Still, when all due allowance is made, there remains the fact that Froebel attributed far too much importance to the series of toys he arranged, and in addition to this he must be held in large measure responsible for the extraordinary amount of mathematical perceptions of which young children have been considered capable, and beneath which many gleams of intelligence may have been extinguished. The psychological error which seems to underlie both these mistakes in pedagogy seems to have been that of making too much of the outer factor in the process of perception. Froebel was quite right and quite modern in refusing to draw any hard and fast line between sense perception and thinking, in saying that the child moves “from perception of a thing, joined with thought about it, up to pure thought.” But he must have failed somehow, sufficiently to grasp the fact that all that is present to sense is not necessarily perceived, that perception depends not merely upon what is presented, but upon previous mind content. The word “apperception,” though apparently somewhat fallen into disfavour of late, has certainly been of service in emphasizing this point. What seems strange is that in the very book, in which we find the theory disregarded in practice, we find Froebel stating the theory itself in the plainest of terms: “The properties and nature of the outer world unfold themselves in exact proportion to the capacities of the child.”--_P., p. 120._ “The child creates his own world for himself; it is at once the expression of his inward realization of the external world and its surroundings, and also the outward representation of his internal mental world, the world of his own subjectivity.”--_L., p. 141._ “Above all, it is the old within the new, which clarifies, unfolds and transmutes itself, thus developing what is new.… We must not require of the child anything not conditioned by his previous achievements.”--_P., p. 169._ No one, surely, can maintain that these words are carried into effect in e.g.: “Could forms of knowledge (mathematical forms) be, for a child of one to three, play forms, and thus forms produced by spontaneous activity? Well, why not? Arrange the eight part-cubes together, and say, ‘One whole.’ But divide it immediately and say, ‘Two halves.’… Or, comparing and connecting and describing by song at the same time that the objects are manipulated: ‘Look here and see! One whole two halves. One half two fourths, two halves four fourths. One whole four fourths. Four fourths eight eighths. Eight eighths one whole.’”--_P., p. 138._ There is certainly no “old within the child” of one to three, which can condition this achievement, nor is there any spontaneity. For the child a little older we have: