340 THE MONTESSORI METHOD
the difference between these pieces being throughout the varying dimensions the same for all, the relative difference diminishes with the increasing size of the pieces themselves. For example, the little cube which has a base of 2 centimetres is double the size, as to base, of the smallest cube which has a base of 1 centimetre, while the largest cube having a base of 10 centimetres, differs by barely 1/10 the base of the cube next it in the series (the one of 9 centimetres base).
Thus it would seem that, theoretically, in such exercises we should begin with the smallest piece. We can, indeed, do this with the material through which size and length are taught. But we cannot do so with the cubes, which must be arranged as a little " tower." This column of blocks must always have as its base the largest cube.
The children, attracted above all by the tower, begin very early to play with it. Thus we often see very little children playing with the tower, happy in believing that they have constructed it, when they have inadvertently used the next to the largest cube as the base. But when the child, repeating the exercise, corrects himself of his own accord, in a permanent fashion, we may be certain that his eye has become trained to perceive even the slightest differences between the pieces.
In the three systems of blocks through which dimensions are taught that of length has pieces differing from each other by 10 centimetres, while in the other two sets, the pieces differ only 1 centimetre. Theoretically it would seem that the long rods should he the first to attract the attention and to exclude errors. This, however, is not the case. The children are attracted by this set of blocks, but they commit the greatest number of errors in using it,