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THE USEFUL AND THE REAL Those who which will attack such an illustration serve the same purpose and must 43 find others satisfy their test of and in doing this they will in all probability pass limits of reality. There is no doubt that the the beyond of cisterns, the coincidence of clock hands, and emptying utility, other seeming trivialities more in ways which are which have more actual do exemplify the handling of rates young children than others real to utility, and they are therefore be welcomed rather than condemned.

Shortly, then, I suggest the continuous development of the idea of a cut or Schnitt of the rational numbers, it at an early age in connection with a treatment of simple measurements, the purpose commencing scientific being to give a true concept of number in its relation to measurement. I make some next reference to algebra, stating first am not to be taken as implying that the subject should be taught before geometry. On the contrary, I am that I convinced from actual experience that geometry should have been studied for two years at least before algebra is commenced.

They develop a detailed knowledge of permake no use of that much larger and ceptory space but more important conceptual space wherein the creations of move and have their being. Travels, adventures, romances, history, and the hundred and one his imagination utterly useless but apparently practical things which interest a boy are situated in this space, and here, as well as in the smaller concrete space of the senses, should the world of thought be exemplified, for these things also are for him.