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from the Jan. No. for 1828 of the JOURNAL OF EDUCATION, " A careful examination of this valuable work will show that iu author has compiled it, - all looks for school use ought to be compiled, from tho resulta of actual experiment and observation in the school-room. It is entirely a practical work, combining the merit of Colburn's system with copious practice da the slate.

- Two circumstances enhanco very much the value of this book. It is very comprehensivo, containing twice the usual quartity of matter is works of this class; while, by judicious attention to arrangement and printing, it is ren derod, perhaps, the cheapest book in this department of education. The brief system of Book-Kooping, attached to the Arithmetic, will be a valuable aid to more completo instruction in common schools, to which the work is, in other rospecto, to peculiarly adapted.

There are several very valuable peculiarities in this work, for which w. cannot, in a notice, find sufficient space. We would recommend a careful ex. amination of the book to all teachers who we desirous of combining goud Woory with copious and rigid practice."

From the Report of the SCHOOL-COMMITTEE or PROVIDESCR.

a Tho books at present used in the schools are, in the opinion of your Como mittee, altogether above the range of thought of the pupila. Works of a natnative character would be better understood, would be more interesting, and would, of course, leach the pupil to read with more taste and judgment. The boy who yotes, in utter disgust, over the book which he reads in schools, will haston home to read with avidity his story-book. The true wisdom would then he, to introluca tha story-book into school, aud thus render his place of education the piace of his amusement,

“Neverthelons, as this subject is one in which time and judgment are necer sary for a selection, and as a chango of this sort, through all the schools, would be productivo of considerable additional expense, your Committee' would secolamend that no change, at prorent, bo mado in books, excupting only the Arithmetic. If a.school, by way of experiment, be established on the monito rial plan, various school-books can bo tried there, and, after a faut opportunity of testing the merits of several, those can be selected which seom bosi adapted to accomplish the purposes of education. Your Committee are, however, of opinion, that it woull be expedient to introduce the system of Arithmetic published by Mr. Smith (subsequently adopted) into all the Public Grammar Schools; and, also, that all the scholan in arithaotic bo laught by classes, and not individually, as is now the prevalent mode."

The above Report was signed by the following named gentlemen -
Rev. F. WarLAND, Jr., D. D., Pres. Browon Univ., (Chairman.)
Rev. THON AS T, WATERMAN,
WILLIAN T. GRINNELL, Esq.

Dated April 24, 1828.

This work is recommonded by the State Commissionen af Vermont to be adopted 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 placen.

ADVERTISEMENT TO THE KEY

WH:CH ACCOMPANILS 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 persors aher having ber a pele suaited, again and again, to review a long anthmetical process, feel, or affect to feel, certain that they have performed it correctly, alth gh the result, by the book, is erronevus. They then apply to their in structer; and, unless he points out their mistake, or performs the opera tion for them, they becoine discouraged, think it useless to try' linger, and the foundation for a habit of idleness is thus imperceptibly estab lished. Now, in a large school, it is always inconvenient, and some. times impossible, for the instrucier 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, lo which reference can be easily and speedily made. The time of the deacher will thus be saved, and the pupil will not have his andor 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 ohject is to lighten the burden of teachers, and facilitate the progress of scholars. To promote, both of these important purposes to is now presented to the public.

M. January, 1834 "

PREFACE

10 TIIE THIRD EDITION.

When a new work is offered to the public, especially on a sijea alsounding with treatises like this, the inquiry is very naturally nade, “Dars this work contain any thing new?" "Are there not a hundred others as good as ths” To the first inquiry it is replied, that there are many things which are believed to be new; and, as to the second, a caudid public, after a careful examination of its contents, and not till then, it is hopest, inust decide. Auntier inquiry may still be made : “ Is this edi. tivy diferent from the precedirgi" Tire answer is, Yes, in inany respects. T'he prescut edition professes to low stóirtly onillie Pestalozzian, or induce tive, plan of teaching. This, however, is not claimed as a novelty. In this respect, li resembles many other systems. The novelty of this work wiil be found to consist in alhering more closely to the true spirit of the Pestalozzian plant ; consequently, in ditering from other systems, it dider less from the Pestalozzian. Tois simiarity will now be shown.

t. The Pestalozzian professes lo unite a conplete system of Mental with Wrilieu Arithmetic. Sy does this.

2. That rejects no rules, but simply illustrates them by mnen. tal questions. So does this.

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

flere it may be asked. “In what respect, then, is this different from that?" To this question it is answered, in the execution of our coinQuin plan.

The following are a few of the prominent characteristics of this work, in whici it is thought to differ from all others,

J. The interrogative systein is generally adopted throughout this work. - 2. The common rules of Arithinetic are exhibited so as to cos. respund with the occurrences in actual business. Under this head is reckoned the application of Rutio to practical purposes Fellowship. &c:

3. There is a constant recapitulation of the s'ubject attended to, stylud“ Questions on the forevniny."

4 The mode of giving the individual results without pointa, then the aggregate of these results, with points, for an answer by which the relative value of the whole is determined, tnus fúrnialaing a complete lest of the knowledge of the pupil. This

in i characteristic difference between this and the forume editions.

5 A new rule for calculating interest for days with monthn.

6. The niode of introducing and conducting the subject of Proportion.

7. The adoption of the Federal Coin, to the exclusion of Ster ling Money, except by itself.

8. The Arithmetical Tables, are practically illustrated, previ. ously and subsequently to their insertion.

.. As this mode of teaching recognizes no anthority but that of reason, it was found necessary to illustrate the rule for the extraction of the Cube Root, by means of blocks, which accom pany this work.

These are some of the predominant traits of this work. Others might be mentioned, but, by the exainination of these, the reader will be qualified to decide on their comparative value.

As, in this work, the common rules rf Arithmetic are retained, perhape the reader is ready to propose a question frequently asked, “What is the Use of so many rules?" " Why not proscribe then?" The reader must nere be reminded, that these rules are tauglit differently, in this system, from the common method. The pupil is tirst to satisfy himself of the truth of several distinct inathematical principles. These deductions, or truths, are then generalized ; that is, brietly samined in the forn of a rule, which for convenience sake, is named. Is there any impropriety in this? On the contrary, is there not a great convenience in it? Should the pupil le left to form his own rules, it is more than probable he might mistake ihe most concise and practical one. Besides, different minds view things different. ly, and draw different conclusions. Is there to benefit, then, in helping the pupil to the most concise and practical method of solving the various problems incident to a business life?

Some ha'.e even gone so far as to condemn the Rule of Threr, or Proportion, and almost all the successive rules growing otit of it. With more reason, they might condemın Long Division, and even Short Division; and, in fact, all the common and fundamental rules of Arithmetic, except Aditi tion ; for these may all be traced to that. The only question, then, is. “To what extent shall we go?". To this it is replied, As far as convenience requires. As the Rule of Three is generally taught, it must be confessed, that almost any thing rise, provided the mind of the pupil be exercised, would be a good substitute. But when tanglit as it should be, and the scholar is led on in the same trains of though that originated the rule, and thus effectually made to see, that it is simply a convenient method of arriving at the restrit of both Multiplication and Division combined, ils ne cessity niay be advocated with as much reason as any fundamental rule, Aa taight in this work, it actually silves more tigrires than Shuurt, compared with Lung Division. Here, then, on the ground of convenience, it would be reasonable to infec. that its retention was more necessary than either. Bui, waiving its utility in this respect, there is another view to be taken of this subject. and that not the least in importance, viz. the ideas or beanty irising from plewing the harmonious relations of numbers. Here is a delightfal field for an inquisitive mind It here ipobibes truth, as lasting as life. When the utility and convenience of this rule are ence concede il, all the other rules gruning ullt of this will demand a place, aud for the same reason.

It may, perhaps, he asked by many, “ Why not take the principle with: out the name?" To this it is ayni replied, convenience forbids. Tho name, the pupil will see, is only an aggregate ferm. given to a process intudying several distint principles. And is there 11o cunvenience in thias

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