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DAVID EUGENE SMITH, LL.D.
COLUMBIA UNIVERSITY, NEW YORK
The following have been controlling ideas in the preparation of this book :
1. In sequence of topics, to follow the plan adopted in the author's Primary and Intermediate Arithmetics, that of recognizing the value of the various courses of study in use in different parts of the country. Whatever originality may be demanded and legitimately shown in the preparation of a text-book, an author is bound to recognize the consensus of opinion as to topics and sequence. For example, modern courses invariably suggest the repetition of the most important portions of arithmetic from time to time, but they favor a somewhat exhaustive treatment of each subject whenever it is under discussion. The extreme spiral system, in which no topic is ever thoroughly treated at one time, but each is repeated until the pupil wearies of it, is psychologically too unwarranted to be considered seriously. On the other hand, the old-time plan of presenting important chapters but once is equally unscientific. Between these extremes lies the mean of the modern courses of study.
2. In arrangement by grades, to recognize the prevailing courses of study in the country, and to outline the work usually covered in the seventh and eighth school years, the author's Intermediate Arithmetic having covered the work of the fifth and sixth years.
3. In the selection of problems, to touch the actual life of this country at this time; to give correct ideas of the business customs of to-day; to embody the mathematical principles in interesting and instructive groups of problems;