Introduction

Abstract

In recent years, a far reaching interest has arisen among university teachers of mathematics and natural sciences directed toward an appropriate training of future teachers at secondary schools, satisfying all desirable needs. This is really quite a new phenomenon. For a long time prior to its appearance, university men were practicing exclusively research of optimal quality, without giving a thought to the needs of the schools, without even caring to establish a connection with school mathematics. What is the result of this practice? The young university student finds himself, at the outset, confronted with problems, which do not remember, in any particular, the things with which he had been concerned at school. Naturally he forgets all these things quickly and thoroughly. When, after finishing his course of study, he becomes a teacher, he suddenly finds himself expected to teach the traditional elementary mathematics according to school practice; and, since he will be scarcely able, unaided, to discern any connection between this task and his university mathematics, he will soon fell in with the time honoured way of teaching, and his university studies remain only a more or less pleasant memory which has no influence upon his teaching.