Froebel as a pioneer in modern psychology

by E. R. Murray

“The hints that are here given suffice to show that the knowledge forms are adapted to children of three and four years of age, and that they incite plays which are both spontaneous and nourishing to heart and intellect.… These few indications for the use of these forms must suffice; they already show sufficiently clearly that the observation and comprehension of them are perfectly suited to the active, intellectual and emotional sides of children three and four years of age, and to actual free play which strengthens intellect and feeling.”—P., p. 185.

Now the “hints” refer to making clear to the child, always in justice, be it remembered, in the concrete, “as perceptible facts only,” such points as “similarity of size with dissimilarity of shape and position, in such words as:

“Twice as long and half as wide,

Half as long and twice as wide,

The same size are we two.”

Certainly children differ very much, and some have a special aptitude for mathematical relations, but to most children under five these words would convey nothing. Half may have a meaning, though at that age and for some time after we hear of “a fair half” and “quarter” is generally used as a name for any fraction recognized as not a half, even if it should be greater. Such words as fourth and eighth can have no meaning for a child who shows no consciousness of difference when shown six, seven or eight objects. At the age of three, an average child recognizes three objects, but when a fourth is added, he proceeds to count one by one, he does not recognize three plus one.

Again, we must repeat that Froebel never intended any mathematical ideas to be forced upon unwilling children. He constantly tells the mother not to force, and he frequently speaks of the child’s “accidental productions which will become a point of departure for his self-development,” through the explanatory rhymes, to be sung by the mother in order to call the child’s attention to the results of his own action. It is true, too, that it is in connection with this kind of work, or play, that Froebel writes of “the knowledge-acquiring side of the game, which is the quickly tiring side.”

But the fact remains that either Froebel made a miscalculation as to what mathematical ideas are within the grasp of children of tender age, or else he attributed too much consequence to what is outside. It is indeed quite possible to present to a child of any age, by means of the cubes of his Fifth Gift, several particular instances of the Theorem of Pythagoras, as Froebel suggests. But though the construction is present to the sense of both child and adult, the career of the child of five or six, who perceives or apperceives the relationship of the squares so presented, may be watched with interest. He is likely to distinguish himself in mathematical research, should he live long enough. Froebel ought to have known, indeed he did know, for he taught it to others, that the child does not “quickly tire” of acquiring knowledge suited to his stage of development by methods equally suitable. From the houses and railway trains, of which at this stage they seem never to tire, children probably gain as much knowledge as Nature means them to absorb by such means. In Froebel’s own hands, with his real and sympathetic understanding of the need for freedom of action, probably no harm was done, but it is easy to see how the ordinary teacher would grasp at the possibility of producing mathematical prodigies through what was supposed to be play.

The same error seems to show itself in various ways, e.g., in some of the reasons Froebel gives for choosing his First Gift, though there is no fault to be found with the choice. He was right in saying that the child first takes in a whole, not a variety of elements, to be combined later. Because of this fact, the ordinary coral and bells, with all its complexity, is just as much a whole to the infant as the woollen ball. But Froebel does seem to have thought that he must make the “outer objects,” or toys from which the child is to gain his earliest ideas, as simple as these ideas, and this certainly implies a wrong view of perception. The same objection might be taken to Froebel’s directions as to how the Third Gift—an 8-inch cube, cut once in each direction—is to be presented; how in order “to furnish to the child clearly and definitely the impression of the whole, of the self-contained, from which fundamental perception everything must proceed,” the box is to be reversed, the lid slipped out and the box is to be lifted “that the play thing may appear as a cube closely united.” But in this case Froebel is “presenting” the first divided unit, “something which may be taken to pieces, arranged and re-arranged and finally re-constructed,” for it is “by this dismembering and re-constructing, and perception of real objects that true knowledge and especially self-knowledge comes to the child.”

A second psychological error, or at least an inconsistency, seems to lie at the root of certain practical directions Froebel gives with regard to the use of his toys. In spite of his iteration and re-iteration that the child’s mind is a unity, that though separation is “permitted for the thinking mind,” there is none in reality, yet in his anxiety for the due fostering of the whole, of the “doing, feeling and thinking” his harmonious development, in actual practice he has an attempted separation which has had bad results. A Kindergarten practice, now discontinued, was to make the children build, either on different occasions, or during different parts of one lesson, what Froebel called (a) Life-forms or Objects (Lebens oder Sachformen), i.e. houses, churches, etc.; (b) Beauty or Picture forms (Schönheits oder Bildformen), i.e. symmetrical designs; and (c) Knowledge or Instruction forms (Erkenntniss oder Lernformen), i.e. squares, triangles, etc. Though this classification is based on the familiar and important “knowing, willing and feeling,” yet it is plain that a child may experience quite as much emotion, probably more, in building a house as in making a star pattern, and that the active side is involved in every kind of construction. Froebel draws a parallel, legitimate to a certain extent, between intellect, feeling and will on the one hand, and truth, beauty and usefulness on the other. Here, however, we can quote him against himself; “Separation is only permitted for the thinking mind.” The useful ought to be beautiful, there is beauty in all truth, and the æsthetic revelation of the world is the world in order. Beauty degenerates into mere ornament and artificiality, when separated from life and use. “Mathematics,” as Froebel wrote himself, “is neither foreign to life, nor deduced from life; it is the expression of life as such: its nature may be studied in life, and life may be studied with its help.… Mathematics should be studied more physically and dynamically as the outcome of nature and energy.”—E., p. 206-7.