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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.

FIFTY-FIRST EDITION, REVISED AND ENLARGED,

WITH

EXERCISES FOR THE SLATE,

TO WHICH IS ADDED A

PRACTICAL SYSTEM OF BOOK-KEEPING

BY ROSWELL C. SMITH.

AUBURN:

PUBLISHED BY II. & J. C. IVISON.

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.

From the Jan. No. for 1828 of the Journal of EDUCATION. "A careful examination of this valuable work wilt 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 tho school-room. It is entirely a practical work, combining the merits of Colburn's system with copious praciice on the slate.

“Two circumstances enhance very much the value of this book. It is very comprehensive, containing twice the usual quartity of matter in works of this class; while, by judicious attention to arrangement and printing, it is rena" dored, perhaps, the cheapest book in this departinent of education. The brief system of Book-keeping, attuched to ihe Arithmetic, will be a valuable aid to sore complete instruction in oummon schools, to which the work is, in other respects, so peculiarly adapted.

" There are several very valuable peculiarities in this work, for which we cannoe, in a notice, find sufficient spuco. We would recommend a careful exsipination of the book to all teachers who are desirous of combining good choory with copious and rigid practice."

From the Report of the SCHOOL-COMMITTEE CF PROVIDENCE.

u Tho books at present used in the schools are, in the opinion of your Com mittee, altogether above the range of ihought of the pupils. Works of a nar. rative character would be better understood, would be more interesting, and jwould, of course, teach the pupil to rend with more taste and judgment. The

boy who pores, in utter disgust, over the book which he roads in schools, will hasten hoino to read with avidity his story-book. The true wisdom would then bo, to introduce the story-book into school, and thus render his place of education thu place of his amusement.

Nevertheless, as this subject is one in which time and judgment are neces orry for a selection, and as a change of this sont, through all the schools, would be productive of considerable additional expense, your Committes' would recoinmend that no change, at present, bo made in books, oxcipling only the Arithmetic. li'a school, by way of experiment, be established on the monitor sia, plan, various school-books can be tried there, and, after u fair opportunity of testing the merits of several, those can be selected which seom best adapteri to accompdish tho purposes of education. Your Committee are, however, of opinion, that it would be expedient to introduce the system of Arithmorie published by Mr. Smith (subsequently adopted into all the Public Grammar

Bohools; and, also, that all the scholars in arithmetic be taught by clašaos, and
bot individually, as is ouw the prevalent mode."

The above Report was signed by the following named gentlemen's
Rev. F. WAYLAND), Jr., D. D., Pres. Brown Univ., (Chairman.)
Rev. THOMAS T. WATERMAN.
WILLIAN T. GRINNELL, Esq.

Daled April 24, 1828.

6-30-43 and

This work is recommended by the State Commissioners of Vermont to ive adopled throughout that state. It is likewise introduced into the public and private schools of Hartford, Conn., by the concurrence both of committees and teachers, and in like manner in various other places.

(RECAP)

3118

ADVERTISEMENT TO THE KEY

WHICH ACCOMPANIES THIS ARITHNETIC.

"The utility, and even necessity, of a work of this description, will scarcely be questioned by those who have had any experience in teaching Arithmetic. Most young persons, after having been persuaded, again and again, to review a long anthmetical process, feel, or affect to feel, certain that they have performed it correcily, although the result, by the book, is erronevus. They then apply to their instructer; 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 idlencss is thus imperceptibly estab. lished. Now, in a large school, it is always inconvenient, and soinetimes impossible, for the instructer 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 ikese imporlant purposes it is now presented to the public.

January, 1834 »

PREFACE

TO THE THIRD EDITION.

WHEN a new work is offered to the public, especially on a subject ahounding with treatises like this, the inquiry is very naturally made, * Does this work contain any thing 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 public, after a careful examination of its contents, and not till then, it is hoped, must decide. Auother inquiry may still be inade : "Is this edi: tion different from the preceding?" The answer is, Yes, in many respects. The present edition professes to be strictly on the Pestalozzian, or inductive, plan of teaching. This, however, is uct claimed as a novelty. In this respect, it resembles many other systems. The novelty of this work will be fomd lo consist in adhering more closely to the true spirit of the Pestalozzian plan ; consequently, in differing from other systems, it differs less from tije Pestalozzian. This similarity will 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 inental questions. So does this.

3. That commences with examples for children as simple as this, is as extensive, and ends with questions adapted to minde as mature.

Here it may be azked, " In what respect, then, is this different from that?". To this question it is answered, 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, Felloroship, &c.

3. There is a constant recapitulation of the subject attended to, styled “ 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

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