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.
Words are men’s daughters, but God’s sons are things.
For words are wise men’s counters,—they do but reckon by them,—but they are the money of fools.
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.
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.