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THE NEW

ADVANCED ARITHMETIC

BY

JOHN w. gpoK

PRESIDENT ILLINOIS STATE NORMAL UNIVERSITY
AND

MISS N. CROPSEY

ASSISTANT SUPERINTENDENT CITT SCHOOLS
INDIANAPOLIS, INDIANA

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SILVER, BURDETT & COMPANY

New York . . . BOSTON . . . Chicago
1902

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PKEFACE.

IT has seemed to the authors of the Normal Course In: Number that there is room for another series of Arithmetics, notwithstanding the fact that there are many admirable books on the subject already in the field.

The Elementary Arithmetic is the result of the ex perience of a supervisor of primary schools in a leading American city. Finding it quite impossible to secure satisfactory results by the use of such elementary arithmetics as were available, she began the experiment of supplying supplementary material. An effort was made to prepare problems that should be in the highest degree practical, that should develop the subject systematically, and that should appeal constantly to the child's ability to think. Believing that abundant practice is a prime necessity to the acquisition of skill, the number of problems was made unusually large. The accumulations of several years have been carefully re-examined, re-arranged, and supplemented, and are now presented to the public for its candid consideration. Not the least valuable feature of this book is the careful gradation of the examples, securing thereby a natural and logical development of number work. No space is occupied with the presentation of theory,—that side of the subject being left to the succeeding book. The first thoughts are what and how, — these so presented that the processes shall be

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easily comprehended and mastered. Subsequently, the why may be intelligently considered and readily underStood.

The Advanced Arithmetic is the outgrowth of a somewhat similar experience in the class-room of a teachers' training-school. For many years an opportunity was afforded to study the effects upon large numbers of pupils of the current methods of instruction in arithmetic. The result of such observation was the conviction that the rational side of the subject is seriously neglected. An effort was made to supplement the ordinary text-book by a study of principles and by explanations of processes. The accumulations of fifteen years have been edited with all of the discrimination of which the authors were capable. Great care has been exercised in the presentation of principles arid in the formulation of processes, to the end that the learner shall have every facility for the use of his reasoning powers, and at no point be relieved from the proper exercise of his mental activity and acumen. It is hoped that the book may contribute somewhat to the movement, now so happily going on, that looks toward the disestablishment of the method of pure authority, and the establishment of a method that makes its appeal to intelligence and reason.

The authors desire to express their appreciation of the excellent suggestions offered by many friends; but especial thanks are due Professor David Felmley, of the Illinois State Normal School, for his discriminating criticisms and valuable assistance.

THE AUTHORS.

SUGGESTIONS.

METHOD is determined chiefly by aim. The answer which the teacher makes to the question, "Why should boys and girls study arithmetic?" will guide him in the details of instruction.

Arithmetic is one of the traditional "three R's." Some knowledge of its processes is necessary to any degree of intelligence. Its highly practical character is conceded by every one.

The arithmetical operations employed in ordinary business affairs are simple, but they must be performed with absolute accuracy and with great rapidity. They are based, primarily, upon the memory. The necessity for perfect familiarity with the fundamental facts of number becomes apparent. Neither accuracy nor rapidity is possible without a thorough mastery of the primary work. This mastery is acquired through constant repetition of the old in connection with the acquisition of the new. One of the teacher's maxims, constantly, must be "Review! Review!! REVIEW!!!

But arithmetic has another and a higher function. It must cultivate that quick intelligence which is able to analyze given conditions and determine what should be done in the particular case.

A true problem in arithmetic is a statement or series of statements in which something is told and something

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