This paper was prepared at the suggestion of the committee as the first of a series on the teaching of elementary mathematics, in the belief that an occasional paper of this nature, with discussions, would be useful.

In the introduction it was suggested that, as secondary education in this country was apparently on the eve of considerable changes, the present was an opportune time for discussing the whole subject of school mathematics; and also that the Society should be prepared to form a scheme of a mathematical course for both teaching and examination purposes.