul awakening, so that they learn to really connect with their surroundings.

At the beginning of the second grade, we will continue with the telling and retelling of stories and try to develop this further. Then the children can be brought gradually to the point of writing down the stories we tell them. After they have had some practice in writing down what they hear, we can also have them write short descriptions of what we’ve told them about the animals, plants, meadows, and woods in the surroundings.

During the first grade it would be important not to touch on issues of grammar, and so on, to any great extent. In the second grade, however, we should teach the children the concepts of what a noun is, what an adjective is, and what a verb is. We should then connect this simply and graphically to a discussion of how sentences are constructed. With regard to descriptions, to thoughtfully describing their surroundings, we continue with what the children began in the first grade.

The third grade is essentially a continuation of the second with regard to speaking, reading, writing, and many other things. We will continue to increase the children’s ability to write about what they see and read. Now we also try to summon up in them a conscious feeling for sounds that are short, long, drawn out, and so on. It is good to cultivate a feeling for articulating speech and for the general structure of language when the children are in third grade—that is, around the age of eight.² At this point, we attempt to convey an understanding of the different types of words and of the components and construction of a sentence—that is, of how punctuation marks such as commas and periods and so on are incorporated into a sentence.

Once again, with regard to telling and retelling, the fourth grade is a continuation of the third. When we take up short poems in the first and second grade, it’s good to make a point of allowing the children to experience the rhythm, rhyme, and meter instinctively, and to wait to make them aware of the poem’s inner structure--that is, everything that relates to its inner beauty—until the third and fourth grades.

At that point, however, we try to lead everything the children have learned about writing descriptions and retelling stories in writing over into composing letters of all kinds. Then we try to awaken in the children a clear understanding of the tenses, of everything expressed by the various transformations of a verb. At around age nine, the children should acquire the concepts for what they need in this regard; they should get a feeling for it, so that they don’t say “The man ran” when they should have said “The man has run”—that is, that they don’t confuse the past tense with the present perfect. Children should get a feeling for when it is proper to say “He stood” rather than “He has stood,” and other similar things that have to do with transformations in what a verb expresses. In the same way, we attempt to teach the children to feel instinctively the relationship between a preposition and its object. We should always make sure to help them get a feeling for when to use “on” instead of “at,” and so on. Children who are going on ten should practice shaping their native language and should experience it as a malleable element.

In the fifth grade, it is important to review and expand on what we did in the fourth grade, and, from that point on, it is important to take into account the difference between active and passive verb forms. We also begin asking children of this particular age not only to reproduce freely what they have seen and heard, but also to quote what they have heard and read and to use quotation marks appropriately. We try to give the children a great deal of spoken practice in distinguishing between conveying their own opinions and conveying those of others. Through their writing assignments, we also try to arouse a keen distinction between what they themselves have thought, seen, and so forth, and what they communicate about what others have said. In this context, we again try to perfect their use of punctuation. Letter writing is also developed further.

In the sixth grade, of course we review and continue what we did in the fifth. In addition, we now try to give the children a strong feeling for the subjunctive mood. We use as many examples as possible in speaking about these things so that the children learn to distinguish between what can be stated as fact and what needs to be expressed in the subjunctive. When we have the children practice speaking, we make a special point of not allowing any mistakes in the use of the subjunctive, so that they assimilate a strong feeling for this inner dimension of the language. A child is supposed to say, “I am taking care that my little sister learn [subjunctive] how to walk,” and not, “I am taking care that my little sister learns to walk.”³

We now make the transition from personal letters to simple, concrete business compositions dealing with things the children have already learned about elsewhere. Even as early as the third grade we can extend what we say about the meadows and woods and so on to business relationships, so that later on the subject matter is already available for composing simple business letters.

In the seventh grade, we will again have to continue with what we did in the sixth grade, but now we also attempt to have the children develop an appropriate and flexible grasp of how to express wishing, astonishment, admiration, and so on in how they speak. We try to teach the children to form sentences in accordance with the inner configuration of these feelings. However, we do not need to mutilate poems or anything else in order to demonstrate how someone or other structured a sentence to express wishing. We approach it directly by having the children themselves express wishes and shape their sentences accordingly. We then have them express admiration and form the sentences accordingly, or help them to construct the sentences. To further educate their ability to see the inner flexibility of language, we then compare their wishing sentences to their admiring ones.

What has been presented in science will already have enabled the children to compose simple characterizations of the wolf, the lion, or the bee, let’s say. At this stage, alongside such exercises, which are directed more toward the universally human element in education, we must especially foster the children’s ability to formulate practical matters of business. The teacher must be concerned with finding out about practical business matters and getting them into the student’s heads in some sensible fashion.

In the eighth grade, it will be important to teach the children to have a coherent understanding of longer pieces of prose or poetry; thus, at this stage we will read a drama and an epic with the children, always keeping in mind what I said before: All the explanations and interpretations precede the actual reading of the piece, so that the reading is always the conclusion of what we do with the material. In particular, however, the practical business element in language instruction must not be disregarded in the eighth grade.

It will be important that we make it possible for children who have reached the fourth grade to choose to learn Latin. Meanwhile, we will have already introduced French and English [as foreign languages] in a very simple fashion as soon as the children have entered school.

When the children are in the fourth grade, we introduce them to Latin by having them listen to it, and we ask them to repeat little conversations as they gradually gain the ability to do so. We should certainly begin with speaking the language for the children to hear; in terms of speaking, we will attempt to achieve through listening what is usually accomplished in the first year of Latin instruction. We will then take this further according to the indications I gave in the lectures on educational theory, to the point where our eighth-grade graduates will have a mastery of Latin that corresponds to what is ordinarily taught in the fourth year of high school. In other words, our fourth graders must accomplish approximately what is usually taught in the first year of high school and our fifth and sixth graders what is usually taught in the second and third years respectively; the remainder of the time can be spent on what is usually taught in the fourth year.

Parallel to this we will continue with French and English [as foreign language] instruction, taking into account what we heard in the theoretical portion of these lectures.

We will also allow those who choose to study the Greek language to begin doing so. Here too, we proceed in the manner we heard about in the theoretical portion. Specifically, we attempt again to develop the writing of Greek letters on the basis of form drawing. It will be of great benefit to those who now choose to learn Greek to use a different set of letters to repeat the initial process of deriving writing from drawing.

Well, you have seen how we make free use of familiar things from the immediate surroundings for our independent instruction in general knowledge. In the third grade, when the children are going on nine, it is quite possible for this instruction to provide them with an idea of how mortar is mixed, for instance—I can only choose a few examples—and how it is used in building houses. They can also have an idea of how manuring and tilling are done, and of what rye and wheat look like. To put it briefly, in a very free way we allow the children to delve into the elements of their immediate surroundings that they are capable of understanding.

In the fourth grade we make the transition from this type of instruction to speaking about what belongs to recent history, still in a very free way. For example, we can tell the children how it happened that grapes came to be cultivated locally (if in fact that is the case), or how orchards were introduced or how one or the other industry appeared, and other similar things. Then, too, we draw on the geography of the local region, beginning with what is most readily available, as I have already described.

In the fifth grade, we make every effort to begin to introduce the children to real historical concepts. With fifth graders, we need not hesitate at all to teach the children about the cultures of Asian peoples and of the Greeks. Our fear of taking the children back into ancient times has occurred only because people in our day and age do not have the ability to develop concepts appropriate to these bygone times. However, if we constantly appeal to their feelings, it is easy enough to help ten- and eleven-year-olds develop an understanding of the Greeks and Asian peoples.

Parallel to this, as I showed you earlier, in geography we begin to teach the children also about soil formations and everything that is economically related to them, dealing first with the specific part of the Earth’s surface that is most readily available.

Greek and Roman history and its aftereffects (until the beginning of the fifteenth century) belong to the sixth grade. In geography we continue with what we did in the fifth grade, taking a different part of the Earth and then linking its climatic conditions to astronomical conditions, examples of which we experienced yesterday afternoon.

In the seventh grade, it is important to get the children to understand how the modern life of humanity dawned in the fifteenth century, and we then describe the situation in Europe and so on up to about the beginning of the seventeenth century. This is one of the most important historical periods, and we must cover it with great care and attention. Indeed, it is even more important than the time immediately following it. In geography, we continue with the study of astronomical conditions and begin to cover the spiritual and cultural circumstances of Earth’s inhabitants, of the various ethnic groups, but always in connection with what the children have already learned about material cultural circumstances—that is, economic circumstances—during their first two years of geography lessons.

In the eighth grade, we try to bring the children right up to the present in history, including a thorough consideration of cultural history. Most of what is included in history, as it is ordinarily taught, will only be mentioned in passing. It is much more important for children to experience how the steam engine, the mechanized loom, and so on have transformed the Earth than it is for them to learn at too young an age about such curiosities as the corrections made to the Emser Depesche.⁴ The things our history books contain are the least important as far as the education of children is concerned. Even great figures in history, such as Charlemagne, should basically be covered only in passing. You will need to do a lot of what I told you yesterday about aids to guiding abstract concepts of time over into something concrete. Indeed, we must do a very great deal of it.

Now I probably do not need to tell you that even the subjects we have discussed so far will help the children develop an awareness of the spirit that permeates everything present in the world, an awareness that the spirit lives in our language, in the geographical elements covering the Earth, and in the flow of history. When we try to sense the living spirit in everything, we will also find the proper enthusiasm for conveying this living spirit to our students.

Whenever we do this, we will learn to compensate our students for what the religious denominations have been doing to humanity since the beginning of the modern era. These religious denominations, which have never made the free development of the individual a priority, have cultivated materialism from various angles. When it is not permissible to use the entire content of the world to teach people that the spirit is active, religious instruction becomes a breeding ground for materialism. The various religious denominations have made it their task to eliminate all mention of spirit and soul from any other form of instruction because they want to keep that privilege for themselves. Meanwhile the reality of these things has dried up as far as the religious denominations are concerned, and so what is presented in religious instruction consists merely of sentimental clichés and figures of speech. All the clichés that are now so terribly apparent everywhere are actually due more to religious culture than to international culture, because nowadays the emptiest clichés, which human instincts then carry over into outer life, are being promoted by the religious denominations. Certainly ordinary life also creates many clichés, but the greatest sinners in this respect are the religious denominations.

It remains to be seen, my dear friends, how religious instruction—which I will not even touch on in these discussions, because that will be the task of the congregations in question—will affect other types of instruction here in our Waldorf school. For now religious instruction is a space that must be left blank; these hours will simply be given over to the religion teachers to do whatever they choose. It goes without saying that they are not going to listen to us. They will listen to their church’s constitution, or to their church gazette or that of the parochial school administration. We will fulfill our obligations in this respect, but we will also quietly continue to fulfill our obligation to summon up the spirit for our children in all the other subjects.

• 1. Steiner is referring here to the fact that the German language at that time was written in Fraktur, a specifically Germanic style of print and handwriting, rather than in the Latin, or Roman, alphabet now universally used for Western European languages.—TRANS.
• 2. The German translates literally as “in their eighth or ninth year” and is sometimes mistranslated in English as “eight or nine years old”; thus references to beginning school in “the seventh year” can be taken to mean that “children shouldn’t go to school until they are seven.” What Steiner said, however, was “in the seventh year of their life—that is, “six-going-on-seven.”—TRANS.
• 3. These distinctions are not as readily detected in current English. In Steiner’s example, the difference is between lerne and lernt; the first is perhaps closest to the process of learning (not yet fact), the second to having learned (fact).
• 4. Emser Depesche: An incident that touched off the Franco-Prussian War of 1870. Bismark publicized an abridged and misleading version of a telegram (known as the “Ems Dispatch”), and the effect of this action was to feed the fury of the opposing parties in France and Prussia.

Now it’s time to divide up the rest of the subjects and distribute them among the various grades.

It should be very clear that when the children are going on nine—that is, in the third grade—they should begin to study an appropriate selection of animals, which we must always relate to the human being, as in the example I presented to you.¹ This should be continued in the fourth grade, so that during the third and fourth grades we consider the animal kingdom scientifically in its relationship to the human being.

In the fifth grade, we begin to add less familiar animals. We also begin the study of botany as I described it in the theoretical portion of our seminar.² In the sixth grade, we continue with botany and begin the study of minerals, which should definitely be done in conjunction with geography.

In the seventh grade we return to the human being and attempt to teach what I pointed to yesterday with regard to what people need to learn about health and nutrition. We also attempt to apply the concepts the children have acquired in the fields of physics and chemistry to developing a comprehensive view of some specific commercial or industrial processes. All this should be developed out of science, in connection with what we are teaching in physics, chemistry, and geography.

In the eighth grade you will have to construct the human being by showing what is built in from the outside—the mechanics of the bones and muscles, the inner structure of the eye, and so on. Once again, you present a comprehensive picture of industrial and commercial relationships as they relate to physics, chemistry, and geography. If you build up your science lessons as we have just described, you will be able to make them incredibly lively and use them to awaken the children’s interest in everything present in the world and in the human being.

Instruction in physics begins in the sixth grade and is linked to what the children have learned in music. We begin the study of physics by allowing acoustics to be born out of music. You should link acoustics to music theory and then go on to discuss the physiology of the human larynx from the viewpoint of physics. You cannot discuss the human eye yet, but you can discuss the larynx. Then, taking up only the most salient aspects, you go on to optics and thermodynamics. You should also introduce the basic concepts of electricity and magnetism now.

The following year, in the seventh grade, you expand on your studies of acoustics, thermodynamics, optics, electricity, and magnetism. Only then do you proceed to cover the most important basic concepts of mechanics—the lever, rollers, wheel and axle, pulleys, block and tackle, the inclined plane, the screw, and so on. After that you start from an everyday process such as combustion and try to make the transition to simple concepts of chemistry.

In the eighth grade you review and expand upon what was done in the seventh and then proceed to the study of hydraulics, of the forces that work through water. You cover everything belonging to hydraulics—water pressure, buoyancy, Archimedes’ principle.

It would be great if we could stay here for three years giving lectures on education and providing examples of all the things you will have to figure out how to do yourselves out of your own inventiveness, but that can’t be. We will have to be content with what has already been presented.

You conclude your study of physics, so to speak, with aerodynamics—that is, the mechanics of gases—discussing everything related to climatology, weather, and barometric pressure. You continue to develop simple concepts of chemistry so that the children also learn to grasp how industrial processes are related to chemical ones. In connection with chemical concepts, you also attempt to develop what needs to be said about the substances that build up organic bodies—starch, sugar, protein, and fat.

We must still apportion everything related to arithmetic, mathematics, and geometry and distribute it among the eight grades.

You know that standard superficial methodology dictates that in the first grade we should deal primarily with numbers up to 100. We can also go along with this, because the range of numbers doesn’t really matter in the first grade, where we stick with simpler numbers. The main issue, regardless of what range of numbers you use, is to teach the arithmetical operations in a way that does justice to what I said before: Develop addition out of the sum, subtraction out of the remainder, multiplication out of the product and division out of the quotient—that is, exactly the opposite of how it’s usually done. Only after you have demonstrated that 5 is 3 plus 2, do you demonstrate the reverse—that adding 2 and 3 yields 5. You must arouse in the children the powerful idea that 5 equals 3 plus 2, but that it also equals 4 plus 1, and so on. Thus, addition is the second step after separating the sum into parts, and subtraction is the second step after asking “What must I take away from a minuend to leave a specific difference?” and so on. As I said before, it goes without saying that you do this with simpler numbers in the first grade, but whether you chose a range of up to 95 or 100 or 105 is basically beside the point.

After that, however, when the second dentition is over, we can immediately begin to teach the children the times tables—even addition, as far as I’m concerned. The point is that children should memorize their times tables and addition facts as soon as possible after you have explained to them in principle what these actually mean—after you have explained this in principle using simple multiplication that you approach in the way we have discussed. That is, as soon as you’ve managed to teach the children the concept of multiplication, you can also expect them to learn the times tables by heart.

Then in the second grade you continue with the arithmetical operations using a greater range of numbers. You try to get the students to solve simple problems orally, in their heads, without any writing. You attempt to introduce unknown numbers by using concrete objects—I told you how you could approach unknown numbers using beans or whatever else is available. However, you should also not lose sight of doing arithmetic with known quantities.

In the third grade everything is continued with more complicated numbers, and the four arithmetical operations practiced during the second grade are applied to certain simple things in everyday life.

In the fourth grade we continue with what was done in the earlier grades, but we must now also make the transition to fractions and especially to decimal fractions.

In the fifth grade, we continue with fractions and decimals and present everything the children need to do independent calculations involving whole numbers, fractions, and decimals.

In the sixth grade we move on to calculating percentages, interest, discounts and the interest on promissory notes, which then forms the basis for algebra, as we have already seen.

I ask you to observe that, until the sixth grade, we have been deriving the geometric shapes—circle, triangle, and so on—from drawing, after having done drawing for the sake of writing in the first few years. Then we gradually made the transition from drawing done for the sake of writing to developing more complicated forms for their own sake—that is, for the sake of drawing, and also to do painting for the sake of painting. We guide instruction in drawing and painting into this area in the fourth grade, and in drawing we teach what a circle is, what an ellipse is, and so on. We develop this out of drawing. We continue this by moving on to three-dimensional forms, using plasticine if it’s available, and whatever else you can get if it isn’t—even if it’s mud from the street, it doesn’t matter! The point is to develop the ability to see and sense forms.

Mathematics instruction, geometry instruction, then picks up on what has been taught in this way in the drawing classes. Only then do we begin to explain in geometrical terms what a triangle, a square, or a circle is, and so on. That is, the children’s spatial grasp of form develops through drawing. We begin to apply geometrical concepts to what they have learned in this way only once they are in the sixth grade. Then we have to make sure that we do something different in drawing.

In the seventh grade, after making the transition to algebra, we teach raising numbers to powers and extracting roots, and also what is known as calculating with positive and negative numbers. Above all, we try to introduce the children to what we might call practical, real-life applications of solving equations.

We continue this in the eighth grade and take the children as far as they can get with it. We also add calculating areas and volumes and the theory of geometrical loci, which we at least touched upon yesterday.

This gives you a picture of what you have to do with the children in mathematics and geometry.

As we have already seen, in the drawing lessons in the first few grades, we first teach the children to have a specific feeling for rounded or angular forms, and so on. From these forms, we develop what we need for teaching writing. In these very elementary stages of teaching drawing, we avoid imitating anything. As much as possible, you should initially avoid allowing the children to copy a chair or a flower or anything else. As much as possible, you should have them produce linear forms—forms that are round, pointed, semicircular, elliptical, straight, and so on. Awaken in the children a feeling for the difference between the curve of a circle and the curve of an ellipse. In short, awaken their feeling for form before their urge to imitate wakes up! Wait until later before allowing them to apply what they have practiced in drawing forms to imitating actual objects. First have them draw angles so that they understand what an angle is through its shape. Then you show them a chair and say, “Look, here’s an angle, and here’s another angle,” and so on. Do not let the children imitate anything until you have cultivated their feeling for independent forms which can be imitated later. Stick to this principle even when you move on to a more independent and creative treatment of drawing and painting.

Then in the sixth grade you introduce simple projection exercises and drawing shadows, both freehand and with a ruler and compass and the like. Make sure that the children have a good grasp of the concept and can reproduce in their drawings what the shadow of a sphere looks like on the surface of a cylinder if the cylinder is here and the sphere here and a light is shining on the sphere:

Yes, how shadows are cast! So a simple study of projection and shadows must take place in the sixth grade. The children must get a conception of it and must be able to imitate how more or less regular shapes or physical objects cast their shadows on flat and curved surfaces. In their sixth school year the children must acquire a concept of how the technical aspect unites with the element of beauty, of how a chair can be technically suited for a certain purpose while also having a beautiful form. The children must acquire both a concept and a handson grasp of this union of the technical and the beautiful.

Then, in the seventh grade, everything having to do with one object penetrating another should be covered. As a simple example, you might say, “Here we have a cylinder with a post running through it. The post has to go through the cylinder.” You must demonstrate what kind of a shape the post cuts in the surface of the cylinder when it enters and exits. This is something to learn together with the children. They must learn what happens when objects or surfaces interpenetrate, so that they know that it makes a difference whether a stovepipe goes through the ceiling at a right angle, in which case their intersection is a circle, or at an angle, in which case it is an ellipse. In addition, this is the year when the children must be taught a good conception of perspective. So you do simple perspective drawing with objects foreshortened in the distance and elongated in the foreground, and you draw objects that are partially concealed and so on. Once again, you combine the technical aspect with beauty, so that you awaken in the children an idea of whether or not it is beautiful when some portion of a wall of a house is concealed by a projection, let’s say. Some such projections are beautiful and others are not. These things have a pronounced effect when they are taught to seventh graders in particular—that is, to thirteen- or fourteen-year-olds.

In the eighth grade, all this is raised to an artistic level. All the other subjects must be handled similarly to the ones we have discussed. We will come back to this in the afternoon and still add a few things to complete our curriculum. Above all, we will have to see how music is developed in the first grade out of elements that are as simple and elementary as possible, and how from the third grade on the transition is made to more complicated things. The point is that the children should be able to take in those aspects of playing an instrument—especially of playing an instrument, but also of singing—that have a creative and formative effect on their capabilities.

As special cases among all the other artistic subjects, we will have to emphasize gymnastics and eurythmy, which must both be developed out of the element of music and the other arts.

• 1. See Practical Advice to Teachers, Rudolf Steiner Press, London, 1988, lecture 7.
• 2. See discussion 9, page 114.

This morning it was pointed out that we can give only general guidelines for music, just as it is possible to give only general guidelines for the visual arts. The details, of course, must be left to the teacher’s independent initiative. If you take these general guidelines in the right way, you will find that, basically, they are able to incorporate whatever you may find reasonable as musical instruction.

In the first, second, and third grades, we will essentially be dealing with very simple musical relationships, which should be applied with a view to developing the human voice and listening ability—that is, we should use the element of music to call upon the individual to use the human voice and the element of sound properly, and also to listen appropriately. I’m sure we all understand this.

Then come the fourth, fifth, and sixth grades. By then we will already be involved in explaining musical notation and will be able to do comprehensive scale exercises. Especially in the fifth and sixth grades, we will be able to go into the different keys and talk about D major and so on. We should wait as long as possible before introducing the minor keys, but by this point they too can be presented to the children.

However, the important thing now is to work from the opposite of our original point of view—that is, to get the children to adapt to the demands of music. This means leaning more toward the esthetic in our teaching. At first the children themselves were the focus, and we had to structure everything so that they would learn to listen and sing. But after having been encouraged in this during the first three grades, the children should then begin to adapt to the artistic demands of music, and the pedagogical element becomes the focus.

In the last two elementary grades—the seventh and eighth—I ask you to take into consideration the fact that the children must no longer have the feeling that they are being “trained” to do something, but must feel that they are making music for the pleasure it gives them, for the sake of enjoying it. This must be the thrust of our instruction in music. Therefore, during these two years the children’s musical judgment can be awakened and educated. We can make them aware of the different character of different pieces of music, of the difference in character between a work by Beethoven and a work by Brahms. In simple ways, therefore, we should encourage the children to form opinions about music. Earlier, it was important to refrain from such opinions and judgments, but now we must cultivate them.

Now it will be especially important to understand one thing. You know I said something very similar this morning about the visual arts—that the way we initially use drawing allows writing to develop out of it. Later, however, drawing is used as an end in itself, and art itself becomes the important thing. As soon as the children progress from utilitarian forms of drawing and painting to developing independent artistic forms—in the third or fourth grade—it is also time to make the musical transition just described. At first we must work to affect the children physiologically; our work must help them adapt to the art of music. There should be a correspondence between these transitions in the graphic arts and in music.

One thing in the state curriculum is to our advantage—that there is no physical education instruction during the first three grades. So we may take the opportunity to begin with eurythmy. It would be very nice if eurythmy could be done in harmony with music instruction in the first grade, so that eurythmy would in fact help the children adapt to geometry and music. Not until the second grade would we begin to develop the gestures for the letters. This would be continued in the third grade, always linking eurythmy to music, geometry, and drawing.

Forms are added in the fourth, fifth, and sixth grades—for concrete and abstract expressions, and so on—since by now the children will have made enough progress in grammar to make this possible. This is continued in the seventh and eighth grades, but the forms become more complicated.

Starting in the fourth grade, this slot in the schedule is divided between eurythmy and physical education. In the fourth, fifth, and sixth grades, instruction in physical education should focus on the movement of the limbs and include everything that has to do with running, jumping, and climbing. Any exercises on gymnastic apparatus should be kept simple.

More complicated exercises involving equipment should not be done until the seventh and eighth grades. Meanwhile, the freeform exercises should be continued, and they should still all involve running, climbing, and jumping. If you go through all of what you’ve been able to conclude, I’m sure you will find that it agrees with the way I have tried to present this.