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HARVARD COLLEGE LIBRARY
FROM THE LIBRARY OF
WILLIAM A. WHITE
JUNE 28, 183

DISTRICT OF MASSACHUSETTS, TO WIT :

District Clerk's office. BE it remembered, that on the fifth day of April. 4. D. 1822, in the Forty-sixth year of the Independence of the United States of America, Cummings and Hilliard, of the said Distriet, have deposited in this office the title of a Book, the right whereof they claim as Proprietors, iu the words following, to wit:

6. First Lessons in Arithmetic on the plan of Pestalozzi. With some Improvements. By Warren Colburn. Second Edition."

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 Histor ical, and other Prints."

JOHN W. DAVIS, Clerk of the District of Massachusetts.

RECOMMENDATION

HARD COLLEGE LIBRARY FROM THE LIBRARY OF WILLIAM A. WHITE JUNE 28, 1930

BOSTON, 15 Nove Sir,

I have made use of the Arithmet which you sometime since prepared, on Pestalozzi ; and have been much gra improved edition of it, which you have am satisfied from experiment, that it is t tual and interesting mode of teaching numbers with which I am acquainted.

Respectfully
your obedient ser-

HENRY
Mr. Warren Colburn.

CT OF MASSACHUSETTS, TO WIT:

District Clerk's office. mbered, that on the fifth day of April. A. D. 1822,

th year of the Independence of the United States of anings and Hilliard, of the said District, have deposited e title of a Book, the right whereof they claim as the words following, to wit: uns in Arithmetic on the plan of Pestalozzi. With ments. By Warren Cotburn. Second Edition." Iy to the Act of the Congress of the United States, enct for the encouragement of Learning, by securing the 3. Charts, and Books, to the Authors and Proprietors during the times therein mentioned :" and also to an ** An Act supplementary to an Act, entitled, An Act ragement of learning, by securing the copies of Maps, ooks, to the Authors and Proprietors of such copies mes therein mentioned ; and extending the benefits

arts of Designing, Engraving, and Etching HistorV W. DAVIS, Clerk of the District of Massachusetts.

[graphic]

r Prints."

Having been made acquainted with treatise on Arithmetic, and having atten ation of his scholars who had been taug this system, I am well satisfied that it i simple and natural way of introducing to the first principles in the science of method here proposed is the fruit of

reflection. The author has had considerable experience as a teacher, added to a strong interest in the subject, and a thorough knowledge not only of this but of many of the higher branches of mathematics. This little work is therefore earnestly recommended to the 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 approved and adopted.

J. FARRAR,

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

PREFACE.

tion. The author has had considerable experia is a teacher, added to a strong interest in the t, and a thorough knowledge not only of this but ny of the higher branches of mathematics. This vork is therefore earnestly recommended to the of those who are employed in this branch of instruction, with the belief that it only requires a ial in order to be fully approved and adopted.

J. FARRAR,

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

As soon as a child begins to use his sense tinually presents to his eyes a variety of one of the first properties which he disc relation of number. He intuitively fixes up measure, and from this he forms the idea less ; which is the idea of quantity.

The names of a few of the first number learned very early; and children freque count as far as a hundred before they learn

As soon as children have the idea of m and the names of a few of the first num able to make small calculations. And this do every day about their playthings, and al affairs which they are called upon to at idea of more and less implies addition; h often perform these operations without instruction. If, for example, one child has and another five, they will readily tell how n have ; and how many one has more than a child be requested to bring three apple: son in the room, he will calculate very many to bring, if the number does not e has learnt. Again, if a child be requestnumber of apples among a certain num

1*

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 of 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 the best, some improvement should be suggested. By following this mode, and making the examples gradually increase in difficulty ; experience proves, that, at an early age, children may be taught a great variety of the most useful combinations of numbers.

Few exercises strengthen and mature the mind so much as arithmetical calculations, if the examples are made sufficiently simple to be understood by the pupil; because a regular, though simple process of reasoning is requisite to perform them, and the results are attended with certainty."

The idea of number is first acquired by observing sensible objects. Having observed that this quality is common to all things with which we are acquainted, we obtain an abstract idea of number. We first make calcu

* See on this subject two essays, entitled Juvenile Studies, in the Prize Book of the Latin school, Nos. I and II. Published by Cummings & Hilliard, 1820 and 1821.

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