PROFESSOR PICKEN AND MR. VON HAAST

Dominion, Volume 7, Issue 2118, 8 April 1914, Page 9

PROFESSOR PICKEN AND MR. VON HAAST

. fTo tho. Editor;) " . No. 11. ' " Sir, —I return to' Mr. Von Haast's letter (of The Dominion, April 1), and take up the running at "the pass men, the mere common drudges." I am not going to assume that this phrase expresses an actual estimate—say by tho University Seriate—of. tho great mass of work douc at the university colleges. Nor shall I waste time in trying to analyse tho object of its use. I pick it up because it affords mo the opportunity to say one of the things I speci-

ally want to say. ■';. , I have, always believed that what wo call the "pass classes" should bo the backbone of university work. I'have never had any sympathy with the view that thoy must be- regarded as a sort of necessary affliction ■ that has to be borne-by university teachers'in order to got the-support of- the public for their real work with (so-called) brilliant students, in the upper reaches. When I was put in charge of a department of study at Victoria College. I sot myself to give effect to this principle, and, in spite of the endless worry it' has meant —indeed, as a direct result pf worrying the thing out with myself,- from every point of view—l am much mqro strongly of that opinion to-day than when it was merely an unexploited idea. .But do not misunderstand me: I claim no monopoly of this idea, which, so far as I know, is- shared by my colleagues'/ Only, 1 have reason.to believe that it is a good deal more difficult to put jnto practice in mathematics—and in theoretical physics—than in most other branches of university work. And I know, that there 'is a very general opinion among teachers of mathematics that it is beating the wind. to", try to. teach the averagestudent the "inwardness" of mathematical science. ' With this opinion I entirely disagree; and the grounds .of .my ever-strengthening adherence, to- tho opposite view are located hi just those pass "students; both men and women, who have taken up the work with the greatest possible enthusiasm in spite of clear recognition that'there exist other much softer and surer ways to that art pf mark-getting which means srece-ss in the University of New- Zealand. • " •'• , This brings me to the next point: .the fact that, in jumping to the conclusion that my reference t& enthusiasm could only be interpreted in terms of students "who have been encouraged to go for honours- in the University examinations," Mr. Von Haast proceeded to reduce my "series" to the . ridiculous figure of two. My main object at this point is to expose the disingenuous nature of my opponent's methods (or, is it only an aspect of that terrible obsession by the examination-idea which sits like a pall on our education system?), ""he obvious conclusion from the statistics adduced is that I have had an absurdly easy time, so far as teaching is concerned/during my_years at Victoria College. Now for the tacts: In 1908, I had, I think, only two students doing higher work. - These had both taken the B.A. degree before I came, and I should never, think of doing other, than "crediting them , to my predecessor." ~,. In 1909 I started fresh with seven higher students, five of whom had been in my hands as "pass students the year before. Two-of these were_ those whom Mr. Von, Haast has mentioned: other two "repeated" creditably, and then retired content with 8.A.; one to her home duties, the.other to a teaching post he had to take jn -the .country ;-the fifth-was : PVW: 0 -Bur.b;dge, now in Jthe University of - Cambridge"-as J 851 Exhibition Science Research Scholar. .(He continued, to be .trained maties tillthe very.ehd of his time here, but I dissuaded him from adding, honours,, examinations, in -mathematics to his double set in physics.) The other two of this group of seven were examples of able students who had begun their course on.the. "exempted" principle: they did good work, but ■ could never get quite into line. In 1910 two more students took up the higher work. One of ithese, in her subsequent course, met with a chapter of accidents, and eventually she .contented herself with "repeating," although she had done a great deal more of the work. The other also "repeated", and then switched off to his: law course; he, by the way, has told' me that the mathematical training is proving, very valuable to his law'. In 1911 a pew factor entered and brought me a class of five men for Differential and Integral Calculus: two from tho "Chemistry Department, two from the Physics Department, and one Insurance man.

The years 1912 and 1913 were lean Tears in the supply of students for liigher work: hut they brought me one man who will take a good honours degree this year, and some good new "pass, students" who have swelled this rear's higher classes to a total of eight students; these years provided space for some special hand-printing work which has proved invaluable to my teaching work, find opportunity for somo .enecial postgraduate work with two Physics research students (of whom the second will follow tho first to Europe in the latter part of this year).

Besides these facts it is pertinent to note that several students who did well in the pass class of mathematics, and wished to proceed further with the subject, had to be advised in their own best interests to take up some other line of workj further, that I know of not more than one student of mathematical ability in tho college who has not made the most of tho opportunities provided bv the coUego for the study of this subject. ■ I am sorry, sir, to have hored you with so long a statement on this point; but facts are the only antidote to poisonous suggestion; and you will see that the:length of my list is n matter of some importance in contrast with the "vanishing quantity" of Mr. Von Haast's estimate. Tho resultant fact is that all the students whose work lies' that way take higher, courses in mathematics; and that the numher in five yonrs has been ftv no means inconsiderable, when all the circumstances are taken into account.

Comint; now to Mr. Von Haast's four propositions for inquiry;— ■ (1) I should welcome an inquiry into the use that my students, of all grades, have made of their training, in .the service of the country; but I want also an inquiry into the effect of more conventional teaching of mathematics. .' ■ : ■ •

(2) There is nothing that would interest me ! more than an inquiry into unacademic routes to degrees of tho TTniversitv of New Zealand; but, apart from that, it_ is a very barren universe ity'territory in which the private conch enn't pick up a living. Look at it tin's way: At Glasgow! used to do six different loctures a week; here, I do anything tin lo eighteen or twenty: and men of Mr. Von Haast's typo want private coaching thrown in I Can it bo the case that that, puzzling phrase ''mere • common drudges" was reallv meant for tho professors, but' got shuffled into the wrong placp? May I add in this connection thnt I did my best for tho students who had a real prievfinco under "compulsory mathematics," by takinrc a vigorous part in the successful offort to remove that barbarism?

(3) rloro your compositor beats me. But if I catch tho idea, I may wot it with an jissuriuice thnt tho College Council' will, at its next meeting, have more exaot statistics of ontrr and enrolment thnn ever before. And as to this constant harping on the magnificent provision of a professor and an assistant for tho teaching of mathematics, pure and applied, let me_ refer again to what I hare mentioned in (2)

above, and state that any less provision would make Univorsity teaching, in mathematics, as I understand it, almost impossible. (4) I should like nothing better than to try to demonstrate the jservico I have rendered this country in warding off all aspirants who have not tho grit to work conscientiously through my pass courses. I happen to know a Good deal about tho futility of much socalled "mathematics" that is learnt for practical purposes; and I have the deepest conviction that tho.only sound basis of good practice is good theory. But, clearly, it is only a.Royal Commissior that can satisfy your correspondent. His fecundity in queries must otherwise run to seed. Speaking

from within, the University Reform Association, I would exhort him, in the words of a. famous "Punch" picture, to "Oomc Insido," were it not for the danger that he might accept the invitation. , . ■

And now let me come to the really courteous part of tho letter, in which I; am politely requested to provide certain information. This I would gladly do more fully than, I fear, is possible at present:— ■ • First of all, I wish -it to be clearly understood that the professors of mathematics Rave most careful consideration to the list.of names they submitted on tho occasion of tho last appointment of an examiner; and that we have in Horace-.Lamb (too great a man in the mathematical world to need any handle to his name) the best man, I believe, that it would bo possible to get for tho post that had! to. be. filled. Hence,, all the ill-effects of the system are reduced to a minimum in this case. ' Indeed, I have little complaint to make of the last papers, 'except on' the ono count, which, is conveniently, left unmentioned by Mr. Von Haasl: viz., that the tilings the students have been "taught to regard as mosij important" are not asked—and could not fairly be asked by an external examiner of four different colleges. By those "things"- I mean the underlying theory. The maxim that "an ounce of practice is worth a torj. of theory" is : not true of mathematics, if "practice" bo denned in examination terms. . Tho easiest route; to examination-passing in mathematics, for the average mind, is by achieving facility in the stock type of "example," to the almost entire neglect of any but the simplest theory. But the effect on tho mind is worse than useless., '.

There happens, however, to lie, in Question 14 of the B.A. paper .in Algebra and Trigonometry, a perfect example of .the impossibly-diificult-intend-ed-to-be-very-simple type of question. '. The "formula." set there is quite' impossible of proof by the .elementary student, fpr even the most ordinary case, such as that of the accompanying numerical example, or such as would arise in the everyday practical calculations of the engineer. K raises one .of the most difficult and abstruse fundamental questions of algebraic theory. The proof for artificially simple cases is "child's play," but useless except as an indication of the general result;.this would bo run off (and would get full marks) by examinees who had not even the remotest idea that it is hopelessly inadequate to the practical uses of the formula. My students would realise sadly that .the worst thing possible had beeii.set, and that the whole of the rest of the fundamental structure of algebra was almost entirely unrepresented in the papers. That is all I shall say at present about (a), (b), (c). Answering query (d), questions 1, 2, 4, 7, and the example (above-mentioned) of 14 of the Paper A are trivial; otherwise the paper is an exceptionally good one. So with questions 1, 3, 5, of Paper B for B:A. But it must.be remembered that sdmo'irivial questions are almost a necessity! examining, to make up for .the inherent unfairness of the- system.. I have.confined these remarks'to'the two-pass B.A. papers. An analysis of all the papers would take a great deal more- time than I can at present give, and space vou would regard as. very "unprofitably filled. _ I As to query (e), evoryone interested knows that the syllabus was a compromise, arrived at with the object of giving each professor : as much liberty as possible in his teaching. Professor Sogar would not agreo to a draft syllabus I had taken greflt rains with; the phrase- "as lisnally denned," characteristic of the new syllabus, was his. I agrped to it, as •making a great advance on the old syllabus. The word "usually" in this connection would at the present timo be a pretty hnrd nut to crack for a British Bench of Supreme Court Judges. But the essence of nv position is that in my view the usual definitions 'of the subject, itnplv a greßt'denl more in the way of fundamental*! than is "usually" admitted, although the In test books on algebra fo? thn use of the Kns;lish public schools show a complete chnnge of front in, this respect. I am afraid this Jotter has run to wearisome length. I have not had time to condense it further. But I am glad to have I'ad the chnnce of clearing up some of the mysteries.—l anvofe.. D. K. PICKEN. ■ April 4, 1914.