Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: CHAPTER III How Arithmetic Has Developed Reasons for studying the subject — The historical development of the reasons for teaching arithmetic has already been considered. For the well-informed teacher there remain two other historical questions of importance. The first relates to the development of the subject itself, and the second to the methods of teaching it. There are good and sufficient reasons for considering briefly the history of arithmetic. In the first place, the child learns somewhat as the world learns.1 " The individual should grow his own mathematics, just as the race has had to do. But I do not propose that he should grow it as if the race had not grown it too. When, however, we set before him mathematics,— be it high or low, — in its latest, and most generalized, and most compacted form, we are trying to manufacture a mathematician, not to grow one."2 This does not mean that the child must go throughall of the stages of mathematical history — an extreme of the " culture-epoch" theory; but what has bothered the world usually bothers the child, and the way in which the world has overcome its difficulties is suggestive of the way in which the child may overcome similar ones in his own development. 1 Cette longue education de l'humanite, dont le point de depart est si loin de nous, elle recommence en chaque petit enfant. — Jean Mac£, L 'Arithmetique du Grand-Papa, 4i4me ed., p. 11. 2 Jas.,Ward in the Educational Review, Vol. I, p. loo. In the second place, the history of the subject gives us a point of view from which we can see with clearer vision the relative importance of the various subjects, what is obsolete in the science, and what the future is likely to demand. Sterner1 has compared the teacher of to-day to a traveller who by much toil has re...