Dr. Robert Duncan-Enzmann, 1949
“On Education: With an emphasis on the careful education of the gifted, for he or she is the one that needs and can best utilize knowledge for the good of all.” – Doc E.
One might ask just what intelligence is. What is this state which is assumed to be so important? Is it real, tangible, and measurable?
Intelligence is indeed real. Intelligence is tangible, measurable, and in the case of mankind, very important.
We might define intelligence as the ability to see the relationships between cause and effect, to see a situation in reality through an examination of its parameters, much as one theorizes on space lattices of crystalline substances by an examination of X-ray diffraction pictures or parameters, or to be able to project information and experience gained in the past to the future, to better deal with that future.
Intelligence is indeed measurable, as may be seen in Lewis M. Terman’s books: The Measurement of Intelligence, Gifted Child Grows Up, Intelligence of School Children, and Mental and Physical Traits of a Thousand Gifted Children. We might think of intelligence as the function of an entity that works better in some than in others because of differences in the construction of the entities – the differences being primarily due to heredity and somewhat due to the environment.
When children are taught to read, they are usually first taught to read letters, then words, phrases, and paragraphs. Reading should be a rapid process; it should be something that is much faster than any human voice could function. Persons should be taught not to read for letters and words but solely for ideas.
One of the most beautiful devices ever thought of for teaching is now in my possession. It is a tachistoscope; it will project words, numbers, sentences, etc., on a screen for periods that will permit only one eye fixation.
Long practice with this apparatus teaches one to read a great amount very quickly and use more than just the eye’s yellow spot. I also believe that it teaches one to use his memory much better and tends to develop the photographic memory. A child with a little practice, say six weeks, can easily remember 36 digits when flashed on a screen for only 1/100th of a second, which permits only one eye fixation.
Repetition is the mother of learning, as the old Latins used to say. Indeed, this is true, and things learned by rote are, when coupled with comprehension, indispensable to quick thinking.
Strangely, repetition by rote is not the only repetition that is helpful to learning. Things repeated over and over when one is sleeping is also useful and will be learned quickly when the sleeper is awake.
For teaching good music and the laws of harmony, or perhaps the multiplication tables and mathematical formulas, or real knowledge of a foreign language, a magnetic recorder placed in her room and run for several hours each night would be most valuable.
In this modern age of enlightenment, the idea of learning by rote is abhorred by many. They prefer to teach one to figure things out. Nothing could be more false. One does not increase the ability to figure things out. The I.Q. is a native capacity. This largely unchangeable I.Q. may only be brought in contact with methods that will aid and equip with systems of knowledge that will act as filing cabinets to work within stock situations.
For this reason, I recommend the teaching by rote of all the multiplication tables up to twenty times twenty. Few persons know it, and it is something needed.
The I.Q. is native. Show it generally helpful methods. Equip it with useful stock answers.
In educating the gifted, those born with a naturally higher I.Q. and therefore ability to think better than the average man – just as racehorses can run faster than truck horses – no expenses should be spared. These persons should have the best that their civilization can provide for their education – in lighting, food, desks, clothes, books, maps, etc. It is justice that these should receive the best because it is to them and not to the masses that humanity owes all its progress. To be sure, in prehistoric times and semi historic times, this progress was due to these intelligent creatures who killed the less cunning or survived disasters where the others perished through lack of cunning. This is not true now, the cunning are not allowed to kill the less cunning, and neither is nature because it would cause chaos in our mechanized world. The less brainy are needed for laborers, clerks, machinists, technicians, etc., in the intelligence pyramid that runs our civilization. The men with high I.Q.s have built a machine that the others can run; however, this machine is not perfect. It can be improved, and only the intelligent can do this work, which will better the lot of all men.
With the facts above in mind, we can see why it is valuable to all of mankind to educate the gifted before all others, so we may all benefit from their superior powers. Certainly, everyone should be educated as well as he can be, but everyone has a limit. Some persons and they are very few, have limits that cannot be measured, but most of the world’s people have a very low mentality and can only absorb a very little bit of the available knowledge. It is unfair to the world to spend great sums on the defectives and neglect the superior because they can shift for themselves or because of some skewed social philosophy. This is unfair to all humanity. People should always be treated in order of their actual importance and not according to their relative weaknesses.
Words change in meaning as time goes on. Dictionaries are made by using a word in ten or twelve typical sentences and deriving a brief meaning from considering them all. There are one thousand words in common use; the average man recognizes five thousand words. The very intelligent man recognizes fifty to one hundred thousand words, and there are a little over a million words in the English language.
When children have finished learning to read and are reading to learn, they begin to use dictionaries. We have some very useful and well-made dictionaries, but they are not yet all that could be desired. For one thing, the dictionaries in a schoolroom should be graded, a simple dictionary, and an intermediate dictionary, and in addition to those two a large dictionary that defines the word. The extensive dictionary should give the history of the word, its roots, Indo-European or other, the language branch it followed, such as Teutonic, Latin, or Slavic, the routes and changes it underwent, including change in its sound and the laws that it followed. All comparisons should be given in the original alphabets with translations. The book should be illustrated.
The first two dictionaries would be relatively cheap. The third would be very expensive if, indeed, it even exists. It would be worth the price, even if it were infrequently used for the reading of this work, it would be entertaining and very educational. By being exposed to such work for many years before studying philology, a smattering of the science would already be learned.
Recognition of Deadwood and Excessive Emphasis on Unimportant Collateral
It would be very healthy for the modern educators if, once in a while, they would read a history of the development of mathematics, physics, medicine, etc., with mathematics as probably the best to observe. Along with a reading of the history of the development of mathematics, educators should study the history of the teaching of these subjects. I mean precisely that they should study the old textbooks and compare them with those of today.
Such a study would lead to a revelation: Mathematics has progressed somewhat since the day of the Greeks; the methods of teaching mathematics have also changed somewhat. Instead of requiring a lifetime to study and comprehend geometry, Euclid’s geometry is finished in the second year of high school. The student is released to study such things as calculus and the new algebra in college. We learn more in a lifetime!
Now, unless we concede that we have reached the ultimate in mathematics or that the human being will have a life of several centuries in a few more decades, we will have to simplify our teaching methods. The deadwood and useless proofs will have to be rejected or simplified. With a few simplifications, the calculus could be finished in high school, releasing the student for other studies.
Personal vanity plays a great part in the publishing of textbooks. Instead of being satisfied with improving the old textbooks, men are forced by their vanity to write more and more books. Undoubtedly this is valuable to science, but there should also be a body of men that look at a textbook and continually improve it through the generations. They should carefully improve the text and illustrations, simplify the proofs adding detail where the books are hazy, slowly improving the work – always and exclusively with an eye to the student’s psychology. Every effort must be toward an appealing text and a book that gives the truth – symbols for nature’s behavior.
Another factor that writers should keep in mind is their pupils’ vanity – vanity being in men and mankind. This also will make the textbooks more pleasing.
On Writing Simple Textbooks
Hundreds of thousands of books are written every year. How many will survive? Perhaps one in one hundred years; this is true for both literary and scientific texts. However, a scientific book fragment may survive for many thousands of years because of its fundamentalness and excellent symbolic representation of nature – the real process.
The literary books survive because of their accurate depiction of man and his ways. Perhaps twenty books per thousand years will endure. The scientific books or methods, such as the Arabic numbers, survive because of their simplicity. Nature is simple, and humans try to make simple symbols for it. As soon as a valid and new symbology system that is simpler than the old appears, the ancient and complicated symbology – epicycles – begins to fade from the scene.
Great men show extreme simplicity in their thinking. It gives them an advantage. Simplicity is something that should be followed in textbooks. Everything should be explained in the sort of language that a little child could understand. The text should be something that can be read with ease and pleasure. No steps should be left out; the whole process in every case should be given.
Another factor should be considered along with simplicity, and that is constant reference to fundamentals. The knowledge of mankind is not very extensive, and it is self-flattery for a teacher to think that he is so far along the road that it is impossible to refer back constantly. He should do this. In all branches of mathematics, the very fundamentals should be reviewed from the bottom up when presenting a new problem, such as giving a lesson in tensors and building up briefly from the Pythagorean theorem.
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