The title of my address is the question with which Professor Temple ended his presidential address two years ago, when he gave such a fascinating review of the impulses and influences, both external and internal, that have promoted the growth of mathematics. Whether he expected an answer I cannot tell; but this Association, since its foundation in 1897, has frequently taken as the theme of its discussions and reports the duty of teachers to show the meaning and inner unity of the subject, and not merely to teach techniques. So it is not out of place to consider from time to time whether we are agreed what this meaning is, and what the techniques have to do with it.

For some years I had been dissatisfied with the methods we were using in my small Primary School, to teach Subtraction. The slower children were unable to grasp the basic principles of Equal Addition, and many errors were made, as the children were using a “parrot” pattern, instead of basing their work on understanding and logical sequence.

Perhaps the most notable achievement of the Mathematical Association since its formation has been the abolition of Euclid. While Euclid remains the greatest mathematical classic, it is no longer used as an instrument of torture on the young. As a school text-book Euclid is dead, replaced by a course in the well-established three stages, in which the type of learning and the degree of logical rigour are adapted to the understanding of the pupil.