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THE PUBLIC SCHOOL

MENTAL ARITHMETIC

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THE PUBLIC SCHOOL

MENTAL ARITHMETIC

BASED ON

MCLELLAN AND DEWEY'S “PSYCHOLOGY OF NUMBER"

BY

J. A. McLELLAN, A.M., LL.D.

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PRESIDENT ONTARIO NORMAL COLLEGE
AUTHOR (WITH DR. DEWEY) OF “THE PSYCHOLOGY OF NUMBER,

PSYCHOLOGY,” ELEMENTS OF ALGEBRA,” ETC.

APPLIED

66

AND

A. F. AMES, A.B.

HONOR GRADUATE IN MATHEMATICS; FORMERLY MATHEMATICAL

MASTER, ST. THOMAS COLLEGIATE INSTITUTE
SUPERINTENDENT OF SCHOOLS, RIVERSIDE, ILL.

New York
THE MACMILLAN COMPANY

LONDON: MACMILLAN & CO., LTD.

1907

All rights reserved

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Set up and electrotyped January, 1899. Reprinted August,
1899 : September, 1901 ; July, 1902 ; May, 1904; August,
November, 1905; February, 1907.

PREFACE

It has recently been stated by a well-known college professor that "boys enter college or training school at eighteen, after having spent from one sixth to one fourth of their entire school life in studying mathematics. Yet they know very little mathematics. In their examination the asking of even three questions shows that they haven't the dimmest idea of what it is all about." This statement, if true, does not prove — as the professor seems to think it does — the justice of the Hamiltonian onslaught on mathematical study.

It simply proves that the prevailing methods of teaching arithmetic are radically wrong. The serious defects in existing methods are mainly due to the fact that they take no account of the real nature of number, and of how the child's mind works in grasping the concepts of number and numerical relations. In other words, arithmetic has never been “psychologized. If there is a science of education and rational methods founded upon it, there must be a psychology of arithmetic, a psychology of language, etc. The onesided theory that education is concerned only with fitting the child for existing civilization has made

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