In the teaching of mathematics as of other subjects the primary determining factor ought to be, but seldom has been, the consideration of the pupil himself—his interests, aptitudes, and capabilities. The teacher should be free to devise the best means of securing his fullest co-operation, and examinations should allow the greatest possible elasticity. It is the reversal of the rational order that has wrought so much harm in the past and that so long delayed and still impedes reform.