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Children. (Touching them with their fingers.) Two cubes.
Mother. (Adding another.) There are three cubes.
Children. (As before.) Three cubes.
Mother. (Taking up the three cubes, and throwing two upon the table.) How many cubes do you see before you?
Children. We see two cubes.
Mother. (Taking up the two, and throwing three cubes upon the table.) How many do you count now?
Children. We count three.
Mother. (Having continued as far as five, and throwing four cubes upon the table.) How many are there now?
Children. There are four.
(When any of the children gave a wrong answer, she took it for granted that the foregoing step was not clear to him; and she returned to the preceding number.)
Mother. (Throwing five upon the table.) How many do you see now?
Children. (After counting them.) We perceive five. In this manner she continued till ten, making the children always repeat the preceding numbers before she went to a new one; and thus, l>y frequent but short repetitions, of a few minutes at a time, they learned with cheerfulness and without fatigue, to count from one to ten.
(The mother should introduce as much variety into these exercises as possible, by making the child count her or his own fingers, the buttons of his jacket or waistcoat, or some other objects near him; and it should never be forgotten, that in order to prevent weariness or disgust, she should give short lessons at a time, but several repetitions of them during the day.)
After having advanced so far as to be able to count from one to ten, the mother now placed an oblong figure before them, saying: Once one.
Children. Once one.
Mother. (Placing a second oblong at a little distance from the first.) Twice one. Children. Twice one.
Mother. (Adding another.) Three times one.
Children. Three times one. Mother. (Adding another.) Four times one.
Children. Four times one.
Mother. Five times one.
Children. Five times one.
Thus she continued till she had ranged ten times one oblong upon the table, at equal distances; and all of them in a straight line; their long sides towards the window, and their short sides towards the door.
Mother. (To the children.) Pay attention: we will look at these oblongs, and see whether we can notice any thing besides; first tell me once more, how many oblongs are on the table.
Children. Ten oblongs are on the table.
Mother. Do they lie close together?
Children. No! they do not lie close together.
Mother. In what manner are they separated? Is the first oblong placed near to, or further from the second, than the second from the third?
Children. No! they are equally distant from each other.
Mother. Right! we have already noticed something of these oblongs—here are ten oblongs at equal distances from each other.
Children. Here are ten oblongs at equal distances from each other.
Mother. Let us try to discover something . more. Could not these oblongs be placed differently, without changing either their number or distance?
Should the children not observe, that they may be placed in a curved as well as in a straight line, the Mother ranges them so as to form a curved line, without changing either their number or distance; and then replaces them in the former straight position. This operation will probably lead them to perceive that they ought to say:
'* These oblongs are ranged in a straight line."
Mother. We have discovered again something new, and lest we should forget it, let us repeat whatever we have observed: here are ten oblongs placed at equal distances, and in a straight line.
Children. Here are ten oblongs placed at equal distances, and in a straight line, &c.
(In/the same manner did the Mother proceed in making the children find out the position of the oblongs with respect to their long and short sides, till they could finally say.)
Children. Here are ten oblongs, placed at equal distances, in a straight line, having their long sides turned towards the window, and their short sides towards the door.
Mother. We can say five different things of these oblongs:
1. That their number amounts to ten.
2. That they are placed at equal distances.
3. That they are ranged in a straight line.
4. That their long sides are turned towards the window.
5. And their short sides towards the door. (The children, after knowing this well,
were desired to turn about, or to shut their eyes; meanwhile she took away two oblongs, and having moved the second nearer to the first, she desired them to face her again, and asked: How many are here now?
Children. (Having counted them.) There are but eight.
Mother. How many were there before?
Children. There were ten.
Mother. How many have I taken away?
Children. You have taken away two (pointing to the vacaut places.)
Mother. Did not these oblongs undergo any other change?