200 



NATURE 



[October 21, 1915 



in distinctions between face value and selling 

 value, and so full of terms among which master 

 and boys are equally at sea. 



Some schools neglect arithmetic sadly, while 

 others give it far more time than its real worth 

 deserves. The latter group are responsible for the 

 bulk of the present-day text-book, in their demand 

 for endless examples. In these schools the cor- 

 rection of the overcrowded time-table will in time 

 reduce the number of periods allotted to arith- 

 metic, and the text-book will be reduced to a 

 fraction of its present size. 



(i) Meantime we have to make the best of 

 present conditions, and Messrs. Godfrey and Price 

 have produced a most usable arithmetic. While 

 compelled to run to above four hundred pages and 

 include all the customary items and tricks (except 

 recurring decimals, for which omission we are 

 thankful), they show in the preface how they 

 would prefer to use the boy's time. Their 

 explanations of difficult points are accurate, con- 

 cise, and clear ; see, for instance, their discussion 

 of fractions. They have regard also to the recom- 

 mendations of various open-minded and wise 

 bodies, such as the Headmasters' Conference, the 

 British Association Committee on type in school- 

 books, and the Mathematical Association Com- 

 mittee. The book is to be highly recommended ; 

 it provides work for the most lavish use of time, 

 and the wise master who limits the time for arith- 

 metic has a wide choice in his selection of work. 



There is much gain in clearness of type by the 

 use of the solidus, for instance, in printing 

 " 19/20 " to stand for nineteen-twentieths, but it is 

 a pity to use the symbol to denote shillings in the 

 same book. 



In elementary schools, also, arithmetic is in a 

 bad way. Not that the boys don't do it well. 

 They do it only too well, and can tackle the most 

 abstruse questions which, if done at all, ought to 

 be done by algebra. Further, they can (or are 

 expected to) tackle questions which are unintelli- 

 gible to the plain, well-educated man ; in these 

 questions conventional meanings, used only in 

 schools, are put upon phrases which are otherwise 

 meaningless. That abomination, the recurring 

 decimal, is firmly entrenched in the elementary 

 school, and children are told to commit to memory 

 the expressions as recurring decimals of all proper 

 fractions with denominator 7. After such enormi- 

 ties it seems quite natural to find the children 

 required to add together 6 days and 23 seconds, 

 or 16 kilometres and 2 millimetres. 



(2) In the " New Concrete Arithmetic " the 



authors are doing the best that is possible in the 



circumstances. The whole gamut of absurdities 



must be included if the book is to sell, and so long 



NO. 2399, VOL. 96] 



as the present excessive allowance of time is given I 

 to the subject it is difficult to provide a sufficient ■ 

 number of varied questions without degenerating ' '■■ 

 at times into unsuitabilities. The idea of first \ 

 presenting every rule in concrete form is good ; \ 

 it might be carried further, and require every 

 question to be such as naturally arises in human • 

 life. It would be still better to require every \ 

 question to be such as arises in the pupil's own \ 

 environment, so that there might be a rural arith- \ 

 metic for the country school and various kinds of '\ 

 industrial arithmetics for town schools. Before 

 such arithmetics are possible, however, the time j 

 allotted to the subject must be severely cut down. 

 For to restrict the book to natural human prob- 

 lems and such bookwork as is necessary for their 1 

 treatment, means the excision of many whole ; 

 sections. 



Let us repeat that we impute no blame to Mr. > 

 Pendlebury and Mr. Leather, who do the best | 

 that circumstances allow. In everything the book ! 

 is as good as others of the kind, and in begin- 

 ning from the concrete it is miles ahead of the ' 

 bulk of thein. j 



(3) In trigonometry also the mathematical i 

 master — or the headmaster or somebody — sets 

 apart too much time for the subject. The time has 



to be filled in, but how can it be done without j 



" Identities " ? Identities being fashionable must be '■ 



included in any book that is to be a success on the i 

 market. Mr. Reed is not to blame ; he cannot 



help himself. First let the time allowed in the I 



school for mathematics as a whole, or for trigono- i 



metry, be cut down, and Mr. Reed will write you j 



a good book. He will discard identities, and iden- j 



tities being gone he will discover that secants and j 



cosecants and tangents have no use except for ! 



the specialist and for the making of identities, and ; 

 he will drop them. 



In the meantime Mr. Reed does what is pos- ; 



sible. He begins the solution of triangles by ; 



formulas most of which result immediately from ; 



geometrical properties. In the only case that pre- | 



sents any difficulty, that in which three sides are \ 



given, the method of solution is due to Prof. , 



Bryan ; expressions are found for the sum and \ 



difference of the two portions into which a side is \ 



divided by a perpendicular from the opposite vertex. \ 



The variety of the questions which are taken ' 



from human life deserves high praise ; it is only ^ 



by long-continued effort that they could have been ! 

 collected. 



We regret, however, to find results left in surd 



form, as on pages 140 and 141, with the remark '% 



that they "may be worked decimally." We should \ 



have expected Mr. Reed to set a good example by j 



"working them decimally" himself. ,] 



