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THE GILBERT ARITHMETICS

THE MACMILLAN COMPANY
NEW YORK. BOSTON • CHICAGO

DALLAS • SAN FRANCISCO

MACMILLAN & CO., LIMITED
LONDON · BOMBAY • CALCUTTA

MELBOURNE
THE MACMILLAN CO. OF CANADA, LTD,

TORONTO

ARITHMETICS

BY
CHARLES H. GLEASON
PRINCIPAL OF THE SUMMER AVENUE SCHOOL
NEWARK, NEW JERSEY

AND

CHARLES B. GILBERT
FORMERLY SUPERINTENDENT OF SCHOOLS, ST. PAUL

NEWARK, AND ROCHESTER
AUTHOR OF “STEPPING STONES TO LITERATURE," "GUIDE
BOOKS TO ENGLISH," " THE SCHOOL AND ITS LIFE,” ETC.

BOOK TWO

PART ONE

New York
THE MACMILLAN COMPANY

1912

AU rights reserved

MATYARD POLLEGE LIBRARY

GHT OF THE
GRADUATE SCHOOL OF EDUCATION

COPYRIGHT, 1910,
By C. B. GILBERT AND COMPANY.

Book II, Books II and III in one volume, printed April, 1912.

PREFACE

The authors have endeavored to present such new material and method, culled from the mass of recent contributions to the subject of arithmetic, as is of real value for children in school, and, at the same time, to retain or restore the admirable features found in the older arithmetics.

The older arithmetics were strongly scientific and treated arithmetic seriously, as a subject demanding systematic presentation, orderly statement, and clear scientific definitions and rules.

They were, however, authoritative in method, ignoring the order in which the mind naturally acquires its knowledge and secures its generalizations, and they gave little heed to the broader, cultural values of the subject.

The principal merits of the newer books are psychological, and consist in the use of the inductive method of presentation and in the employment of practical and vital problems. Their weakness is in the failure to present arithmetic as a science deserving careful and orderly development.

The method of presentation in these books is inductive, until principles have been thoroughly established and illuminated. Then the principles are stated “in good set terms." After such statement has been made it is utilized, and illustrations and problems are founded upon it.

The books recognize both the merits and the limitations of the so-called “spiral plan.”

Up to a certain point this plan is psychologically sound. Repeated experiences, if attended with the interest incident to the addition of new features at each recurrence, unques

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