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To which is ADDED,

By Roswell, C. SMITH.


J. H. A. FRost, PRINTER.

- - District Clerk's Office. BE IT REMEMBERED, That on the twentieth day of December, A. D. 1827, in the fifty-second year of the Independence of the United States of America, RICHARDSON & LORD and S. G. GOODRICH, of the said District, have deposited in this Office the title of a book, the right whereof they claim as proprietors, in the words following, to wit:

“Practical and Mental Arithmetic on a new plan, in which Mental Arithmetic is combined with the use of the slate: containing a complete system for all practical purposes; being in Doliars and Cents. Second Edition, revised and enlarged with exercises for the slate. To which is added, a Practical System of Book Keeping, by Roswell C. Smith.”

In conformity to the act of the Congress of the United States, entitled “An Act for the Encouragement of Learning, by securing the Copies of Maps, Charts and Books, to the Authors and Proprietors of such Copies, during the times therein mentioned:” and aiso to an Act entitled “An Act supplementary to an Act, entitled, An Act for the Encouragement of Learning, by securing the Copies of Maps, Charts and Books to the Authors and Proprietors of such Copies during the time therein mentiomed ; and extending the benefits thereof to the Arts of Designing, Engraving and Etching Historical and other Prints.”

Clerk of the District of JMassachusetts.


2. THE present Edition is not only revised and corrected but very materially enlarged and improved. Whenever novelty and improvement are claimed for a publication of this nature, it seems incumbent on the author to state wherein the novelty consists, and to show how that novelty is an improvement. This will be now attempted in a few particulars, in which this work will be found to be mainly new. 1. JMere mental arithmetic, in this work, is made subservient to the use of the slate. The grand object is to convey instruction to children in language which they understand Their knowledge of things is always greater than their knowledge of words, the signs of things. And of all studies of which they are capable, Arithmetic is best suited to exercise and expand their reasoning faculties. The subject has been sometimes accounted above the capacity of boys under 10 or 12 years of age; and the profound and intricate science of language, the first principles of which, are, but with intense application, apprehended by the adult philosopher, has been sagely substituted as the more simple and pleasant exercise of infantile intellect. Arithmetic as usually taught, it is confessed, is sufficiently intricate. At worst, however, it is obviously better comprehended by children than English Grammar ; and taught as it might be, it is thought to be better adapted to their age than any other study. Children necessarily begin the actual use of Arithmetic at an early period, in their sports and interchange of toys about the streets: and by a proper process, it is easy to make them see that the Arithmetic of books and schools is precisely of the same kind, as that which they use every day in buying apples and exchanging marbles. Now the plan of this publication is, in the first place, to set the pupil at work upon this simple practical arithmetic which he already comprehends; and gradually to lead him to extend his operations to more intricate cases. The next step is to make him comprehend distinctly the reasons why he performs his operations, and how he arrives at his conclusions. Let the pupil be interrogated on these points, his own ideas drawn forth, and if erroneous, corrected by familiar questions and remarks. In doing this he arrives by a natural process of inductive reasoning at the substance of the rules for solving problems, involsing the same principles. After having performed upon the

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Too, . - ~ - PREFACE. t iii To 5 - + slate,one of two practical examples of the same nature, and upon which he can reason; and after questioning him as before, on the reasons of his operutions and results, let him commit perfectly to memory the rule, which his own reflections have thus developed, and which is, of course laid down in this work. The way will then be prepared to proceed by an easy gradation to more complex practical examples on the slate, and finally to the introduction of abstract numbers, as the last part of the whole course; for the obvious reason, that abstract ideas are the most difficult of attainment. 2. The four tables of the ground rules are located separately, and practical questions are given on each, illustrative of their nature and use. Similar questions are likewise given on the other tables, such as those of Weights, JMeasures, Currencies, &c. The propriety of making the scholar understand the nature and use of these tables before committing them to memory is sufficiently obvious. - 3. In giving the answers to the arithmetical questions, the aggregate of several has been given instead of each answer separately. By this means, the pupil is prevented from taking the answers from the book, instead of solv. ing the problem for himself: while at the same time the teacher is relieved from the burden of a continual examination of every operation. 4. Nearly the whole is on the “interrogative system” and the answers are unusually bricf. 5. The money calculations are almost wholly in Dollars and Cents, the exceptions being barely sufficient to exemplify the former currency of the country, and that in only a very few of the rules. The above system of connecting the process of mental arithmetic with that of the slate, is thought to be an improvement of no small importance. The Author has frequently known pupils who had completed a course of mental arithmetic, entirely unable to perform any operations on the slate, whose mental'exercises extended only to small sums and a short process; and who never seemed to imagine that their mental calculations were in any manner to facilitate or introduce the use of figures. It is thought best in general not to show the pupil how to perform any of his operations. Instead of this, let him be asked such questions as tend to unfold the principles. When he wishes to be shown, ask him, how he would do it? Having obtained his answer give him some simple o to test his principle by. Let him seek the result on the slate, and he will readily, perhaps, see the absurdity of his proposed method. For instance; you ask him how he would bring quarts into pecks? he would perhaps inadvertantly say “multiply.” instead of “divide.” Then tell him to bring 8 quarts into pecks by that rule. Let him multiply by 8–Ask him how much it makes. The same principles may be adopted in the ordinary course of instruction throughout the volume. There are several improvements in the rules, the value of which has been readily acknowledged by every one who has examined them. The object being to secure the greatest amount of usefulness, the nature of the sums, of various authors has been without hesitation adopted, whenever occasion required. . Of the former edition, the principal complaints, the author has heard from adults were, that it was “too simple;” and from children, that “it made their heads ache with thinking.” These were the objects intended to be accomplished by the Author. He meant to divest the subject of that rubbish of needless perplexity and artificial mystery, with which past ages had encumbered it; and to destroy that mechanical machinery with which Dullness has been taught, without effect to mimic the labours of Industry. If, however, in the oietion of “too much simplicity,” a deficiency of practical detail be implied, it is confidently expected that the present edition will not be found “too simple.” October, 1827. ROSWELL C. SMITH.

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