A KEY то CHASE'S COMMON SCHOOL ARITHMETIC, WITH EXPLANATIONS AND REMARKS UPON THE PECULIAR FEATURES OF THE WORK, AND OPERATIONS OF THE MORE DIFFICULT EXAMPLES. By A. P. STONE. WORCESTER : PUBLISHED BY A. HUTCHINSON. 1853. HARVARD Entered according to Act of Congress, in the year 1852, by A. P. STONE, In the Clerk's Office of the District Court of the District of Massachusetts. PREFACE. THE following Key has been prepared for the purpose of furnishing a fuller explanation of some of the more difficult portions of Chase's Common School Arithmetic than could be given in the body of the book without rendering it objectionable on account of size and prolixity, and also for the purpose of calling attention to some of the peculiar features and excellences of that work. So long as the present method of teaching mathematics prevails, and text books are prepared upon the principles which, at present, govern their construction, there will often be found a necessity for a more extended elucidation of principles, rules, and examples than is convenient or desirable to incorporate into a text book for the use of pupils. Especially will this be true if the work is an elementary one, where great prominence should be given to leading principles and their applications, unencumbered with diffuse explanations and unnecessary details, which rather serve to prevent the learner from obtaining a clear and ready perception of the thing to be acquired. In the study of arithmetic, it is also oftentimes desirable, on the part of both teacher and pupil, to have the answers to the examples in a separate work, whether they are or are not inserted in the text book. To meet these wants, to some extent at least, has been the object of the following pages. An experience of nearly four years in the use of the Common School Arithmetic, where classes of all grades of proficiency 3 have made it their principal text book, has impressed the author of this Key very favorably in regard to the superiority of that arithmetic as a manual for learners. This experience, and valuable suggestions from others, have been his guide in the preparation of the Key. Wherever explanations and illustrations have been deemed necessary, they have been given as fully as was thought proper, regard always being had to the reasonable limits desirable in a work of this kind. In several instances operations have been performed, or their results indicated, to save the teacher the drudgery of what would be to him mere mechanical labor—a service which the author believes teachers will fully appreciate. Although the Key has been prepared partly at the suggestion of Mr. Chase, the author of the Arithmetic, and with his approbation, it is proper to state here that he should not be held responsible for any portion of it. And it is equally proper that acknowledgments should here be made, as they most cheerfully are, for his kindness and assistance in examining and correcting the sheets as they have come from the press. Should it be found that the Key approximates, even, to the Arithmetic, in point of simplicity, completeness, and adaptedness to its purpose, its merits will equal the expectation of the author. MILLBURY ACADEMY, Mass., December 16, 1852. SUGGESTIONS TO TEACHERS AND OTHERS. THE favor with which the Common School Arithmetic has been received, by those qualified to judge of its merits, fully entitles it, as its friends believe, to a candid examination by Teachers, School Committees, and others interested in education, and especially in the department of mathematics. The work has been examined by some of the best teachers of the day, and has received their highest commendation; and especially has it stood well the test of the school room; a trial without which no text book can present its claims for general introduction or use. In several instances where it has been taken up with seeming objections, and in some cases with positive prejudices, against it, a further acquaintance with its character, and a trial of it in the school room, have entirely removed those objections and prejudices, and won for it almost unqualified praise. The testimony of well-informed professional teachers, who have given it a fair examination and trial, has always been in its favor. Some of the essential features of the work, in which it differs, more or less, from most arithmetics, may here be briefly alluded to. At the commencement of the work, Decimals are introduced with Whole Numbers, and their operations are taught in connection. This seems much more philosophical than to reserve the consideration of Decimals, to be taken up with Fractions after the pupil has learned all the fundamental rules of operation in Whole Numbers. The numeration and notation of Whole Numbers and of Decimals are so similar, that there can be no good reason for separating them; and they have, also, such an intimate relation to each other, that it seems incomplete to teach one without the other. No more time is necessary to teach them both in connection than to teach one without the other. The examples in Numeration and Notation, and in the other fundamental rules, are specially designed to give the pupil a clear understanding of the first principles of the science and of their application, and to prepare him, by an easy progress, for the more difficult portions. |