•The THE MACMILLAN COMPANY MACMILLAN & CO., LIMITED LONDON BOMBAY CALCUTTA THE MACMILLAN CO. OF CANADA, LTD. TORONTO ARITHMETICS BY CHARLES H. GLEASON PRINCIPAL OF THE SUMMER AVENUE SCHOOL NEWARK, NEW JERSEY AND CHARLES B. GILBERT FORMERLY SUPERINTENDENT OF SCHOOLS, ST. PAUL 66 NEWARK, AND ROCHESTER AUTHOR OF STEPPING STONES TO LITERATURE," 66 GUIDE BOOK TWO PART ONE New York THE MACMILLAN COMPANY 1912 All rights reserved PREFACE THE authors have endeavored to present such new material and method, culled from the mass of recent contributions to the subject of arithmetic, as is of real value for children in school, and, at the same time, to retain or restore the admirable features found in the older arithmetics. The older arithmetics were strongly scientific and treated arithmetic seriously, as a subject demanding systematic presentation, orderly statement, and clear scientific definitions and rules. They were, however, authoritative in method, ignoring the order in which the mind naturally acquires its knowledge and secures its generalizations, and they gave little heed to the broader, cultural values of the subject. The principal merits of the newer books are psychological, and consist in the use of the inductive method of presentation and in the employment of practical and vital problems. Their weakness is in the failure to present arithmetic as a science deserving careful and orderly development. The method of presentation in these books is inductive, until principles have been thoroughly established and illuminated. Then the principles are stated "in good set terms." After such statement has been made it is utilized, and illustrations and problems are founded upon it. The books recognize both the merits and the limitations of the so-called "spiral plan." Up to a certain point this plan is psychologically sound. Repeated experiences, if attended with the interest incident to the addition of new features at each recurrence, unques |