divisor seventy-five is multiplied (as before,) by the four hundred, and the product is set down under the first three figures of the dividend, and there are two thousand and seven hundred remaining. This remainder is set down in the next line, because seventy-five is not contained in two thousand seven hundred any number of hundred times. And so of the residue of the process. When there is danger that an advanced class will forget the value of the denominations they are handling, they are required to express the value of each figure in full, throughout the whole process, in the manner above described. I shall never forget the impression which a recitation by a higher class of girls produced upon my mind. It lasted an hour. Neither teacher nor pupil had book or slate. Questions and answers were extemporaneous. They consisted of problems in Vulgar Fractions, simple and compound; in the Rule of Three, Practice, Interest; Discount, &c., &c. A few of the first were simple, but they soon increased in complication and difficulty, and in the amount of the sums managed, until I could hardly credit the report of my own senses, so difficult were the questions, and so prompt and accurate the replies. ty, should the place be lost, of being obliged to recommence the solution. GRAMMAR AND COMPOSITION. their Great attention is paid to grammar, or, as it is usually called in the Plan of Studies,the German language. But I heard very little of the ding-dong and recitative of gender, number make up so great a portion of the grammatical and case,-of government and agreement, which exercises in our schools, and which the pupils are often required to repeat until they really lose all sense of the original meaning of the terms they use. Of what service is it for children to reiterate and reassert, fifty times in a single recitation, the gender and number of nouns, about which they never made a mistake hands? If the object of grammar is to teach even before a grammar book was put into their children to speak and write their native language with propriety, then they should be practised upon expressing their own ideas with elegance, distinctness and force. For this purpose, common every-day phraseology is first to be at tended to. As their speech becomes more copious, they should be led to recognize those slight shades of distinction which exist between words almost synonymous; to discriminate between the literal and the figurative; and to frame sentences in which the main idea shall be brought out conspicuously and prominently, while all subordinate ones,-mere matters of circumstance or qualification,-shall occupy humbler or more retired positions. The sentences of some public speakers are so arranged, that what is collateral or incidental, stands out boldly in the foreground, while the principal thought is almost lost in the shade;—an arrangement as preposterous as if, in the Senate chamber, the forum or the parade-ground, the president, the judge, or the commanding officer, throng of non-officials and incognitos should ocwere thrust into the rear, while a nameless cupy the places of dignity and authority. Grammar should be taught in such a way as to lead out into rhetoric as it regards the form of the expression, and into logic as it regards the se quence and coherency of the thoughts. If this is so, then no person is competent to teach grammar who is not familiar, at least, with all the leading principles of rhetoric and logic. A great many of the exercises in arithmetic consisted in reducing the coins of one state to those of another. In Germany there are almost as many different currencies as there are states; and the expression of the value of one coin in other denominations is a very common exercise. It struck me that the main differences between their mode of teaching arithmetic and ours, consist in their beginning earlier, continuing the practice in the elements much longer, requiring a more thorough analysis of all questions, and in not separating the processes, or rules, so much as we do from each other. The pupils proceed less by rule, more by an understanding of the subject. It often happens to our children that while engaged in one rule, they forget a preceding. Hence many of our best teachers have frequent reviews. But there, as I stated above, the youngest classes of children were taught addition, subtraction, multiplication and division promiscuously. And so it was in the later stages. The mind was constantly carried along, and the practice enlarged in more than one direction. It is a difference which results from teaching, in the one case, from a book; The Prussian teachers, by their constant habit and in the other, from the head. In the latter of conversing with the pupils; by requiring a case the teacher sees what each pupil most complete answer to be given to every question; needs, and if he finds any one halting or failing by never allowing a mistake in termination, or on a particular class of questions, plies him with in the collocation of words or clauses to pass questions of that kind until his deficiencies are uncorrected, nor the sentence as corrected to supplied. pass unrepeated; by requiring the poetry of the In algebra, trigonometry, surveying, geome.reading lessons to be changed into oral, or writ try, &c., I invariably saw the teacher standing before the black board, drawing the diagrams and explaining all the relations between their several parts, while the pupils, in their seats, having a pen and a small manuscript book, copied the figures, and took down brief heads of the solution; and at the next recitation they were required to go to the blackboard, draw the figures and solve the problems themselves. How different this mode of hearing a lessson from that of holding the text-book in the left hand, while the fore-finger of the right carefully follows the printed demonstration, under penal ten prose, and the prose to be paraphrased, or expressed in different words; and by exacting a general account or summary of the reading lessons, are,-as we may almost literally say,— constantly teaching grammar; or, as they more comprehensively call it,—the German language. It is easy to see that Composition is included under this head,-the writing of regular "es. says" or "themes" being only a later exercise. Professor Stowe gives the following account of the manner of teaching and explaining the different parts of speech. "Grammar is taught directly and scientifi manner. cally, yet by no means in a dry and technical On the contrary, technical terms are carefully avoided, till the child has become familiar with the nature and use of the things designated by them, and he is able to use them as the names of ideas which have a definite exist ence in his mind, and not as awful sounds, dimly shadowing forth some mysteries of science into which he has no power to penetrate. "The first object is to illustrate the different parts of speech, such as the noun, verb, adjective, adverb; and this is done by engaging the pupil in conversation, and leading him to form sentences in which the particular part of speech to be learned shall be the most important word, and directing his attention to the nature and use of the word, in the place where he uses it, For example, let us suppose the nature and use of the adverb is to be taught; the teacher writes upon the blackboard the words here, there, near, &c. He then says, 'Children, we are all together in this room, by which of the words on the blackboard can you express this?' Children, We are all here.' Teacher, Now look out of the window and see the church The fact what can you say of the church with the second word on the blackboard? Children, The church is there.' Teacher, The distance between us and the church is not great; how will you express this by a word on the blackboard? Children,- The church is near.' that these different words express the same sort of relations is then explained, and accordingly, that they belong to the same class, or are the same part of speech. The variations of these words are next explained. Children, you say the church is near, but there is a shop between us and the church; what will you say of the shop ?' Children, The shop is nearer.'Teacher, But there's a fence between us and the shop. Now when you think of the distance between us, the shop, and the fence, what will you say of the fence? Children,- The fence is nearest.' So of other adverbs. The lark sings well. Compare the singing of the lark with that of the canary bird. Compare the singing of the nightingale with that of the canary bird." I heard excellent lessons on the different meanings which roots, or primitive words assame, when used with different affixes or suffixes. An analagous lesson in our language would consist in giving the meanings of the different words which come from one root in the Latin, as, convene, intervene, prevent, event, advent, &c.; or accede, recede, succeed, exceed, proceed, secede, precede, intercede, &c. THE ALPHABET. JExtract from the report of H. WILSON, County intendent of Allegany.] The following are the methods generally used: 1st. The twenty-six letters are presented to the child in rapid succession three or four times a day. 2d. One letter only at a time; let it be written on the black-board, and when it is thoroughly learned, place another near it, proceed in the same way until all are mastered; care should be taken that those already learned are not forgot. ten as the child proceeds, &c. When one letter has been learned, let the child have a small slate and try to make the letter on that, or let a small black-board be procured and let him chalk the letter on that, &c. 3d. Divide the alphabet into lessons of a few letters each, let these form the names of objects familiar to the child, as follows: cat, dog, hen, bird, &c. The letters in each word, let it be is learning the letters in the word selected for the borne in mind, form a lesson. When the child lesson, let the teacher tell him an anecdote about the object, something that will please him. 4th. Divide the alphabet into lessons, and class together on a black-board or card the let ters that have a similar form, thus: ij, lf, tr, hk, num, oce, bd, pq, vxz, wy, sag, double letters, th, sh, ch, ph, terminations, ing, tion, ple, ble. Each division is a distinct lesson; the teacher should point out the similarity and differences in the shapes of the letters, &c.-thus in the first lesson, the dotted letter j differs from the i in its greater length and curve at the bottom; the land fare of equal length, the one has a square top, the other a curved one, and so on to the others. In double letters and terminations, the teacher should carefully give, and practice the child in their proper sounds, as without it he would not be able to perceive them from the combinations of the letters. The child should not be permit ted to pass on to a new class until he has fully mastered the one before him. 5th. Words and letters are taught at the same time. Show the child the first letter in the Bible, I, and let him find it then wherever it occurs in the first verse. Having done this, show him the second letter, n; let him find every n in the first verse. He should then be informed what I-n spells. This enables him to read the first word in the Bible; let his second lesson be the next word in the Bible, the letters of which and their combinations should be learned as be fore. Proceed in the same manner through each successive lesson, till he can read the first verse in Genesis. "In the beginning, God created the heaven and the earth." 6th. Present the child with a picture of some object, having the name on the card in capitals. It may be a dog, &c. The word is shown to the child, and he is referred to the picture for the Super-meaning, after having pronounced it. The child To compile some of the various modes that have been recommended for teaching the alphabet, and from these to suggest the best, is all that the undersigned has aimed to accomplish; he presumes this is all the department expects at his hands; and could he persuade himself that this expectation would not be wholly disappointed, he could then believe that, at least, some service had been rendered to the cause of general education. may then be taught these three letters, and that One word is sufficient for a lesson, and when the they perform the same office as the picture, &c. letters in this are thoroughly learned, take another word and proceed as before. The teacher should accompany each lesson with an interesting anecdote respecting the object, &c. Set the child to draw the letters designed for the lesson... or the picture of the object, upon the black-board or slate. (We shall continue the subject in our next.) CLASS BOOKS OF ESTABLISHED REPUTATION. FOR COMMON SCHOOLS AND ACADEMIES. PUBLISHED BY BAILEY'S ALGEBRA. JENKS & PALMER, No 131 Washington st., Boston, stitutions where the modern improvements are adopt and for sale by the following houses: New-York City-ed. Collins, Brother & Co., Robinson, Pratt & Co, Huntington & Savage, A. V. Blake, Mark H. Newman, Roe Bailey's First Lessons in Algebra, for Academies and Lockwood, Geo. F. Coolidge & Brother, Mahlon Day Common Schools. Key to the above for Teachers. & Co., Daniel Appleton & Co. Albany-Oliver Steele, The above Algebra is on the inductive plan, and is deE. H. Pease. Troy-Stedham & Redfield. Utica-Ben-signed for those not versed in the science. It is used nett, Backus & Hawley. Rochester-David Hoyt, Wm. as a class book in the Public Schools of Boston, and in Alling. Buffalo-W. B. & C. E. Peck, and by Booksel- various schools and academies of high character in all lers and Traders generally. The following works for parts of the United States. Education are particularly recommended to the notice of those interested in the subjects, as containing the modern improvements, and calculated to lessen the labors of teaching and learning, and at the same time to make thorough and practical scholars. This series is considered by Teachers and others to be the most valuable and popular now before the public. The Rules and Instructions for avoiding common errors were originally inserted in this series by the author, and form their peculiar characteristics. Wherever used, and they are extensively introduced, the books have given entire satisfaction. PARLEY'S SCHOOL BOOKS. The Histories contain maps and engravings, and be ing in general use in the schools and academies in our country, may be considered as standard books for the instruction of youth in History. EMERSON'S ARITHMETIC, (in Three Parts.) Part 1, contains easy lessons for beginners. Part 2, contains lessons for all scholars. Part 3, contains the higher operations. Key to. Parts 2 and 3. Questions to Part 3. This series of Arithmetics is in use in the schools of New-York, Philadelphia, and Boston, and in other in GOODRICH'S UNITED STATES. Goodrich's History of the United States, adapted to the capacity of youth. Revised and enlarged from the one hundredth edition, and brought down to Tyler's administration. Goodrich's and Emerson's Questions to the above. The above History of the United States is among the most popular works of the kind. It is in use in the Boston Schools, and has a high and extensive popularity. WORCESTER'S DICTIONARIES. and Academies, containing nearly 9000 more words than Worcester's Elementary, adapted for use in Schools any other School Dictionary. Do. Comprehensive, (Pronoucing and Explanatory,) designed for the same, and for general reference. This Dictionary is recommended by persons of the highest literary merit, as "combining advantages as a Pronouncing Dictionary, superior to all others," and as being a "a most comprehensive, correct, and useful compendium." RUSSELL'S ELOCUTIONARY SERIES. 1. Russell's Lessons in Enunciation. 2. Do. Rudiments of Gesture. 3. Do. Exercises in Elocution. MUSIC BOOKS FOR SCHOOLS. The Common School Songster, for advanced learners; by the same. Published under the sanction of the Boston Academy of Music. The Young Lady's Vocal Class Book, designed for families and the higher schools; by the same. Publish ed un ler the sanction of the Boston Academy of Music. The above form a progressive series for the use of families and schools. MISCELLANEOUS. School Committees, Teachers, &c. desirous of exam. ining any of the above will be supplied without chargeIn addition to the above, always for sale, at satisfactory prices, a complete assortment of School, Music and Miscellaneous Books, Stationery, &c. WILLARD'S HISTORICAL WORKS. PUBLISHED BY A. S. BARNES & Co. The works of Mrs. Willard, late of the Troy Female Seminary, are receiving the stamp of approbation wherever they are made known. School Teachers, Trustees, Town and County Superintendents, are invited to examine these works, with reference to their adaptation to Common and Select Schools of the country. Published by A. S. Barnes & Co., Philadelphia, and Pratt, Woodford & Co, New-York. Willard's History of the United States, a Republic of America, illustrated with maps and engravings. Two Editions. The Academical or Library Edition, 8 vols. Abridged or School Edition, 18 mo. The large work is designed as a Text Book for Academies and Female Se minaries, and will be found to be a valuable Library book, for every District School. The small work, being an abridgement of the same is designed as a Text Book for Common Schools. The same publishers have in press, and will publish on the 15th of June, a new and splendid Edition of Willard's Universal History, illustrated with numerous maps and engravings, designed as a Text Book for Academies and Schools. Teachers forming new classes in Universal History are invited to examine this work before deciding upon the Text Book they will adopt. VALUABLE SCHOOL BOOKS, PUBLISHED BY HUNTINGTON & SAVAGE, 216 PEARL STREET, NEW-YORK. The Geography of the Heavens, and Class Book of Astronomy, 1 vol. 18mo., accompanied by a Celestial Atlas, imperial 4to, neatly colored. Contents of the Atlas. 1. Plan exhibiting the relative magnitudes, distances, and positions of the different bodies which compose the Solar System. 2. The Visible Heavens in January, February, and March. 3. The Visible Heavens in October, November, and December. 4. The Visible Hea. vens in July, August, and September. 5. The Visible Heavens in April, May, and June. 6. The Visible Heavens in the south polar regions for each month in the year. 7. The Visible Heavens in the north polar regions for each month in the year. 8. The Planisphere of the whole Heavens, on Mercator's Projection. By E. A. Burritt, A. M, with an Introduction by Thomas Dick, LL. D., author of the Christian Philosopher. Written expressly for this work. Astronomy for Beginners, with a Map and twentyseven Engravings. By Francis Fellowes, A. M. Familiar Lectures on Botany; practical, elementary, and physiological: with an appendix containing descriptions of the Plants of the United States, the Exotics, &c.; also a Dictionary of the Symbolical language of Flowers.-1 vol. imperial 12mo., by Mrs. Almira H. Lincoln. Botany for Beginners; an Introduction to Mrs. Lincoln's Lectures on Botany, for the use of Common Schools and the Younger Pupils of Higher Schools and Academics. By Mrs. Lincoln Phelps, 1 vol. royal 18mo. Familiar Lectures on Natural Philosophy, for the use of Schools and Academies, 1 vol. 12 mo. Natural Philosophy for Beginners; designed for Common Schools and Families. By Mrs. Phelps, author of Familiar Lectures on Botany," &c. 1 vol. 18mo. Familiar Lectures on Chemistry, for the use of Schools and Academies. By Mrs. Phelps (formerly Mrs. Lin. coln,) 1 vol. 12mo. Chemistry for Beginners; designed for Com. Schools and the Younger Pupils of Higher Schools and Academies, with Engravings By Mrs. Phelps,1 vol. 18mo. A Dictionary of the English Language: Abridged from the American Dictionary, for the use of Primary Schools and the Counting-House. By Noah Webster, LL. D. 1 vol. duodecimo, 550 pp. A Dictionary for Primary Schools. By Noah Web1 vol. 16mo., 330 pp. ster. The Child's Picture Defining and Reading Book, by the Rev. Thomas H. Gallaudet. The Malte Brun School Geography and Atlas, 288 pages royal 18mo. and 32 engravings from original designs. By S. Griswold Goodrich. A practical Grammar of the English language, or an introduction to Composition; in which the constructions of the language are classified into Predications and Phrases, by Edward Hazen, author of "The Symbolicae Spelling Book," "The Speller and Definer," and " Popular Technology, or Professions and Trades." Peter Parley's Geography for Children; illustrated with 9 maps and 75 engravings. Peter Parley's History of the World, 75 engravings. A New Introduction to the Science of Algebra; de. signed for Students in Colleges and the higher Schools and Academies. By Silas Totten, M. A., President of Washington College, Connecticut. The Ecclesiastical Class Book, or History of the Church, from the birth of Christ, to the present time; adapted to the use of Academies and Schools. By Charles A. Goodrich. 1 vol. 18mo. Elements of Criticism by Henry Home, Lord Kaimes, Judge of the Court of Sessions in Scotland, &c. &c., with Analyses and Translations of the Illustrations. Lives of the Signers of the Declaration of Independ. ence, with an Introduction, giving a short sketch of the causes which Jed to the Declaration of Independence, containing seven beautiful engravings on steel, among which is one taken from Col. Trumbull's celebrated picture of the "Signing of the Declaration of Independence." 1 vol. imperial 12mo. pp. 479. Townrow's Stenography; prepared expressly for Schools and private instruction. A number of recommendations from the highest sources, could be appended to each of the above mentioned works; but, from their extended and very general use, the publishers deem this unnecessary. H. & S in addition to their own publications, keep an assortment of School, Miscellaneous, and Classical Books, and Stationery, which will be sold on the most favorable terms. VALUABLE SCHOOL BOOKS, PUBLISHEED BY JOHN PAINE, Hartford, Conn. SMITH'S SCHOOL GEOGRAPHY, illustrated by numerous cuts. The questions and answers are adapted to the object in view, and calculated to impart instruction in a pleas ing and interesting manner. It is accompanied by a large and valuable Atlas. Many of the maps have been recently redrawn and newly engraved, and all arranged from the latest and best authorities. A system of emblems and abbreviations is adopted throughout the whole showing the Government, Religion, State of Society, Population, Navigation, &c., of the more important countries at a single glance. Though the Atlas is much enlarged and greatly improved, the price remains the same as heretofore. SMITH'S PRACTICAL AND MENTAL ARITHME. TIC, 18mo, in which mental arithmetic is combined with the use of the slate, being a complete system for all practical purposes. KEY to the above, designed for teachers only. SMITH'S NEW ARITHMETIC, 12mo, in three parts. Part first, a mental course for every class of learners. Part second, consisting both in theory and practice. Part third treats of the more advanced studies in mathematics. Tilustrated by diagrams and cubical blocks. Key to the same, designed for teachers only. REQUISITES FOR ACADEMIES, SEMINARIES AND SCHOOLS. Published by O.O.WICKHAM, 77 FULTON-STREET, NEW-YORK. FOR DISTRICT SCHOOLS. 1. The School Ledger, which will last as a Register for a School in the proportion of 36 scholars, six years, eight months to the year, substantially bound; price for single copies, $1.25, and when 5 or more copies are ordered, $i each. The same, which will serve as a Register for a School of 22 scholars, 4 years, 8 months to the year, cloth backs; 50 cents single, or 13 copies for $5. 2. The Trustees' and Clerks' District Record for the Common Schools of the State of New-York, containing the School Act, and instructions of the State Superintendent, and ruled for the Clerks' and Treasurers' Accounts, substantially bound, in sizes of 1, 2, 3 and 4 quires of foolscap paper, at the rate of 33 cents per quire. 3. The Teachers' Certificates, on which are entered at given periods, the Attendances, Recitations and Deportment of the pupils, being filled up from the regis ter, with a list of studies upon the back, printed either with colored inks or on colored paper; price sets. per doz.; 50 cts. per hundred. 4. Regulations of District Libraries, comformable to law, approved of by the State Superintendent, and suited to the size of ordinary books; 25 cts. per hundred, (but put in with libraries ordered, gratis.) FOR ACADEMIES, SEMINARIES AND SELECT 1. The School Register. sufficient for the account of 3. Academical and High School Diploma, illustrated by a beautiful lithograph engraving of the "Hill of Science;" plain, 8 cts. The same, colored, 124 ets. 4. The Pupil's Album of Chirography, a comparative Record of Penmanship, prepared for 500 specimens, on good paper; 37 cts. The same, for 300 specimens, 25 cts. 6. School Rewards, beautifully engraved on steel; plain per doz., 4 cts. The same colored, per doz., 6 cts. O. O. W., is also agent for the sale of Blake's Dis trict Library, 252 pages each. Nine volumes are already published, and others will be added at short intervals-they are printed on fine paper and handsomely bound, and will be sold at the low price of 45 cts. per volume. M. A. ROOT'S PHILOSOPHICAL THEORY & PRACTICE OF PENMANSHIP. A System of Twelve Books, in Three Parts. PUBLISHED BY Appollos W. Harrison, 81 SOUTH-SEVENTH-ST., PHILADELPHIA. The object of this system is to furnish to Common or District school teachers, the means of accomplishing | all with their pupils in the art that the best writing masters can. THE PRIMARY PART Is for beginners, and is peculiarly adapted to their youthful capacities. The lessons are so arranged that This it is believed will be fully realized on trial, and tised first, according to similarity of formation; then, short, long, and capital letters are classed and pracat a less cost for books, than for the use of blank writ-alphabetically in single letters and words, so as to ing books. It has been ascertained by careful analysis, that Root's Writing Books, average four times as much writing for the pupil, as the same number of blank books; and as the cost for each number is but a trifle more than for blank books, they must be much the cheapest, at least by more than one half. Besides there is a great saving of time to be teacher, the copies being all set in a fac-simile of the beautiful hand of the author. PLAN AND USE OF THE SYSTEM. The arrangement is such, as to enable teachers who use them, to superintend, and rapidly advance very large classes with comparatively little labor. Every exercise to be practised, and letter to be imitatel, is fully and clearly explained in bold type upon the same page with the lesson. This, and the ready set copies, with cuts illustrating and exhibiting both the correct and false positions of the hand and pen, enables any one of common capacity, who will read, think, and exercise his own judgment, not only to teach himself, but become with the aid of these books, a thorough and successful teacher of practical writing. The whole plan is pleasing, interesting, and effectual; entirely new and original with the author. fix the form of cach letter in the pupil's mind. Each lesson is alternated with exercises, to give facility of action to the muscles, and establish the correct nianner of holding the hand and pen. THE INTERMEDIATE PART, Though a proper successor to the primary, may be used as a com mencement by pupils somewhat advanced, or self instructors. It will produce a practical business style. It comprises as exercises, single small letters, entire words, capital letters, alphabetical sen tences, and a series of bold exercises for acquiring great freedom and command of hand. THE FINAL PART. Contains off-hand or whole arm exercises, capital letters, select sentences of one and two lines each, and business transactions; such as Notes, Orders, Drafts, Receipts, &c., and the ornamental branches of the art, comprising Round Hand, German Text, Old English, &c. Each part although gradually progressive, and designed to be used in regular succession; is so planned as to make a complete series of itself, and may be used independently of the others. The whole forming the most complete, philosophical, practical, and economical system ever before published, |