▲ CALIFORNI A MENTAL ARITHMETIC BY WILLIAM J. MILNE, PH.D., LL.D. PRESIDENT OF NEW YORK STATE NORMAL COLLEGE, ALBANY, N.Y. NEW YORK.:. CINCINNATI... CHICAGO PREFACE There are many who believe that Mental Arithmetic is one of the most valuable studies in a school curriculum. There can be no doubt that if the subject is properly taught it develops a habit of concentration of mind, which is one of the most desirable ends to be attained by any scheme of education. This habit is not acquired, however, by constantly performing operations with small numbers or by solving many easy problems which require but little mental effort, but rather by working examples of gradually increasing difficulty, until the pupil is enabled with effort to solve problems whose solution might seem to be almost impossible, without resort to ciphering. This habit of concentration, when once it has become established, makes the acquisition of knowledge rapid and delightful, and the development of intellectual power noticeably great. The plan adopted in this book contemplates not only the attainment of this end, but also another object of equal importance, the development of the reasoning faculty. The problems are arranged upon a pro541525 gressive plan, and the pupil is guided by explanations and suggestions until he is able to devise methods of solution for himself. The book thus follows the method of development which has proved so successful in the author's other works. It will be seen at once that the book is not a collection of easy problems designed to give the student practice in the simple processes of arithmetic, nor is it an exercise book to accompany a work on written arithmetic. It may be used with profit to supplement such a work, and it gives, also, abundant drill in computing; but it constitutes in itself an independent book, furnishing such a thorough course in arithmetic, that it will give to pupils who master it not only more than common skill in computing, and more than ordinary ability in reasoning, but also a firm grasp of the general principles of the science. W. J. M. |