PREFACE In deciding the form of arrangement for this book the authors accept the fact that each of the two well-defined types of text-books in arithmetic has advantages. A teacher may prefer either one or the other, according to circumstances or training; and the same teacher might conceivably, in the exercise of the best pedagogic judgment, use under one set of conditions a text-book of one type, and when conditions changed employ a book of the other kind. With books of the type arranged for the recurrent treatment of topics the market is well supplied. Some of the extreme books of this recurrent form are, it is true, too fragmentary in arrangement to give the pupil that feeling of mastery which is his right and his reward. But excellent books of this type, which avoid its perils and provide all its good features, are now available. There is, however, great need for arithmetics having the topical arrangement but thoroughly modern in spirit and in material. That need this book is written to supply. The leading principle that has made the Wentworth books the standard in America for a generation has been followed: Present the reason briefly but clearly, then furnish such an amount of practice that the pupil cannot forget the principle. Theory is reduced to a minimum, and practice is abundant, in both abstract and concrete work, since the experience of a century proves beyond question that each of these two lines must be treated fully to prepare the pupils for life. The concrete problems are modern in the best sense. Those that seem to be real are real; modern business customs are followed, and the needs of the future citizen are always kept in mind. But in this book is found no trace of the unfortunate tendency of some of our recent writers to consider an example concrete when it treats of topics or contains technicalities that no pupil understands and few teachers are expected to know. This volume covers all of the topics ordinarily studied in the seventh and eighth school years. Under each topic there are found an unusually large number of well-graded · examples, and at frequent intervals collections of problems without numbers have been inserted as exercises in terse mathematical statement. The topics properly close with sets of exercises that relate to the vocational interests of our people, to the end that pupils may leave school with the real applications of arithmetic to common life clearly in their minds. A few recreations are given in the Appendix, that the lighter side of arithmetic may be seen along with its more serious aspect, and a large amount of drill work has been added for the use of pupils who may be in need of more work than is commonly required. Any corrections or suggestions relating to the work will be thankfully received. The authors hope that teachers who recognize the strong features of the topical arrangement, who wish for an abundance of well-graded problems requiring thought in their solution, who are sympathetic with the movement to replace the obsolete by the genuine applications of arithmetic to the American life of to-day, who are opposed to certain of the extreme attempts of the present time that are sure to result disastrously to scholarship, that such teachers will find in this work a sane, modern, and helpful treatment of the subject. II GEORGE WENTWORTH |