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PREFACE

This book is intended for pupils in Grades VII and VIII. It covers the work as generally taught in a majority of the schools in this country. Most of our elementary schools extend through eight school years, and the topics studied are generally rather uniform. For systems in which the junior high school begins in the seventh grade the Junior High School Mathematics, Books I, II, and III, published in this series, will be found well arranged, but for the more common type of school the work of Grades VII and VIII will for a long time be of the nature herein set forth.

For the convenience of teachers the book has been divided into four chapters, each chapter containing sufficient work for a half year. Teachers

may omit as many exercises as necessary to allow for carrying out this plan. Indeed, one of the greatest failures on the part of teachers using any textbook is due to the fact that they feel that all exercises must be solved. A textbook should be the servant of the teacher, not the master, and under each topic the teacher should choose only such exercises and as many of them as are necessary to secure good work on the part of the pupils.

The arrangement of the book is topical, so that a pupil stays long enough with a subject at one time to acquire that feeling of mastery which is his right and privilege. Along with this sequence of topics, however, there are several features which are noteworthy. One is the Little Examinations, a brief series of tests covering each chapter in turn; a second feature is the Review and Drill section, also placed near the end of each chapter, and furnishing a cumulative review of all preceding work; a third is the sets of Problems without Numbers and Problems for Completion, each of which requires new lines

of independent thought on the part of the pupils; and a fourth is the Material for Frequent Drill found on page 315. By the aid of these features a teacher may be assured that the pupil is instructed in and kept refreshed upon those essentials of computation without which he cannot hope to succeed. There have also been inserted several elementary psychological tests relating to arithmetic, which may be used or not in the discretion of the teacher.

In the theory of the work the authors have no more sympathy with the idea that a pupil should be told to do a thing in a certain way, with no knowledge of why this way is the right one, than they have with the notion that he must explain every operation with all the care that a textbook writer would show. They believe that every process should be learned with an appeal to the pupil's understanding, and that thereafter it should become entirely mechanical; and in this way each operation has been presented in this book.

A feature of the book is the large number of modern applications to the actual needs of our American people, but these applications are not permitted to exclude the abstract drill work without which no pupil has ever become a good computer. To balance adequately the abstract and the concrete, the drill work and the applied problem, the review work and the new material, has been one of the earnest endeavors of the authors in the preparation of this series.

The authors hope that their effort to prepare a perfectly usable textbook, free from those eccentricities which, while attracting momentary, attention, fail to give the pupils the power they need, will prove helpful to the schools of the country.

GEORGE WENTWORTH
DAVID EUGENE SMITH

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