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BOSTON:
SAN BORN, CARTER AND BAZIN.
PORTLAND: SANBORN & CARTER.

1856.

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DISTRICT OF MASSACHUSETTS, TO WIT:

District Clerk's Office. BE IT REMEMBERED, that on the twenty-fifth day of May. A. D. 1826, and in the fiftieth year of the Independence of the United States of America, Warren Colburn, of the said District, has deposited in this office the title of a book, the right whereof he claiins as author, in the words following, to wit:

Arithmetic upon the Inductive_Method of Instruction. being a Sequel to Intellectual Arithmetic. By Warren Colburn, A. M."

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 an act, en. titled, “ An act supplementary to an act, entitled, An act for the en. couragement 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.

RECOMMENDATIONS.

From B. A. GOULD, Principal of the Public Latin School, Boston

Boston, 22d Oct., 1822. DEAR SIR,

I have been highly gratified by the examination of the second part of your Arithmetic. The principles of the science are unfolded, and its practical uses explaineů with great perspicuity and simplicity I ihink your reasonings and illustratio's are peculiariy happy and original. Tliis, together with your “ First Lessons," forms the most lucid and intelligible, as well as tho most scientific system of Arith raetic I have ever seen.-Its own merits place it beyond the need of connendation.

With much esteem,
Sir, your obedient servant,

B. A. GOULD
Mr. WARREN COLBURN.

From G. B. EMERSON, Principal of the English Classical School,

Buston.

Boston, 222 Oct., 1822 DEAR SIR:

I have carefully examined a large portion of your manuscript, and do not hesitate to recommend it very highly to every person who wishc3 to teach arithmetic intelligibly. The arrangement is very much better, the explanations more convincing, and the rules, from the mode in which they are introduced, are clearer and simpler, than can be found in any book on the sucject with which I ain acquainted I am, with great respect,

Yours, &c.

G. B. EMERSON, Mr WARREN COLBORN.

PREFACE

It will be extremely useful, though not absolutely necessary, tai pupils of' evory age to study the “ First Lessons," previous to commencing this lieatise. There is an intimate connexion between the two, though this is not dependent on the other. It is hoped that this will be found less diflicult than other treatises on the subjeci, for those who have not studied the “ First Lessons."

Pupils may commence thu “ First Lessons” to advantage, is soon as they can read the examples; and even before they can read, it will be found very useful to ask them questions from i.. This may be done by other pupils who have already studied it. Those who commence early, inay generally ubtain sutlicient knowledge of it by the time they are eight or nine years old. They may then commence this.

This Sequel consists oí two parts. The first contains a course of exampies for the illustration and application of the principles. The second part contains a developement of the prir:ciples. The articles are numbered in ihe twe, so as to correspond wiili each other. The two parts are to he studied ingether, when the pupil is old enough to comprehend the second part by reading it himself. When he fias performed ali tlie examples in an article in the first part, he shone boos required to recite the ci rresponding article in the second part, not verbatim, but to give a good account of the reasoning. When the principle is well undersiood, the rules which are printed in Italics should be committed to ineniory. At each recitation, the first thing should be to require the pupil to give a practical example, involving th; principle to be explained, and then an explanation of tho principle itself.

When the pupil is to learn the use of figures for the first time, it is best to explain to hin the nature of then as in Art. to about three or four place“; and then require him to write some numbers. Then give him some of the first examples in Art. II., withicul telling him what to do. He will disc.ver what is to be done, and invent a way 10 do it. Let him perform several in his own way, and then suggest wune method a litie different from his, and uearer the common

method. If he readily comprehends it, he will be pleased with it; and adopt it. If he does not, his mind is not yet prepared for it, ard should be allowed to continue his own way longer, and then it should be suggested again. Afier he is familiar with that, suggest another method, somewhat nearer the cominon method, and so on, until he learns the best method. Never urge him to adopt any method until he understands it, and is pleased with it. In some of the articles, it may perhaps be necessary for young pupils to perform more examples than are given in the book.

When the pupil is to commence multiplication, give him one of the first examples in Art. III., as if it were an example in Addition. He will write it down as such But if he is familiar with the “ First Lessons," he will probably perform it as multiplication without knowing it.

When he does this, suggest to him, that he nced not write the number but once. Afterwards recommend to him to write a number to show how many times he repeated it, lest he should forget it. Then tell him that it is Multiplication. Proceed in a similar inanner with the other rules.

One general maxim to be observed with pupils of every age, is never to tell them directly how to perform any exanıple. If a pupil is unable to perform an exainple, it is generally because he does nou fully comprehend the object of it. The object should be explained, and some questions asked, which will have a tendency to recal the principles necessary. If this does not succeed, his mind is not pre. pared for it, and he must be required to examino it more by himself, and to review some of the principles which it involves. It is useless for him to perform it before his mind is prepared for it. After he has been told, he is satisfied, and will not be willing to examine the principle, and he will be no better prepared for another case of the same kind, than he was before. When the pupil knows that lie is not to be told, he learns to depend on himself ; and when he once contracts the halit of understanding what he does, he will not easily be prevailed on to do any thing which he does not understand.

Several considerations induce the author to think, that when a principle is to be taught, practical questions should first be proposed, care being taken tu select such as will show the combination in the simplest manner, and that the numbers be so small that the operation shall not be difficult. When a proper idca is ford of the nature and use of the combination, the method of solving these questions with large numbers should be attended to. This method, on trial has s'ic ceeded beyond his expectations. Practical exaır ples not only show at once the objeet to be accomplished, but they greatly assist

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