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ADAPTED TO ALL GRADES OF

SCHOOLS, ACADEMIES, AND COLLEGES.

Published by IVISON, PHINNEY & CO., 48 & 50 Walker St., N. Y.

The most COMPLETE, PRACTICAL, and SCIENTIFIC SERIES of MATHematical TextBooks ever published in this country.

(IN TWENTY VOLUMES.)

THESE books are unequalled in style, typography, and binding; in gradation, new and original methods, and practical applications.

With the improvements and additions recently made, it is the only series by one author, adapted to every grade of scholarship in the Common School, Academy, and College, published in this country.

Although comparatively new, the books of this series have a large and increasing sale in almost every State in the Union; and are now used in hundreds of the Schools, Seminaries, and High Schools of NEW ENGLAND.

TERMS OF INTRODUCTION.

As an inducement, in addition to their merits, the class-books of this series will be furnished for first introduction, in exchange for whole books of a corresponding grade by other authors, that may be in use, on the following terms, viz:

Introduction. Retail Price.

Progressive Primary Arithmetic, in exchange for old book and
Progressive Intellectual Arithmetic,

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New Geometry and Trigonometry, full bound. 450 pp. 8vo.

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Conic Sections and Analytic Geometry, full bound, 8vo.
Differen. and Int. Calculus, (in press,)

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The Key to Geometry and Trigonometry, Conic Sections and Analytical Geometry, will be sent to teachers prepaid on receipt of one dollar. Keys to the Arithmeics and Algebras are also published.

A beautiful Pictorial Arithmetical Table Book, for Primary Schools, is in preparation.

Specimen Copies of any of the above Text-Books will be mailed to teachers for examination, on receipt of one half the retail price.

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THE

MASSACHUSETTS TEACHER.

JANUARY, 1862.

Volume XV. GEORGE A. WALTON, Editor for this month. Number 1.

SALUTATORY.

THE Editor of the present number of the Teacher begs to be indulged in a brief apology.

In issuing the first number of a volume of any periodical, it is usually considered politic to present it in its most attractive features. But, dear reader, if you look for such a treat in the present issue of the Teacher, we fear you will be disappointed. Only last Saturday did we know that editorial honors were ours; much less did we dream of being placed in the chair so soon. But now we are told that by Saturday next, without fail, we must compose or select, in some way provide and arrange matter for this number of the journal. Help us, Hercules! What, we, a poor schoolmaster, in the field with half a regiment at our back, with calls to our post early and late, can we cull with sufficient care or draw from our own resources, anything worthy the patronage of the Teacher's progressive, critical readers? and all in six short days? Your generous response we know, and need not crave pardon for the wide margin we shall leave for improvement; but at once assume that you will excuse any plain, crude matter which may be here presented, in anticipation of the good things, we can promise shall follow, (if you as contributors do your duty.)

THE TEACHER A STUDENT.

THE man who attempts to teach, without being himself an attentive student, will as surely fail as he who attempts to command without having first learned to obey. This proposition is limited to no branch of instruction; in every department the teacher must classify and review, if not originate. What text-book in Reading or Spelling, in Arithmetic or Algebra, in French or Latin, is so complete as to require no revision, no eradication of errors, no additional illustrations? The most perfect book must be adapted to the spirit of the teacher and conditions of the learner; in all, there will be here too little, there too much; this, though its author be the superior of all its teachers; for it is useless to assume that any one can secure the fullest and readiest comprehension of a subject in the exact methods of another.

We commisserate the honest brute in the traces of a treadmill, spurred on by the whiz of the circling saw; but, when he has once secured an easy footing upon the steps of the treadle, we can conceive that he might toil up towards the receding post with some spirit; nor is it difficult to imagine him after the secret of his failure is discovered, with patience still laboring on. But when we see a teacher going the same treadmill round of a text-book for the twentieth time, moving to the same clatter, and turning out blocks of the same length, we behold a more pitiable object still. The process is stultifying to a teacher; and certainly not less so to the pupil.

It matters not what the study, the plan of developing it mus> be intelligently comprehended by the teacher, or the highest success in his art cannot be attained; the increments of it may be ever so thoroughly impressed, but to clothe it with beauty, its natural order, its various applications, and its secret charms, must first be conceived in the mind of the teacher.

Hence, incidentally, the folly of attempting to teach what we are learning, lesson by lesson, in advance of our pupil. And hence the necessity for the broadest culture, whatever we teach.

But to impart with vigor and freshness, the mind must be continually in a receptive state, craving new and varied aliment to be assimilating with what it possessed before. To be successful in a

high degree, we apprehend the teacher must be actuated by the same spirit which prompts an author. And, in a certain sense, every teacher should be an author. Having come to consider the practical uses of his subject, he will at once decide to leave to maturer age many topics, or consult the circumstances of the life pursuits of his pupils as to what he shall present or omit. Take in illustration, Arithmetic :

Select the best book of the many excellent ones in this department, and every teacher will reject something and desire to add much. But beyond the faults of the book, there is a want of adaptation the best book cannot meet. The book is only designed to be the text. The higher branches of the mathematics, (only higher because presented to maturer minds, perhaps,) algebra and geometry, must have a natural sequence in all their unfoldings; but if such an order exists in the steps of arithmetic, few of its authors have been successful in its embodiment. And the teacher must observe as he teaches, reärrange and modify till he has an order of his own. By the same process he will determine what prominence shall be given to the various branches of his subject. He will not fail to observe how large a part the two fundamental rules play in all future, and especially in all business operations. If we do not mistake, a child is better off with a thorough knowledge of these, with fractions, vulgar and decimal, and the simplest applications of per centage, than with the ordinary tuition in reductions, compound numbers, proportion, duodecimals, cube and square root, equations, progressions, positions, permutations, and combinations, and all the et ceteras, though we would, by no means, discourage the study of these.

Circumstances must determine the policy of dwelling longer or shorter upon any particular topic, or whether it is desirable to exhaust one before proceeding to another. No time will be considered lost which is spent in an honest discussion of the conditions or the principles involved in a problem. To secure such a comprehension of principles that they can be practically applied, will tax the ingenuity to the utmost. Examples must be multiplied indefinitely; their forms and conditions must be repeatedly varied; practical examples must be substituted for abstract, and other numbers for those in the book, again and again, where the principle

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