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8thly, The custom, prevalent in French schools taught on the Lancasterian system, of the drafts (gallicè, groupes) or small classes, saying all their lessons in an under tone or whisper. It appears that the submonitor and his pupils, in a small class of this kind, can distinguish words and sounds thus pronounced as well as in the usual loud tones to be heard in English Lancasterian schools.

Mention should also be made of the advantages offered in France by the “ Superior primary schools” which are established in each department for the carrying on the education of such boys as may have distinguished themselves at the “ Elementary schools,” and thus obtained exhibitions (Gallicè, bourses), as well as of those boys whose parents may be willing to pay for further instruction in the arts, sciences, languages, &c. SUGGESTIONS AS TO CERTAIN ADVANTAGES AND DISADVANTAGES OBSERV

ABLE IN THE SIMULTANEOUS, BELL'S, AND LANCASTER'S SYSTEMS OF EDUCATION.

It is most desirable, when children are instructed in religion or morals, that the teacher should have a matured and well regulated mind, and as on these subjects children of different ages and talents are often equally well informed, or, at least, are equally capable of receiving information, in this most important part of education the simultaneous method is peculiarly applicable. Upon any other subjects taught in the school, however, gallery lessons are likewise useful, particularly when followed by questioning by the monitors in their classes, or by requiring the children to state in writing the substance of what they have heard.

By Lancaster's arrangement of desks, writing may be well taught to the whole school at one time.

The drafts, or very small classes, are adapted to the teaching of reading, spelling, and linear drawing, In the last, for instance, the submonitor having the printed copy before him, will exert himself to set an example to his few pupils; and they, being nearly on a par with each other and with him, will strive to equal his copy.

Bell's system of large classes with monitors and assistant monitors, is suited for giving instruction in arithmetic, for ascertaining the comparative abilities of a number of children in reading or spelling, for teaching history, chronology, grammar, and etymology; by this system the children may likewise be easily induced to question each other upon any of the subjects taught. As a method of teaching religion, however, this last exercise is by no means to be recommended.

The monitorial systems, whether of Bell or Lancaster, are supposed occasionally to render those children who are monitors dictatorial and conceited. In girls' schools such an effect, as shown in the manners and appearance of the elder children, would be most objectionable. This danger would be in a great measure avoided by the plan subsequently suggested, in which the monitors and submonitors become pupils in their turn, and are often placed upon an equal footing with the other children.

For reasons then such as those just mentioned, it is thought that two schoolrooms are required ; if possible, on the same floor, and in that case, with a wide glass door between them. One room should be fitted up on Lancaster's plan, with desks in the centre, and a space at the sides for “ drafts,” or small classes. The other room, in which should be a gallery capable of holding half the number of children in the school, should be fitted up on Bell's plan, and when the whole school was assembled here (except at meal time, for then it would be most convenient for the children, whose homes are distant, to remain in this room), it would be divided into eight (or six) large “ classes," with monitors and assistant monitors. Two of such classes would form a “ subdivision ;" four classes, a “division; and each of the eight (or six) classes would be broken into drafts, under submonitors, with five, six, or seven children in each.

The several objects to be attained by means of these arrangements may be thus briefly pointed out :

The master might address children on the gallery in one room, either in “ divisions,” “ subdivisions,” or even in classes if thought desirable, whilst the remainder of the school was taught under the superintendence of the “ general monitor,” to read, spell, or draw by submonitors in the desk room. When the children were assembled in the gallery room, the submonitors would constitute the two upper classes.

When the school was conducted on Lancaster's plan (provided the master was not occupied in giving a gallery lesson to other classes or divisions), the monitors and assistant-monitors might receive from him particular instruction. In fact, by this system, one great fault in the monitorial method of teaching, viz., the small amount of instruction received by the monitors, would be avoided.

For the purposes of addressing the whole school at one time, or of teaching writing—the desk-room would be preferred to the gallery-room.

As the offices of “general monitor,” and “monitor,"'* would have a small weekly payment attached to them, and those of “assistant-monitor” and “sub-monitor," would be the necessary steps by which to rise to these, the master would have many opportunities of stimulating his pupils by the hope of advancement or the fear of the contrary.

This, then, my dear Sir, is a very humble illustration of the way in which, in my opinion, we should proceed in forming a general system of instruction for the national schools in England ; and I would beg to mention in reference to it, that in judging of the different educational institutions in France and elsewhere, I have always been on my guard against the very natural error of supposing, that because a school under the superintendence of a master-mind, succeeds, that the method adopted in it is applicable to all other schools ; for in our case, where regard must be had to economy, I conceive that would be the best system which should best aid one master of average abilities in communicating to a number of children, by means of certain books, the amount of knowledge he possesses, or may acquire. Very faithfully yours,

* In schools containing more than 150 children, an assistant-master (or mistress) would doubtless be a useful addition, although it is believed that a good “general monitor,” would in most cases be sufficient. With regard to the monitorial system of teaching generally, it is, however, to be observed, that it seldom, if ever, succeeds, unless such weekly payments are given to the monitors as shall induce the elder and better educated children to remain in the school as teachers. In the Central School at Westminster, the senior monitors or apprentices receive 5s. weekly, and the junior monitors not less than 9d.

T. L. WOLLEY.

PRINCIPLES BETTER THAN RULES IN TEACHING

ARITHMETIC. Dear Sir,--The only thing I have to offer at present towards your Magazine, is a translation of a French elementary treatise on arithmetic, which appears to me capable of enabling schoolmasters to teach the principles and explain the groundwork of the rules, in accordance with the remarks which you have made in your excellent essay on the “Importance of Language,” p. 31. The book I allude to is entitled Elements of Decimal Arithmetic," and merely comprises a familiar explanation of the four simple rules and fractions, together with the elements of ratios and proportions. It is the book approved of by the University of France, for use in the elementary schools throughout that country, and is the production of a good mathematician, professor of that science in the University of Strasbourgh. The French must be allowed, I think, to possess the faculty of explaining, in lucid and simple language, the principles of the exact sciences, in a much higher degree than English writers ; I know at least, in my time at Oxford, and, I believe, at Cam. bridge, their works on all branches of pure mathematics, were in very general use. I think, too, it will be allowed, that nothing can be more repulsive, or less capable of exercising and satisfying the reasoning powers, for which the study of mathematics is usually recommended, than the quaint and absolute rules (usually stereotyped), omitting any allusion to the reasons on which the rules are founded, which distinguish the usual arithmetic books. The French work, on the contrary, leads the student from one step to the next by insensible progress, and reasons out each rule by recalling the previous step already mastered; so that the whole forms one connected chain of reasoning, like that so beautifully displayed in Euclid's Elements. Surely such a method of instruction must be better suited to the purposes of educationto the drawing out, and training by use, the faculties of the mind, than any system of cramming stereotyped rules by rote.

We have not far to look for examples of the sort of rules of which I complain in our English school books. I will take a work composed by an eminent mathematician, LL.D. and F.R.S, &c., &c., improved and corrected up to 1835, and of course stereotyped. The editor of this improved work, which, we are told, has “always maintained the highest reputation,” as witnessed “by the numerous editions published since the death of its illustrious author,” nevertheless confesses, that the origi. nal work is “ in several respects not so perfect and perspicuous in its plan, nor so plain and practical in its details, as the present advanced state of arithmetical science requires." He truly observes :-"Nothing can be more uninteresting and repulsive to the mind of uninitiated

youth, than the dry and technical manner in which the first rules are generally exemplified and taught, and by this means the pupil, at his commencement, too frequently contracts an improper aversion to this necessary branch of knowledge.” Accordingly, in the present edition, " the greatest care has been taken to smooth the way of the learner, and to explain the general principles, and illustrate the practice of the science.” There will, therefore, be nothing unfair in my taking this book as an example of its class, with the latest improvements.

Now imagine, Sir, (perhaps I should rather say remember, infandum jubeo renovare dolorem”), the hopeless feelings of boy or girl, age from eight to twelve, thus initiated into the mysteries of simple division.

Rule. “1. Having written down the divisor and dividend, consider if the divisor be less than, or equal to the same number of the left-hand figures of the dividend ; if so, write the figure expressing the number of times it is contained in the quotient; but if not, take one place more of the dividend figures than are in the divisor, and write the number of times they contain it in the quotient as before.

“2. Multiply the divisor by the quotient figure.

"3. Subtract [or substract as we always called it], the product from the same dividend figures.

“ 4. To the remainder affix the next dividend figure, and write in the quotient the number of times the divisor is contained in this number; multiply the divisor by the last quotient figure, and subtract the product from the last-mentioned number; then proceed as before, from the beginning of this article, till all the dividend figures are used." Now if that is not simple division, I should like to know what is !

“Multiplication is vexation,

“ Division is as bad,” &c. To many a poor plodding lad, I have no doubt it seems very like a complete division of sound from sense, and confirms him in an opinion to which he has long been inclined, that words are only meant to conceal a person's meaning. “ Ignotum omne pro magnifico," however, think the parents, and nothing are they so anxious for, as that “ Our Will should be a scholar at summing." But, I forgot, we have not done with simple division yet; accordingly, there follow no fewer than eight contractions, as they are called. Thus, “1. Division by any small number, [to be learnt after division by a large one.] 2. When ciphers are annexed to the divisor. 3. To divide by 1 with any number of ciphers annexed. 4. When the divisor is the product of two or more numbers not greater than 12. 5. When you are pretty ready at division. 6. To divide by any number of nines. 7. When there is a fraction in the divisor, (this comes about 46 pages before it has been explained what a fraction is, whether vulgar or otherwise.) 8. To multiply by a mixed number. These are the contractions.” Now the boy will indeed be a numskull, if he has not learnt not only what simple division is, but what is the meaning of contraction also ; which illustrates what you so justly observe about the importance of understanding English. Dip into what page we will of this manual for cramping the brains of childhood, we cannot fail to meet with some excellence; but for terseness and a sort of conciseness, of which Tacitus himself might be proud, I do not remember to have seen “ the beat of this,”

MIXED REDUCTION.-Rule. Bring down the given number to a denomination, which is contained exactly in that required; then bring it up to the required denomina

tion ! ,

The admiration expressed by Moliére's Bourgeois gentilhomme, when he learns for the first time from his master of philosophy, that he has been speaking prose for the last 40 years without knowing it, is something akin to that which I feel for the great masters of science who have contrived to involve the simplest elements of arithmetic in such a cloud of words as we find in these books.

But, however simply and plainly the rule might be worded, I still decidedly object to the method, I might call it the Chinese method of teaching mere rules, and not first tracing out the course of reasoning which conducts to the rules, and thus demonstrating the principles on which they rest. Arithmetic is clearly a branch of demonstrative science; and it appears to me to be altogether a misapplication of the great principle of exercising the faith of children, to insist upon their taking for granted, and never learning in fact, the principles of this science. The introduction of faith here, I think, tends to confound all just views of its propriety in those higher parts of knowledge which are within its true province. If the translation of the French arithmetic seems to you deserving of a place in your sheets, your readers will be able to judge whether my estimate of its superiority to those in common use is well-founded. Yours very truly,

T.T. [We hope that our kind correspondent will give us a free translation of the valuable little book to which he refers, adapting it, wherever necessary, to the use of English schools.—Ed.]

HINTS ON CATECHISING. REGULATIONS IN THE DIOCESE OF TOURS. In the last two volumes of the Educational Magazine, there was a valuable series of “ Hints on Catechising," collected from various authors, including extracts from old visitation queries and injunctions. We shall be glad of the help of our correspondents, and particularly of the gentleman who furnished the former series, in the continuation of so important and interesting a “catena.” It is a happy circumstance of the times, that within the last month or two, the attention of the clergy has been authoritatively called, in more than one diocese, to the duty of obeying the rubrics and canons. We know nothing that would tend more certainly, or more directly, to the promotion of sound education, in the schoolroom as well as in the church, than the simple observance of the rubrics at the end of the catechism, the first of which enjoins, that the curate of every parish shall diligently upon Sundays and holy-days, after the second lesson at evening prayer, openly in the church, instruct and examine

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