THE NEW YORKİ ASTOR, LENOX AND Entered according to Act of Congress, the year 1849, by In the Clerk's Office of the District Court of the District of Massachusetts Entered according to Act of Congress, in the year 1858, by TEMPERANCE C. COLBURN, Widow of Warren Colburn, In the Clerk's Office of the District Court of the District of Massachusetts Entered according to Act of Congress in the year 1863, by TEMPERANCE C. COLBURN, Widow of Warren Colburn, in the Clerk's Office of the District Court of the District of Massachusetts ADVERTISEMENT. THIS book has returned by purchase into the pos session of the heirs of the late WARREN COLburn, and will hereafter be published for their benefit. The Introduction, by GEORGE B. EMERSON, gives some valuable hints as to the proper use of the book. The Original Preface, in which the design and plan of the work are stated at length by the Author, has been restored. A careful perusal of this Introduction and Preface is earnestly recommended to all teachers who make use of the book. Cambridge, June, 1868. H. O. HOUGHTON. INTRODUCTION. THIS little book has now been in constant use for forty years, and its value has been proved by the entire and admiring approbation of thousands of the best teachers. Yet its very simplicity has prevented many persons from seeing how really profound and comprehensive it is, and that it actually develops every essential principle in elementary arithmetic. Want of attention and the previous use of poorer books have also misled many persons as to the proper and true mode of using it. It is strictly a mental arithmetic, and, if faithfully used in the way intended by the author, it evolves from the mind of the learner himself, in a perfectly easy and natural manner, a knowledge of the principles of arithmetic, and the power of solving, mentally and almost instantly, every question likely to occur in the every-day business of common life. It can be well taught only by a teacher who perfectly understands it, and who knows how to teach. Such a teacher will not allow the lesson to be previously studied by the pupil. Each section is intended to teach some ́one process up to a certain point. If, in the course of the section, questions occur which the class cannot readily solve without previous study, the teacher has only to interpose, at the point where the class fails, or begins to fail, addi tional questions of the same kind, somewhat easier man those in the book. If, at the end of the section, the class be not perfectly ready in the solution of the questions, the teacher ought to go over the section again, with the class, or to add, at the end of the section, a sufficient number of similar questions to render the solution easy and instanta neous. By allowing the class to study the lesson beforehand, not only is much time lost, but the exercise is turned into a poor sort of mechanical process not much better than the common ciphering. Its mental character ceases almost entirely. As an exercise in exact reasoning, the mental solution of questions is very valuable; not less so than geometrical demonstration, and preferable in the fact that it is purely mental. It is thus an admirable preparation for the attainment of the faculty of ready and sharp logic, to be applied to the business of common life, where the mental habit alone is available. Its great value for children is in its shortness and its clearness. For example:What is 1 of of? Answer: of of of is; for of is; of is; of is; therefore, of of of } is } Similar examples are found in almost every section in the book. Now, the going faithfully through many such processes, every day for years, at the age at which mental habits are formed, must have the effect of forming habits of clearness, accuracy, and exact reasoning, which, once fully formed, will always exert a happy influence over the mind. This book ought not to be used with beginners only. Its effect upon those far advanced is even better and more striking. It might be continued, with the greatest advan tage, till the end of every course of instruction, and, if sc continued, would have the constant effect of sharpening the perception and varying the ability of analysis, of giving perfect readiness in the mental solution of all com mon problems, and of fixing the habit of clearness, quickness, and accuracy in the process of exact reasoning. GEORGE B. EMERSON May, 1863. |