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INTERMEDIATE ARITHMETIC

BY

DAVID EUGENE SMITH, LL.D.

PROFESSOR OF MATHEMATICS IN TEACHERS COLLEGE

COLUMBIA UNIVERSITY, NEW YORK

GINN & COMPANY

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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 Arithmetic, 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 fifth and sixth school years, reserving for the author's Advanced Arithmetic the work of the seventh and eighth 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;

to touch the genuine interests of pupils in the story of our national resources and industries rather than to dwell upon the technicalities of minor trades in which they have no immediate or prospective concern; and to come in contact with human life rather than with those phases of science which are quite as foreign to the interests of boys and girls as are the mere abstract problems of numbers.

4. In the matter of abstract drill work, to recognize the fact that a large number of “problems without content" are necessary to concentrate the attention on the operations and to acquire the computing habit. The numbers selected have been those demanded by the conditions of the present day, the fractions and compound numbers being those in common use rather than those never met in business, and the integers being the ordinary ones of daily life. Very large numbers have generally been used only in such applied problems as represent the real conditions that the children meet in their geography, their elementary science, and their newspaper reading.

5. In the matter of illustrations, to recognize that pictures aid in the understanding of certain number relations, that they are often helpful in suggesting simple material for the teacher's use, and that they may be legitimately used in rendering more interesting and real various groups of problems.

In fine, the book is written for the use of those teachers who wish to preserve the best that was in the old-style arithmetic, with its topical system and its abundant drill, while giving to it a modern arrangement and securing “ mental discipline” through problems of to-day rather than through the tiresome, meaningless, unreal inheritances of the past.

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