MATHEMATICS IN ENGLISH SCHOOLS 173 



the age of eighteen he has looked into the matter further and 

 found it not to repay attention : he has decided that .^-chasing 

 is not his vocation. Probably he is right and his teachers are 

 wrong ; yet whether they are right or wrong they have to satisfy 

 the examiner, whose demands are stale but persistent. 



The adoption of some such policy as that put forward by 

 the committee might bring about something like a renaissance 

 in English schools. This has actually been effected at Winchester, 

 where reform on the lines indicated has been gradually brought 

 about ; the conventional schoolboy attitude toward mathe- 

 matics has been changed entirely, as is patent to such impartial 

 spectators as classical house-masters. The most serious 

 opposition to a general movement this way will come from 

 teachers ; examiners generally cede to a fairly universal demand. 

 There are plenty of keen, efficient teachers who cannot persuade 

 themselves that their dear old haunts are blind alleys; year 

 after year they go on trying to make silk purses of sows' ears, 

 trying to turn their sensible, clumsy, ordinary pupils into 

 skilled analysts. They are wasting their energies just as sadly 

 as their colleague who teaches Greek to a middle form. Perhaps 

 they would have more sympathy and insight if they had once 

 been average boys themselves. 



If time can be saved from algebra, there is no difficulty 

 in using it. Why should a three-dimensional boy be tied 

 down to a two-dimensional geometry ? Given the time, there 

 is much that could be done to strengthen his sense of space- 

 intuition. There is a movement in France to amalgamate 

 definitely the teaching of plane and solid geometry from the 

 outset but the particular shape taken by this movement might 

 not suit English needs ; it involves a simultaneous formal 

 treatment of the two branches and I doubt whether we ought 

 to be formal in teaching " solid." We used to try this via 

 Euclid's eleventh book but the result was poor. Still the idea 

 of simultaneous treatment is sound, if difficult to work out. 

 It might take the form of an informal reference to three 

 dimensions, accompanying the formal two-dimensional course. 

 In this way, for instance, might be introduced those simple 

 considerations about parallel and perpendicular planes and 

 lines that are so fundamental and yet so little understood by 

 the general public and the matter of so much confusion of 

 language in every-day life. There might be an amplification 



