Page:Popular Science Monthly Volume 68.djvu/169

 Rh of public instruction with a view to encouraging the introduction of 'Mèray's method' in the teaching of geometry. During last year this method was employed in at least thirty of the French schools, and very enthusiastic reports of improvement were received. The method is expounded in 'Nouveaux Eléments de Géometrie par Méray,' as well as in several of the French journals. One of its important features is the introduction of the notions of displacements and the group of displacements into elementryelementary [sic] geometry.

While reform movements in mathematical instruction are not new, yet the present movement is without a parallel both with respect to its extent and with respect to its vigor. The question naturally arises whether the mental inclinations of civilized races are undergoing gradual changes so that concepts which at one time give pleasure and power to the youthful mind, at other times are beyond the capacity of the average mind, or whether we are becoming more sympathetic with the difficulties which have to be overcome in mental development and take greater precautions to make the steps natural. Whatever may be the cause, it seems probable that readjustment will be effected without departing very far from the older methods. The most likely changes in elementary instruction are those which Klein has been so actively advocating; viz., the early introduction and frequent use of the concept of a function and the teaching of the elements of analytic geometry and the differential and integral calculus at a much earlier period, before the student begins to specialize.