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extreme right, the teacher or some designated pupil reads the first word as spelled on the slate in his hand, while all the others compare this spelling with that which they have before them. If all the slates agree in this spelling no sign is made, and the reader gives the spelling of the next word. When any one finds on his slate a different spelling from that given by the reader, he immediately lifts his hand. The teacher then calls successively upon those whose bands are up, to give the spelling from their slates, and the class is called upon to choose the right spelling. The word is then assigned for further study, and the class is requested to refer to the dictionary adopted as authority, and bring a decision at the next recitation. When the list has been completed, (which will after a little practice occupy no more time than an ordinary oral spelling lesson) the lesson for the next day is given and taken down by the pupils in the same manner as the first.

The lists of words when finally corrected, are to be neatly written in small blank books kept for this purpose. By this means each pupil makes a spelling book for himself, and the lists are ready at wand for review lessons, which should be given as often as once each week.

The advantages of this method of teaching orthography, are mainly the following:

1st. No words are embraced in the lesson but those of which the pupils know the meaning, and which they will therefore be likely to use. The class of words under which the lesson is given, is itself an approximate definition, and the interest of the pupils is certain to lead them to seek the definite meaning of each word.

2d. It will lead to the acquisition of many new words. Each pupil will be eager to find the names of all the parts of the object taken, or all the words in the given class, and thus a spirited enquiry will be set on foot, which will increase both the knowledge of things and the knowledge of words.

3d. Each pupil spells every word, and as he writes it several times, his attention is fixed so often and so distinctly upon it 'that its form becomes familiar, and is more certainly remem. bered.

4th. The exercise in penmanship is an incidental advantage, abundantly sufficient to compensate for the cost of the blank books and the time spent in writing the lessons.

By a little care in the arrangement of lessons, they may be made nearly exhaustive of all the words which the pupil will need to learn.

The following headings of lessons will be suitable for beginners, and will suggest others :

1. Material for houses—as wood, timber, boards, brick, stone, lime, hair, nails, &c. 2. Parts of a house-as sill, post, rafter, brace, beam, roof, door, chimney, &c. 3. Rooms in a houseas parlor, kitchen, cellar, hall, pantry, &c. 4. Parlor furniture. 5. Kitchen furniture. 6. Dining-room furniture. 7. Bed-room furniture. 8. Table furniture. 9. Kinds of meat. 10. Kinds of bread and cake. 11. Modes of cooking-as fry, bake, &c. 12. Condiments. 13. Table drinks. 14. Garden vegetables. 15. Fruit trees. 16. Forest trees. 17. Evergreens. 18. Wild flowers 19. Cultivated flowers. 20. Weeds. 21. Parts of a tree. 22. Shrubs and bushes. 23. Parts of a human head. 24. Parts of the arm. 25. Parts of the trunk. 26. Parts of the leg. 27. Domestic quadrupeds. 28. Domestic fowls. 29. Birds. 30. Wild animals. 31. Parts of a horse. 32. Food of animals.

33. Trades. 34. Tools of a carpenter. 35. Things made by carpenters. 36. Farmers' tools. 37. Farm products. 38. Parts of a wagon. 39. Parts of a shoe. 40. Parts of a coat. 41. Articles of dress for a boy. 42. Articles of dress for a girl. 43. Colors. 44. Tastes. 45. Sounds. 46. Temperatures. 47. Liquids. 48. Qualities of surface. 49. Acts of the mind. 50. Acts of the arm and hand. 51. Acts of the legs and feet. 52. Acts of the eye. 53. Acts of other senses. 54. Acts of a horse. 55. Acts of birds. 56. Names of men. 57. Names of women. 58. Titles of civil officers. 59. Titles of military officers. 60. Celebrated warriors. 61. Celebrated orators. 62. Names of sciences. 63. School studies. 64. Duties of a pupil. 65. Divisions of land. 66. Divisions of water. 67. Rivers of New England.

These classes, of which the above are given simply as exam ples, may be continued till the common words expressing things, actions and qualities, are all learned.

For learning derivative words, a single prefix, as con, or in, may be given, and when its significance as a prefix is thor oughly comprehended, the pupils may make their lessons of words having this prefix. Then another prefix may be taken, and so on till all the prefixes have been taught. In like manner proceed with the suffixes. Afterward take a single radical word, as act, or fact, and let the class give all the derivatives they can form, first with the prefixes, then with the suffixes, and finally with both.

In addition to the above spelling lessons, every teacher ought occasionally to read slowly short passages from some book to his spelling classes, and require them to write what he reads. They may be instructed in connection with this exercise, to leave a proper margin to their manuscript, to indent or begin back of the margin line, their paragraphs, and also the use of capital letters and punctuation points.


In the solution of every arithmetical problem, there are two distinct classes of operations; the one class is purely rational, the other as purely numerical. The former concerns the logical relations of the quantities considered in the problem; the latter, the operations to be performed on the numbers which represent those quantities.

Take, for example, the simple question of the cost of 5 bushels of corn at 50 cents a bushel. · Its solution requires us to determine which are the quantities to be considered, and what their relations are to each other. By purely logical reasoning, or by common sense as some would say, we decide that the quantities are the bushel whose price is given-the five bushels whose price is sought-the fifty cents, the money equivalent or price of the one bushel-and an unknown quantity, the money equivalent or price of the five bushels. The relations of these four quantities are simply as follows, viz: the 1 busbel and the 50 cents, its equivalent in value, are the standards of measurement of the 5 bushels and their money equivalent. An axiom now tells us that the equals or equivalents, 1 bushel and 50 cents, will be contained respectively in the equivalents, 5 busbels and their price, an equal number of times; and hence we infer that since 5 bushels is five times 1 bushel, the price of 5 busbels will be five times 50 cents. This is the rational solution of the problem. The purely rational processes are here finished, and the rational answer is reached. But there comes now another process, a purely numerical one, which must be passed before the numerical answer to the problem is obtained. This is the combination of the two factors, 5 and 50, by multiplication, into the single product, 2.50.

Had the statement been that two men bought 5 bushels of corn in 3 weeks, for 50 cents a bushel, the problem would have remained essentially the same ; but in the rational processes we should have rejected the 2 men and 3 weeks, as quantities not to be considered in the solution.

This example exhibits not only the two classes of operations, but also something of their relative amount and character, The rational or logical are many and various, differing with each new problem, and often profound and difficult ; the numer. ical are few and simple.

The study of Arithmetic, therefore, embraces two departments : 1st, The study of numerical operations; and 2d, The study of the rational conditions of problems. The aim of the first, is to learn the art of computing abstract numbers; that of the second, is to acquire the ability to reason clearly on the relations of quantities, and their connections in each new problem. To acquire the greatest facility in the performance of these two classes of operations, is the aim of practical Arithmetic; to understand thoroughly the reasonings in the two, is

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to understand the science of Arithmetic. Two things so dig. tinct and different as the operations of numbers, and the relations of quantities, obviously ought not to be confounded in teaching. Each has its own modes of action, and should have its own separate and special methods of training. The purely numerical operations being few and simple, may be made, by proper training, so familiar and babitual as to be performed almost without effort. Memory takes the place of calculation. Let, for example, the sum and product of 8 and 7 be asked of an expert arithmetician, he answers instantly, and without conscious effort, 15 and 56.

He does not stop to seek the answer by any fresh process of reasoning; he simply quotes it from his previously acquired knowledge. In the same way will he go through long series of numbers, combining or resolving them with the greatest rapidity and ease, aided simply by his familiar knowledge of the particular results.

This principle is already in use in teaching the multiplication table. The pupil is drilled in this till all the products of any two numbers up to 12 times 12 are perfectly memorized. But it does not seem to be generally understood that the principle is equally applicable and equally valuable in additions, subtractions and divisions as it is in multiplication. It is not uncommon to see a boy, who will tell you at once that 7 times 9 is 63, counting his fingers to find out that the sum of 7 and 9 is 16.

Evidently a great advance would be made, and a great advantage gained, in teaching Arithmetic, if, by a well arranged system of drill exercises, all the combinations of the lower numbers could be made as familiar as the multiplication tablo is sometimes made. At least, the following will be found prao. ticable and desirable.

1st. The multiplication table to be continued to 20 times 20, and made thoroughly familiar.

2nd. The addition of any two numbers below 100. 3d. The difference of any two numbers below 100.

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