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carried on in the true University spirit, is very far removed from ordinary 

 specialisation, and involves very wide extension of interest and learning ; whereas, 

 if carried on in a preparatory spirit, it is necessarily limited. 



In a very short time this student had published three original papers which 

 seem to me of considerable importance, though perhaps on a somewhat obscure 

 subject, and I see that they are now quoted as marking a substantial advance in 

 knowledge. 



Of course this is the exceptional case of the exceptionally able student; but I 

 think it illustrates two things — firstly, the prevalence of the conventional attitude 

 that preparation on school lines is necessary even for the post-graduate student; 

 secondly, the fact that what is really necessary to the University student is 

 the purpose, and that with this before his eyes he may safely be introduced to new 

 fields of work. 



One result of the conventional attitude is that those who have distinguished 

 themselves at school in some subject are often assumed to have a special aptitude 

 in it, and to be destined by Nature to pursue the same subject at the University, 

 whereas their school success may only prove that they are abler than their fellows, 

 and that this ability will show itself in whatever subject they may take up. 

 Such students would sometimes on coming to the University be all the better for 

 a complete change of subject, without which the continuance of the school studies 

 too often means a perpetuation of the school methods. 



Another result is that when teachers are always playing a somewhat mechanical 

 part in a systematised course, receiving duly prepared pupils and preparing them 

 again for the next stage, such an atmosphere of preparation is produced that 

 many persons continue to spend the greater part of their lives in preparation 

 without any reasonable prospect of performance. 



I am well aware that, on the other hand, there always have been and are 

 now many earnest and accomplished University teachers who are pursuing the 

 methods that I advocate, whose teaching is always inspired with a purpose, 

 whose pupils are stimulated to learn in the spirit of inquiry, and who consequently 

 exercise a personal influence that is profound and enduring. I am deeply con- 

 scious how much I owe to some such teachers with whom I have studied and to 

 others whom I have known. But still it does remain true that this is not yet the 

 atmosphere of ordinary University education, that it does not yet invigorate the 

 ordinary University student, and that to him the passage from school to the 

 University does not necessarily mean a transition from mental discipline and 

 preparation to mental activity and performance. 



The distinction that I have in my mind between University and school teaching 

 may be expressed in this way. At school no subject should be taught to a class as 

 though it were intended to be their life work; to take an example, it too often 

 happens at present, owing really to excessive zeal on the part of school teachers, 

 that mathematics is taught as though each member of the class were destined to 

 become a mathematician ; consequently only the few scholars with a real aptitude 

 for mathematics become interested, and the remainder are left behind. On the 

 other hand, at the University each subject should be studied as though it really 

 were the life work both of teacher and student. Thus, to take the same subject 

 as an illustration, the mathematical student will attend the full courses of 

 his professors and will follow them with the interest of a mathematician ; 

 whereas for the scientific student it will only be in those branches of 

 mathematics which concern him that the interest of his special science will put 

 him on terms of equality with the mathematical student. If I may choose an 

 illustration which is familiar to myself, any student of mineralogy can easily be 

 interested in and benefit by a course in spherical trigonometry, because it is one 

 of the tools of his trade, but to send him to lectures on differential equations 

 would be only to discourage him. On the other hand, the student of chemistry 

 would rather be interested in the latter. To each of them certain branches of 

 mathematics as taught by an ardent teacher afford a real intellectual training, but 

 neither would gain much if compelled to follow a general University course of 

 mathematics designed for mathematicians. 



It will be observed that I have endeavoured to confine myself to the subject 

 of University education and not to say much, except by way of contrast, con- 

 cerning school teaching. 



1910. 3 f 



