We notice that the child continues to be confused between the two last pieces in the growing scale, being for a long time unconscious of such an error after he has learned to put the other pieces in correct order. Indeed 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 from 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 be 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, and only after they have for a long time eliminated every error in constructing the other two sets, do they succeed in arranging the Long Stair perfectly. This may then be considered as the most difficult among the series through which dimensions are taught.
Arrived at this point in his education, the child is capable of fixing his attention, with interest, upon the thermic and tactile stimuli.
The progression in the sense development is not, therefore, in actual practice identical with the theoretical progression which psychometry indicates in the study of its subjects. Nor does it follow the progression which physiology and anatomy indicate in the description of the relations of the sense organs.
In fact, the tactile sense is the primitive sense; the organ of touch is the most simple and the most widely diffused. But it is easy to explain how the most simple sensations, the least complex organs, are not the first through which to attract the attention in a didactic presentation of sense stimuli.
Therefore, when the education of the attention has been begun, we may present to the child the rough and smooth surfaces (following certain thermic exercises described elsewhere in the book).
These exercises, if presented at the proper time, interest the children immensely. It is to be remembered that these games are of the greatest importance in the method, because upon them, in union with the exercises for the movement of the hand, which we introduce later, we base the acquisition of writing.
Together with the two series of sense exercises described above, we may begin what we call the "pairing of the colours," that is, the recognition of the identity of two colours. This is the first exercise of the chromatic sense.