Fig. 11.––The Broad Stair.
Fig. 12.––The Long Stair.
(2) Ten wooden prisms, colored brown. The length of the prisms is twenty centimeters, and the square section diminishes from ten centimeters a side to the smallest, one centimeter a side. (Fig. 11.)
The child scatters the ten pieces over a light-colored carpet, and then beginning sometimes with the thickest, sometimes with the thinnest, he places them in their right order of gradation upon a table.
(3) Ten rods, colored green, or alternately red and blue, all of which have the same square 35 section of four centimeters a side, but vary by ten centimeters in length from ten centimeters to one meter. (Fig. 12.)
The child scatters the ten rods on a large carpet and mixes them at random, and, by comparing rod with rod, he arranges them according to their order of length, so that they take the form of a set of organ pipes.
As usual, the teacher, by doing the exercises herself, first shows the child how the pieces of each set should be arranged, but it will often happen that the child learns, not directly from her, but by watching his companions. She will, however, always continue to watch the children, never losing sight of their efforts, and any correction of hers will be directed more towards preventing rough or disorderly use of the material than towards any error which the child may make in placing the rods in their order of gradation. The reason is that the mistakes which the child makes, by placing, for example, a small cube beneath one that is larger, are caused by his own lack of education, and it is the repetition of the exercise which, by refining his powers of observation, will lead him sooner or later to correct 36 himself. Sometimes it happens that a child working with the long rods makes the most glaring mistakes. As the aim of the exercise, however, is not that the rods be arranged in the right order of gradation, but that the child should practise by himself, there is no need to intervene.
One day the child will arrange all the rods in their right order, and then, full of joy, he will call the teacher to come and admire them. The object of the exercise will thus be achieved.