and Shillings' tables. This method of instruction has also a counterpart; an arithmetical table of this kind, applied to the first four rules, without the amount of each combination annexed, is placed on the wall, or other convenient place. In the former instance, the monitor told the class, 9 and 9 are 18, and they wrote it. He now subdivides the class; and they assemble, successively, in circles of twelve boys, around the tables of figures on the wall. They have their numbers, insignia of merit, prizes, &c. as in other divisions of classes. The monitor then puts the question to the first boy-How much are 9 and 4? and the boy is expected to tell the amount-13. If he cannot answer correctly, the monitor puts the question to another boy, till he finds one who can: and he takes precedence, and the badge of merit from the boy who is unable to answer the question. The boys in this class are called out, in successive companies of twelve each, to answer questions of this nature, applicatory to the similar lesson they have that day been performing on the slate; and he varies the questions, as, How much are 9 and 9?-take 9 from 18-what remains?How much are 9 times 9? -How many times 9 in 81?

Whilst one company of twelve boys (the number need not be restricted to twelve, but it can hardly be more than twenty, with propriety) are performing this task, the remainder of the class continue at

their

their seats, writing what the monitor dictates, till the first division of twelve have finished their lesson. Then another division goes out, to the same lesson on the card; and they return to write on the slate. This is done every day, till the whole class has performed their lesson both ways. This method serves as an introduction to Numeration, which, it will be seen in the sequel, is only taught in a practical way.

The next is the Simple Addition class. Each boy in every cyphering class, has a slate and pencil; and we may consider, that the subject now before us relates to the best method of conveying the knowledge of arithmetic to those who are unacquainted with it. They usually begin with small sums, and gradually advance to larger; but, boys who have been well instructed in the preceding class, are not only qualified for this, but have a foundation laid for their future proficiency in every branch of arithmetic. As the reader will observe, + the whole of this method of teaching is closely connected with writing it not only unites a mental exertion with itself, but always renders that mental exertion, however great or small, visible to the teacher; and enables him to say, with certainty, that his pupils have performed their business. The monitor, or subordinate teacher of the class, has a written book of sums, which his class are to do; and F 3

he

he has another written book, containing a key to those sums, on a peculiar plan, which will be described, and which fully shows how they are to be done*.

In the first place, when his class are seated, he takes the book of sums-suppose the first sum is as follows:

+

He repeats audibly the figures 27,935, and each boy in the class writes them; they are then inspected, and if done correct, he dictates the figures 3,963, which are written and inspected in like manner : and thus he proceeds till every boy in the class has the sum finished on his slate.

*

Any boy who can read and numerate a little, is able to perform this duty as well as the principal monitor. The boy who reads the sum cannot be idle: if he is, the whole class must be so too; and, whilst teaching others, he is rapidly improving himself.

He

He then takes the key, and reads as follows:

FIRST COLUMN.

7 and 9 are 16, and 3 are 19, and 5 are 24. down 4* under the 7, and carry 2 to the next.

Set

This is written by every boy in the class, inspected as before, and then he proceeds.

2 and 7 are 9,

I carried are 20. next.

SECOND COLUMN.

and 6 are 15, and 3 are 18, and 2

Set down 0 and carry 2 to the

THIRD COLUMN.

3 and 6 are 9, and 9 are 18, and 9 are 27, and 2 I carried are 29:-Set down 9 and carry 2.

FOURTH COLUMN.

4 and 8 are 12, and 3 are 15, and 7 are 22, and 2 I carried are 24.-Set down 4 and carry 2.

FIFTH COLUMN.

1 and 2 are 3, and 2 I carried are 5.

* When the teacher reads, set down 4 under the 7 and carry 2 to the next, the lads who are inspecting the manner in which the boys in this class perform their sums, see that each boy writes down the 7 under the 4, and that they do the same with the amount; to be set down in every succeeding column.

Total, in figures, 54,904lbs. Total, in words, fifty-four thousand, nine hundred and four pounds.

The whole of a sum is written in this manner, by cach boy in the class it is afterwards inspected by the monitor, and frequently by the master; and it is a method, in particular, well adapted to facilitate the progress of the scholars in the elementary parts of arithmetic.

Its good effects are deducible from principle, as well as practice. For youth to be conversant in arithmetic, it is needful that the most frequent combinations of figures which occur in the first four rules, should be familiar to their memory. Now, + the frequent recurring of one idea, if simple and definite, is alone sufficient to impress it on the memory; without sitting down to learn it as a task; and, in the method of tuition just described, every boy is ✦ obliged to repeat it at least twice. First, the impression it makes on his mind, when listening to his monitor's voice, and the repetition of that impression when writing it on the slate. When a certain quota of sums are done, the class begins anew: and thus + repetitions gradually succeed each other, till practice secures improvement, and removes boys individually into other classes and superior rules, when each boy has a suitable prize, which our established plan appropriates to the occasion.

+