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But this operation of adding or subtracting, for instance, is intellectual, not mechanical or audible; of course, we cannot ascertain how many times a boy repeats his sum before it is brought to his master for inspection : steady boys may do it five or six times, but the idle and careless seldom do it more than once; here is much time lost, and a remedy adapted to the case is not in the teacher's power.

Again, when sums are brought up to the master for inspection, each boy's must be individually attended to; here is another great loss of invaluable time. Perhaps, twenty boys have sums ready for inspection at once, and 'nineteen wait, sit, idle, or talk, while the twentieth is at his master's desk, with his sums.

Nor is this all : if an incorrigible dunce happens to show up his sumś first, and, as is often the case, adds new blunders to mistakes, he may easily delay his master, and the boys who are waiting to follow him in succession, for some time; and a few instances of this sort, arising from carelessness, inattention, or incapacity on the part of the scholars, will completely derange the business of a morning, and keep a number of their school-fellows unemployed.

Independent of this, it is disgusting to teachers of any description to be continually plodding over the same ground of elementary arithmetic. Same

ness,

ness, in every instance, produces listlessness; and variety is ever productive of agreeable sensationis, I have seen a respectable schoolmaster, well versed in the mathematics, have a dozen boys standing round his desk, waiting for him to attend to their sums, while he has been listening to a slow boy, repeating his sum, till he has bitten his lips with vexation,

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To prevent this dulness, I have invented an e entire new method of teaching arithmetic, that commences when children begin to make their figures. The folļowing is the arrangement of the , cyphering classes:

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VI
Class 1; Combination of figures.

2, Addition.
3, Compound ditto,
4, Subtraction.
5. Compound ditto.
6, Multiplication.
7, Compound ditto.
8, Division.
9, Compound.ditto.
10, Reduction.
11, Rule of Three.
12, Practice.

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The first object is to teach children to make their figures. In order to do this, the class learning to make figures are assembled under the monitor, in

one

one part of the school, by themselves, 1 It is to be observed, the same boys who are in one class,tach to cording to their proficiency in reading, are in another, according to their progress in arithmetics that, when the school is cyphering, the classes are organized on the annexed plan of the cyphering classes; when they are reading, they are arranged on the plan of the reading classes, given in a preceding page. They always, on the commencement of school, come in, in their different reading classes; and, when cyphering, afterwards, separate to their several arithmetical classes: after having performed the cyphering, they return to their reading classes, before they go out of school. This changing abouť from class to class, in which three fourths of the whole schoolare concerned, is attended with but littlebustle, and no confusion. It is usually done in less than five minutes; and the school-room is so large, it will take near that time to go round it. If there are any boys who cannot cypher, they remain under the monitor's care, for instruction in reading, while the others are cyphering. The modes of teaching arithmetic are so simple and easy, that all the boys in the school, who can read and write text-hand in four letters, are put in the first cyphering class.

It is not uncommon to find boys thus instructed, who learn to write and cypher remarkably well, in six months, who never handled a pen, or were taught by any other method. Before boys go into arith

metic

métie it is needful they should learn to make the figures : on my plan, they learn to make and combine them at the same time. The class of boys, who are learning to make their figures, form, in the institution,

THE FIRST CLASS OF ARITHMETIC.

In the tuition of this class, the boys who constitute it, are not limited to number: any boy, for whom it is requisite, is immediately placed in it. Instead of teaching them to make figures in the order of the nine digits, as is usually done, by writing occasionally in copy-books, they haye each a slate. The monitor takes a long Addition table, which combines not only units with units, but tens with units: a thing in which the pupil's greatest difficulty, as to simple and compound Addition,

The monitor reads from this table:

9 and I are 10, 9 and 2 are 11, &c. 25 and I are 26, 25 and 2 are 27, 25 and 3 are 28, 25 and 4 are 29, 25 and 5 are 30, 25 and 6 are 31, 25 and 7 are, 32, 25 and 8 are 33, 25 and 9 are 34; or other variations of the same table.

When these are dictated, each boy writes them on his slate: the monitor and senior boys in the class,

assisting

assisting in teaching the beginners, to make the figures, till they can make them themselves. The monitor also varies the tables:

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Take 9 from 10, 1 remains; 9 from 11, 2 remain; 9 from 12, 3 remain, &c.

He also uses the Multiplication table, and reverses it in the same manner: 6 times 2 are 12, 2 in 12 6 times.

In the same way he teaches them the Shillings' and Pence tables The knowledge of figures which the children acquire; by this method is great; and the improvement of this class in making the figures, does much credit to the class and teachers. It is true, the class are told all they are to do i but, in doing what they are bidden, they acquire a ready knowledge of the figures; whilst they are insensibly led into the habit of giving attention to all they do, and taking pains in doing it. By making their figures so many times over, they unavoidably attain freedom in making them; and this is the best step that can possibly be taken to facilitate their improvement in the next stage of their progress in arithmetic.

The same variation and tables, without the total, or answer to the monitor's question, applies to Subtraction, Multiplication, Division, and the Pence

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