Thinking and learning to think

by Nathan Christ Schaeffer

Examples.

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.

Symbols for water.

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.

Sources of error.

Elementary instruction.

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.

More advanced instruction.

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 the scientists have invented to facilitate their thinking.