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INTELLECTUAL

ARITHMETIC,

UPON THE

INDUCTIVE METHOD

Xnstruction.

BY WARREN COLBURN, A. M.

STEREOTYPED AT THE BOSTON TYPE AND STEREOTYPE FOUNDRA

HALLOWELL, ME.:
GLAZIER, MASTERS, & SMITH.

BOSTON :
MILLIARD, GRAY, & Co

1836.

DISTRICT OP MASSACHUSETTS, TO WIT:

District Clerk's Odioe. BE it rememberod, that on the twenty-third day of March, A. D. 1826, in the fiftieth your of the lodependence of the United States of America, Cummings, Hilliard, and Company, of the said District, have deposited in this office the title of , boxok, the right whereof they claim as proprietors, in the words following, to wit:

"Intellectual Arithinotic, upon the Inductive Method of Instruction. 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 houks, tu the authors and proprietors of such copies, during the times tkerein inentioned :" and also to an act, entitled, “ An Act, supplementary to an gat, entitled, An Act for the encouragement of learning, by securing the copies of mups, charts, and books, to the authors and proprietors of ouch copies during the times therein mentioned ; and extending the benefits thereof to the urts of designing, engraving, and etching historical, and other prints."

JOHN W. DAVIS,
Clerk of the District of Massachusetts

RECOMMENDATIONS.

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Boston, 15 November, 1821. I have made use of the Arithmetic and Tables, which you sometimo since prepared, on the system of Pestalozzi; and have been much grar ified with ibe improved edition of it, which you have shown me. I am satisfied, from experiment, that it is the most effectual and interesting trole of teaching the science of numbers with which I am acquainted.

Respectfully,
Your obedient servant,

HENRY COLMAN.
Mr. Warren Colbury.

Having heen made acquainted with Mr. Colburn's treatise on Arithmetic, and having aiteuried an examination of his scholars, who had been laugh accoriling to Hois system, I an well satisfied that it is the most easy, simple, and valural way of introducing young persons to the first priüriples in the science of numbers. The method here proposed is the Frunt où inuch study and reflection. The author has had considerable ex. perience as a teacher, added to a strong interest in the subject, and a thorough knowledge 110k only of this out of inany of the higher branches of mathematics. This line work is therefore earnestly recommended to dhe notice of those who are employed in this branch of early instruction, with the belief that it only requires a fair trial in order to be fully approve ad and allopied.

J. FARRAR,

Prof Math. Harvard University. Campridge, Nov. 16 1821.

in Au vuklub Libri

GIFT OF
JULIUS R. WAKEFIELU

MAY 4 1932

PREFACE.

As soon as a child begins to use his senses, nature contin'ually presents to his eyes a variety of objects; and one of the first properties which he discovers, is the relation of number. He intuitively fixes upon unity as a ineasure, and from this ne forms the idea of more and less; which is the idea of quantity

The names of a few of the first numbers are usually learned very early; and children frequently learn to count as far as a hundred before they learn their letters.

As soon as children have the idea of more and less, and the names of a few of the first numbers, they are able to make small calculations. And this we see them do every day about their playthings, and about the little affairs which they are called upon to attend to. The idea of more and less implies addition; lience they will often perform these operations without any previous instruction. If, for example, one child has three apoles, and another five, they will readily tell how many they both have ; and how many one has more than the other. Ifa child be requested to bring three apples for each person in the room, he will calculate very readily how many to bring, if the number does not exceed those he has learnt. Again, if a child be requested to divido a number of apples among a certain number of persons, he will contrive a way to do it. and will tell how many each must have. The method which children take to do these things, though always correct, is not always the most expeditious.

The fondness which children usually manifest for these exercises, and the facility with which they perform them, seem to indicate that the science

numbers, to a certain extent, should be among the first lessons taught to them.*

To succeed in this, however, it is necessary rather to furnish occasions for them to exercise their own skill in performing examples, than to give them rules. They should be allowed to pursue their own method first, and then they should be made to observe and explain it; and, if it was not

* See on this subject two essays, entitled Juvenile Studies, in the Prize Book of the Latin school, Nos. I. and Il., published by Cum. mings & Hilliard, 1920 and 1821.

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