ioO REPORTS OX THE STATE OF SCIENCE. 



Sshoulcl include simple sums involving money and the common weights and 

 measures, vulgar fractions, decimals, and proportion by the method of unity. 



' In all cases an endeavour should be made to frame schemes of 

 arithmetic teacliing with some reference to the circumstances of the 

 school ; and the course of arithmetic should include the drawing of lines 

 and plans, practical measurements, and the construction of such things as 

 cubic centimetres, if the scheme of hand and eye training taken in the 

 school permits of this being done. In this manner this subject will be 

 correlated with drawing, elementary physics, and the scheme of hand and 

 eye training. It v/ill also be possible to connect the sums with the sulj- 

 ject-matter of other lessons. Thus, to be effective interest sums should be 

 preceded by simple lessons on savings banks, relative safety of various 

 investments, and usurer's interest. Such sums should be limited strictly 

 to simple numbers. 



' For older scholars exercises in land measuring are valuable ; and the 

 occasional actual measurement of a field, or of the playground if no field 

 is available, will be a useful supplement to indoor instruction. Even in 

 the school it is possible to find suitable practical exercises in the measure- 

 ment of bulks, weights, and areas of common schoolroom objects. 



' For both older and younger girls problems relating todomestic ccononiy 

 and thrift are especially useful, and in country schools the sums should 

 frequently have reference to the produce of the farm and the field. It is 

 also desirable that, as far as possible, the current market price of the com- 

 modities named should be used in the questions. 



' The commercial applications of arithmetic commonly found in text- 

 books could generally be advantageously replaced by algebra, pi-actical 

 geometry, and the mensuration of the simpler solids and surfaces. The 

 division of ai'ithmetic and algebra into distinct subjects is much to be 

 deprecated. Much will be gained by the very early substitution of 

 letters for numbers in .some of the ordinary arithmetic, and by the early 

 introduction of the ideas of negative quantities and simple equations. 



' Practice should thus be of five kinds : — ■ 



' (1) Preparatory experimental exercises to show the necessity and 

 meaning of what is coming. 



' (2) Numerical exercises, in the rules and processes that are being 

 taught, dealing with very small quantities. 



' (3) Exercises combining these rules with others, and also containing 

 larger numbers. 



' (4) Recapitulation, including oral (or, where possible, written) 

 answers to questions on previous work. These should be given with as 

 little technical nomenclature as possible, and without ciphering abbrevia- 

 tions ; i.e., each figure should have its full value assigned to it. 



' 5. Exercises in pure ciphering, to cultivate speed, accuracy, and the 

 habit of concentration. 



' It is not, however, necessary that large quantities should be in- 

 volved. Accuracy is not obtained by working long .sums, but is rather 

 the result of mental concentration and experience.' ' 



A course of work conceived in the spirit of these suggestions would 



1 ' The Teacliing of Arithmetic' From Sutjgestions for the Consideration of 

 Teachers aiul others concerned in the Work of Public Elementary Scliools. Board of 

 Education. Cd. 2638, 1905. Price M. 



