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in proportion, By the method of arithmetic just described, every boy in each class is told by the teacher all he is to do; and his sole business is to do it, so often as to become quite familiar with it. In the succeeding method, the boy's business is to do 'every thing without instruction.

Each arithmetical class is called out according to the list, in companies of twelve. To each class is allotted a proper sum, according to the rule they are in. This sum is written on a card, with ink; or on a board, with chalk. The twelve boys stand round the sum they are to work; and the board, on which the sum is, is suspended from the wall. The teacher is provided with a key to the sum, similar to those before described. Each semicircle have their insignia of merit, &c. and each boy gives precedence to any other boy who excels him in performing his lesson. The teacher then requires the first boy to add the first column, if in Addition; or to multiply the first figure, if in Multiplication. He is to do this aloud, extempore, without any previous knowledge of the sum, or assistance from his teacher in performing it. If he mistakes, it is not the monitor's business to rectify the mistake, but the next boy is to try if he can do it: and if none of the twelve can answer right, it must be done by the monitor. When many mistakes in a whole class occur, such boys must practise more in the methods first described, before they are tried this way. The

former

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former method affords an easy introduction to this. The same advantage is possessed by both, that neither teacher nor learner can be idle. Our system of emulation enables me to combine encouragement and reward with it, in a manner more than usual in schools where this is practised. The last method being such as is usually taught in some schools, it requires a boy of superior abilities, to teach those who are inferior to himself in proficiency. The improvement I have made is by introducing the key, which reduces it to a mere system of reading on the monitor's part. If the boys repeat the sum, extempore, naming the total, according to the key in the teacher's hand, they are correct; if their account differs, the monitor immediately detects the error, when it becomes the business of the next boy in

the class to correct it. On this plan, any boy who + can read, can teach; and the inferior boys may do the

work usually done by the teachers, in the common mode: for a boy who can read, can teach, ALTHOUGH HE KNOWS NOTHING ABOUT it; and, in teaching, will imperceptibly acquire the knowledge he is destitute of, when he begins to teach, by reading.

There is yet another way of trying the proficiency of the scholars, after they have been used to both the preceding methods of tuition: the teacher places each boy in a situation where he cannot copy from, or be assisted by, any other, who has the same task to perform. He gives him a sum, according to the

rule

rule he is in, and requires him to make a key to the sum, in a correct manner. If he can do this readily, à number of times, it is a proof that he is conversant with the rule he is in; and, when practice has deeply impressed it on his memory, he may advance to another rule. The first class, or combination of figures, is examined the same way. The tables in Addition åre written on the slate, without the amount, thus : 6 and 6 are--the boy who is examined, is required to add the amount--12. If he can do this, with every combination of figures, in the Addition and other tables, he is then fit for cyphering. By the old method of teaching arithmetic, there is usually + a great consumption of printed books of arithmetic; the new method almost entirely supersedes them. The same economy applies to another expensive + article of consumption in schools, cyphering books; in which the scholars usually write down all the sums they do. The expeditious progress they make, both in writing and accounts, is so great, they need only commit to writing a very short specimen of their sums, for the satisfaction of their parents; and even that is not absolutely needful. By using their pencils well, they acquire an equal facility in the use of their

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INSPECTION,

HAVING detailed a method of tuition for the several classes, it will be obvious, that, on the admission of boys into the school, they should be classed according to their proficiency. Those who have not learnt their letters, will be placed in the A, B, C, class; those who know all their letters, but do not know how to combine them, are placed in the two-letter class. Such as can spell in two letters, but not in, three, are placed in the three-letter class; the four and five-letter classes are organized, and receive additions, on the same principle. After this it is considered, boys should read for the improvement of their minds; and are classed accordingly, in the Testament or Bible. The arithmetic classes are.constituted in the same manner. Each boy should be examined before he is classed. The lessons for every class being determined on, and the name of each class, descriptive of the lessons, learnt by it; no other lessons can be taught to each class than those appointed for it. Boys should be removed from one class to another, as soon as they are proficient in that to which they belong. Thus, a boy in the A, B, C, having learnt to distinguish all his letters, should be removed to the next, or mono-syllable class of two letters; and, when he is proficient in that he should be removed higher, and so on. As the scholars are all arranged in different classes, many of them will soon make a proficiency, by these expeditious modes of teaching; and, as they cannot learn more than what is appointed for the class cannot remove themselves--nor can their monitor remove them—they must remain where they are, losing 'time, and making no progress, unless the system of inspection I am about to describe, pre> vented the evil. A monitor is appointed as inspec tor-general of reading: he keeps a list of every class of reading in the school. Whenever a new scholar enters, another monitor, whose business it is, examines what progress in learning the pupil has made, and appoints him to a class accordingly. The first duty of the inspector of reading, is to see, that each scholar's name is duly entered on the list of the class to which he is sent on commencing school. This is a matter of consequence. If any omission be made in the entry of each boy's name, it is possible the inspection may be conducted well, and yet the boy, whose name is omitted, be passed by: and, whatever his improvement may be, he may remain stationary.

many

The monitor of each class keeps a list thereof. It is also his duty to see the inspection conducted, so that no boy is passed by who is in his class. But the inspector of reading keeps a list of every class of reading in the school; and, when his lists are correct, he proceeds to duty, but not before.—He begins his inspection, by desiring the monitor of

the

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