SMITH'S PRACTICAL AND MENTAL ARITHMETIC. From the JOURNAL OF EDUCATION. "A special examination of this valuable work will show that its author has compiled it, as all books for school use ought to be compiled, from the results of actual experiment and observation in the school-room. It is entire. ly a practical work, combining the merits of Colburn's system with copious practice on the slate. "Two circumstances enhance very much the value of this book. It is very comprehensive, containing twice the usual quantity of matter in works of this elass; while, by judicious attention to arrangement and printing, it is rendered, perhaps, the cheapest book in this department of education. The brief system of Book-Keeping, attached to the Arithmetic, will be a valuable aid to more complete instruction in common schools, to which the work is, in other respects, so peculiarly adapted. "There are several very valuable peculiarities in this work, for which we cannot, in a notice, find sufficient space. We would recommend a careful examination of the book to all teachers who are desirous of combining good theory with copious and rigid practice." ADVERTISEMENT TO THE KEY WHICH ACCOMPANIES THIS ARITHMETIC. The utility, and even necessity, of a work of this description, will scarcely be questioned by those who have had any experience in teaching Arithme tic. Most young persons, after having been persuaded, again and again, to review a long arithmetical process, feel, or affect to feel, certain that they have performed it correctly, although the result, by the book, is erroneous. They then apply to their instructor; and, unless he points out their mistake, or performs the operation for them, they become discouraged, think it useless" to try" longer, and the foundation for a habit of idleness is thus imperceptibly established. Now, in a large school, it is always inconvenient, and sometimes impossible, for the instructor to devote the time necessary to overlook or perform a very simple, much more a complex, question in Arithmetic. This is at once obviated by having at hand a Key, to which reference can be easily and speedily made. The time of the teacher will thus be saved, and the pupil will not have his ardor damped by being told that "his sum is wrong," without learning where or how. This work is not designed for, and can scarcely become a help to laziness; its object is to lighten the burden of teachers, and facilitate the progress of scholars. To promote both of these important purposes it is now presented to the public. MUS Entered according to Act of Congress, in the year 1835, by CARTER, HENDEE & CO. In the Clerk's Office of the District Court of Massachusetts. 46 8.W.BENEDICT & CO., Stereotypers and Printers, No. 16 Spruce street, New York. 641. PREFACE. When a new work is offered to the public, especially on a subject abounding with treatises like this, the inquiry is very naturally made, "Does this work contain anything new? "Are there not a hundred others as good as this? To the first inquiry it is replied, that there are many things which are believed to be new; and, as to the second, a candid pub lic, after a careful examination of its contents, and not till then, it is hoped, must decide. Another inquiry may still be made: "Is this edition different from the preceding?" The answer is, Yes, in many respects. The present edition professes to be strictly on the Pesta lozzian, or inductive, plan of teaching. This, however, is not claimed as a novelty. In this respect, it resembles many other systems. The novelty of this work will be found to consist in adhering more closely to the true spirit of the Pestalozzian plan; consequently, in differing from other systems, it differs less from the Pestalozzian. This similarity wil now be shown. 1. The Pestalozzian professes to unite a complete system of Mental with Written Arithmetic. So does this. 2. That rejects no rules, but simply illustrates them by mental questions. So does this. 3. That commences with examples for children as simple as this, is as extensive, and ends with questions adapted to minds as mature. Here it may be asked, "In what respect, then, is this different from that?" To this question it is auswered, In the execution of our common plan. The following are a few of the prominent characteristics of this work, in which it is thought to differ from all others. 1. The interrogative system is generally adopted throughout this work. 2. The common rules of Arithmetic are exhibited so as to correspond with the occurrences in actual business. Under this head is reckoned the application of Ratio to practical purposes, Fellowship, &c. 3. There is a constant recapitulation of the subject attended to, styled 66 Questions on the foregoing." 4. The mode of giving the individual results without points, then the aggregate of these results, with points, for an answer by which the relative value of the whole is determined, thus furnishing a complete test of the knowledge of the pupil. This is a characteristic difference between this and the former editions. 5. A new rule for calculating interest for days with mouths. 6. The mode of introducing and conducting the subject of Proportion. 7. The adoption of the Federal Coin, to the exclusion of Sterling Money, except by itself. 8. The Arithmetical Tables are practically illustrated, previously and subsequently to their insertion. 9. As this mode of teaching recognizes no authority but that of reason, it was found necessary to illustrate the rule for the extraction of the Cube Root, by means of blocks, which accompany this work. These are some of the predominant traits of this work. Others might be mentioned, but, by the examination of these, the reader will be qualified to decide on their comparative value. As, in this work, the common rules of Arithmetic are retained, perhaps the reader is ready to propose a question frequently asked, "What is the use of so many rules?" "Why not proscribe them The reader must here be reminded, that these rules are taught differ ently, in this system, from the common method. The pupil is first to satisfy himself of the truth of several distinct mathematical principles. These deductions, or truths, are then |