ON STUDIES MOST SUITABLE FOR ELEMENTARY SCHOOLS. 447 



' 10. That the rule foi' cube root should be omitted. 



'11. That tliose parts only of the English tables of weights and 

 measures which are in general use should be taught ; and that long 

 questions in reduction {e.g., square miles to square inches) should be 

 avoided. 



' 12. That in money sums the system of decimalising money at sight 

 should be largely used, and that answers should, as a rule, not be required 

 beyond the nearest penny. 



' 13. That, in pass examinations in arithmetic, the use of algebraic 

 symbols should not be prohibited. 



' 14. That rough checks should be constantly employed in arithmetical 

 work. 



' 15. That in many cases a rough estimate might usefully precede the 

 detailed work of an arithmetical computation. 



' IG. The Committee consider that the mental training afforded by 

 arithmetic is largely impaired by the existing tendency of text-books to 

 classify problems and to establish each type as a separate rule.' 



Report of Committee of Institution of Civil Engineers. 



The Committee of the Institution of Civil Engineers issued a schedule 

 of questions to 120 representatives of (a) teachers in engineering colleges ; 

 (6) headmasters in secondary schools at which it was believed special 

 attention was paid to scientific training ; and (c) engineers not engaged 

 in teaching. The following questions were submitted in mathematics, 

 and the percentage of I'eplies in favour or against is shown for each : — 



' Is it desirable that the teaching of mathematics at school should be 

 arranged with a view to attain all or any of the following objects 1 — 



' 1. The practical use of arithmetic, with the special object of obtaining 

 correct results independently of the mere study of arithmetical methods.' 

 (Yes, 81 ; No, 19.) 



'2. The encouragement of the use of contracted methods.' (Yes, 91 ; 

 No, 9.) 



' 3. The encouragement of exercises in mental arithmetic' (Yes, 94 ; 

 No, 6.) 



' 4. The teaching, at this stage, of what Professor Perry has called 

 " practical mathematics," of the use of logarithms, of elementary trigono- 

 metry (limited, for example, to right-angled triangles), of the general 

 ideas of projective geometry, including points and lines at infinity, and 

 the use of the slide-i-ule.' (Yes, 85 ; No, 10 ; omit slide-rule, 5.) 



' 5. The elimination from instruction in mathematics of such matters 

 as cube-root extraction and elaborate algebraic equations, which are 

 purely intellectual gymnastics without any direct usefulness.' (Yes, 90 ; 

 No, 10.) 



The result of this inquiry led the Committee to make the following 

 recommendations : — 



' Instruction in mathematics should be given by methods differing 

 considerably from those usually adopted in the teaching of this subject 

 merely as an intellectual exercise. The geometrical side of mathematics 

 should be fostered, and before they leave school boys should be conversant 

 with the use of logarithms, and with at least the elements of trigono- 

 metry, including the solution of triangles. It is also of importance that^ 



