PREFACE.

THE public favor shown to this little work has induced the author to stereotype it, that it may be sold as low as possible to the infant and primary schools, to whose use it is adapted. The author's school, where children entered at the earliest age, and were carried through all the branches of a useful, as well as polite education, afforded him an opportunity of personally testing the operation of the plan here adopted, not only in its immediate effect upon the infant's mind, but also in its influence upon the future progress. The idea of pictures was thoroughly examined, and the plan tried, before that of using counters was preferred. Pictures pleased the eye of his little pupils for a moment, but, being fixed and unchangeable, they soon lost the charm of novelty, and he was obliged again to resort to counters, which, being susceptible of endless variety and change, without taxing the infantile mind too far, give it exercise enough. The task should be made pleasant to the child, but not so much so as to render mental exertion unnecessary. Many years' experience in teaching, not only arithmetic, but every other branch, on the plan of Pestalozzi, will, the author hopes, entitle his judgment, in this particular, to a candid consideration.

The increasing use of this little work would excuse any mention of recommendations, but the publishers cannot refrain from saying that this alone is recommended for beginners as an introduction to Colburn's First Lessons and the larger Arithmetics, by T. H. Palmer, in his "TEACHER'S MANUAL," and by George B. Emerson, in his "SCHOOL AND SCHOOLMASTER.'

BOSTON, June, 1844.

THE

CHILD'S ARITHMETIC.

VARIOUS articles may be used for counters, and, perhaps, the greater the variety, the more interest will be excited in the little pupils. But, as it is desirable not to confuse their ideas, only one kind of counters should be used at first, and the best, on some accounts, are flat pieces of wood, about an inch long and half as wide; and, as only 5 will be necessary, they may be made exactly alike; for, if the child can distinguish them, when told that the first is 1, the second 2, &c., he will think that no other can be called 1, or 2, and if you place what was called 1 in the fifth place, he will still call it 1, as he did before.

LESSON I.

Having provided the 5 counters, call the little class around you, and require them to put their hands behind them, to prevent their handling the counters unless told to do so. Then put down 1, and say, there is 1. Let each child repeat after you, 1. Then put down another, and say, there is 1 more, and 1 and 1 more make 2. Then take both up, and, putting 1 down again, ask how many you put down. If no child in the class can answer, you must say 1, and require them to repeat 1. Then put down another, saying as before, 1 and 1 more make 2. Let them repeat always. Do not proceed to the third counter 1*

until they can count 2. When you put down the third, say, 1 and 1 more are 2, and 1 more makes 3. Then take all up, and go over the same process again, until the children can count 3. This will require a great stock of patience, but it is important that the child be advanced no faster than he perfectly comprehends. There is no fear of impatience on the part of the children, for until they feel perfectly acquainted with 3, they will not be anxious to try a larger number.

Be sure to put down but 1 at a time, and when it is time to put down a fourth, put down 1 and (always requiring the class to repeat after you) say, 1; then, putting down another, say, 1 and 1 make 2; then, putting down another, say, 1 and 1 are 2, and 1 more makes 3, and 1 more makes 4.

Go through the same process when you put down the fifth. Be particular to name the units or single ones of which the number 5 is composed. This lesson will require a considerable time to be well understood, but it is better to dwell too long than too short a time upon it. The exercise may be varied by using beans, cents, blocks, fingers, &c., for counters. Indeed, it will greatly increase the interest the children take in the exercise, if little wooden or pewter men, such as are found at the toy-shops, be used. These are far superior to pictures, because their position and number can be readily changed.

Il.

After the children have thus learned to count 5, put down 2 counters at once, and ask the first child how many there are down. It is possible that he cannot tell. He must, at any rate, be required to put his finger upon 1, and say, 1 (then, putting his finger upon the other, let him say)

and 1 more makes 2. It is very important that the child be required to touch each counter.

Then let the next count in the same manner, till each of the class has tried, and if one miscounts, let the next correct him.

When it is evident that they can all count 2, put down 3 counters at once in a line, and let the highest put his finger upon each, saying, 1 and 1 are 2, and 1 more makes 3. Let each try as before, touching and correcting.

So put down 4, and then 5, proceeding carefully in the same manner, and continuing the exercise upon each number until you are satisfied that all the children understand it. Vary the exercise with the different sorts of counters.

III.

Put down the whole 5 in a line, previously taking care to chalk or ink as many spots as there are counters, that, when you take up any counters, the spots may assist the child to tell how many are taken up.

When the counters are laid upon the spots above mentioned, take up 1, and ask how many are gone. Then put it down again, and take up 2. asking how many are gone, as before. Let the child say, 2 ones, or 1 and 1, which make 2. Then put

all down, and take up 3, then 4, and 5, in the same manner. To make this lesson more interesting, set up five of the pewter men, and, knocking 1 down, ask how many are down; then set him up, and knock down 2, and so on.

IV.

This lesson is the reverse of the third. Place the 5 counters on the 5 spots, and then, taking away 1, ask how many are left. Let the child put his finger upon each, and count as in Lesson I.