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THE GREGG PUBLISHING COMPANY
NEW YORK BOSTON CHICAGO SAN FRANCISCO
ENGLAND: 21 HARRINGTON STREET, LIVERPOOL

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PREFACE

UNTIL recently upper elementary and high school work in mathematics was planned for the pupil who was expected to continue it in the university. Although logical, its arrangement was neither psychological nor pedagogical. Some progress, however, has been made recently in adapting the study to the needs and abilities of pupils.

In the junior high or intermediate school, work in mathematics in the seventh, eighth, and ninth grades should be complete in itself and at the same time preparatory to senior high school work. No effort should be made to "finish" arithmetic in the eighth grade and algebra in the ninth, while denying the child the interest and beauty that lie in geometry and trigonometry until his taste for mathematics has been destroyed. Nor will alternate bits of formal algebra, geometry, and trigonometry solve the problem. The result is a mastery of none and a confusion in all.

Experience has proved that the necessary elements of arithmetic can be taught and certain definite skill developed in the first six grades. In the seventh grade business applications of arithmetic with the simplest elements of bookkeeping should be given. In the eighth grade mensuration should be taught experimentally or through observational geometry, and, through that, in a natural and meaningful way,

the very beginnings of algebra. Optional courses should be offered in the ninth grade.

Experience has shown that much of the content and the whole of the subject matter must be changed to make the course of study fit the needs of the pupils. The definite aims of Book One of this series are: 1. To train the pupil in that part of arithmetic used in

everyday business which he can understand. 2. To develop his skill in rapid calculation by short

cuts and time tests. 3. To show the necessity for checking, and to develop

the habit of checking. 4. To develop the habit of thrift by planning budgets,

keeping accounts, and becoming familiar with

savings banks. 5. To train the pupil in the simplest elements of

bookkeeping 6. To study a few common applications of arithmetic

for their social and economic value more than for their mathematical content.

In presenting each phase of the subject, actual business practice has been carefully followed. For this reason the terms base, rate, and percentage are not used.

The whole subject of percentage is closely interwoven with the already familiar fractions. The various applications are not presented as new mathematical topics, but as new uses in business of the same arithmetic.

The various methods of calculating interest are omitted, for they are not used in business and serve only to confuse the pupil. The general method is

given in order that he may thoroughly understand the principle of interest; then interest tables are presented, so that he may know business practice.

The usual work in bank discount is omitted because it rightly belongs in a high school arithmetic. In the child's relation to a bank he needs to know how to open an account; how to make checks and keep stubs; how to indorse checks and fill out deposit slips; and how money works for him if put in a savings bank. These things are given, as are other phases of social and business practice, but only those for which a child can feel a need or can see a need in his near future.

A sane and practical pedagogy has been consistently followed. First, the use is shown; then, a feeling of the need is created as a motive for learning; and finally, the topic is developed in a simple, natural way, with sufficient applications and practice to give the pupil a sense of mastery.

The graph is given, not in an isolated chapter to be taught or not as the teacher wishes, but it is used throughout to illuminate different phases of the subject. That is, mathematical language is given more meaning by the use of graphs or mathematical pictures, just as the English or a foreign language is made more interesting and more intelligible by illustrative pictures.

Book One of the series is planned for a year's work in the seventh grade, or the first year of the junior high or intermediate school, and will follow in unbroken sequence the sixth grade work of any standard arithmetic series.

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