ON STUDIES MOST SUITABLE FOR ELEMENTARY SCHOOLS. 445 



suitable for the course of theorems proposed. The whole or parts of 

 these schedules have been adopted as the basis of requirements in 

 geometry for the Previous Examination at Cambridge, Responsions at 

 Oxford, and the Local Examinations connected with these two univer- 

 sities, 'other examinations which have been modified so as to found 

 geometrical teaching upon experimental work with the use of instruments 

 and numerical measurements and calculations are those of the London 

 Matriculation, Army and Navy Entrance and Lower Civil Service ; with 

 the result that in most secondary schools, not only in this country but 

 also in India and the Colonies, the work in elementary geometry has 

 altered greatly ; though it must be admitted that in actual practice reform 

 has not gone far in the average school. 



The recent improvements in the character of school geometry have 

 been shared by other mathematical subjects, such as arithmetic, algebra, 

 and trigonometry, to the advantage of them all. It is recognised that 

 the work of accurate drawing and measuring, with numerical calculations, 

 is far better adapted to the intelligence of pupils in schools, even when its 

 practical value is left out of consideration, than a rigid system of deduc- 

 tive geometry. In good schools, geometry and trigonometry have, indeed, 

 become in their earlier stages largely arithmetical, while algebra is 

 introduced as generalised arithmetic ; and there is good ground for the 

 belief that this rational and co-ordinated treatment of school mathematics 

 will be generally adopted in the course of a few years. 



The views expressed by the Committees of the British and Mathe- 

 matical Associations as to desirable improvements in the teaching of 

 arithmetic are subjoined, and also the recommendations relating to this 

 subject contained in a report recently presented by a committee of the 

 Institution of Civil Engineers. From these extracts it will be seen that 

 there is a consensus of opinion among men of science, mathematical 

 masters, and engineers, as to the fundamental importance of practical 

 work, the need for simplification, the use of contracted methods and of 

 logarithms in numerical calculations, and the omission of those parts of 

 the subject which have no relation to the common experiences of life. 



Recommendations of British Association Committee} 



' In regard to arithmetic, the Committee desire to point out, what has 

 been pointed out so often before, that, if the decimal system of weights 

 and measures were adopted in this country, a vast amount of what is now 

 the subject-matter of teaching and of examination could be omitted, as 

 being then useless for any purpose. The economy in time, and the advan- 

 tage in point of simplification, would be of the greatest importance. But 

 such a change does not seem likely to be adopted at present ; and the 

 Committee confine themselves to making certain suggestions affecting 

 the present practice. They desire, however, to urge that teachers and 

 examiners alike should deal with only those tables of weights and measures 

 which are the simplest and of most frequent practical use. 



' In formal arithmetic, the elaborate manipulation of vulgar fractions 

 should be avoided, both in teaching and in examinations ; too many of the 

 questions that appear in examination papers are tests rather of mechanical 



' Extract from the Report of a Committee of the British Association on the 

 Teaching of Elementary Mathematics. Eej^rt of the Belfast Meeting, 1902, p. 473. 



