Ten silver dimes equal one gold or silver dollar.
Twenty nickle pieces equal one gold or silver dollar.
One hundred copper pennies equal one gold or silver dollar.
On the following day a new concrete table was prepared, and the dollar sign, figures, symbols, and decimal point were substituted for the words in the written work. The relative values of the lower denominations to one another were taught, and tables constructed and written. The different denominations of paper money up to the fifty-dollar bill were added to the coins; and this money—about one hundred and fifty dollars—was used in business transactions, which gave review of the number relations already learned, and taught those necessary to the construction and comprehension of the remaining tables. At the end of eight months the children could use and write numbers to one hundred and fifty, and the signs and (decimal point); and understood the value of position in notation to three places to the left and two to the right of a decimal point. Also, in the oral work with money, they readily used the fractions one half, one fourth, one tenth, one twentieth, and one hundredth; and most of them could write from memory the usual tables from one to twelve. In this first year no effort was made to do a defined kind or amount of work; the children spent from twenty to thirty minutes each day at some mathematical work, but progress and variety depended on their interest and capacities. A visitor who had spent forty years in teaching sat through one of these primary sessions. He expressed pleasure and surprise at the work of the children in science, reading, and other branches, but was incredulous, at first, about the work in number with the money at their desks, and the written work in figures and signs at the blackboards. He went around among the children, tested them, and watched to see if there were not some trick of parrot-like performance. Finally, convinced of the genuine comprehension of what they were doing by these children of six and seven, he said: "I should not have believed it on the statement of any man or woman whom I have known; but I have seen it with my own eyes."
It is a matter of regret to me that growing burdens of care forbade the development of the number work during the second and third years on the lines begun in the first year. To spend from a half-hour to an hour a day for ten years at mathematics, with no better results than the average boy and girl of sixteen can show, looks like a great waste of time and energy. May not the cause be twofold: First, that the beginning work is made silly by its simplicity, and insipid by being related to nothing interesting; second, that processes like the subtraction of large numbers and long division are pressed upon the child before his powers are adequate to their comprehension?
