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Few School Books have perhaps proved more generally useful than Colburn's Mental Arithmetic. Yet Colburn's work has this fault, with classes taking their first lessons in figures. They advance to a certain point when they must be put back and begin anew, for the reason that their capacity cannot grow with the advance so suddenly made from the simple principles of numbers: the operation is repeated until pupils tire and become discouraged in consequence. Nothing can more certainly dampen the warm and curious impulse, with which a child opens upon anything new when rightly presented to hin.

I consider your "First Lessons in Numbers" as admirably guarded in this respect, and most cordially recommend them as a desideratum much needed in our schools for the use of that class of children for whom they were intended. I am, most truly, Yours,

Auburn, May 20, 1846.

C. A. PARSONS.

It is believed that children may be profitably instructed in mental arith metic, as one of their earliest exercises. The works that have been mostly in use, for this purpose, are Colburn's Mental Arithmetic, and Emerson's First Lessons. The former is too difficult forbeginners, and is seldom mastered, except by the most gifted of the class. The latter is too puerile, and confines the attention too much to sensible objects. We think Mr. Thomson has avoided the faults of both. His system "commences with practical examples which relate to familiar objects and require the simplest combinations. The pupil is then introduced to others involving the same principle but somewhat harder, special care being taken to make the transition very gradual, so that instead of being disheartened at the ruggedness of the way, he shall be stimulated to take the next step by the hope of victory."-Cayuga Patriot.

Mr. Thomson has already been very successful as the author of several works of a higher character-and it will be a source of pleasure to many who have become acquainted with his former efforts, to learn of his present work for the young. This, it will be noticed, is intended as comprising the first lessons in numbers, and SIMPLICITY has therefore been sought in all its rules as well as in all its examples. Every effort seems to have been made to bring all things relating to it down to the youngest capacity. As one example it may be mentioned, owing to the fact that "children comprehend and remember words more easily than figures, and reason upon them with so much greater facility, the numbers and tables in the first part of the book, are expressed in words." Taken as a whole, it is admirably adapted for the class for whose benefit it is specially intended-and we rejoice to learn that it has already been very generally introduced into most of the schools in this vicinity.-Auburn Daily Advertiser.

PRACTICAL ARITHMETIC.

From Prof. V. DREW, A. M. Prin. of Eng. and Classical Institute, N. Y. City-to PROF. WEST, Principal of Rutgers Institute, New York.

Dear Sir,-By request of the publishers, I present you a copy of "Thom. son's Practical Arithmetic"-a work which I have just adopted in school. My rule has been, not to recommend a book which I have not fully tested by use but, in the present case, I must say, from a fair examination, I consider this Arithmetic as decidedly the best that has appeared. In nearly every Article something is gained in the mode of presenting the subject,

perspicuity, and precision being remarkable throughout. Notwithstanding the late improvements in such works, I should not be surprised should this production soon become the general favorite.

New York, May 4, 1846.

V. DREW.

Extract from Rev. SAMUEL J. MAY, late Principal of State Normal School, Lexington, Mass.

JAMES B. THOMSON, ESQ.-Dear Sir:-I have given some time to the examination of your "Practical Arithmetic;" and am happy in being able to speak of it in terms of high commendation. The plan is excellent, and the execution of the plan, so far as I have examined, is thorough. It is the best offspring, I have yet seen, of the improved method of teaching Arith. metic. Wishing you an ample reward for your labors, in the preparation of books, to assist in the instruction of the young, I remain your sincere friend,

Syracuse, May 6, 1846.

SAMUEL J. MAY.

From L. W. HALL, A. M. Author of Moral Philosophy, and Principal of Ravenna High School, Ohio.

J. B. THOMSON, Esq.-Dear Sir,-I have derived much satisfaction from an examination of your "Practical Arithmetic," and my appreciation of its merits will be best expressed by the statement of the fact that I intend to introduce it into my school, at the earliest practical moment. Its thorough ly practical character is what gives it great value in my estimation, and in this respect it greatly excels any Arithmetic with which I am acquainted. Ravenna, Ohio, May 19, 1846: L. W. HALL.

From Rev. GEO.W. THOMSON, Principal of Onondaga Academy, New-York.

MR. THOMSON-Dear Sir-From the examination I have been able to give your "Practical Arithmetic," I consider it a valuable addition to that class of books. It contains many improvements and items which are not found in other Arithmetics. Your edition of "Day's Algebra," I am also very much pleased with. I shall introduce both of them into my school as soon as possible. Very respectfully your obedient servant, GEO. W. THOMSON.

Onondaga Academy, May 25, 1846.

From E. A. SMITH, Esq. Cor. Secretary of Queens Co. Teachers Association, N. Y.

MR. THOMSON-Dear Sir-I recently received from your publishers a copy of the "Practical Arithmetic', of which you are the author. Permit me to express my gratification at the internal evidence of merit which it exhibits. The lucid arrangement exceeds any thing of the kind that I have hitherto seen; the progression from simple easy examples to those which are more complex, and especially the illustrations of the different rules by examples drawn from the every day occurrences of life, are all exceedingly well adapted to impart a real knowledge of the science of Arithmetic, and are altogether preferable to the mechanical sameness, which has so long prevailed, and which will continue, until the mere abstract expositions are laid aside. The juvenile mind needs tangible objects, familiar examples, which may be grasped without difficulty, and to which the process of reasoning may be successfully applied. Finally, I hope your book may come into genral use; and I am satisfied that to be appreciated it has only to be seen and exam. ined. Very truly Yours, ELIJAH A. SMITH.

Hemstead, Jan. 31, 1846.

Thomson's First Lessons.

MENTAL

ARITHMETIC,

OR

FIRST LESSONS IN NUMBERS.

FOR CHILDREN.

BY JAMES B. THOMSON, A. M.

AUTHOR OF PRACTICAL ARITHMETIC, 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.

1846.

HARVARD COLLEGE LIBRARY

GIFY OF

BESIGE ARTHUR PLANETOL
JANUARY 25, 1823.

Entered according to Act of Congress, in the year 1846,
BY DURRIE & PECK,

in the Clerk's Office of the District Court of Connecticut.

H. OLIPHANT, PRINTER,

Auburn, N. Y.

PREFACE.

At what precise age a child should begin to go to school, or commence the different studies, it is not our province to decide. Whatever may be the diversity of opinion on this point, all practical teachers seem to agree, that Mental Arithmetic is among the first exercises, which should be presented to the youthful mind. The correctness of this sentiment is corroborated by the ease with which children understand simple combinations of numbers, their fondness for these exercises, and the obvious advantages which may be derived from them. But in order to become interesting or profitable, it is manifest, this branch, as well as others, must be taught in such a manner that the pupil shall understand it. The examples therefore must, at first, be simple, containing small numbers, and have reference to sensible objects with which the learner is acquainted; the transition from easy to more difficult questions must be very gradual; and the reason for every step in the solution distinctly seen.

It is believed that much dislike for the study of Arithmetic, and much unnecessary discouragement, have been/ occasioned by the abruptness of the transitions from easy to difficult questions. It is too often forgotten that the powers of the child's mind, like those of his body, are feeble; that while familiar mental exercises which he can comprehend, afford him the highest delight, he turns from intricate questions, which he does not and cannot understand, with indifference and disgust.

It is the design of this little work to furnish a series of mental exercises in numbers, adapted to the wants and capacities of children. It commences with practical examples which relate to familiar objects and require the simplest combinations. The pupil is then introduced to others involving the same principle but somewhat harder, special care being taken to make the transition very gradual, so that instead of being disheartened at the ruggedness of the

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