By means of toys, handwork and games, as well as various private individual experiments, a child touches on most sides of mathematics in the nursery class. In experimenting with bricks he must of necessity have considered relative size, balance and adjustment, form and symmetry; in fitting them back into their boxes some of the most difficult problems of cubic content; in weighing out "pretence" sugar and butter by means of sand and clay new problems are there for consideration; in making a paper-house questions of measurement evolve. This is all in the incidental play of the Nursery School, and yet we might say that a child thus occupied is learning mathematics more than anything else. Here, if he remained till six, he did a certain amount of necessary counting, and he may have acquired skill in recognising groups, he may have unconsciously and incidentally performed achievements in the four rules, but never, of course, in any shortened or technical form. Probably he knows some figures. It is best to give these to a child when he asks for or needs them, as in the case of records of games. On the other hand he may be content with strokes. Various mathematical relationships are made clear in his games or trials of strength, such as distance in relation to time or strength, weight in relation to power and to balance, length and breadth in relation to materials, value of material in relation to money or work. By means of many of his toys the properties of solids have become working knowledge to him. Here, then, is our starting-point for the transition period. AFTER THE NURSERY STAGE Undoubtedly the aim of the transition class is partly to continue by means of games and dramatic play the kind of knowledge gained in the Nursery School; but it has also the task of beginning to organise such knowledge, as the grouping into tens and hundreds. This organisation of raw material and the presenting of shortened processes, as occur in the first four rules, forms the work also of the junior school. To give to a child shortened processes which he would be very unlikely to discover in less than a lifetime, is simply giving him the experience of the race, as primitive man did to his son. But the important point is to decide when a child's discovery should end and the teacher's demonstration begin.