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PREFACE

Whatever may be his future course in life, every child should have a thorough knowledge of the fundamental processes of arithmetic. No one subject serves so well to develop in the young accuracy, speed, and logical habits of mind as does the early training in arithmetic.

This text-book is new and is intended for pupils in the second, third, and fourth grades. It contains five chapters, each of which should constitute the work for half a year. The first chapter may be used in the last half of the second year, and scholars should master the whole book by the end of the fourth year.

Each subject is developed by forcing the scholars to approach it logically by means of a series of questions, the answers of which are easy to discover and probably are known already by the pupils. The utmost pains has been taken to put in the text no words or phrases that might seem hard or confusing to the pupils.

The shortest and best method of learning arithmetic is by solving problems. This book contains a great number of examples and problems, which have been selected and graded with care.

For the study of arithmetic in higher grades it is absolutely necessary that each pupil should have at his tongue's end the different combinations in addition and in multiplication. Subtraction is taught easily as the reverse of addition, and division as the reverse of multiplication. The greatest stress is laid upon repetition in interesting variations until each young scholar is able to give in an instant the correct answer to any simple question in

addition, subtraction, multiplication, and division. These processes have been made as easy as is consistent with good teaching, and have been presented in a manner most attractive to the beginner. At the same time he is taught to know his combinations and never to use the awkward and inaccurate method of counting in place of adding or multiplying.

Easy fractions and the more common measures are introduced early and will be found of use in stimulating the interest of the pupils in their work. Common fractions have been treated in a manner that compels the beginners to understand them thoroughly and at the same time to do some logical thinking.

A very short treatise has been presented on each of the following subjects: denominate numbers, decimal fractions, and bills and receipts. On these subjects enough has been included in the book to assist greatly the work in the fifth and sixth grades.

The author is indebted to many eminent teachers for valuable suggestions and criticisms. He desires to acknowledge his special indebtedness to Mrs. Mary Ziek Andre of Cedar Rapids, Iowa, who has made suggestions and furnished material of great value.

Every effort has been made to avoid errors in text and in answers. The author will be very grateful to any one for corrections, criticisms, or suggestions.

EXETER, NEW HAMPSHIRE

GEORGE WENTWORTH

SUGGESTIONS TO THE TEACHER

This text-book is designed to be introduced not earlier than the last half of the second school year. Each chapter constitutes the work for a half year. In many schools it is deemed preferable not to introduce a text-book in arithmetic before the beginning of the third year; but much depends upon the character of the preliminary work. The child's early lessons in numbers must be related closely to his experience with things; hence sense training should serve as the foundation for a rational study of numbers.

Lack of power to image is the source of much of the weakness and inaccuracy in arithmetic. Systematic training in observation and in visualization is necessary to the development of the imaging power. It will be observed that in this book much use has been made of visualization as a means of fixing the number facts of the fundamental operations.

The purpose of the exercises that should characterize the period preceding the introduction of the text-book is not to teach color or form or sound, but to develop in the pupil the power of attention through the systematic training of his senses.

The following exercises will serve as a suggestive guide for this preliminary work.

Eye training. 1. Require four or five children to stand in a row before the class. The pupils in their seats notice the position of the pupils in front. The children in their seats bow their heads, and the teacher changes the order of the scholars in front. Teacher gives command, "Heads up!" Now ask who can arrange the pupils in front in the order they were at first.

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