474 REPORT— 1902. 



not merely be required from all candidates in any one examination, but 

 also be applied to all examinations throughout the country. In order to 

 secure the uniformity thus postulated, the Committee, thinking that no 

 text-book had been produced fit to succeed Euclid in the position of 

 authority, and deeming it improbable that such a book could be produced 

 by the joint action of selected individuals, suggested the publication of an 

 authorised syllabus. In their second report they discussed the merits of 

 a particular syllabus — that of the Association for the Improvement of 

 Geometrical Teaching ; but, in spite of such commendation as was then 

 expressed, the syllabus has not been generally adopted. 



It is still true that (in the words of the former Committee) ' in this 

 country a.t present teaching is guided largely by the requirements of 

 examinations.' For some time to come the practice of the country is not 

 unlikely to allow examinations to retain at least a partial domination 

 over teaching in schools. Accordingly, if the teaching is to be improved, 

 it seems to be a preliminary requisite that examinations should be modi- 

 fied ; and, where it is possible, these modifications in the examinations 

 should leave greater freedom to the teacher, and give him more assistance 

 than at present. 



On the other hand, there is a tendency in this country whereby, in 

 such matters as teaching and examination, the changes adopted are only 

 gradually effected, and progress comes only by slow degrees. Accordingly, 

 the general recommendations submitted in this report are such that they 

 can be introduced easily and without any great alteration of the best 

 present practice. It is the hope of the Committee that the recommen- 

 dations, if adopted, will constitute merely the first stage in a gradual 

 improvement both of teaching and of examinations. For the most part 

 only broad lines of change are suggested : this has been done in order to 

 leave as much freedom as possible to teacliers for the development of tlieir 

 methods in the light of their experience. 



Is Uniformity imjwrative ? 



The Committee do not consider that a single method of teaching 

 mathematics should be imposed uniformly upon all classes of students ; 

 for the only variations then possible would be limited by the individuality 

 of the teacher. In their opinion, different methods may be adopted for 

 various classes of students, according to the needs of the students ; and 

 corresponding types of examination should l)e used. 



It is generally, if not universally, conceded that a proper training in 

 mathematics is an important part of a liberal education. The value of 

 the training depends upon the comprehension of the aims of the mathe- 

 matical subjects chosen, upon the grasp of the fundamental notions 

 involved, and upon the attention paid to the logical sequence of the 

 arguments. On the other hand, it is freely claimed that, in the training 

 of students for technical aims such as the profession of engineering, a 

 knowledge of results and a facility in using them are more important than 

 familiarity with the mathematical processes by which the results are 

 established with rigid precision. This divergence of needs belongs, how- 

 ever, to a later stage in the training of students. In the earliest stages, 

 when the elements of mathematics are being acquired, tlie processes 

 adopted can be substantially the same for all students ; and many of the 

 following recommendations are directed towards the improvement of thoge 

 processes. 



