diately follow, and when they have spelt the word, the leader repeats another, and so on through the card; the children at the same time keeping their finger to the word they are spelling, so that if a child be inattentive it is sure to be detected.

We pursue, likewise, the following method of teaching the writing alphabet. The children who are about five years old are supplied with slates, on which is engraved the whole alphabet, the same as on copper-plate copies, thirteen letters on each side of the slate, some in capital letters, others in text; the children then put the pencil into the engraving, and work it round into the shape of the letter, which they cannot avoid doing as the pencil will keep in the engraved part; in this way they learn not only to read anything written but also to form their letters correctly.

CHAPTER XI.

NUMBER.

VARIOUS METHODS OF TEACHING THE
RUDIMENTS OF ARITHMETIC.

"It is not the possessing, but the right management of any valuable advantage, which makes it desirable."

THE advantage of numerical knowledge has never been disputed. Its continual and universal application to the business of life renders it a most indisputable acquisition to all ranks and conditions of men. The practicability of imparting the rudiments of arithmetic to very young children, has been satisfactorily shewn by the infant school system; and it has been found likewise that it is the readiest and surest way of developing the thinking faculties of the infant mind. Since the most complicated and difficult questions of arithmetic, as well as the most simple, are all solvable by the same rules and on the same principles, it is of the utmost importance to give children a clear insight into the primary principles of number. For this purpose we take care to shew them, by visible objects, that all numbers are combinations of unity; and that all

changes of number must consist, either of adding to, or taking from, a certain stated number. After this, or rather, perhaps I should say, in conjunction with the instruction by visible objects, we exhibit to the children the signs of number, and make them acquainted with their various combinations; and lastly we bring them to the abstract consideration of number; or what may be termed mental arithmetic. If you reverse this, which has generally been the system of instruction pursued-if you set a child to learn its multiplication, pence and other tables,-before have shewn it by realities, the combinations of unity which these tables express in words-you are rendering the whole an abstruse, difficult and uninteresting affair to the infant mind; and, in short, giving it knowledge which it is unable to apply.

you

As far as regards the general principles of numerical tuition, it may be sufficient to state, that we should begin with unity, and proceed very gradually, by slow and sure steps, through the simplest forms of combination to the more comprehensive. Trace and retrace your first steps -the children can never too thoroughly comprehend the first principles or facts of number.

We have various ways of teaching arithmetic in use in the schools; I shall speak of them all, beginning with a description of an instrument of great utility and much used in Infant Schools.

THE TRANSPOSITION FRAME AND THE
METHOD OF USING IT.*

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TIE frame is 16-in. square, and made of wood, twelve wires pass through it at equal distances; on which wires seventy-eight moveable balls are to be placed beginning with one on the first, two on the second, three on the third, &c. up to tewlve. It is an excellent instrument for an intant school, as with it you may teach the first principles of grammar, arithmetic and geometry.

It is to be used as follows:-Move one of the balls to a part of the frame distinct from the rest. The children will then repeat, "There it is, there it is." Apply your finger to the ball, and set it running round. The children will immediately change from saying, "There it is," to "There it goes, there it goes."

It is to be understood that this Frame is for teaching the children altogether in the gallery.

When they have repeated "There it goes" long enough to impress it on their memory, stop the ball; the children will probably say," Now it stops, now it stops." When that is the case move another ball to it, and then explain to the children the difference between singular and plural, desiring them to call out, "There they are, there they are ;" and when they have done that as long as may be proper, set both balls moving, and it is likely they will call out, "There they go, there they go," &c. &c.

By the natural position of the balls, they may be taught to begin at the first. The master raising it at the top of the frame, says, What am I doing? Children answer, Raising the ball up with your hand. Q. Which hand? A. Left hand. Then the master lets the ball drop, saying, "One, one." Raise the two balls, and propose questions of a similar tendency; then let them fall; the children will say, "Twice one:" raise three, and let them fall as before, the children will say, "Three times one." Proceed to raise the balls on every remaining wire, so that they may say, as the balls are let fall, four times one, five times one, six times one, seven times one, eight times one, nine times one, ten times one, eleven times one, and twelve times one

We now proceed as follows; 1 and 2 are 3, and 3 are 6, and 4 are 10, and 5 are 15, and 6 are 21, and 7 are 28, and 8 are 36, and 9 are 45, and 10 are 55, and 11 are 66, and 12 are 78.

Then the master may exercise them backwards, saying, 12 and 11 are 23, and 10 are 33, and 9 are 42, and 8 are 50, and 7 are 57, and 6 are 63, and 5 are 68, and 4 are 72, and 3 are 75, and 2 are 77,