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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 Dollars and Cents. Stereotype Edition, revised and enlarged with Exercises for the Slate. To which is added a Practical System of Bookkeeping. BY ROSWELL C. SMITH.

THE publishers particularly invite the attention of teachers to this work, in the belief that it is a great and important improvement in the art of teaching Arithmetic. It is the production of an experienced and accomplished instructer of youth, who has availed himself of observations made in a long course of experience. Every part of this work has been carefully adapted to the business of teaching, and every page has been tested, by the use of the work in the author's school.-The design of the author has been to instruct the learner in the principles and practice of Arithmetic. This he has endeavored to do by slow gradations, beginning with the simplest ideas, and gradually ascending in the scale of knowledge, till the pupil is master of the whole field of Arithmetical combinations.-A fundamental principle of the work, is, to present no difficulty which the learner is unable of himself to surmount. In accordance with this maxim, the first 20 pages contain no rules nor exercises for the slate. It commences with examples so simple, that children 5 years old, will readily comprehend them. These illustrate the principles of addition, after which the Table is inserted, followed by intellectual exercises, explanatory of its practical utility. The remaining tables of simple Subtraction, Multiplication and Division, are exemplified in a similar manner.Thus by a mere mental process, the pupil is effectually taught the ground rules of Arithmetic, and this may be accomplished without any other assistance than the book, and the operations of his own mind.-The pupii on this plan, is required to think, and having become familiar with the individual operations required to solve a series of arithmetical questions, these operations are then summed up, and stated in the form of a rule. This rule he is then required to commit to memory, not however, without having been previously interrogated, to be assured of his complete comprehension of the same. The interrogative system is generally adopted throughout this work.

The common rules of arithmetic are exhibited so as to correspond with the occurrenees in actual business.

There is a constant recapitulation of the subject attended to, styled "Questions on the foregoing."

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.

A new rule for calculating interest for days with months.

The mode of introducing and conducting the subject of Proportion.

The adoption of the federal coin, to the exclusion of sterling money, except by itself. The arithmetical tables are practically illustrated, previously and subsequently to their insertion.

The work has been recommended by the Vermont and Rhode Island School commissioners for use throughout those states, and it is also extensively in use in Massachusetts, Connecticut, New York, and other parts of the country. It is used in many places on the score of economy, aside from its intrinsic merit, it being one of the cheapest books extant, embracing all that is valuable in the two systems, mental and practical, at the usual price of a treatise on one. The following certificate will show the reception of the work in Providence.

Petition of the Teachers of the Public Schools in Providence, to the Town-Council and School Committee

"We, the undersigned, Teachers of the public Schools, beg leave to represent to the Hon. Town-Council and School Committee;-That we have for a long time been sensible that the system of Common Arithmetic, ordered to be used in the Public Schools, has many defects, and it is not so well adapted to initiate the pupils into the science of figures, as an elementary book in such schools ought to be;-That a work adapted to any age or capacity of pupils, by an experienced Teacher, was a great desideratum. Your petitioners believe that such a work has lately been presented to the public by Mr. ROSWELL C. SMITH.

We view it superfluous to point out what we consider as the defects of the one, or the superior merits of the other.-It may be sufficient, for the present, that we merely express to your Honors and the gentlemen of the School Committee, our decided preference of Mr. Smith's Arithmetic to any other now in use, with which we are acquainted;and we most earnestly entreat that you would authorize its immediate introduction into the Public Schools.

Oliver Angell, Jos. B. Pettis, Origin Bachelor, Edward W. Baker,
Joseph C. Gardner, William P. Tuft, Alfred B. Lee.

The above petition was refered to

Rev. F. WAYLAND, JUN. D. D. Pres. of Brown Uni.

Rev. T. T. WATERMAN.
WM. T. GRINNELL, Esq.

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The said Sub-Committee, after having visited the Public Schools in Boston for the purpose of obtaining general information on the subject of education, made their report, from which the following is an extract;-"Your Committee are of opinion, that it would be expedient to introduce the System of Arithmetic published by Mr. Smith, into all the Public Grammar Schools; and also, that all the scholars in arithmetic be taught by classes, and not individually as is now the prevalent mode."

The Town-Council accordingly directed that "The System of Arithmetic, by Roswell C. Smith," be used in all the Public Schools in this town.

Highly favourable notices of this work have been made in several of the periodicals of the day. From many the following have been selected.

From the National Philanthropist and Investigator.

This long expected work has at length made its appearance***. If long experi. ence in teaching arithmetic, an ardent desire to remedy ascertained defects in the usua modes of teaching it, and a laborious, patient and systematic course of study and experiment for the attainment of this object, with the use of all the light that could be collected from men and from books, in relation to the theoretical principles and practical details of the subject, could enable any one to produce an improved treatise upon Arithmetic, the history of this work renders it probable that the object has been accomplished. In its principle, the present edition professes to be Pestalozzian, or inductive.—In or der to render it such, it was not, however, thought necessary to throw away written and practical arithmetic, in order to advance, or exalt the mental process, and the phi losophical elucidation; nor to reject rules, because it is irrational to learn them by rote, without illustration;-nor to disconnect the simplicity of a juvenile commencement of the subject, from a depth of research, in its progress, adapted to the maturity of manhood. To have done either of these, would have been thought contrary to the true spirit of the Pestalozzian plan. Names have been made to succeed ideas, yet names, as the convenient signs of things, have nevertheless, been retained.

His course we conceive to be a sober medium between the extremes of the inductive and synthetic systems, or rather, a specimen of the rational and alternate use of both, according to their proper spirit and design.

From the United States (Philadelphia) Gazette.

Mental Arithmetic.-A small, closely printed volume, entitled Practical and Mental Arithmetic, &c. &c. appears to us to possess much merit, and some degree of nov. elty. The plan of combining mental Arithmetic with the use of the slate, is good; and we should suppose that Mr. Smith's work (the book before us) would be found useful to teachers and learners-especially considering the simplicity of its arrangements and the care which the author has taken in forming his table of questions, without which no school book can be considered as complete.

WALSH'S ARITHMETIC.

WALSH'S MERCANTILE ARITHMETIC, a new edition, thoroughly revised by the author. For several years past this work has been out of the author's control, but during this period he has been continually collecting materials with which to enrich it, when it should again come into his hands. These improvements have all been incorporated into this edition, and are accompanied with an entirely new system of Book-Keeping-which it is confidently believed, surpasses in simplicity and usefulness, any other elementary system extant. This alone it may truly be said, is worth the whole price of the

book.

There is appended to this edition, a short treatise on Gauging and Mensuration. Re commendations could be procured, were it desirable, from hundreds of the most practical and intelligent Merchants, Shipmasters, and Instructers. It is undoubtedly the best Mercantile Arithmetic extant, and is used in some of the first seminaries in New England in instructing those who intend to pursue any Mechanic or Mercantile occupation

NOYES'S PENMANSHIP.

NOYES'S SYSTEM OF PENMANSHIP. One of the most popular and useful systems extant.

LESSONS IN ENUNCIATION.

LESSONS IN ENUNCIATION, Comprising a statement of Common Errors in Articulation, and the Rules of correct Usage in Pronouncing; with a course of Elementary Exercises in these branches of Elocution. To which is added an Appendix, containing Rules and Exercises on the mode of Enunciation required for Public Reading and Speaking. By William Russell, Ed. Journal of Education (first series).

GOODRICH'S GEOGRAPHY AND NEW ATLAS.
CH'S
OUTLINES OF MODERN GEOGRAPHY, on a new plan carefully
adapted to youth, with numerous Engravings of Cities, Manners,
Costumes, and Curiosities; accompanied by an Atlas.

This Geography is thought to possess peculiar advantages.

The elementary and most important parts are put into the form of question and answer, a form which experience has shown to be more successful for beginners than any other; These parts are distinguished by being in large type; and are intended to be studied during the pupil's first course.

The pupil having gone through the work once and fixed these outlines in his mind is then led into the details of the subject, being required on his second course to commit the whole, both in large and small type. [It will be observed that this plan is designed for those who begin the study with this work. But where the pupil has already become somewhat acquainted with the subject from an introductory work, he may be required to attend to the whole subject on his first course; and the publishers have no hesitation in saying it will be found more comprehensive by far than any other work of the same price and size.]

Being thus led gradually into the subject, instead of aversion to the study, and the habit of being satisfied with half formed ideas, the result of a difficult arangement, and requiring him to overload his memory with details which he does not understand, his interest will be excited and half the labor of teaching will be saved; while he will lastingly possess himself of more facts than by any other method.

The difficult names have their true pronunciation given them. This peculiarity will at once be esteemed a great improvement.

The use of initial letters in giving the boundaries of countries, has been found exceedingly useful, requiring the pupil to examine his maps to determine the answer, while they serve only as a clue to it. This plan, first used in this work, has been found of so much consequence as to be adopted as an original peculiarity in a late Geography, claiming it as a great improvement.

The author has adopted Malte Brun's 5th division of the earth (Oceanica) comprehending a vast number of islands in the Pacific Ocean.

The work represents Mexico and South America according to their present political divisions.

The Review, given at the end, is thought to be of particular value. It will be a scrutinizing test of the scholar's proficiency; will lead him to make comparisons, which are the foundation of inference and opinion; will invigorate his mind, and will establish the facts in his memory; and tend to make him a thorough geographer.

This, if faithfully used, it is believed will be more and more highly appreciated, the longer it is used.

In fact the Geography itself has always experienced the most flattering reception and is acknowledged by all who have examined it to be fully equal to any rival work. Some objection has however been made to the Atlas, and in most cases, the only objection to the work has been on that account. The publishers have therefore been at the expense of procuring several new and valuable plates, and now offer

A NEW ATLAS

OF THIRTEEN MAPS, which they have no hesitation in saying, possesses advantages over any other School Atlas ever published in this country.

As the plan of this Atlas is somewhat different from any other, an explanation of it will be given.

THE MAP OF THE WORLD is on a much larger Scale than is usual, and the Countries are on this nearly as fully delineated as they usually are on separate Maps, and the whole subject is brought before the eye of the pupil in bold relief. This being the case, the pupil is enabled and should be required, to study a good part of his time on this Map, the advantage of which is that he constantly keeps in mind the relative positions of the different countries which he is liable to lose sight of while using different and isolated Maps.

THE MAPS OF THE UNITED STATES AND EUROPE, are also on the same. liberal scale, and new Maps of North and South America, Asia and Africa, have been added, of a size corresponding to their consequence.

The MAP of OCEANICA, which is in no other Atlas, is very interesting, as embracing New Holland and the immense clusters of other islands in the Pacific Ocean, in å separate division according to the plan of the celebrated French Geographer Malte Brun and other late writers on the subject. It is also peculiarly valuable as representing the relative situations of Asia and America in a different light from what they usually appear, showing as it were, the other side of the world; and calculated to correct the false impressions which the pupil imbibes, from seeing these countries as on a common map, where the western coast of America appears at the greatest possible distance from the eastern coast of Asia.

The peculiarity, however, which is believed gives this Atlas an advantage over any other, is in the

OUTLINE MAPS

Of the World, the U. States, and New England, to be filled up by the pupil. The two latter have been added to the new Atlas, the former having been so highly appreciated. The exercise of filling up these Maps it is thought will materially facilitate the progress of the pupil, and so impress the positions of towns, mountains, rivers, &c. in his mind, that they will never be eradicated.

A Plate is also given, showing on a large scale the comparative heights of mountains and lengths of rivers, &c.

MORSE'S GEOGRAPHY.

This work has become a standard, in most of the High Schools and Academies in the United States. The talents of the present Editor, Mr. S. E. Morse, as a Geographer, are too well known to be questioned. The valuable materials, collected by his father during forty or fifty years' service, he has digested and concentrated in this work, with ability, and particular attention to the present wants and improved state of Schools: Perhaps no Geographer was ever more extensively quoted, or followed in his plans, than the late senior author of this work. It is supposed that upwards of 500,000 volumes of his geographical works have been published in America and in various parts of Europe: his large Geography has been there republished, in quarto.

Extract from a notice of this work in the Journal of Education, Oct. 1829.

"We consider the authors of the present work as advancing two distinct and well founded claims to public patronage. In the first place, Doctor Morse was emphatically and truly the Father of American Geography; and in the second place, he has kept up with the age in the progress of improvement."

Improved ATLASES Ancient and Modern, accompany this work.

WORCESTER'S SECOND BOOK.

A SECOND BOOK FOR READING AND SPELLING. By Samuel Worcester, author of a Primer for Schools. Second Edition, Stereotype. This work is designed to be used next after Mr. Worcester's or any other Primer or First Book, and to be the attractive medium for conveying further instruction to those children who have acquired the rudiments of reading and spelling. For this purpose, it is embellished with a great number of original cuts, illustrative of the reading lessons, which are short and written in a simple and familiar style, and on subjects which most interest and engage the attention of children-the words contained in them being such as they use and understand. At the end of each reading lesson the most important of these words are collected into columns and arranged according to the difficulty of spelling them, and so divided and italicised as to aid the scholar in determining the correct pronunciation, for which he might otherwise be at a loss. It is expected that in this way both the reading and spelling lessons may be learned at the same time. Those who have used Mr. Worcester's Primer are aware of his peculiar talents in rendering these usually dry subjects' interesting to children, and to them it is sufficient to say that his Second Book has the same simple and attractive character as the first.

GOODRICH'S HISTORY U. S. A.

A HISTORY OF THE UNITED STATES OF AMERICA, on a plan adapted to the capacity of youth, and designed to aid the memory by a systematic arrangement and interesting associations. By Rev. C. A. GOODRICH, author of Outlines of Geography.

. It is written in a plain, easy and intelligible style,-its arrangement of the subject is elear and natural, and it is rendered extremely interesting to youth by the introduction of lively anecdotes and narrations, which serve to illustrate points in the history.

This work has passed through nearly forty editions, and is used in the first seminaries of the U. States. It has lately been introduced into the Boston High School, and is considered to be better calculated for the purposes of education than any similar work now before the public.

The following, copied from Mr. Emerson's prospectus of the Wethersfield Female Seminary, is of weight as proceeding from one of the most experienced teachers in New England.

By using it the last season, the high opinion which I had formed of its worth was confirmed and raised. The author is uncommonly happy in his arrangement of facts; in presenting a simple, concise and luminous view of the subject which in its nature is peculiarly complex and intricate; in dividing the time into eleven periods; in tracing causes and effects;-in publishing the principal and subordinate parts in type of different sizes; and in presenting reflections for the benefit of the youthful mind." "The style is

easy, neat and remarkably perspicuous, and suited to improve the taste of the learner. On this account this little compend appears peculiarly adapted to the use of Schools." With respect to the plan of Mr. Goodrich's History, it is only necessary to say that it has been adopted in treating of English History, and the work is one of the most popular n England. In comparing it with other School Histories, the Journal of Education says "If any other circumstance is necessary to explain the fact, that it has run through more than thirty editions, it may be found in its better adaptation to the real wants and actual state of our schools than the other works."

EMERSON'S QUESTIONS.

QUESTIONS AND SUPPLEMENT TO GOODRICH'S HISTORY OF THE UNITED STATES. By the Rev. Joseph Emerson, Principal of the Female Seminary in Wethersfield, Conn.

Extract from the Preface.

"Till within a few years, perhaps no School Book has been more needed than a good History of the United States. This most unhappy deficiency has been in a good degree supplied by the excellent and popular work of Mr. Goodrich. My first perusal of this book convinced me that it was the best extant, for the purpose intended. This conviction has been increased by a more intimate acquaintance with it and much experience. In proportion to the time, it has probably had a greater circulation than any other school book of equal size, Murray's excepted."

This Supplement consists of Questions on Mr. G.'s history, and others to which the answers are given, and of notes intended to amplify the most interesting portions of the History in which Mr. G.'s notices are too concise. It is thought that both these works together, form the most complete and useful epitome of the U. S. History ever published.

BLAIR'S CHRONOLOGY.

OUTLINES OF CHRONOLOGY, ANCIENT AND MODERN, being an Introduction to the Study of History, on the plan of the Rev. David Blair, with numerous engravings.

WHELPLEY'S COMPEND.

A COMPEND OF HISTORY FROM THE EARLIEST TIMES; comprehending a general view of the present state of the world, with respect to the Civilization, Religion and Government; and a brief dissertation on the importance of Historical Knowledge. By Samuel Whelpley, Eleventh edition with corrections and improvements by Rev. Joseph Emerson, Principal of the Female Seminary at Wethersfield.

Of Whelpley's Compend, the Rev. Mr. Emerson says, in the Prospectus of his Female Seminary, "For many years I have been solicitously inquiring for the best Compend of General History for the use of Schools That which I consider by far the best, which I have yet examined, is the Compend of Mr. Whelpley. My estimation of this work has been rising for more than ten years, while I have been engaged in reading and teaching it more than ten times through. It is not a mere compilation or abridgement in the words of others-his style is his own-a style, perhaps not less distinctly marked than that of any other prose writer in the language.

FROST'S GRAMMAR.

ELEMENTS OF ENGLISH GRAMMAR with Progressive Exercises in Parsing. By John Frost, late Principal of the Mayhew Grammar School, Boston.

From the Masters in the Boston Public Reading and Grammar Schools. BOSTON, September 12, 1829.

Mr. JOHN FROST,-Dear Sir, We have attentively examined your Grammar, and we do not hesitate to say that it appears to us better adapted to the younger classes in Common Schools, than any other work with which we are acquainted. You have, indeed, omitted much that is essential to a full and thorough treatise, and which ought to be studied in our higher schools, but this we consider a great recommendation of your book. By giving the subject a bolder outline, simplifying the phraseology of Murray, and especially by introducing copious examples and exercises, you have removed many difficulties, and have made Grammar, we think an easy study for children. We are pleased to see that you have not departed w.dely from the principles of Murray,-to whose larger work, we consider yours an excellent introduction.

Abraham Andrews.
N. K. G. Oliver.

Charles Fox. Cornelius Walker.
Wm. J. Adams, Barnum Field.

R. G. Parker.
Saml. Barrett.

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