PROCEEDINGS OV SECTION J. 719 



Research Scliolarsliips — botli of considerable value — the examination 

 test has been superseded by the more reliable method of nomination. 



As year after year passes by there is a tendency to add to the 

 number of subjects of a school curriculum. It is on this account all 

 the more necessary that the strain on the memory should be reduced 

 to a minimum, and further desirable that all superfluous portions of a 

 subject be excised. A teacher should have a reason for every part of 

 the subject which he teaches, just as an examiner should be able to 

 say why it is important that the candidate should know what he is 

 asked about. The importance of mathematics in education is fully 

 realised, yet I do not think we can give satisfactory reasons for much 

 that is taught. Take arithmetic, for instance. Twenty years ago 

 arithmetic seemed to be dealt with largely from the commercial aspect. 

 This, perhaps, is not strange in a country whose prosperity was due 

 to its commerce, and at a time when scientific training was practically 

 unknown in schools. Interest, discount, exchange and barter, alli- 

 gation, medial and alternate partnership, stocks and shares, loomed 

 large on the boy's arithmetical horizon. Most of these rules have 

 passed into oblivion, though a vestige remains in stocks and shares 

 which still remain a sine qua non for a boy's arithmetic proficiency. 

 Personally I think that with the exception of interest, which is a mere 

 matter of percentage, the problems of the stock exchange, of the in- 

 surance office, and of the discounter's profession are best omitted 

 from a general course of arithmetic. They are part of commercial 

 arithmetic, and are best taught by a specialist in the technical school. 



Another application of the pruning knife should be to recurring 

 decimals. I have a vague recollection of rules for recurring decimals 

 which caused me considerable perplexity at school. I have never 

 had occasion to teach arithmetic, and I have never needed the rules 

 in my own calculations, so that I am ignorant of their nature at the 

 present moment. Any special rules for dealing with recurring decimals 

 are unnecessary, because five significant figures — or six at the outside — 

 are sufficient for all practical purposes to represent magnitudes. With 

 six figures we have a degree of accuracy of at least one in a hundred 

 thousand, and at most one in a million. It is rarely one has to do 

 with quantity whose measurement justifies more than five figures. 

 Every teacher knows how difficult it is to correct in pupils the abuse 

 ■of figures. It is best, I think, to insist on restricting numbers to five 

 or six figures, on the understanding that the purpose is not to shorten 

 the work but to drop all figures which are meaningless. In most 

 arithmetical textbooks it is the custom to require decimal sums to be 

 worked out to a definite number of decimal places, irrespective of the 

 total number of figures. This is illogical. The result should be re- 

 quired correct to five significant figures, irrespective of the decimal 

 place. Working on this principle no notice need be taken of recurring 

 decimals : the five significant figures are made up without taking par- 

 ticular notice of any recurrence. 



In dealing with the simplification of arithmetical expressions the 

 result is often left as an integer, with a fraction of a high and incom- 



