processes, and have acquired some mastery of their uses, a relief from the tedium of long arithmetical calculations becomes a matter of great importance. No one can become a rapid computer without short methods, and, considering that the problems of daily life that call for arithmetical treatment do not have answers with them, no one can be certain of his results without means of checking calculations. Every expert accountant uses them, and the more expert he is the more he uses them. In fact, expertness consists very largely in the ability to shorten calculations and to apply rapid checks. Constant use of these sections should be made through the seventh and eighth grades. Definitions, processes, rules, and even special subjects are worked out under the guidance of the principle: "First its informal, though rational, use, and afterwards conscious recognition of its formal use." Definitions of merely technical terms are given when called for by the development and where the need for them arises. Book III is a complete arithmetic. All the essentials are given a topical treatment here. The earlier topics, that were carefully taught in Books I and II, are here rounded out sufficiently for elementary school needs. The later topics are carefully taught and applied in numerous directions. The unities of the standard arithmetical subjects are carefully preserved. Part I reviews thoroughly all the fundamental operations with whole numbers; provides ample material for drill-exercises at suitable places; teaches carefully the operations on fractions, common and decimal, the laws of percentage and interest and their simpler and more common applications. Part II reviews, from a higher point of view, the topics previously taught, brings out a little of the science, adds the more difficult applications of percentage and interest, and while completing the mensuration of the common geometrical forms makes use of a little rudimentary practical geometry and general number. The general number brings out and emphasizes the unities of arithmetical topics and laws, and the geometry illuminates the arithmetic and general number and arouses an interest in and an appreciation for the constructive work of the builder. For the convenience of teachers in reviews, and for aid in estimating the rate of progress from time to time and the stage of advancement, summaries of the work of both parts are given at the end of this book, as was done in Books I and II. The author's acknowledgments for suggestions and ideas are due to numerous arithmetical writers and teachers. He desires to express his obligations to Miss Katherine M. Stilwell, of the University of Chicago School of Education; to Miss Ada Van Stone Harris, Supervisor of Primary Schools, Rochester, N. Y., both of whom read much of the proof. He desires most heartily to thank Mr. F. W. Buchholz, of the Chicago Normal School, whose unceasing diligence and pains with the manuscripts and the proofs have wrought distinct improvements on nearly every page of the book. Chicago, June, 1908. THE AUTHOR. |