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From Wm. B. Greene, A. B., Principal of Milford Academy.
MILFORD, Nov. 29, 1845.

J B. Thomson, Esq.-Dear Sir,-I have examined your Practical Arithmetic, and am pleased to observe the clearness and precision with which the subject is presented-the same that have so highly characterized your Algebra and Geometry, and so happily adapted them to the capacities of the young.Such a work has long been needed in our schools and academies. It meets my views so well, that I have introduced it into my school.

Yours, truly,

WM. B. GREENE.

Notwithstanding the number of Arithmetics before the public, the general opinion among practical teachers is, and they are best qualified to judge, that in many respects they are not adapted to the use of our schools, and the improved method of instruction. Thomson's Practical Arithmetic is admirably adapted to supply these wants.

The plan of the work is, first to give the pupil a knowledge of the rule by solving a number of examples; that is, by induction; then to analyze the principles separately; and, finally, to sum up these separate principles into a General Rule. The plan is philosophical and the only true one, and is most. admirably executed. The definitions and rules are expressed in a simple and lucid mauner, so that every child can understand them;-each rule is commenced with practical examples, well adapted to explain the principles of the rule; the numbers in them at first are small, and gradually increase to larger combinations, as the mind of the pupil is expanded, and is able to comprehend

them.

The Notes and Observations interspersed through the work, contain much information which it is essential for the learner to possess in order to have a full understanding of the rule, which is not to be found in other Arithmetics. The correction of the Tables of Compound Numbers, giving the Standard Units of Weights and Measures adopted by the General Government, are of the highest importance to those who are preparing to transact business, and show that the author has gone into a thorough investigation of his subject. We cordially recommend the work to all who want a Practical Arithmetic. Give it a fair hearing, and it cannot fail to "win its way" at once, to the approbation and favor of the public.-New Haven Courier.

Mr. Thomson enjoys an enviable reputation as a maker of school books, both from his own decided merit, and also as being associated with President Day of Yale College. Perfectly familiar with the wants of scholars, from years of faithful, successful teaching; perfect master of the branches necessary to be taught; enthusiastic in his love of his profession; and possessed also of much literary ability, in which quality mere school book makers are apt to be defficient; and enjoying the distinguished opportunity of the suggestion and assistance of Dr. Day; the public would have a right to be greatly dissatisfied if the result was not such a book as few could equal and none surpass.

Mr. Thomson has already published a number of books, being portions of "Day & Thoinson's serics;" the present one now added to the list, is, so far as we can judge, not only equal to the rest, but superior. It teaches the pupil by examples, leading him thus to a knowledge of the rule; when this is attained he is made to retrace his steps, analyze the process and understand what he has done.-New Haven Daily Herald.

Thomson's Practical Arithmetic, is an improvement on most school books of this description-inasmuch as it is eminently practical; simplifying the most difficult parts of common Arithmetic, so as to bring results readily and almost intuitively to the mind of the scholar Nothing disheartens the new beginner so much as a severe array of figures which he is required to subdue by a cold and unattractive rule, which is as much a hyeroglypic as the problem itself; but let him see it in the light of a practical, common sense question, and he will accomplish by induction, almost immediately, what would take him much longer to figure out by the old process-and be more clearly impressed on the mind. This seems to have been the primary object of the author, who, in connection with President Day, is publishing a new and valuable series of books for Schools and Academies.-New Haven Register.

PRACTICAL

ARITHMETIC,

UNITING THE

INDUCTIVE WITH THE SYNTHETIC MODE OF INSTRUCTION:

ALSO, ILLUSTRATING THE

PRINCIPLES OF CANCELATION.

FOR SCHOOLS AND ACADEMIES.

By JAMES B. THOMSON, A. M. EDITOR OF DAY'S SCHOOL ALGEBRA, LEGENDRE'S GEOMETRY, &C.

NEW HAVEN :

DURRIE & PECK;

LOOMIS & PECK, PHILADELPHIA;

J. C. DERBY & CO., AUBURN, N. Y.;

G. H. DERBY & CO., GENEVA, N. Y.

1484507

1863, May 1,

Entered according to Act of Congress, in the year 1845,
BY JEREMIAH DAY and JAMES B. THOMSON,
in the Clerk's Office of the District Court of Connecticut.

N. B. A KEY to Practical Arithmetic, containing the answers, numerous suggestions, &c., is published for the use of Teachers.

PECK & STAFFORD, Printers,

New Haven.

PREFACE.

Ir has been well said, that "whoever shortens the road to knowledge, lengthens life." The value of a knowledge of Arithmetic is too generally appreciated to require comment. When properly studied, two important ends are attained, viz: discipline of mind and facility in the application of numbers to business calculations. Neither of these results can be secured, unless the pupil thoroughly understands the principle of every operation he performs. There is no uncertainty in the conclusions of mathematics; there should be no guess-work in its operations. What then is the cause of so much groping and fruitless effort in this department of education? Why this aimless, mechanical" ciphering," that is so prevalent in our schools?

The present work was undertaken, and is now offered to the public, with the hope of contributing something towards the removal of these inveterate evils. Its plan is the following:

1. To lead the pupil to a knowledge of each rule by induction; that is, by the examination and solution of a large number of practical examples which involve the principles of the rule.

2. The operation is then defined, each principle is analyzed separately, and illustrated by other examples.

3. The general rule is now deduced, and put in its proper place, both for convenient reference and review; thus combining the inductive and synthetic modes of instruction.

4. The general rule is followed by copious examples for practice, which are drawn from the various departments of business, and are calculated both to call into exercise the different principles of the rule, and to prepare the learner for the active duties of life.

1

It is believed that much of this guess-work in "figuring," and its concomitant habits of listlessness and vacuity of mind, have arisen from the use, at first, of abstract numbers and intricate questions, requiring combinations above the capacity of children. Taking his slate and pencil, the pupil sits down to the solution of his problem, but soon finds himself involved in an impenetrable maze. He anxiously asks for light, and is directed "to learn the rule." He does it to the letter, but his mind is still in the dark. By puzzling and repeated trials, he perhaps finds that certain multiplications and divisions produce the answer in the book; but as to the reasons of the process, he is totally ignorant. To require a pupil to learn and understand the rule, before he is permitted to see its principles illustrated by simple practical examples, places him in the condition of the boy, whose mother charged him never to go into the water till he had learned to swim.

These embarrassments are believed to be unnecessary, and are attempted to be removed in the following manner: 1. The examples at the commencement of each rule are all practical, and are adapted to illustrate the particular principle under consideration. Every teacher can bear testimony, that children reason upon practical questions with far greater facility and accuracy than they do upon abstract numbers.

2. The numbers contained in the examples are at first small, so that the learner can solve the question mentally, and understand the reason of each step in the opera

tion.

3. As the pupil becomes familiar with the more simple combinations, the numbers gradually increase, till the slate becomes necessary for the solution, and its proper use is then explained.

4. Frequent mental exercises are interwoven with exercises upon the slate, for the purpose of strengthening the habit of analyzing and reasoning, and thus enable the learner to comprehend and solve the more intricate problems.

5. In the arrangement of subjects it has been a cardinal point to follow the natural order of the science. No principle is used in the explanation of another, until it

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