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DISTRICT OF MASSACHUSETTS, TO WIT:
District Clerk's Office. BE it remembered, that on the Twenty-third day of March, A. D. 1826, in the fiftieth Year of the Independence of the United States of America, Cummings, Hilliard, and Company, 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:
" Intellectual Arithmetick, upon the Inductive Method of Instruction. By Warren Colburn, A. M."
In conformity to the Act of the Congress of the United States, enlitled “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, 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."
JOHN W. DAVIS, Clerk of the District of Massachusetts.
Boston, 15 November, 1821. I have made use of the Arithmetic and Tables, which you sometime since prepared, on the system of Pestalozzi ; and have been much gratified, with the improved edition of it, which
have shown me. Í am satisfied from experiment, that it is the most effectual and interesting mode of teaching the science of numbers with which I am acquainted.
Having been made acquainted with Mr. Colburn's treatise on Arithmetic, and having attended an examination of his scholars who had been taught according to this system, I am well satisfied that it is the most easy, simple, and natural way of introducing young persons to the first principles in the science of numbers. The method here proposed is the fruit of much study and reflection. The author has had considera. ble 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,
Prof. Math. Harvard University. Cambridge, Nov. 16, 1821. TOCMESE LISTY
As soon as a child begins to use his senses, nature contina 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 measure, and from this he 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 ; hence they will often perform these operations without any previous instruction. If, for example, one child has three apples, and another five, they will readily tell how many they both have; and how many one has more than the other. If a 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 divide 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 cxercises, 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
* 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.