This system in which a child is constantly moving objects with his hands and actively exercising his senses, also takes into account a child’s special aptitude for mathematics. When they leave the material, the children very easily reach the point where they wish to write out the operation. They can thus carryout an abstract mental operation and acquire a kind of natural and spontaneous inclination for mental calculations.
To become acquainted with the material, a teacher should not just look at it, study it in a book, or learn its use through the explanations of another. Rather, she must exercise herself with it for a long time, trying in this way to evaluate through her own experience the difficulties of, or the interests inherent in, each piece of material that can be given to a child, trying to interpret, although imperfectly, the impressions which a child himself can get from it. Moreover, if a teacher has enough patience to repeat an exercise as often as a child, she can measure in herself the energy and endurance possessed by a child of a determined age. For this final purpose, the teacher can grade the materials and thus judge the capacity of a child for a certain kind of activity at a given stage of his development.
In brief, the teacher’s principle duty in the school may be described as follows: She should explain the use of the material. She is the main connecting link between the material, that is the objects, and the child. This is a simple, modest duty, and yet it is much more delicate than that found in the older schools, where the material simply helps the children to understand the mind of the teacher, who must pass on her own ideas to a child, who must in turn receive them.
The objects in our system are instead a help to the child himself, he chooses what he wants for his own use, and works with it according to his own needs, tendencies and special interests. In this way, the objects become a means of growth.
The work of education is divided between the teacher and the environment.
When we think about mixed ages, we must make sure we aren’t starving children intellectually or physically … we should not have a supermarket, but just what is essential.