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From the Jan. No. for 1828 of the JOURNAL or Education. “A careful 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 entirely a practical work, combining the merits of Colburn's system with copious practice en the late.

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 eannot, 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."

From the Report of the SCHOOL-COMMITTEE OF PROVIDENCE. "The books at present used in the schools are, in the opinion of your Committee, altogether above the range of thought of the pupils. Works of a nurrative character would be better understood, would be more interesting, and would, of course, teach the pupil to read with more taste and judgment. The boy who pores, in utter disgust, over the book which he reads in schools, will hasten home to read with avidity his story-book. The true wisdom would then be, to introduce the story-book into school, and thus render his place of education the place of his amusement.

"Nevertheless, as this subject is one in which time and judgment are necessary for a selection, and as a change of this sort, through all the schools, would be Froductive of considerable additional expense, your Committee would secoinmend that no change, at present, be made in books, excepting only the Arithmetic. Ifa.school, by way of experiment, be established on the monitorial plan, various school-books can be tried there, and, after a fair opportunity of testing the merits of several, those can be selected which seem best adapted to accomplish the purposes of education. Your Committee are, however, of opinion, that it would be expedient to introduce the system of Arithmetic published by Mr. Smith [subsequently adopted] into all the Public Grammar Bchools; and, also, that all the scholars in arithmetic be taught by classes, and not individually, as is now the prevalent mode."

The above Report was signed by the following named gentlemenRev. F. WAYLAND, Jr., D. D., Pres. Brown Univ., (Chairman.) Rev. THOMAS T. WATERMAN,

WILLIAM T. Grinnell, Esq.

Dated April 24, 1828.

This work is recommended by the State Commissioners of 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 places.

ADVERTISEMENT TO THE KEY

WHICH ACCOMPANIES THIS ARITHMETIC.

"The utility, and even necessity, of a work of this description, wiß carcely be questioned by those who have had any experience in teaching Arithmetic. Most young persors after having been persuaded, again and again, to review a long anthmetical 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 in structer; and, unless he points out their mistake, or performs the opera tion for them, they become discouraged, think it useless • to try' lunger, 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 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 these important purposes it is now presented to the public.

“January, 1834 "

10 THE THIRD EDITION.

ऐ WHEя a new work is offered to the public, especially on a subject abounding with treatises like this, the inquiry is very naturally made, 4. 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. 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 Pestalozzian, or induc tive, 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 ditlero less from the 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 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

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Here it may be asked. “In what respect, then, is this different from that?" To this question it is answered, In the execution of our comThe following are a few of the prominent characteristics of this work, in which it is thought to differ from all others,

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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 " 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, tnus furnishing a complete test of the knowledge of the pupil. ́This'

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is a characteristic difference between this and the formos editions.

A new rule for calculating interest for days with months. 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, previ ously 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 accom pany 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, perhape 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 nere be reminded, that these rules are taught differently, 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 generalized; that is, brietly summed in the form 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 he left to form his own rules, it is more than probable he might mistake the most concise and practical one. Besides, different minds view things differently, and draw different conclusions. Is there no benefit, then, in helping the pupil to the most concise and practical method of solving the various Droblems incident to a business life?

Some have even gone so far as to condemn the Rule of Three, or Proportion, and almost all the successive rules growing out of it. With more reason, they might condemn Long Division, and even Short Division; and, in fact, all the common and fundamental rules of Arithmetic, except Addi 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 else, provided the mind of the pupil be exercised, would be a good substitute. But when taught as it should be, and the scholar is led on in the same train of thought that originated the rule, and thus effectually made to see, that it is simply a convement method of arriving at the result of both Multiplication and Division combined, its necessity may be advocated with as much reason as any fundamental rule, As taught in this work, it actually saves more figures than Short, compared with Long Division. Here, then, on the ground of conventence, it would be reasonable to infer. that its retention was more necessary than either. But, 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 of beauty arising from viewing the harmonious relations of numbers. Here is a delightful field for an inquisitive mind It here imbibes truths as lasting as life. When the utility and convenience of this rule are once conceded, all the other rules growing out of this will demand a place, and

for the same reason.

It may, perhaps, be asked by many, "Why not take the principle with. out the name?" To this it is again replied, Convenience forbids. The name, the pupil will see, is only an aggregate term. given to a process imbodying several distinct principles. And is there no convenience in this

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