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BEINDUS.

THE

GRAMMAR-SCHOOL ARITHMETIC;

BEING

BOOK SECOND

OF THE

ANALYSIS OF WRITTEN ARITHMETIC,

DESIGNED FOR

PUBLIC AND PRIVATE SCHOOLS,

CONTAINING

llental, Slate, and Blackboard Exercises.

BY

S. A. FELTER, A. M.,

@RADUATE OP TIE STATE NORMAL SCHOOL, AND LATE OP TIE BROOKLYN COLLEGIATE AND

POLYTECINIC INSTITUTE, AUTHOR OF AN ARITUJETICAL SERIES, ETC.

NEW YORK:
PUBLISHED BY CHARLES SCRIBNER & CO.

HADLEY BROTHERS, CHICAGO, ILL.
THOMPSON, BIGELOW, & BROWN, BOSTON, Mass.

GL. PUTNAM & Sons
Books & Statuttery,

ASSOCIATION BUILDING
COR. 4 AVE. & 23 BT.'s.

N.Y.

[blocks in formation]

Entered according to Act of Congress in the year 1864, by

S. A. FELTER, In the Clerk's Office of the District Court for the Southern District of

New York.

Entered according to Act of Congress in the year 1868, by

S. A. FELTER, In the Clerk's Office of the District Court for the Southern Distriet of

New York.

PREFACE.

WITHIN the past few years, a radical change has taken place in the ideas respecting instruction in Arithmetic. The formulas of Mental Arithmetic are now applied to the solution of questions in Written Arithmetic, and instead of problems for illustration only, sufficient work is required to give accuracy, rapidity, and a complete familiarity with commercial transactions. Arithmetical puzzles, and improbable conditions in the commercial problems are almost entirely discarded, and questions emphatically practical are now desired.

Teachers now recognize the natural as the logical order of subjects, and the order of simplicity as best adapted to the natural unfolding and growth of the mind. Pupils are taught to reason from cause to effect rather than to follow the blind direction of rules, to walk unaided rather than to be carried like deformed cripples.

In most of the published text-books on arithmetic there has been, however, less change. As formerly, they contain a paucity of problems, a large amount of theory but little practice, much of the why, but little of the how and the moro complex subjects are thrust upon the attention of the pupil before his mind is sufficiently developed to master them. Proportion or the Rule of Three, Reduction of Currencies, Duodecimals, Permutation, and the Progressions receive undue prominence and are allowed to take the place

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