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When the children are quite firm in it, and understand perfectly the nature of the operation, the mother may give the exercise inversely, by decomposing the combined number 2. Thus:
(Placing 2 cubes upon the table.) Once 2 are twice 1.
Childr. Once 2 are twice 1.
Moth. (Taking one of the cubes up.) The half of 2 is 1.
Childr. The half of 2 is 1.
Moth. (Replacing the cube next t6 the first.) Once 2 are twice 1.
Childr. Once 2 are twice 1.
Moth. (Adding a third.) Once 2 and the half of 2 are 3 times 1.
Childr. (Always looking at the cubes.) Once 2 and the half of 2 are 3 times 1.
Moth. Twice 2 are 4 times 1.
Childr. Twice 2 are 4 times 1.
Moth. Twice 2 and the half of 2 are 5 times 1.
Childr. Twice 2 and the half of 2 are 5 times It
Moth. 3 times 2 are 6 times 1.
Childr. 3 times 2 are 6 times 1.
Moth* 3 times 2 and the half of 2 are 7 times 1.
Childr. 3 times 2 and the half of 2 are 7 times 1.
Moth. 4 times 2 are 8 times 1.
Childr. 4 times 2 are 8 times 1.
This is continued till 10 times 2 are 20 times 1. The mother enunciates, and the children repeat the whole of the lesson; which is followed by many and varied questions, all relating to and arising from the same. As it is essential, deeply to impress on the children's minds this in itself so simple, but to them so apparently complicated relation of unity to a combined number, and of the parts of a combined number to unity, the greatest possible variety must be introduced, in order to vivify the instruction; for which purpose the following examples may assist mothers, who are desirous of attempting this most useful and interesting branch of elementary instruction.
Moth. (Throwing a number of cubes, say 15, upon the table.) How many times 2 are here?
Childr. 7 times 2 and the half of 2.( Should any of the children make a mistake, they must count again till they are right.)
Moth. Right! but how many times 1 are in 7 times 2 and the half of 2?
Childr. In 7 times 2 and the half of 2 are 15 times 1. Moth. Why?
Childr. In 7 times 2 are 14 times 1; the half of 2 is once 1; 14 times 1 and once 1 are 15 times 1.
The children, before giving the answer, should always repeat the question; by so doing, the mother sees whether it has been understood.
Many teachers will consider the observance of this rule as superfluous; perhaps, as an absurdity; but they are mistaken; it has the most decided influence on the development of the faculties of the mind; and the teacher should never forget that the child has not only to learn, but deeply to engraft upon his mind what he himself has long known; but not acquired without great trouble and frequent repetition.
This rule, especially in arithmetical and geometrical exercises, is strictly observed in Pestalozzi's school: and it is undoubtedly owing to its being put into practice, from the first easy and simple steps, that the pupils can solve with facility by head the most difficult and complicated problems. Adding Numbers.
In order to introduce as much variety as possible into these first exercises, the mother may place the cubes in two columns, not too far asunder.
In the column at the left hand, the number of cubes, according as she adds, 1 or 2, &c. increases from 1 to 9, or from 1 to 10, &c. In the right column, the number of cubes may continue the same.
a. The number of cubes in each column is pronounced, without mentioning the sum which they produce.
b. The sums produced by the single rows
of both columns are stated.
c. a and b are combined.
a. The number of cubes in each column is pronounced, without mentioning the sums they produce, as:
Before the mother proceeds, the children must be able to give these combinations readily, and to answer any question relating to them.
Moth. Shew me where are 6 and 1?
Childr. Here. .. .
Moth. Where are 3 and 1? How many are in this row?
Childr. In this row are 4 and 1, &c.
h. The sums contained in the single rows of both columns are stated.
1st row contains 2
Moth. In this row are how many times 1?
Childr. 6 times 1.
Moth. Where are 8 times 1?
Childr. Here, &c.