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.
Hear a parable. A teacher sat down to dinner. The waiter handed him the bill of fare. The proprietor followed the waiter to the kitchen, directed him to cut out the names of the eatables which had been ordered, and to carry these names on plates to the dining-room. “It is not these words,” exclaimed the guest, “that I desire to eat, but the things in the kitchen for which these words stand.” “Isn’t that what you pedagogues are doing all the time, expecting children to make an intellectual meal on words such as are found in the columns of the spelling-book and attached on maps to the black dots which you call cities? My boy gravely informs me that every State capital has its ring, because on his map there is always a ring around the dot called the capital of a country.” The teacher was forced to admit that there is, alas! too much truth in the allegation. In the afternoon he took revenge. Knowing that the proprietor had a thousand-dollar draft to be cashed, he arranged with the banker to have it paid in silver coin. When the landlord saw the growing heap of coin, he exclaimed, “If I must be paid in silver, can you not give me silver certificates?” “Did you not intimate to me,” said the teacher, tapping him on the shoulder, “that it is the real things we want, and not words and symbols which stand for realities?” The landlord was obliged to admit that in the larger transactions of the mercantile world it saves time and is far more convenient to use checks, drafts, and other symbols for money than it would be to use the actual cash. In elementary transactions, like the purchase of a necktie, it is better to use the cash, to think and deal in real money, but when it comes to the distribution of five and one-half million dollars among the school districts of Pennsylvania, it is better to draw warrants upon the State Treasurer, to use checks and drafts, and to think in figures, than it would be to count so much coin, and send the appropriation in that form all over a great commonwealth.