Children. (Attentively examining them.) Yes. You have moved that (pointing to it) nearer to the other.

Mother. Very well! Do Do you observe any other change?

Each of the Children. I see no other. Mother. What did you notice respecting the oblongs before you turned about?

Children. There were ten placed at equal distances, in a straight line, their long sides turned towards the window, and their short sides towards the door.

Mother. What change did they undergo whilst you turned about?

Children. There were but eight left, and one of them was moved nearer to another. All the rest remained as before.

Mother. Exactly so!

These and many other changes, by diminishing or increasing the number of oblongs, by making the children find out whatever can be observed with respect to their position, &c. are particularly calculated to fix their attention.

The Mother may vary these first exercises,

by drawing lines in different directions, cir

cles, triangles, squares, &c. Thus:

The children repeating, One line, one circle, one triangle, one square *.

Children. One line, one circle, one ▲, one □, One line and one line.

One circle and one circle.

One triangle and one triangle.

One square and one square.

Children. One line, one circle, one triangle,

one square.

One line and one line.

One circle and one circle.

One triangle and one triangle.

One square and one square.

One line, and one line, and one line.

One circle, and one circle, and one circle.

* This exercise should be performed with chalk, standing

at a large slate placed upon an easel.

One triangle, and one triangle, and

one triangle.

One square, and one square, and

one square.

• As soon as the children are aware, that any number whatever is composed of unities, it would be superfluous to let them any longer repeat all the unities of a collective number; and after having continued to draw

1 line, 1 circle, 1 triangle, 1 square.

2 lines, 2 circles, 2 triangles, 2 squares. 3 lines, 3 circles, 3 triangles, 3 squares. 4 lines, 4 circles, 4 triangles, 4 squares; to be continued to twelve.

Each lesson, after having been well exercised, either with tangible objects or the above signs, is then to be repeated without making use of either, till the children are quite firm in their operations, and able to answer any question proposed to them relative to each lesson.

Counting backward.

The Mother draws

Then

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Children say, 2 lines, 1 line.

She draws

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Children, 3 lines, 2 lines, 1 line.

Children, 4 lines, 3 lines, 2 lines, 1 line. This to be continued, beginning with 5, then with 6, 7, &c. to 20.

Counting forward and backward combined. The Mother draws one line, and below it two lines. Then, at a small distance, two lines and one below, as,

Children repeat, 1 line, 2 lines; 2 lines, 1 line. They repeat the same operation with various figures.

Draw each of you,
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And say, 1 line, 2 lines, 3 lines. 3 lines, 2 lines, 1 line.

And say, 1 line, 2 lines, 3 lines, 4 lines: 4 lines, 3 lines, 2 lines, 1 line.

The same to be continued to twenty.

As soon as the Mother is quite satisfied that her little ones not only take delight in these operations, but can give ready and correct answers in regard to any of them, she may with safety proceed to a second step, in the following manner :

Mother. (Placing one cube on the table.) Once 1.

Moth. (Pointing to the one cube.) Once 1, (adding a second to it,) more once 1, are twice 1.

Childr. Once 1, more once 1, are twice 1. Moth. (Pointing to the two cubes on the table.) Twice 1 more once 1 (adding a third cube) are 3 times 1.

Childr. Twice 1 more once 1, are 3 times 1.