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COPYRIGHT, 1899,

BY

1. B. LIPPINCOTT COMPANY.

ELECTROTVPED AND PRINTED BY J. B. LIPPINCOTT COMPANY, PHILADELPHIA, U. S. A.

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PREFACE.

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That Arithmetic is both a science and an art is not only generally conceded, but emphatically affirmed. One, therefore, investigating the methods of instruction adopted in school-rooms would logically expect to find both aspects of the subject distinctly put in evidence. What is universally acknowledged and proclaimed as essential and vital to any true system of arithmetical education the investigator, however, would fail to find distinctly characterizing either the instructions given by the average teacher or the work required of the average pupil. What we mean is, that if he saw anything notable, he would see Art conspicuous in the foreground, while Science, if visible at all, sat mute far back. There might be seen, to be sure, remarkable skill displayed in many instances, and results brought forth with surprising facility; but, in it all, Science, that alone imparts life to action and informs the mind, would have little or no part.

The great error is that arithmetical exercises and problems are too frequently-nay, almost invariably—set up like so many ten-pins, to be knocked down by mechanical action, without any inquiry as to the underlying and fundamental principles upon which action is based. In a word, the schools, with little exception, are not making the best use of

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Arithmetic as an educational force by ignoring the fact that it has principles to be explained, induction and analysis to explain them, and a philosophical reason for every step necessary to be taken.

The text-books used may sometimes be seriously at fault, want of time may be an impediment, and other hindrances may be numerous; but the live and intelligent teacher will find in the least scientific treatise food for quickening thought and moulding the mental state. It must be admitted, however, that the teacher, in the conscientious performance of his duty, has a difficult environment, and needs all the help that text-books can furnish him.

The book that we now introduce to the public we have aimed to make what it assumes to be,-a Practical Arithmetic; -practical, not so much by devising short processes and labor-saving schemes as by laying a scientific foundation to be studied and mastered as the essential preliminary to the intelligent and skilful use of any device of mere art ; practical, therefore, as a teacher's true assistant, bringing to his hand a full supply of definitions, inductive steps, illustrations, principles, analyses, syntheses, processes, rules, and suggestions, needful to him in his high vocation,-a vocation that is highest when most devoted to “bright-eyed Science," and lowest when it rests content with the pretentious and empty forms of mere mechanic art.”

The text-book, even in its best estate, replete with science and art-full, can have little philosophical efficiency except when intelligently used as a means to an end. In the schoolroom, where a book is expected to promote the high aims of education, the intelligent use of it must begin, if it begins at all, with the teacher; for it is he alone whose very office it is, through voice and action, to stir into quickening force the words of the text, that otherwise may fall as good seed upon sterile ground. Every teacher ought to know—what every pupil soon learns—that “to hear illustrations and explanations from living lips is a different thing from struggling through them on the printed page.” Every page is to be learned, however,-mastered,—and made emphatically the pupil's own; and, as a suggestion pertinent here, we quote the philosophic words of John Locke: “The great art to learn much is to undertake a little at a time.

The author would gladly express his thanks to all who in any way made contributions of help. To one friend, whose devotion to the work never faltered, he acknowledges lasting obligation.

J. M. R.

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