The problems of mathematical instruction in elementary and secondary schools are of great professional importance to the physics teacher. In particular, the physics instructor of collegiate standing is much interested in the following question: "Is the mathematical equipment which the college freshman brings from the secondary school all that his teacher in physics would like it to be?" Specific as this question is, it is an organic part of the wider problem of secondary and elementary education in general and cannot be treated aside from the broader educational trends prevailing in our school. In view of the complexity of the subject, the present paper does not claim to offer an exhaustive analysis but merely attempts to serve as a startin...