TRANSACTIONS OF SECTION L. 819 



5. The use of angles greater than two right angles. 



G. That the exact treatment of incommensurables be regarded iis a branch 

 of higher mathematics. 



The report also suggests that in pass examinations the sy&tera should be 

 gradually introduced of requiring that a candidate, iu order to secure a pass, 

 should evince some power besides that of being able to write out bookworlc; the 

 solution of riders and questions requiring the use of instruments would thus be 

 encouraged. 



The most important suggestions under the head of arithmetic and algebra are 

 those proposing that the barriers between arithmetic, algebra, and geometry 

 should be broken down, and the early introduction of graplis ; there are many 

 other suggestions of too detailed a nature to be considered individually now. 



The Arithmetic and Algebra Report may be briefly summed up iu the folloW' 

 ing words : — 



The Committee recommend — 



(a) that easy viva voce examples should be frequently used in both arith- 

 metic and algebra ; 

 (i) that great stress should be laid on fundamental principles ; 



(c) that, as far as possible, the rules Avhich a pupil uses should be general- 

 isations from his own experience ; 



(d) that, whenever practicable, geometry should be employed to illustrate 

 arithmetic and algebra, and, in particular, that graphs should be used 

 extensively ; 



(e) that many of the harder rules and heavier types of examples, which 

 examinations alone compel us to retain in a school curriculum, should be 

 postponed. 



Finally, I should point out that the report has been drawn up with a special 

 view to the acquirement of brain-power, which is the most important considera- 

 tion at this stage of a student's career ; but nevertheless if these recommendations 

 are adopted I feel sure the engineers, whom we have to thank for bringing matters 

 to a head by introducing the discussion last year, will find great improvement in 

 the boys sent to them from the various schools — improvement not only in brain- 

 power, but also in mathematical power. 



19Q2. - 6 I 



