PEDANTRY OF SCHOOL ARITHMETIC

Dominion, Volume 12, Issue 134, 1 March 1919, Page 9

PEDANTRY OF SCHOOL ARITHMETIC

THE GREAT AND GROWING IMPORTANCE OF NUMBER ITS FAULTY TEACHING (By P. L.' Combs', MX) The Arabic numerals, regarded from the standpoint of function, are simply an addition to the alphabet. In the 'course of speech and intercourse it is necessary to express With precision soma qualitative or qualitative estimate of the subject under discussion. To 6ecure accuracy we figure out this estimate and set forth a sum total. Some GO years of popular and research science have greatly added to the importance of figures. What was once picturesquely stated in allusive words is now accurately set forth in serried columns of numerals. Pepvsian accounts of the great'plague are replaced by bills of mortality; quality in, a. cow, once a theme for the bucolic argot, is now indicated in - decimals; our buildings, our bridges, bur ships, our machines are 1 but the concreted equivalents of reams of calculation. Bureaux of statistics the world over are fast-becoming first rank Government Departments., It hardly needs a poetic vision to anticipate the .time when they will tuck the Treasuries under their wing as deferentially handled sub-Departments., ■ A Statistical Civilisation. All this shows how highly civilised we are becoming. . To savages (and women) no exercise of the intellect is more distasteful than calculation. The disciplined. and rigorous view to-day taken of truth and causation is best reflected in the increased extent to which every activity human and meolanical of modern times is set forth in. figures. The core of politics, as Gladstone first testified, is finance. ITo those who cannot read figures finance is a dead Heal, wages, profiteering, / patriotic societies, eugenics, public opinion, are all dependent for their clear and reliable interpretation upon mathematical analysis. Number, if not superseding spoken language, is rising, even for colloquial purposes, to a parity with it. /

. Yet We Shy at Figures. Yet, except for freaks, who, like, chess players, Tevel in the complications of the process for its own sake, no one willingly reads figures. They , are not thrown on the picture screens. No popular novelist or magazine' writer would dream of starting'his story with an array of numerals— though it were only a laundry bill. ■ The Finance Minister weaves his fluent web of ipouuds,. shillings, and pence, conscious that notVone listener in a hundred is alert, interested; or critical. His 1 reputation for,wizardry is enhanced by expounding what no one else can or cares to understand. A nation of mathematicians would scotch the profiteer by way of a, breakfast appetiser. He eludes with impudent unconcern the exasperation of a democracy that'is loath to cipher. Even the monthly grocer's bill, with its breathtaking rises for salt' and salad oil, receives but grudged attention. Arithmetic, if not' a dead, is at least to most of us a repellant language.

We Should Read Figures Avidly. In a civilisation where every problem precipitateaHtself into figures this is not as it should be. I Cause and remedy' /for suoh a. 1 vital _ defect need discussion. ', To 'a rjnite remarkable degree, the responsibility for this distaste for number lies with the school., The home, if not- the colleague, should'be the coadjutor of the school in • itji'efforts towards a general culture. One-half a child's ideas, at least •onehalf of..its vocabulary, might he fairly expected to .derive from home nurture. But figuring the home can rarely teach. It'would be'easier to impart French or magnetism. The technique of number is 1 as' arduous as that of piano-playing. It requires a specialised skill in instruction beyond the acquirement of any average parent. The school, therefore, to a quite unique extent has the mathematics bf the nation left to its care. If . interest, in'figures, a willingness to use them, an ability to demonstrate by their' aid, a quickness' to see the vital significance of a numerical analysis are am. indication . of welt-taught, arithmetic, the school fails lamentably.. It so fails, not because the subject is not thoroughly, even drastically,, taught (as the •"results" subject iti neglect would spoil the record of any State school), it fails because of the'pedantry of its content. What is Scholastic Pedantry? "It is worth while being precise at this point. A subject becomes pedantic when ceasing to have sufficient vital lipplica-1 tion to the world of affairs, it • becomes I the .happy' hunting-ground of scholars brought'up on it, indurated to it. The school, owing to the lack of shiWl, public opinion in regard to ij;s aims and methods,. has pedantry as its besetting sin. • Etymology clinches this contention. 1 Pedantry and pedagogue ' are words of common derivation. '■ Scholasticism (i.e., the wisdom" of the schools) is a byword ,for its insipid and _wire-drawn disquisitions. The reason is obvious, when.outeiders, | through indifference or. inability, fall, to! interfere, the .habit of the inati-. tution. takes possession of it heart and 'Soul*,' A generation in control, dominated ;by an aocepted tradition, imposes it

( oa its successors, and 60 on ad infinitum. This vicious cycle is rendered easier of imposition by fhe plastic docility of the average _ child. Now, primary school arithmetic drew its. first breath under , Pestallozi. He had in view (a) calculaI tion for the purposes of domestic life and petty business, (b) a gymnastic in • the subject for which he had a personal partiality.' Our own monitorial and subsequently board schools took over and elaborated the Pestallozian system. Examination suppr-added by our system. still further narrowed and stiffened the ._ subject. It set to it a scope, against any novel expansion of which there was resistance from tho habit o ithe school. Just as now that double entry bookkeeping is so necessary to every ohild's education, there would bo reluctance (i.e., the inertia of a,habit-bound institution) to take it up. Antfijuated Sums and Rules. The consequence to-day is a series of rules and type sums in our school arithmetics, some, like "Partnership" already antiquated, some, sjich as compound interest . without 'logarithms obsolescing, many, such as compound proportion, of purely scholastio application. (The writer, except for examination, has never had to do a compound proportion sum since lie passed the Sixth Standard over twenty years ago). Much of the •arithmetic,. notably fractions, is pure gymnastics—a mere exercise of specialised skill without the justification afforded by chess—that it serves a recreative purpos.e ; Lack of Striking Applications. Against such increase in mechanical facility there need ba no protest, if only it; were later on given pertinent application, but it is at this point that the soliool mathematics .break down most completely. It is true that timid inno- . vations in the form of "barometer" 6ums and "milk" sums creep into the annual test cards, but a bold and vigorous attempt to use number, to explain' our business and political activities, and thus to justify the expenditure—quite —made niton its teaching, seems still, long distant. Yet, as at first suggested,: we have scores of institutions and national undertakings • whose operations must 1m checked and interpreted in terms of figures or not at all. ■ Banks, joint stock - companies, i loan agencies,_ post office and, railways, the annual national statistics,, the wages question, the land question, the whole of economics,, our finance, our sociology, bristles with numerical aspects concerning which popular notions are most often I disastrously fallacious. Teach Not Sums But Accounting. . Reformation is not hard to deduce from the foregoing. Double entry accounting as the clue to one's personal and to civic finance is a prime essential. How few of our farmers attempt anything 'remotely resembling it lawyers lmve learnt to their profit since war taxation was imposed. How many of our swollen businesses are .managed without it the writer can only judge from his own private knowledge, but the general ignorance of, and indifference to, national and high finance in times when Governments are; the big spenders is common testimony. Following double entry should come education as to the nature and operations of joint stock companies. The subject is saturated with historical aiidi human interest. All the class' as possible shareholders or consumers are vitally concerned to get the drift, of this subject—far mot'e'so than to leariii the formulae for a right-angled triangle. One might, very well start a joint stock company in connection with the school itself, unless traditions too ' to be flouted stood in the way. Banking would follow joint stock as a subject; overdraft and foreclosure would, no lonser bo a mystery, nor need that' .contentious subject the note issue be avoided from any point of view. The new course among things that will occur to readers, though not' to the writer, would certainly include a sort of national and local stocktaking. Municipal and county council balance-sheets, thpse also of big local trading and manufacturing concerns would, be scrutinised and expounded. The thorny subjects of private .or irablic enterprise might be pet out in imoartial The national scone of the arithmetic will be suggested'by a perusal of the .Year Book. Work among 1 simplified tables derived therefrom give a proportioned outlook to discussions on tariffs, taxes, revenues, mortalities, weather conditions, etc. | Tho Solution of Half Our Modern | , Problems. . The total effect of the course thus cursorily sketched in can hardly be denied. It would give to all the processes and /results of numerical calculation a, vital significance—a realistic bearing absent from the abstract- or formal operations of.current text-books. The writer argues jit would do more. One-half the world at present fails to realise how the other half lives. It'also fails, to. reach a. solution, because it is unable, to figure it out. A democraoy that had not merely learned to use but to like figures 'would come to an understanding of pauper and profiteer. \ftterly beyond the power of scorn and no .'bad rival for the intuitions of sympathy. Undoubtedly. arithmetic should be tought. Do the schools .malteach it take the. bloomy off . it and destroy its promise? , For the reasons above given the writer thinks they do.