Friedrich Froebel.
"The definitely productive exercises begin with the third gift."
Susan E. Blow.
1. The third gift is a wooden cube measuring two inches in each of its dimensions. It is divided once in its height, breadth, and thickness, according to the three dimensions which define a solid, and thus eight smaller cubes are produced.
2. We pass from the undivided to the divided unit, emphasizing the fact that unity still exists, though divisibility enters as a new factor.
3. The most important characteristics of the gift are contrasts of size resulting in the abstraction of form from size; increase of material as a whole, decrease of size in parts; increase of facilities in illustrating form and number.
The new experience to be found in this first divided body is the idea of relativity; of the whole in its relation to the parts (each an embryo whole), and of the parts in relation to the whole.
The form of the parts is like the form of the whole, but, in shape alike, the dissimilarity is in size; the fact becoming more apparent by a variety of combinations of a different number of parts: thus the relations of numbers are introduced to the observation of the child together with those of form and magnitude.
4. The third gift was intended by Froebel to meet the necessities of the child at a period when, no longer satisfied with the external appearances of things, he strives to penetrate their internal conditions, and begins to realize the many different possibilities of the same element.
5. The geometrical forms illustrated in this gift are:—