1 66 SCIENCE PROGRESS 



about him. So much I think we may make fairly sure of if 

 we go to work in the right way and I wish to make some 

 suggestions later on as to how these ends may be attained. 

 But when it is said that mathematics develop the memory, 

 the logical and reasoning facult}', the power of generalisation — 

 develops all these powers as applied not only to mathematics 

 but also to general activities — well, I hope that it may all 

 be true but I have not met with the proof. And unless these 

 developed powers can be carried over from mathematics into 

 general activities, the effect of the teaching is of no significance 

 in the education of the average boy ; the average boy is not being 

 trained for a mathematical career. 



Boys certainly are apt to leave behind them in school any 

 good habits that they may have formed there. They go even 

 further and leave their habits in the particular class-room where 

 these were engendered. Cases of this kind are typical : A boy 

 who is practising decimals in mathematics is found unable to 

 divide by a thousand in the laboratory ; he may be studying 

 cylinders in mathematics but breaks down over the sectional 

 area of a cylinder in the workshops ; a senior class is bowled 

 out by their classical master over a question of sesterces. 

 These cases are too familiar to be a matter of surprise to 

 any one who supervises the work of more than one department ; 

 but to the specialist they are a continual offence. The only 

 remedy is to have a good splice between different departments, 

 so that what is learnt in one class-room may be applied in 

 another. A mathematical question set in a physics class-room 

 takes a boy unawares ; it comes in a strange form — it is an 

 unusual stimulus and does not automatically provoke the 

 expected reaction. We want to make a boy's knowledge and 

 acquired habits responsive to all sorts of stimuli ; hence the 

 need for that system so dear to educationists and such a 

 bugbear to practical teachers — correlation. 



The point of this illustration is, that if it be so difficult to 

 " carry over " mental habits from one department to another 

 within a school, how much more difficult is it to "carry over" 

 from school into after-life. Perhaps this object would be 

 better attained (if it be attainable) by providing for it more 

 deliberately. For instance, the study of geometry ought to 

 teach that it is necessary to verify hypotheses. The framing 

 of hypotheses depends on a cultivated power of guessing, a 



