98 MATHEMATICS 



apt to produce upon the pupil the impression that 

 Mathematics was an arid subject out of relation 

 with everything outside itself. The repulsive effect 

 upon most minds produced by a subject so pre- 

 sented is held to be the chief explanation of the 

 low standard of the knowledge attained by a 

 large proportion of the pupils. The newer kind 

 of teaching is based upon the idea that the interest 

 of the pupil should be stimulated at every point by 

 directing his attention to actual or possible applica- 

 tions of what is being learned ; in fact by showing 

 him that Mathematics is really connected with 

 certain aspects of the actual world, and is an 

 instrument which can be employed for a variety 

 of practical ends. The newer methods based upon 

 a wider view of the functions of the teaching, and 

 upon a more enlightened apprehension of the 

 Psychology of the immature mind, have their 

 characteristic dangers when pushed too far, and 

 have in fact led to a certain amount of reaction in 

 favour of the older methods. It is certain that the 

 newer methods of teaching make incomparably 

 greater demands than the older methods upon the 

 skill and alertness of mind of the teacher. It is 

 probably true that the results obtained by an 

 incompetent teacher, who attempts the reformed 

 methods, may in some respects even fall short of 

 those he might have obtained under the older system. 

 The disestablishment of Euclid's Elements of 

 Geometry which, until some years ago, had the 



