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.