ON STUDIES MOST SUITABLE FOR ELEMENTARY SCHOOLS. 449 



' Lessons in arithmetic will thus be of three kinds, which may bo 

 roughly described as theoretical, practical, and problem lessons respec- 

 tively. In lessons of the first kind the scholars, under the guidance of the 

 teacher, should construct the process or rule ; the practice lessons may be 

 devoted to the acquisition of neatness, accuracy, and speed in applying 

 the rules which have been worked out : but the best proof of effective 

 teaching in arithmetic is the ability of the scholars to work problems, and 

 good results cannot be expected if undue attention is paid to abstract or 

 difficult examples. 



' Throughout the school the instruction in arithmetic should be made as 

 realistic as possible. Infants should learn by the aid of actual objects, 

 such as bricks, beans, cubes, or balls in a frame, to analyse numbers from 

 three to ten, and combinations of these numbers not exceeding twenty, 

 or, in other words, to find out in what different ways these numbers may 

 be arranged. The use of sets of objects will make it possible from the 

 very beginning to teach the children to add, rather than to count by 

 units ; the latter bad habit, once formed, is very difficult to eradicate, and 

 will affect adversely the arithmetic throughout the school. 



' Multiplication tables should not be learnt before they have been con- 

 structed and understood, and are therefore out of place in an infant school. 

 When the children have mastered the principles underlying the simple 

 rules and the construction of the multiplication table, it will be found 

 advantageous to insist on great rapidity and accuracy in the mechanical 

 operations involved. 



' Even in the later stages recourse to concrete illustrations is advisable. 

 For example, in dealing with areas and volumes, the idea of measurement 

 by unit area or volume should be illustrated by building up areas or volumes 

 out of unit squares or cubes. Physical illustrations of least common 

 multiple and highest common factor may readily be devised by the teacher. 

 Diagrams should be freely employed ; and squai'ed paper can be used with 

 advantage in all exercises relating to mea,surement, and is the best means 

 of introducing the idea of scale. 



' To enable this practical work to be done every school should be 

 provided with — 



' (a) Foot-rulers graduated in inches and tenths of an inch, and also in 

 centimetres and millimetres. (These should have square edges.) 



' (6) Cords with feet, yards, and metres marked upon them, 



' (c) Imitation coins. 



' (d) A pair of common scales with the smaller weights, such as ounces, 

 pounds, kilogrammes, decagrammes, and grammes. 



' (e) Measures of capacity, such as a pint pot. 



' (/) Squared paper or tracing cloth. 



' Plain paper also, owing to its cheapness and easy divisibility, will be 

 found to be of very great value for illustrations. 



' With this simple apparatus the scholar should be taught to perform 

 the actual operations of shoppihg that involve the use of money and 

 weights and measures, to measure in inches and centimetres the various 

 objects in the school, and to estimate lengths and weights. 



' There is much to be said for allowing a considerable interval of time 

 to elapse between such experimental practice and the introduction of more 

 formal numerical applications and rules. 



' Certain elementary " rules " must be taught in all schools. These 



1906. G G 



