ON STUDIES MOST SUlTABt.E FOR ELEMENTARY SCHOOLS. 455 



Go-ordiiialion with Ueomelry and Algebra, 



Whatever geometry admits of arithmetical exercises or illustrations 

 should 1)6 introduced where it is of use. Even if formal goomftiy and 

 algehra are not taught in elementary schools, there is no reason why thoy 

 should not be used as grapliic and generalised arithmetic re,spectiv(?ly 

 where the circumstances of the school and staff arc favourable. This has 

 ))oen done in some schools and from the work that has been sul)nutted to 

 us it is evident that success has been achieved. For instance, at the 

 Newhall Council .School, Burton-on-Trent, the experimental geometry 

 scheme for Standards Y. and VI. — that is, for boys of about ten to twelve 

 years of age — is largely arithmetical in character. The course includes 

 the construction and measurement of simple geometrical figures and the 

 chief properties of these figures of service in mensuration are illustrated 

 by the results. At the New Seaham Boys' School, also, a decidedly 

 practical character is given to the work, which includes measurements of 

 lengths, areas and volumes, drawing plans to scale, simple surveying, the 

 use of such instruments as calipers and the millimetre screw-gauge and 

 of tables of logarithms. 



Algebra as generalised or shorthand arithmetic should be introduced 

 when the use of algebraic symbols in expressing relationships briefly or 

 simplifying problems is appreciated. Pupils will soon learn to write 

 algebraic expressions of arithmetical rules or relationships ; and when 

 they understand clearly the nature of a formula and the principle of 

 proportion as the equality of two ratios, they are in a position to make 

 intelligent use of the simple formulae and tables relating to mensuration, 

 physics, chemistry and engineering to be found in pocket-books used 

 by pi-actical men. They will be far better employed in the evaluation of 

 selected formuhe, using tabulated data from such' works, than in con- 

 tinually working at tiresome frivolities of currency. In actual business, 

 boys are not likely to be concerned much with calculations involving 

 interest, discount or other elaborate commercial calculations ; it is much 

 more de.sirable to give them a practical and sensible knowledge of 

 the principles and tools of arithmetic than to drill them in the use of 

 rules which they will rarely have an opportunity of applying in their 

 daily work. If a boy has been taught arithmetic by scientific methods 

 and not as a collection of artifices, he will have little difficulty in respond- 

 ing to the demands made upon him when he leaves scliool, whether ho 

 enter the office or the workshop. 



Correlation of Malhcmatical with other Work. 



At present much time is wasted in schools by teaching the various 

 subjects separately ; not only might time be saved but the work might be 

 made far more interesting and far more profitable to children, if it were 

 often to involve a variety of exercises and the complete working out of 

 some scheme. Experiments are needed in this direction. Th.e following 

 suggestions are made by Professor Armstrong for a series of lessons : — 



Suggested Lessonn on Jf/es, 



*Ask the children their ages and write upon a blackboard a list of 

 names, with the age in years and months in order of age. Some may 



