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The Rudolf Steiner Archive

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Search results 5611 through 5620 of 6552

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295. Discussions with Teachers: Discussion Thirteen 04 Sep 1919, Stuttgart
Translated by Helen Fox, Catherine E. Creeger

Interest = Principal × Rate × Time $$I = \frac{PRT}{100}$$ 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.
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.
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.
295. Discussions with Teachers: Discussion Fourteen 05 Sep 1919, Stuttgart
Translated by Helen Fox, Catherine E. Creeger

In this way multiplication can easily be developed and understood from addition, and you thus make the transition from actual numbers to algebraic quantities: \(a × a = a2\), \(a × a × a = a3\).
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.
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.
295. Discussions with Teachers: First Lecture on the Curriculum 06 Sep 1919, Stuttgart
Translated by Helen Fox, Catherine E. Creeger

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.
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.
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.
295. Discussions with Teachers: Second Lecture on the Curriculum 06 Sep 1919, Stuttgart
Translated by Helen Fox, Catherine E. Creeger

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.
295. Discussions with Teachers: Third Lecture on the Curriculum 06 Sep 1919, Stuttgart
Translated by Helen Fox, Catherine E. Creeger

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.
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.
295. Discussions with Teachers: Closing Words 07 Sep 1919, Stuttgart
Translated by Helen Fox, Catherine E. Creeger

The time has been so short that, for the rest, I must simply appeal to the understanding and devotion you will bring to your work. Turn your thoughts again and again to all that has been said that can lead you to understand the human being, and especially the child.
296. Education as a Social Problem: Historical Requirements of the Present Time 09 Aug 1919, Dornach
Translated by Lisa D. Monges, Doris M. Bugbey

This idea is not the result of a brainstorm, it is something born of the deepest needs of our age, something that corresponds in the highest degree to our present time. There are many people who say they do not understand this, that it is very difficult. In Germany, when people said over and over that these things are difficult to understand, I said to them that I certainly do make a distinction between these ideas and what one has become accustomed to understand during the last four or five years. There one thought it easy to understand things I could not understand—so I said—things that merely had to be commanded to be understood. The Supreme Headquarters or another place of authority commanded that matters had to be understood, then they certainly were crammed into one's head. They were understood because one was commanded to understand.
296. Education as a Social Problem: The Social Structure in Ancient Greece and Rome 10 Aug 1919, Dornach
Translated by Lisa D. Monges, Doris M. Bugbey

If we wish to understand the task of the anthroposophical science of the spirit in the present and immediate future we must consider the character of mankind's evolution since the middle of the fifteenth century.
This was not possible, nor was it the task of mankind in earlier epochs of our post-Atlantean evolution. If we want to understand this great change in the middle of which we find ourselves, we must focus our attention still more precisely upon such matters as I characterized yesterday.
No attention is paid to this in modern history, which is a fable convenue, as I have often stated. Whoever is able to understand the concepts of mankind prior to the middle of the fifteenth century knows that they were full of imagery, that they actually were imaginations.
296. Education as a Social Problem: Commodity, Labor, and Capital 11 Aug 1919, Dornach
Translated by Lisa D. Monges, Doris M. Bugbey

I should like to speak briefly about three concepts which, if they are fully understood, can bring about an understanding of outer social life. I say expressly outer social life because these three concepts originate from people's cooperation in outer affairs.
He was of the opinion that not only the views I had advanced but also those to be found in my books, are infantile. Well, I understand such a judgment. I understand it especially well when the man is a university professor. I understand it for the reason that science, which he represents, has quite lost all imaginative life and considers infantile what it does not comprehend.
This indeed is how it must happen. What is a commodity will be feelingly understood by a science that gains understanding through pictures, and by no other science. In the society of the future a proper understanding of labor will have to be a dominating element.
296. Education as a Social Problem: Education as a Problem Involving the Training of Teachers 15 Aug 1919, Dornach
Translated by Lisa D. Monges, Doris M. Bugbey

From the various matters we have considered here you will have gathered that among the many problems under discussion today that of education is the most important. We had to emphasize that the entire social question contains as its chief factor, education.
What man is as an active being is externally brought to completion in the physical configuration of these three members of his whole organism: Head-man, or nerve-sense man; Chest-man, or rhythmical man; Limb-man, or metabolic man. It is important to understand the differences between these three members, but this is very uncomfortable for people today because they love diagrams.
Whereas the egotistical point of view makes man more and more abstract, theoretical, and inclines him toward head-thinking, the unegotistical point of view urges him to understand the world with love, to lay hold of it through love. This is one of the elements which must be taken up in teacher training; to look at prenatal man, and not only feel the riddle of death but also the riddle of birth.

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