MATHEMATICS AT VICTORIA COLLEGE.

Dominion, Volume 7, Issue 2128, 21 April 1914, Page 4

MATHEMATICS AT VICTORIA COLLEGE.

(To tile Editor.)

Sir. —Professor Picket)'s'idta of "playing the game" is typical of his frauso of mmd with regard to tho .jaciiate. He is to have lioenco to abuse its members, to jew at mid belittle them, but if ho is criticised tor his lofty attitude, ho cries out that he is insulted. Ho does-not realise the arrogance of his tone, tho dictatorial air with which he assumes that what he says Must bo right; that ail who hold other views are anti-reformers, aud the bant of T3ni»

vorsity education, that his expression of discontent with the University is the last ivord en tho subject. Ho puts everyone in his plaqe, m if they were boys in his class. Hβ once' believed that the- Minister of Education was progressing nicely, bnfc now he must give him a bad mark, because of tlto Minister's association with those backward boys of Otago. Tie- Professor cannot see the bad taste—to put it mildly— of treating in the same way the council that employs htm; ho' picks out the good boys and pats them on the head for their progress. Thig attitude lie thinks right and proper. It is part of his pajicy to make the council a v aiero echo of the Professorial Board, and the I chairman of tuo latter body tlto virtual dictator of the college. The public is not yet alive to the danger of the domination of our University by professors, but a few mow letters from Projissor i Picket! will awaken it to the situation.

Now for tho main question, the teachins; of mathematics a* Victoria College. I assorted that a University existed Dtiraarily for the benefit of the rank and file, who should be- given a. sound grounding in the principles oftheir subjects, and at tho same time receive such ■» training as''would enable thorn to tajfn their learning to practical account. _ The Professor, who began by maintaining that a University existed for the uuFpose of enabling the teacher to develop his subject along the lines of the most up-to-date ideas at his command, now agrees that tb* pass classes are the backbone ef the University, Ho does not claim a monopoly of the ideal For this concession much thanks. I wciii ou to say that the Professor, on his own confession, was out of bis element, and that ho bad developed into a specialist in a branch of philosophical roatheiaatjes considered from an abstract point of view, and that he could . not regard with any sympathy the teaching of mathematics at the University considered in its relation to its practical everyday use. Here we join issue. The Professor says lam too deep for him. But that is not the point. Tho issue is whether, on his own showing, h« is not too fteop for the 'yerage New Zealand pass student! , lie. complains that he has been unfairly vilified ever since ho set himself to do ins duty to tlie State. " Let. Him remember that in the present controversy it Was be who put himself "on the earpet," and condemned himself. The professors of mathematics framed their own syllabus. They got the Senate to appoint a great man in the mathematical world as examiner, the bast man for the post. He set papers that in the wain meet with even tho professor's ajipteva!. The etaicents take up the work with the greatest possible, enthusiasm, and yet tk© professor finds himself in. a desperate difficulty, and, being a recognised specialist, makes apparently simple questions impossibly 'difficult,' .instead of -making apparently impossibly difficult questions quite- simple by a lucid exposition. Where does the 'fault, lie? Auy reasonable, man,.''readme the prolessor's letters, will reply "with the teacher."

Professor Pickens's two long letters only_ corroborate' my contentions. He. admits that his record of honours pained in the University examinations is two second-classes in six years, and that tho siumber of students who during the last six years have been attracted by his lectures to do higher work has been smell indeed. He has wardedoif aspir* s ants for sKLthemaiioal training whom lie thought unsuitable, but whose abilities might have been developed by a teacher, of tho "practical" school, tie says ho knows a good deal about tho futility of much so-called '■mathematics" that, ie 'learned for practical purposes. It is evident that the professor's bent is to abstract theory, or, as he has, towards the philosophical side of mathematics." Hβ teaches his own original work a»d develops his subject, along the lines of the most up-to-dato ideas at his command before the eyes ot his students. That seems U bo why the Professor has been above the heads of many of his students during the last six years. He has spent twenty years in becoming a specialist in mathematics, and does not realise that the development of what is new to him after all those years of stady may be incomprehensible, to those students who com© with only a secondary.school knowledge- cf tho subject.

Tha fact is, that the professor belongs to a .school of mathematics that is not .suited to the circumstances of Now Zealand. There are two schools, tho philosophical or "unpractical" (a.s it is sometimes called), to which the professor belongs, and tho "practical," The . former school, as can be

seeu from tho professor's let* ters, attaches roost importance to the underlying theory; the "inwardnfcss" of mathematics. It wants.

above all things., to be logical, not to deal with the practical β-jtplication of a theory until tlie whole of that theory, however complicated, has been expounded, A "teacher of music of the "philosophical" school would not teach pupil the practical side of ruu&i« until tilts latter had gnisped the underlying theory, and "Nelly Bly" ami the ''Harmonious Blacksmith" might bo made impossibly difficult by the t«acher, if only the poor pupii coukl bo induced ; to see their true inwardness and to realise that iii-these simple melodies might I lurk difficult and abstruse fundamental questions of musical theory. To this school evidently belonged tho two engineer officers of whom Lord Roberts writes. It became necessary in Burniah to bridge a small stream. The officers were asked if they could do so. They rotited into their tent and spont the day wrestling with the problem ju the light of the underlying theory. Thoir 1 training had made the apparently j siinplo problem almost impossibly tliffi- 1 cult for them. They emerged late iu the day, ready fov action, only to find that two nakoii niggers bad ran the bridge off already iuid got full marks, although they ha 4 not the remotest idea, i that some of the roost difficult a«cl abstruse lunula mental questions were involved in its construction. And tho eu-gineci-a went back to'their tent realising i —to use the naive words of the profes- ] sol- —"that the worst thing possible had' feen set." ' . j Lot- us see what a mathematician, Professor ferry, has to say about tho "impractical" school of mathematics, bearing in mind that ho is probably as much an extremist on the practical a& Professor Pickon is on the theoretical side. "Twenty years ago," lie says, "mnlli'Omatics continued to be taught in what may be called the orthodox way, a way that succeeded fairly well with students who were font! of abstract reasoning, 3 per cent, of all etiuleiite, anil trmtoi failed with tho other 07 |K>r cent." - - 1-Jo |toe 9 on to say that practical merliotls arc its use now in all the publift scSiools whiM'i; natural Kcicnw; is Iftught, and in all science and cngiiioeriuK coll«Sges, and lie concludes thus: "Tile average student cannot understand abstract, reasoning;; his teacher has no knowfedue of him. and pursues hit-Eersnely'ig-wraHt war. wendering how it i? that' *o manv student* ars stupid, or *1&» h* roadere ,t!i»t fe? *ini J &J.

The practical school, ca the ether hand, considers of primary importance t'ho relalicn of mathematics to every-

day lit'o and its application to the solution of practical problems. It prefers the concrete n> the abstract, ami every

day is reinforcing its concrete. The philosophical' school liad a vogue Tor a while, birt ft. reaction has sot in. As the Professor says, the latest books on algebra for the use of English public schools show a ceßipklo change of front, The modern tendency is to introduce mere of the practical element into the teaching of mathematics, to rnako tho subject for pass students prao tical, and to leave abstract theories to advanced studonte. For instance, the ; calcuhis is sow introduced into, nmtljfi-

natical curricula at a much earlier \ stage than was thought possablo soiM % rears ago. And well-Eeowu mathemati- j *.ians contend that the introdufitioft ftf f -he practical element is 'producing the | iwst beneficial results in connection =, irith the education of the large body of | pupils, who learn iaathematics. not- to s qualify for some special profession only. » lut as part of their general education. 5 Ths Professor's answers to the little ; arternal examination paper that I set * him illustrate his predilection for ab- j straofc theory. I asked liim to take \ Professor Lamb's papers and point out I [inter alia) whieli questions & student properly taught on any rational system | :ould not fairly he expected to answer, ; ivhieh contained matter that Professor ! Pickeia had taught his students to "regard as bciug unimportant stuff, not . worthy of it man's serious attention," and, which rocant to be very simple the professor's teaching had made impossibly difficult for his students. His reply is : that of the two fi.A. pass papers eight questions are trivial and that one is a perfect example of the inapossibly-diffi-ralt'inteiided-to-be-very-Bimpb typo of question, and that the whole of the rest jf the fundamental structure of algebra nas almost entirely unrepresented m j* the papers. Which, beina interpreted.. 1| means that Professor Lamb set straightforward practical questions on abstract' theories. The ' .ques- - tions which the Matter stigmiv- a fcises as trivial comprise division, simplification of elgebraic formulae., logarithms, a simple practical trigonometrical : | problem, a question that goes to the 3 baeis of quadratic equations, a geometn- | sal problem, and two geometry questions i get to test'tho candidates' ability m f drawing and construction. Are aU these j ttiatters "unimportant stuff, not worthy [ i man's serious attefttion" ? His bug- ; boar, ouestioa 14, the . impossibly ( JimcMlt ono, asks ttm candidate j to prove a logarithm* forn»Ha mi to simplify » nanwricaJ , ■ ssampte- | Other mathematicians consider thie ■, nuflstioß a simpte and straightforwara " t on*, and canucrt, find iiv it the desperate ! difficulties that the professor conjures | up. li will b& observed that except in | tfie c-ase of tho impossibly difficult nues- j tion tie professor has not given a direct |i answer to my questions. My last qws- s tion, for instance, was: "Does he teacli jj mawefflatics in accordance with the syl- i labus?" This is evidently' An. "jmpos- h sibly-difSeult-intended-to-hß'vejy-simpJe- f type of question," for this ia ms j answer: "The syllabus was a cortpro' | mise. . .' • lii my view the usual de- : | Initions ol tho subject imply a great | deal more in the way of fundamentals g than is usually admitted." If lus. stuients are taught to answer apparejitiy simple questions in this way, no wonder thev find difficulties iu the estenm exwnuiations. (Perhaps Professor ;PicUen will give'you his draft syllabus and let us compare it with th-a Cambridge syllabus.) The professor asserts that "the underlying theory" of aistliomatics cannot fairly' be. asked by an external exnhiiner of four different- colleges. If the theory can bo , taaght- clearly so' that the students can understand it, \yliy, when he grasps it, cm he not esjjoimd it-MmsfitHo-aii external csasti- - iner ? Are ibe main eleasntary -theories of mathesaatits so uncfystallised and so nebulous that tho four professors «ranot agree upon them and'that test hook : writers cannot expound the.ro? Aμpareniiy the prefessoi" thinks so, for ha says: '"'So much of what is really jttost \ important that a student of lMatlrartuy tics should have read and understood is so intrinsically difficult and at present time so anerystalliscd that it is almost impossible to set fair examination questions upon it without the most hitimato knowledge of the point -of view fwin •which students have boen taught. "If this be soi what is the use_of the professor deseribinK mathematics in their syllabus as "high algcka, higher trigonometry, spherical astronomy, asusually flfifineti," whew apparently-they raniiot agree upon tl» most ijni?ortant part of mathematics, the "underlying theory/' tho "inwardness," tW "Wiidametrtale." What noiiseiise it all is? The method of teaching mathematics at --our tfnivcrsity Cc-llego js of the greatest importance t<? the community. The University should be brought into closer touch with the' commerce and industry of the country, and its pi-ofe-ssora be links between ths academic and tl?o practical. There is a large. army of teachers to he trained at the- tJaivorsity College to teacli our children tho elements of mathematics. There a,re many Government Departments whose officers should utilise the University for their niatkomatieal training, such, for instance, as the Audit, Electoral, Statistical, Actuarial, Insurances Astronomical, iSlectrical, Surrey, Public Works, Superannuation, There are our professional men, such as engineers, surfoynrs, actuaries to be traineci. Where the abstract theoretical method attracts one siudent, the practical method attracts and interests twenty. The importance of the subject wu-st ha my excuse for-the length of this 1-et-tcr. I—l1—I am. etc., H, F. VOX HAAST.

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Messrs, Abraham and Williams, Ltd., wiH holil a stock sals at Johnsonville on WeWsday,' April 22, «miineueiitg at 2 \o l>.m> ___^_