Fig. 42.––Arithmetic Frame.
If, instead of the piece 1, we were to take pieces as long as the rod 10, we could count 10, 20, 30, 40, 50, 60, 70, 80, 90. In the didactic material there are frames containing cards on which are printed such numbers from 10 to 90. These numbers are fixed into a frame in such a way that the figures 1 to 9 can be slipped in covering the zero. If the zero of 10 is covered by 1 the result is 11, if with 2 it becomes 12, and so on, until the last 9. Then we pass to the twenties (the second ten), and so on, from ten to ten. (Fig. 42.)
For the beginning of this exercise with the cards marking the tens we can use the rods. As we begin with the first ten (10) in the frame, we take the rod 10. We then place the small rod 1 next to rod 10, and at the same time slip in the number 1, covering the zero of the 10. Then we take rod 1 and figure 1 away from the frame, and put in their place rod 2 next to rod 10, and figure 2 over the zero in the frame, and so on, up to 9. To advance farther we should need to use two rods of 10 to make 20.
The children show much enthusiasm when learning these exercises, which demand from them 113 two sets of activities, and give them in their work clearness of idea.
In writing and arithmetic we have gathered the fruits of a laborious education which consisted in coordinating the movements and gaining a first knowledge of the world. This culture comes as a natural consequence of man’s first efforts to put himself into intelligent communication with the world.
All those early acquisitions which have brought order into the child’s mind, would be wasted were they not firmly established by means of written language and of figures. Thus established, however, these experiences open up an unlimited field for future education. What we have done, therefore, is to introduce the child to a higher level––the level of culture––and he will now be able to pass on to a school, but not the school we know to-day, where, irrationally, we try to give culture to minds not yet prepared or educated to receive it.
To preserve the health of their minds, which have been exercised and not fatigued by the order of the work, our children must have a new kind 114 of school for the acquisition of culture. My experiments in the continuation of this method for older children are already far advanced.