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HARVARD
UNIVERSITY
LIBRARY

47X130

DISTRICT OF MASSACHUSETTS, to wit:

District Clerk's Office.

BE IT REMEMBERED, That on the twenty-first day of January, A. D. 1825 in the fifty-third year of the Independence of the United States of Ameri ca, 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 Dollars and Cents. Stereotype 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 also 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 times therein mentioned; and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints." JNO. W. DAVIS,

Clerk of the District of Massachusetts.

iii

RECOMMENDATIONS.

From the Jan. No. for 1828 of the JOURNAL OF 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 cf actual experiment and observation in the school-room. It is entirely a practical work, combining the merits of Colburn's system with copious practice on the slate.

"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 class; while, by judicious attention to arrangement and printing, it is ren dered, 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 compiete 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 cannot, 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 narrative 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 neces sary for a selection, and as a change of this sort, through all the schools, would be productive of considerable additional expense, your Committee would recommend that no change, at present, be made in books, excepting only the Arithmetic. If a 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 Graminar Schools; 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 gen tlemen :

Rev. 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 Vermont to be adopted throughout that State. It is likewise in. troduced 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.

PREFACE

TO THE THIRD EDITION.

WHEN a new work is offered to the public, especially on a subject abounding 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 now; 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 inductive 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 differs 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

as mature.

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 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, Fellowship, &c.

3. There is a constant recapitulation of the subject attende.¿ 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 fur nishing a complete test of the knowledge of the pupil. This is a characteristic difference between this and the former editions 5. 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, previously and subsequently to their insertion.

9. As this mode of teaching recognises 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 accompany 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 de cide on their comparative value.

As, in this work, the common rules of arithmetic are retained, perhaps the reader is ready to propose a question frequently asked, "What is the use of so ma ny rules?" "Why not proscribe them?" The reader must here 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, briefly 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 ft? Should the pupil be left to form his own rules, it is more than probable he might mistake the most concise and practical one. Besides, dif- . ferent 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 problems 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, ail the common and fundamental rules of arithmetic, except Addition; 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 convenient 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 convenience, 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 without 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? Shall the pupil, when in actual business, be obliged to call off his mind from all other pursuits to trace a train of deductions arising from abstract reasoning, when his atten ion is most needed on other subjects. With as much propriety the name o captain may be dispensed with; for, although the general, by merely suron ng his captain, may summon 100 men, still he might ca' on each se tely, although not quite so conveniently With these remarks, the subject will ba

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