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The School Commission of the City of oostam

ADMINISTRATIO:1 LIBRARY

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PREFACE

This work has been prepared to meet a demand for a book which shall present the great essentials of arithmetic as required in Grades V and VI of our schools. The authors have not attempted to make a book of methods for teachers or to provide for the technical education of pupils in any special vocation; but they have furnished the teacher with the labor-saving material needed in a thorough course in arithmetic, they have motivated every process, they have suggested fields for the development of interesting local problems, they have suggested a large number of appropriate projects, and they have given to the pupils those fundamental elements of the subject which assure the command of numbers that will be needed in after life.

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

may

omit such exercises as are necessary for carrying out this plan. Indeed, in general, a teacher should learn the importance of omitting exercises whenever those exercises do not relate to the experiences or probable needs of the pupils. In a rural community all problems relating to the farm may properly be given, while many of those relating to the city or to manufacturing should be omitted. Similarly, in a city school many problems relating to agriculture will concern the pupils only remotely, and hence only a few exercises of this kind need be given.

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; and a third is the sets of Problems without Numbers and the Problems for Completion, each of which requires new lines of independent thought on the part of the pupils. By the aid of these features a teacher may be assured that the pupil is kept refreshed

upon those essentials of computation without which he cannot hope to succeed and that he is trained in independent thinking in arithmetic. There have also been inserted several elementary psychological tests relating to arithmetic, and these 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 presented with a definite motive, that it 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.

The applications are more numerous and more real to the pupil than is usually the case in textbooks, 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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