Thinking and learning to think by Nathan C. Schaeffer (ebooks that read to you .txt) đź“–
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THINKING IN THINGS AND IN SYMBOLS
The rote system, like other systems of its age, made more of forms and symbols than of the things symbolized. To repeat the words correctly was everything, to understand the meaning nothing; and thus the spirit was sacrificed to the letter.
Herbert Spencer.
Words are men’s daughters, but God’s sons are things.
Johnson.
For words are wise men’s counters,—they do but reckon by them,—but they are the money of fools.
Hobbes.
It is only by the help of language (or some other equivalent set of signs) that we can think in the strict sense of the word; that is to say, consider things under their general or common aspects.
Sully.
IITHINKING IN THINGS AND IN SYMBOLS
Within half a mile of the Susquehanna River a teacher was asking the class, “Of what is the earth’s surface composed?” “Of land and water,” was the reply. In answer to a question by the superintendent concerning the earth’s surface, one boy declared that he had never seen the earth. He had been acquiring words without the corresponding ideas. Turning to another boy, this official said, “Will you please show me water?” With a gleam of satisfaction on his face, the lad raised his atlas, pointed to the blue coloring around the map of North America, and said, “That is water.” “Will you please drink it?” The expression on the faces of teacher and pupils indicated that all felt as if some one had committed a blunder. Where did the blunder lie? Had the teacher taught what should not be learned? Surely, every child should learn how water is indicated on a map. Did the boy use language wrong in idiom? By no means; for, as every student who has handled a lexicon well knows, many words have both a literal and a tropical, or figurative, meaning. If, pointing to an object, the teacher says, “This is a desk,” he uses the word is in its literal sense. On the other hand, if he points to a division on the map of the United States, and says, “This is Pennsylvania,” he does not mean that the colored surface to which he is pointing is the real State of Pennsylvania (if it were, a political boss could pocket it, and carry it the rest of his days without further trouble). What is meant is, that a given space on the map indicates or represents Pennsylvania, the word is being used, in the latter instance, in a figurative sense. Whether the word is, in the expression, “This is my body,” should be understood in a literal or in a figurative sense has been discussed for ages in the Christian church. In the answer of the boy we strike a distinction in thought that lies at the basis of good teaching in all grades of schools, from the kindergarten to the university,—namely, the distinction between thinking in things and thinking in symbols. In one sense of the word, all thinking is symbolic; for the percepts, concepts, and images of external objects which the mind employs in the thinking process are symbolic of the things for which they stand. But in advanced thinking, and especially in scientific investigations, objective symbols, such as words, signs, letters, equations, formulas, technical terms and expressions, are utilized to facilitate the thinking process. Take the age questions in mental arithmetic that have been prematurely inflicted upon so many pupils in the public schools. So long as the mind consciously carries A’s age and the wife’s age, using the clumsy instruments of arithmetical analysis, the thinking is difficult indeed. As soon as x is made the symbol of A’s age, and y the symbol of the wife’s age, so that the conditions of the problem can be thrown into algebraic equations, the difficulty vanishes. In the algebraic solution the mind drops all thought of A’s age and the wife’s age while manipulating the signs and symbols of the equation, and restores the meaning of the symbols only when their value in figures has been found. The algebraic solution is a genuine specimen of thinking in symbols, and illustrates the labor-saving machinery which the human mind employs, more or less, in all the most difficult scientific investigations.
What is a symbol? It is a mark, sign, or visible representation of an idea. The mathematician uses the symbol to represent quantities, operations, and relations. The chemist uses the symbol to indicate elements and their groupings or combinations. The theologian applies the term symbol to creeds and abstract statements of doctrine. The grips, countersigns, and passwords of a secret society may be spoken of as symbols of the ideas, aims, and principles of the organization. Often the symbol is chosen on account of some supposed resemblance between it and that for which it stands, as when black is made the symbol of mourning, white of purity, the oak of strength, and the sword of slaughter. “A symbol,” says Kate Douglass Wiggin, “may be considered to be a sensuous object which suggests an idea, or it may be defined as the sign or representation of something moral or intellectual by the images or properties of natural things, as we commonly say, for instance, that the lion is the symbol of courage, the dove the symbol of gentleness. It need not be an object any more than an action or an event, for the emerging of the butterfly from the chrysalis may be a symbol of the resurrection of the body, or the silver lining of the cloud typify the joy that shines through adversity.” Frequently the symbol is chosen arbitrarily, or because it is the first letter of the word which denotes the quality, substance, thing, or idea for which the symbol stands. Generally the symbol is a visible representation, but it may also address the other senses, notably the ear and the sense of touch. The Standard Dictionary excludes the portrait from the extent or scope of the symbol, and confines it to the representation of that which is not capable of portraiture, as an idea, state, quality, or action. It is well to bear this limitation in mind during the present discussion.
A few illustrations will serve to fix the sense of the word symbol. In some parts of America the tramps have a system of symbols of their own, a given mark on the front gate indicating a good place to ask for a meal, another indicating a cross dog in the rear yard. That which the tramp fears or likes is not the mark which he sees, but a very real thing which that mark suggests to his mind. A number of the apostles were fishermen by trade. The fish became a very significant symbol in the days of early Christianity. The letters in the Greek name for fish are the initial letters of the expression, Jesus Christ, God’s Son, Saviour. It is one of many instances showing how the human mind delights in heaping symbol upon symbol to conceal precious meanings from the uninitiated.
What was the mental condition of the lad spoken of at the beginning of this chapter? The boy knew the real thing long before he knew the first symbol for water. Without doubt he had tasted it, played in it against his mother’s will, been washed in it against his own will, for months before he learned the first symbol for water used in common by him and others, which was probably the spoken word. Up to that time he thought of water in some mental picture or image which had been formed upon the eye and then upon mind somewhat as the picture is formed through the art of the photographer. Up to the time that he learned the spoken word for water this liquid suggested mental pictures which constituted a thinking in things[1] rather than in symbols, using the latter term according to the limitation set by the Standard Dictionary. On entering school he was taught to read; he added to the ear-symbol the eye-symbol,—that is, the written or printed word, which he may have associated at first with the real thing, or with the spoken word; of course, very soon with both, if correct methods of teaching were followed. Next, he was taught the map-symbol. The blunder which the teacher on the banks of the Susquehanna had committed consisted not in teaching how water is indicated on a map, but in not pointing to the majestic river near the school-house, and associating the water in its channel with the representations of water on a map. If the boy studied Latin or Greek, he was taught new symbols for water in the corresponding words of these languages. If he studied chemistry, he early learned the composition of water, and was thenceforth taught to write it H₂O, a symbol enshrining a new truth and lifting him to higher planes of thought by giving him a new instrument as well as new materials of thought.
Half the errors in teaching arise from the fact that the teacher does not constantly bear in mind the distinction between the symbol and the thing for which the symbol stands, thus giving rise to confusion in the mind of the learner. A class was bounding the different States of the Union. At the close of the recitation the superintendent suggested that the class bound the school-house. It was bounded on the north by the roof, on the south by the cellar, on the east and west by walls. The geography classes of an entire city were caught in that way. Either the pupils had not been taught, or else they had forgotten the difference between the real directions and the ordinary representation of them on the surface of a wall map. Sometimes the confusion exists in the mind of the teacher as well as in the minds of the pupils. Then he expects them to learn one thing while he teaches them another. By the methods formerly in vogue the pupil was expected to learn the sounds of the letters from their names; the pronunciation of the word from the names of the letters which compose it; the names, forms, and sounds of letters from the word taught as a whole; the musical sounds from the notation on a musical staff; the ideas of number, of fractions, from the corresponding symbols; the units of denominate numbers and of the metric system from the names used in the tables of weights and measures; the flowers of the field from the nomenclature of the botany; the substances and experiments in chemistry from the descriptions and pictures of a text-book. Such teaching has given rise to endless lectures, editorials, and discussions upon the use of the concrete in teaching, upon the value of thinking in things, upon the importance of object-lessons, laboratory methods, and the like.
But there is another side to the question. There comes a time in the development of the pupil when he must rise above the sticks and shoe-pegs and blocks of the elementary arithmetic, and learn to think in the symbols of the Arabic notation. Later he must learn to think in the more comprehensive symbols of the algebraic notation. He must learn to think the abstract and general concepts of science, and, in thinking these, to use the devices, technical terms, and other symbols which
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