Some of the fundamental ideas acquired only through laborious lessons by our common school methods are here learned intuitively, naturally, and spontaneously. An interesting study which completes that already made with the "hundred chain" and the "thousand chain" is the comparison of the respective square chain and cube chain. Such differing relations showing the increasing length are most illustrative and make a marked impression upon the child. Furthermore, they prepare for knowledge that is to be used later. Some day when the child hears of "geometric progressions" or "linear squares" he will understand immediately and clearly.
It is interesting to build a small tower with the bead cubes. Though it will resemble the pink tower, this tower, which seems to be built of jewels, gives a profound notion of the relations of quantity. By this time these cubes are no longer recognized superficially through sensorial impressions, but their minutest details are known to the child through the progressively intelligent work which they have occasioned.
PART IV
GEOMETRY
I
PLANE GEOMETRY