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UPON THE

INDUCTIVE METHOD OF INSTRUOTION:

BEING

A SEQUEL

то

INTELLECTUAL ARITHMETIC.

BY WARREN COLBURN, A. M.

STEREOTYPED AT THE BOSTON TYPE AND STEREOTYPE FOUNDRY.

PHILADELPHIA :
* PUBLISHED BY URIAH HUNT.

BOSTON:
HILLIARD, GRAY, LITTLE, AND WILKINS.

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Lista SOLLEGA

(in oct 1929

LIBRARY

Mers. Many R. Hanne
DISTRICT OF MASSACHUSETTS, To win:

District Clerk's Office. BE IT REMEMBEREI), 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 elaims 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, en. titled, “ An act for the encouragement of learning, by sccuring the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned ;” and also an act, entitled, “ 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 thercin 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 explained with great perspicuity and simplicity. I think your reasonings and illustrations are peculiariy happy and original. This, together with your “ First Lessons,” forms the most lucid and intelligible, as well as the most scientific system of Arithmetic I have ever seen. Its own merits place it beyond the need of commendation.

With much esteem,
Sir, your obedient servant,

B. A. GOULD. · Mr. WARREN COLBURN.

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

Boston.

Boston, 22d 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 wishes 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 sutject with which I am acquainted. I am, with great respect,

Yours, &c.

G. B. EMERSON Mr. WARREN COLBURN

PREFACE.

It will be extremely useful, though not absolutely necessary, for pupils of every age to study the “ First Lessons," previous to commencing this treatise. 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 difficult than other treatises on the subject, for those who have not studied the “ First Lessons."

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

This Sequel consists of two parts. The first contains a course of examples for the illustration and application of the principles. The second part contains a developement of the principles. The articles are numbered in the two, so as to correspond with each other. The two parts are to be studied together, when the pupil is old enough to comprehend the second part by reading it himself. When he has performed all the examples in an article in the first part, he should be required to recite the corresponding article in the second part, not verbatim, but to give a good account of the reasoning. When the principle is well understood, the rules which are printed in Italics should be committed to memory. At each recitation, the first thing should be to require the pupil to give a practical example, involving the principle to be explained, and then an explanation of the principle itself.

When the pupil is to learn the use of figures for the first time, it is best to explain to him the nature of them as in Art. I., to about three or four places; and then require him to write some numbers. Then give him some of the first examples in Art. II., without telling him what to do. He will discover what is to be done, and invent a way 10 do it. Let him perform several in his own way, and then suggest syme method a little different from his, and nearer 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, and should be allowed to continue his own way longer, and then it should be suggested again. After he is familiar with that, suggest another method, somewhat nearer the common 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. Ile will write it down as such. But if he is familiar with the “ First Lessons,” he will probably perform it as multiplication without know. ing it. When he does this, suggest to him, that he need 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 manner 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 example. · If a pupil is unable to perform an example, it is generally because he does not 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 prepared for it, and he must be required to examine 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 he is not to be told, he learns to depend on himself; and when he once contracts the habit 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 to select such as will show the combination in the simplest manner, and that the numbers be so smal, that the operation shall not be difficult. When a proper idea is formed 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 succeeded beyond his expectations. Practical examples not only shop at once the object to be accomplished, but they greatly assist

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