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.”  I do not particularize further, because I know that good teachers will at once see the principle aimed at, and supply the other requisite lessons:  the object of this book being rather to shew the principle of the thing, than to go into detail.

CHAPTER XII.

ARITHMETIC.

The arithmeticon—­How applied—­Numeration—­Addition—­Subtraction—­ Multiplication—­Division—­Fraction—­Arithmetical tables—­Arithmetical Songs—­Observations.

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“In arithmetic, as in every other branch of education, the principal object should be to preserve the understanding from implicit belief, to invigorate its powers, and to induce the laudable ambition of progressive improvement.”—­Edgeworth

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The advantage of a knowledge of arithmetic has never been disputed.  Its universal application to the business of life renders it an important 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 arise either from adding to or taking from a certain stated number.  After this, or rather, perhaps I should say, in conjunction with this instruction, 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 you have shewn it by realities, the combinations of unity which these tables express in words—­you are rendering the whole abstruse, difficult, and uninteresting; and, in short, are giving it knowledge which it is unable to apply.