[Illustration: Board with hooks, in ranks of nine, and rings]
The whole apparatus is a rectangular piece of wood about 3/4 of an inch thick, and about 3x1-1/2 feet of surface. It is painted white, and the horizontal bars are green, so that the divisions may be apparent at a distance; it has perpendicular divisions breaking it up into three columns, each of which contains rows of nine small dresser hooks. It can be hung on an easel or supported by its own hinge on a table. Each of the divisions represents a numerical grouping, the one on the right is for singles or units, the central one for tens, and the left side one for hundreds: the counters used are button moulds, dipped in red ink, with small loops of string to hang on the hooks: it is easily seen by a child that, after nine is reached, the units can no longer remain in their division or "house," but must be gathered together into a bunch (fastened by a safety pin) and fixed on one of the hooks of the middle division.
Sums of two or three lines can thus be set out on the horizontal bars, and in processes of addition the answer can be on the bottom line. It is very easy, by this concrete means, to see the process in subtraction, and indeed the whole difficulty of dealing with ten is made concrete. The whole of a sum can be gone through on this board with the button-moulds, and on boards and chalk with figures, side by side, thus interpreting symbol by material; but the whole process is abstract.
The piece of apparatus is less abstract only in degree than the figures on the blackboard, because neither represents real life or its problems: in abstract working we are merely going off at a side issue for the sake of practice, to make us more competent to deal with the economic affairs of life. There is a place for sticks and counters, and there is a place for money and measures, but they are not the same: the former represents the abstract and the latter the concrete problem if used as in real life: the bridge between the abstract and the concrete is largely the work of the transition class and junior school, in respect of the foundations of arithmetic known as the first four rules.
Games of skill, very thorough shopping or keeping a bankbook, or selling tickets for tram or train, represent the kind of everyday problem that should be the centre of the arithmetic work at this transition stage; and out of the necessities of these problems the abstract and semi-abstract work should come, but it should never precede the real work. A real purpose should underlie it all, a purpose that is apparent and stimulating enough to produce willing practice. A child will do much to be a good shopkeeper, a good tram conductor, a good banker; he will always play the game for all it is worth.
CHAPTER XXIV
EXPERIENCES BY MEANS OF DOING
In the Nursery School activity is the chief characteristic: one of its most usual forms is experimenting with tools and materials, such as chalk, paints, scissors, paper, sand, clay and other things. The desire to experiment, to change the material in some way, to gratify the senses, especially the muscular one, may be stronger than the desire to construct. The handwork play of the Nursery School is therefore chiefly by means of imitation and experiment, and direct help is usually quite unwelcome to the child under six. There is little more to be said in the way of direction than, "Provide suitable material, give freedom, and help, if the child wants it." But the case is rather different in the transitional stage. As the race learnt to think by doing, so children seem to approach thought in that way; they have a natural inclination to do in the first case; they try, do wrongly, consider, examine, observe, and do again: for example, a girl wants to make a doll's bonnet like the baby's; she begins impulsively to cut out the stuff, finds it too small, tries to visualise the right size, examines the real bonnet, and makes another attempt. At some apparently odd moment she stumbles on a truth, perhaps the relation of one form to another in the mazes of bonnet-making; it is at these odd moments that we learn. Or a boy may be painting a Christmas card, and in another odd moment he may feel something of the beauty of colour, if, for example, he is copying holly-berries. No purposeless looking at them would have stirred appreciation. Whether the end is doing, or whether it is thinking, the two are inextricably connected; in the earlier stages the way to know and feel is very often by action, and here is the basis of the maxim that handwork is a method.
This idea has often been only half digested, and consequently it has led to a very trivial kind of application; a nature lesson of the "look and say" description has been followed by a painting lesson; a geography lesson, by the making of a model. If the method of learning by doing was the accepted aim of the teacher then it was not carried out, for this is learning and then doing, not learning for the purpose of doing, but doing for the purpose of testing the learning, which is quite another matter, and not a very natural procedure with young children. Many people have tried to make things from printed directions, a woman may try to make a blouse and a man to make a knife-box; their procedure is not to separate the doing and the learning process; probably they have first tried to do, found need for help, and gone to the printed directions, which they followed side by side with the doing; and in the light of former failures or in the course of looking or of experimenting, they stumbled upon knowledge: this is learning by doing.
Therefore the making of a box may be arithmetic, the painting of a buttercup may be nature study, the construction of a model, or of dramatic properties may be geography or history, not by any means the only way of learning, but one of the earlier ways and a very sound way; there is a purpose to serve behind it all, that will lead to very careful discrimination in selection of knowledge, and to pains taken to retain it. If this is fully understood by a teacher and she is content to take nature's way, and abide for nature's time to see results, then her methods will be appropriately applied: she will see that she is not training a race of box-makers, but that she is guiding children to discover things that they need to know in a natural way, and ensuring that as these facts are discovered they shall be used. Consequently neither haste nor perfection of finish must cloud the aim; it is not the output that matters but the method by which the children arrive at the finished object, not forty good boxes, but forty good thinkers. Dewey has put it most clearly when he says that the right test of an occupation consists "in putting the maximum of consciousness into whatever is done." Froebel says, "What man tries to represent or do he begins to understand."