PRINCIPAL OF PENNSYLVANIA STATE NORMAL SCHOOL, AND AUTHOR OF A "The highest Science is the greatest simplicity." PHILADELPHIA SOWER, POTTS & COMPANY 530 MARKET ST. AND 523 MINOr St. Entered according to Act of Congress, in the year 1876, by In the Office of the Librarian of Congress, at Washingtou. STEREOTYPED & PRINTED BY THE INQUIRER P. & P. CO., LANCASTER, PA 48X284 PREFACE. ROGRESS in education is one of the most striking characteris PROGRES tics of this remarkable age. Never before was there so general an interest in the education of the people. The development of the intellectual resources of the nation has become an object of transcendent interest. Schools of all kinds and grades are multiplying in every section of the country; improved methods of training have been adopted; dull routine has given way to a healthy intellectual activity; instruction has become a science and teaching a profession. This advance is reflected in, and, to a certain extent, has been pioneered by, the improvements in the methods of teaching arithmetic. Fifty years ago, arithmetic was taught as a mere collection of rules to be committed to memory and applied mechanically to the solution of problems. No reasons for an operation were given, none were required; and it was the privilege of only the favored few even to realize that there is any thought in the processes. Amidst this darkness a star arose in the East; that star was the mental arithmetic of Warren Colburn. It caught the eyes of a few of the wise men of the schools, and led them to the adoption of methods of teaching that have lifted the mind from the slavery of dull routine to the freedom of independent thought. Through the influence of this little book, arithmetic was transformed from a dry collection of mechanical processes into a subject full of life and interest. The spirit of analysis, suggested and developed in it, runs to-day like a golden thread through the whole science, giving simplicity and beauty to all its various parts. (iii) |