i 7 2 SCIENCE PROGRESS 



of the work here considered to be non-essential." Again " we 

 do not wish to fetter any teacher in his endeavour to provide 

 what he considers the best general education for his pupils ; 

 we wish rather to restrict the demands of examiners to things 

 of real moment, in order to give greater freedom to educators 

 who are anxious to progress." 



It is interesting then to see what are the principles on which 

 the report determines the portions of algebra that are " of real 

 moment." The first principle appears to be as follows : " That 

 within the range of work selected the teaching should be 

 thorough, so that at each stage a boy may acquire the facility 

 necessary to enable him to pass on to the next stage without 

 being hindered by lack of skill in the preceding manipulations." 

 This should dispose of the fear that it is intended to frame 

 an algebra course consisting entirely of ideas, an airy nothing 

 with no substantial element for a boy to get his teeth into ; a 

 diet like Falstaffs " twopennyworth of bread to such a 

 monstrous deal of sack." This is not the intention at all — 

 " within the range of work selected the teaching is to be 

 thorough." But the work selected should form a series of 

 stepping-stones leading somewhere, not a parade-ground for 

 practising the goose-step. 



The second limiting principle is as follows : " That a boy 

 should not be required to possess more manipulative skill 

 (in algebra) than will enable him to deal with such parts of 

 the subject as for the reasons either detailed above or other- 

 wise generally admitted ought to form part of a liberal educa- 

 tion ; in other words, manipulative processes should be 

 developed, in the elementary course, just so far as they are 

 really subsidiary to the aims of that course and no further — 

 not as mere curious exercises." 



A description in detail of the results deduced from this 

 limitation would probably be out of place in the present article ; 

 it is enough to indicate that the results are considerable. If 

 algebra teaching were confined to the essentials recommended 

 by the committee of the Mathematical Association a very 

 important change would come over the conditions under which 

 the average schoolboy works. At present his algebra drags 

 on till he reaches the only goal that is set before him — Littlego 

 or Responsions. At the age of twelve he has learnt what an 

 equation is, what it is for and how to solve it, if it be easy. At 



