A better idea of these may be obtained through a manipulation of the blocks and an arrangement of the geometrical forms in their regular order.
The child, if he were taught as Froebel intended, would make his first acquaintance with numbers in the nursery, beginning in a very small way and progressing slowly. The pupils of the kindergarten are a little older, and having already a slight knowledge of numbers (though not of course in their abstract relations) are able to accomplish greater things.
The child can, with our guidance, make all possible combinations of the parts of the number Eight. The principles of Addition, Subtraction, even Multiplication and Fractions, can also be mastered without one tear of misery or pang of torture. He grasps the whole first, then by simple processes, building with his own hands, he finds out and demonstrates for himself halves, fourths, and eighths, sometimes in different positions, but always having the same contents.
Method and Manner of using the Gift.
Even yet we must not suffer this to become work. The exercises should be repeated again and again, but we must learn to break off when the play is still delightful, and study ways to endow the next one with new life and charm, though it carry with it the same old facts. What we want to secure is, not a formidable number of parrot-like statements, but a firm foundation for future clearness of understanding, depth of feeling, and firmness of purpose. So, at the beginning of the exercise, we should not ask John if he remembers what we talked about last time, and expect him to answer clearly at once. Because he does not answer our formal questions which do not properly belong to babyhood, we need not conclude he has learned nothing, for a child can show to our dull eyes only a very tiny glimpse of his wonderful inner world.
Let our aim be, that the child shall little by little receive impressions so clearly that he will recognize them when they appear again, and that he shall, after a time, know these impressions by their names. It is nothing but play after all, but it is in this childish play that deep meaning lies.
A child is far less interested in that which is given him complete than in that which needs something from him to make it perfect. He loves to employ all his energies in conceiving and constructing forms; the less you do for him the better he enjoys it, if he has been trained to independence.[41]
Pedantry and dogmatism must be eliminated from all the dictations; the life must not be shut out of the lessons in order that we may hear a pin drop, nor should they be allowed to degenerate into a tedious formalism and mechanical puppet-show, in which we pull the strings and the poor little dummies move with one accord.
Yet most emphatically a certain order and harmony must prevail, the forms must follow each other in natural sequence, the blocks must, invariably, be taken carefully from the box, so as to present a whole at the first glance, and at the close of the lesson should always be neatly put together again into the original form and returned to the box as a whole.[42]
And now one last word of warning about doing too much for the children in these exercises, and even guiding too much, carrying system and method too far in dictation. We must remember that an excess of systematizing crushes instead of developing originality, and that it is all too easy even in the kindergarten to turn children into machines incapable of acting when the guiding hand is removed.