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that you will be troubled with either obstinacy or sulkiness. Good humour is remarkably diffusive, and you will soon find the children becoming what the teacher is.]

[We have a large number of communications in reply to the request of R. B. K., all of them giving evidence of attention to the subject of arithmetic. We select but two, in consequence of our limited space.]

SIR, Your correspondent, R. B. K., requests information as to the best method of teaching Compound Proportion, to a class of twenty-five boys:-I beg leave to lay before you the method practised in the school in which I serve as Pupil Teacher, observing, that our master attaches great importance to this rule, as one which, when judiciously taught, is calculated to exercise the minds of children in a most beneficial manner.

I will illustrate our method by a simple example.-If in 6 days 12 men earn £10, how much will 8 men earn in 16 days?

Form a diagram similar to the accompanying one, having 5 spaces (or 7, &c., according to the number of terms); place the 3 terms of supposition along the top, so, that the term like the answer, shall be in the 3rd place:-put each of the terms of demand under their like, in the spaces below.

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Next take the third term, and each pair of terms, and state them as in simple Proportion, thus-If £10 be earned in 6 days, will more or less be earned in 16 days? (more); the greater term is therefore put in the second place.

Again, if £10 be earned by 16 men, will more or less be earned by 8 men ?(less); the less term is, therefore, put in the second place. The statement will then assume the accompanying form.

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By Multiplication the question becomes a simple Rule of Three statement, and is worked out in the same manner.

Our scholars are accustomed to work all the questions in Compound Proportion, twice;— the first time using figures only--the second, a written explanation of the process is required similar to that given above.

HENRY HOUGHTON.

One of your correspondents wishes to know of an easy and simple way to teach Compound Proportion.

"Experience teaches wisdom," is the old and true proverb. There are many ways in which this rule of arithmetic is taught, and I see that, in almost every school, a different method is adopted. I find the method which I use, if not altogether the easiest to learn, yet the most simple when understood. This method is called that of "Cause and Effect;' and if your correspondent will give it a good trial in his class of twenty-five, for a short time, I believe he will be repaid. Children do not understand what is meant by the letter , which is placed for the unknown term, unless it is made very clear to them. Mr. Hind's, "Principles of Arithmetic," treats well on Cause and Effect. respondent has not seen this method, I will subjoin an example.

If our cor

If 120 men in 3 days of 12 hours each, can dig a trench 30 yards long, 2 feet broad, and 4 deep, how many men would be required to dig a trench 50 yards long, 6 feet deep, and 14 yards broad, in 9 days of 15 hours each.

Here the unknown term is men.

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1st Effect: 90 × 2 × 4:

2nd Ditto. 150 x 6 x 41.

120 × 3 × 12: X x 9 x 15:: Writing these terms fractionally and cancelling the factors common to both numerator, and denominator, we have

30 X 3 X 2 = 180 Men.

The rule is, multiply the two extremes together and the two means.

If the unknown term is in the means, take them for the divisor, if in the extremes, take them for the divisor. D. B. A,

G. W., an unpaid teacher in a Ragged School, would feel greatly obliged if the Editor of the "Papers" would kindly furnish her with a series of "Notes" of Bible and Secular Lessons for an Infant class. Any suggestions he may have the goodness to offer, will be most gratefully received. Perhaps, at some convenient time he would kindly propose a system of organization for this school; it assembles for two hours, three times a week. G. W. fears that such a school does not quite enter within the province of the "Papers;" but ventures to prefer the above request, from a feeling of the importance of the work. It is a labour of love, but a hard task for one who greatly needs guidance and instruction in the management of a school.

[We gladly insert the communication of G. W., and shall feel obliged to any of our subscribers engaged in Ragged Schools, if they will favour us with a sketch of the modes of organization or other plans they have found to work with efficiency. We are happy to say, that our correspondent's fears are quite groundless, the province of the "Papers" extends to all and every kind of institution, which has for its object the right education of the masses of our youthful population. The greater the difficulties the teacher has to encounter, the greater shall be our sympathy.

G. W. is recommended to obtain either Stow's Training System," or "Model Lessons for Infant School Teachers." Both these books supply not only Notes of Bible and Secular Lessons, but also the best methods of using them]

ANSWERS TO EXAMINATION PAPERS ON SCHOOL

MANAGEMENT.

(CONTINUED FROM NO. XIX.)

III. METHOD-INSTRUCTION.

QUESTION I.

Next to Religious and Moral training nothing is so important in elementary schools as the Reading Lesson. For, apart from the fact that an ability to read with intelligence is the most valuable of all attainments, it being the key to all others, it is when rightly conducted the most efficient instrument for developing and cultivating the various powers of the mind. Its influence on all the faculties is direct and powerful, while that of object or other collective lessons is at best but supplementary and weak; and these in fact succeed best, except in the case of infants, when based on previously prepared reading lessons. To the reading lesson and its concomitants, dictation and abstracts, one-third at least of school time should be devoted.

The graduation of the reading-lesson is intended to secure accuracy, case, fluency, and expression.

Accuracy of pronunciation depends on the culture of the ear, combined with distinct and forcible enunciation of every sound in a word. Ease depends on familiarity with the words, and requires the culture of the eye; hence the importance of fixing the attention during the reading lesson. Fluency is the combination of accuracy with ease. Expression depends on an intelligence of what is read, and on sympathy with the feelings of the author.

To secure this progress in a school a careful graduation to suit the states of the children is essential.

The first lessons should consist entirely of words with which the ear of children is familiar. Saxon words, and those in every day use, are the first

that should be presented to the eye; and in these lessons children should remain until the eye is as familiar with them as the ear, or in other words until they can read them with ease. The best lessons we know for this purpose are those published in the First Book of the Sunday School Union.

The next step is to extend a child's acquaintance with language, and hence lessons gradually introducing words used in every day life, but not common to childhood should be presented taking care that the increasing difficulty is in the phraseology and not in the matter of the lessons.

Another stage would require the introduction of difficult matter and as a consequence an increase in the amount of difficult language.

The principle then on which the graduation of the reading lesson should be conducted is that of presenting first to the eye, the words with which the car is already familiar; secondly, the further addition of words, whose meaning may be readily conveyed to the mind, and whose form and sound may be easily made familiar to the eye and

ear;

and thirdly, the introduction of such difficulties in matter and language as will require a vigorous analysis on the part of the teacher, with considerble mental effort on the part of the children.

The great difficulty in the graduation of the reading lesson is the want of suitable books. Those best adapted to our purpose are the books published by the Irish Educational Board; or those by Mc'Culloch.

The processes through which a reading lesson should pass, depend on the stage of the children.

In the earlier stages, the lesson should be printed or written on the slates; it should then be read, word by word, clause by clause, sentence by sentence, by the children individually, the teacher shewing them how, but throwing as much upon them as possible. It should then be read simultaneously for the purpose of emphasis

and expression. During the lesson the interest of the children should be excited, by getting them to talk of the things of which they are reading, or of the meaning of the words. After it is read, it should be spelt and then written or printed on the slate from dictation.

In the later stages, the reading lesson should be read individually in the drafts, that the children may be better prepared for any assistance to be received from the teacher. After the individual reading in the draft, with mutual correction under the supervision of a monitor, the meaning and derivation of words should be given to a class of two drafts, by an apprentice. After which the different classes forming a section should pass to the gallery for examination, analysis, and supplementary instruction by the teacher, to be followed by simultaneous and individual reading; the teacher should give the example in tone, emphasis, and expression, and finally the lesson should be reproduced, either as an abstract or by dictation, to ascertain whether the eye has been properly employed during the previous processes. QUESTION II.

Grammar should be taught so as to make children acquainted with language as the vehicle of thought. Hence attention should be directed in the first lesson to simple sentences and not as is usually the case to classes of words. The relation which the words in the sentences sustain to the things they represent, and to each other, so as to express thought, should be pointed out. Afterwards the simple sentence should be gradually increased, by the addition of qualifying words and clauses to the subject and predicate; and this process should be continued until by a carefully graduated series of lessons the child is made acquainted with the different classes of words used, their definite office, the modifications to which they are subject, and the various modes in which they may be arranged.

In thus teaching Grammar it is necessary to observe that no word

should be introduced into a sentence until the mind is ready for the idea it conveys, and no modification or inflection of a word should be allowed to be made until the difficulty of giving the precise meaning without it is felt.

Grammar and Composition should be taught together. Let half an hour daily be devoted to them; on one day there should be oral instruction, and on the next the formation of sentences on the model of the previous day. For instance if on Monday the oral instruction had been to show how the subject might be extended by means of an adjective (as a ripe apple falls,") on Tuesday the children should be required to form on their slates a number of sentences illustrating the same case.

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Dictation lessons should make a a child familiar with the structure of words and with the peculiar difficulties of the language, and this may be best done by a graduated series of lessons.

1. Words of like endings as bid, did, hid, kid, lid; bend, lend, mend, send.

2. Words with silent letters, knee, dumb.

should be spelt as it has been written, and if a boy finds that he and his neighbour do not agree, let him hold out his hand, and then be required to spell as he has written it; the two ways of spelling the word should then be put down on the black-board, and the sense of the class taken as to which is right, after which all the class should write the word in its correct form. At the end of the sentence, the slates should be inspected, and if any child's slate now contain mistakes, he should be required to produce them three or six times correctly. Thus proceed to the end of the lesson or till the time allotted to it has expired.

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3. With double vowels and con- ing, its functions are the same with sonants as piece, cabbage.

4. Primitives and Derivatives as shade, shadow; fiercely, fierceness; care, careful, careless.

5. Words nearly alike in sound but different in meaning; as device, devise. 6. Peculiar difficulties, as- 66 Eight heifers and ewe sheep were chewing the cud beneath the tough boughs of an ancient yew tree in that beautiful field."

Teaching should be made Collective during oral instruction by the practice of mutual correction combined with vigorous interrogation; and during the written exercises by a constant oversight and thorough revision. The certainty of such revision will do much to secure that diligent application without which the most skilful teaching is inefficient. To the correction of dictation exercises especial attention must be given. This correction should appeal to the eye not to the ear; hence after a sentence is dictated, each word

those assigned to geometry in a high state of education; it is the Euclid of elementary schools," Hence it should be so taught as to furnish material for the cultivation of the reasoning powers. Its great object is the discipline of the mind; and for this it furnishes great facilities as its principles are capable of easy demonstration and ready application.

To attain these objects a dogmatic style of teaching must be avoided, the reason of every process must be made apparent, the principles must be demonstrated, and examples of their application in household economy constantly given. A great defect in the ordinary examples is their being connected with subjects of which the majority of children have no ready conception. To remedy this the teacher should form examples having special reference to the circumstances of his children's parents, and to the particular modes of business pursued in his locality.

Oral teaching combining demonstration of principles and dictation of exercises, individual application to written or printed examples, and constant advancement of the proficient, are the things essential to success.

They can be secured only by an organization based on ability in Arithmetic. The practice of teaching Arithmetic in the reading section is as false in principle as it is fatal to success. "It often happens that the same child will make very different progress in different branches, many a boy will shoot a head of his class-fellows in reading and yet fall short in the reading section of them in arithmetic,' and vice versa.

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In organizing for Arithmetic the classification is a matter of considerable moment, as in the best formed classes, if there be periodical examination and removal, there must be some who are either below the average of the class, or are ignorant of the principles taught in it. Now, it would be an absolute waste of time to teach the informed and the uninformed together; hence they should be placed in drafts according to the attainments. In each classes two or more principles should be taught. Those that have mastered the first principle should be placed in the higher draft, and should be seated in the desk silently working examples from cards, while the new comers and the rest in the remaining draft should be taken round a black board for instruction, in the first principle taught in the class. On another day the lowest draft should be left in the desk for silent working, and the higher one taken out for instruction in the other principle. Such a classification and method by adapting the instruction to the state of the children, tend to ensure its collectiveness.

QUESTION IV.

These have relation to the children, the teacher and method.

1. With respect to the children. Their position requires attention for the purpose of inducing a love of neatness and order. If seated at desks in

parallel rows each child should be immediately behind his neighbour; if standing at drafts the boys on the sides of the semicircle should be equal in numbers and exactly opposite. The posture of the children should be erect for the sake of health, neither leaning nor lounging should be permitted. All talking should be prohibited. Employment should be secured for all. The slightest deviation from what is required with the least wandering of the attention should be checked at first. 2. With respect to the teacher.

His eye should take in all; every child should feel how utterly impossible it is to escape its notice; his voice should be no louder than is necessary for the class to hear,-noise creates noise; his manner should be firm, conveying the impression that it is quite hopeless to attempt to do wrong with impunity.

3. With respect to method.

The interrogation should be rapid, not addressed to the children in turn, but irregularly, so that each child may feel the importance of being attentive. It should be at once addressed wherever there is a vacant look, a wandering eye, or any other symptom of inattention.

The answering should be individual, and if not immediate, or if wrong, others should indicate their ability to answer by putting out their hands. The teacher should never correct an answer himself so long as he can procure it from the class.

G.

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