REFORM OF TEACHING 97 



opportunities will arise for the application of 

 Mathematics. It is clearly essential for an adequate 

 fulfilment of these demands upon Mathematical 

 Science that the requisite knowledge and skill 

 should be forthcoming in ample measure. Accord- 

 ingly, in the consideration of the means of increasing 

 national efficiency, so far as it depends upon 

 scientific training, questions relating to mathema- 

 tical education and research must receive a con- 

 siderable share of attention. The essential requi- 

 sites as regards Mathematics are much the same as 

 in other branches of knowledge. They consist in 

 a thoroughly well thought out system of instruction, 

 graduated according to the needs of various classes 

 of students, in the training of a competent body 

 of teachers of every grade, and in the encourage- 

 ment of mathematical research in the Universities 

 and other higher educational establishments. 



Many reforms have been introduced of late 

 years in the school teaching of Mathematics. The 

 powerful influence of the Mathematical Association, 

 which has focussed and sifted the views of the 

 most thoughtful and observant of the teachers of 

 the subject, has contributed much to the intro- 

 duction of improved methods of teaching ; and the 

 Universities have also effected something by means 

 of changes in the syllabuses of their more elementary 

 examinations. The older traditional teaching of 

 Mathematics in schools, by its undue insistence 

 upon the purely abstract side of the subject, was 



