THE INFLUENCE OF EXAMINATIONS

A

ON EDUCATION.

By C. H. SAMPSON, M.A.

Fellow of Brasenose College, Oxford.

T the recent meeting of the British Association a very interesting interim report was presented to the Educational Science Section on behalf of the Committee on the Influence of Examinations upon Education. The report specifies nine points which have been laid before persons of experience in school and university teaching, and gives extracts from fifty-six replies. No attempt is made to arrive at a general conclusion, and the difficulty of any such attempt is obvious. But many interesting and suggestive criticisms of examinations in general and certain particular examinations are recorded, and deserve our careful attention. After many years of experience in Oxford as a college tutor and also as a Delegate of Local Examinations, I venture to offer one more opinion on one aspect of the general question and on sundry matters of a more detailed character.

It is unfortunate, but apparently inevitable, that in such a discussion as this the weakness rather than the strength of examinations should be so constantly emphasised. No one troubles to prove, possibly because no one cares to dispute, the general propositions that examinations have their rightful sphere as discriminating and stimulating influences in educational work, and that in some form or other examinations are the accepted means of testing individual fitness for professional and other purposes in the work of ordinary life. And yet hardly anyone expresses any real wholehearted satisfaction with the manner in which existing examinations are worked. Can we suggest any general explanation of the dissatisfaction so commonly expressed both by teachers themselves and by those who have to judge of the results that follow from examinations?

I cannot help feeling that teachers too often lose confidence in themselves and in their teaching work as the centre of all true education. There is a tendency to exalt examinations into a position unjustifiable in theory and unsatisfactory in practice to all concerned. In theory examinations are made for education, and not education for examinations. In practice the syllabus of examinations is the only working ideal of education in the minds of many teachers, with the inevitable result that sooner or later they are angry with the examination for not being what their fancy painted.

I know quite well that much of this tendency springs from the absolute practical necessity of preparing a certain number of individual pupils for some definite competition on which their future careers may depend. But the absorbing interest of these special efforts ought not to obscure the sense that the general training of character and intellect is the teacher's real work. No examination can possibly cover all the ground that teaching ought to cover. If teaching is concentrated solely

on one special examination, failure ends either in undue depression or in fitful criticism, and success may be pleasant for the moment, and yet barren of abiding results.

Those who have read the report will remember a very comprehensive criticism quoted from "S. 25." I cannot help thinking that he has a too exalted view of the possible functions of examinations. He says, with perfect truth, that the training of character is a most vital part of a master's work. He then complains that the reports of examiners are practically useless, because " they do not deal with training of character." To my mind, training of character is one of those parts of our work of teaching that we must be content to leave to some more abiding test than any examiner can devise. Inspection may bring with it in the future the "many days of close contact and the advice and encouragement" which "S. 25" cannot find in our examination system. Meanwhile, cannot the members of a teaching staff do more in the way of taking counsel with and encouraging one another than they sometimes seem able to do?

The effect of this ultra-specialisation on the pupils cannot be more clearly illustrated than in the criticisms made in this report on entrance scholarships at Oxford and Cambridge. We know at Oxford too well the dangers indicated. I am quite ready to admit that within the twenty-one years of my experience there has been some advance in the standard of scholarship examinations. But I am also quite sure that the attitude of schoolmasters towards these examinations has changed out of all proportion to this advance. So far as classical scholarships are concerned, the trouble is not serious. The range of the examination is (in general) wide enough to set a reasonable standard of work for the last year, or even the last two years, at school. If only modern languages were more effectively represented (as they probably will be when the proposed Final School of Modern Languages is in working order), there would not be much ground of complaint. In the case of other subjects, this quite uncalled-for specialisation is to all true friends of education a source of grave regret. This tendency is at its worst, in my judgment, in schools where mathematics is kept apart from natural science. I have lately been talking to two scholars, one elected for mathematics and one for natural science. They come from quite different schools, in both of which there is excellent teaching given in both subjects, but in separate departments and to separate sets of boys. The mathematical scholar is utterly ignorant of any form of natural science, and the science scholar knows no mathematics beyond the merest rudiments. We are endeavouring to counteract this tendency by incorporating a fairly comprehensive "general paper in our examinations for mathe matical scholarships. The whole subject of science scholarships is surrounded with difficulties as to the scope of the examination. It is easier to recognise our duty to encourage science than to know how best to carry it into effect. Possibly it

may be wise to offer a scholarship for mathematics and some branch of natural science taken together. Many criticisms on examinations as directly affecting schools arise in connection with the work of such bodies as the Oxford and Cambridge Joint Board or the Delegacy or Syndicate of Local Examinations. It is inevitable that a given school should, when examined by one of these bodies, be subject to certain regulations as to the form and subject matter of the examinations which hamper its freedom of choice. No one is more conscious than those who are engaged in such work of the great difficulty of adapting the scheme of examination to the need of all sorts and conditions of schools. So far as the Oxford Local Examinations are concerned (and of these alone I can speak from personal experience), the steady increase in the number of those whom we examine is a constant source of encouragement, in spite of what one critic in this respect calls our flagrant ignorance of the average schoolboy. We are constantly receiving, often asking for, and constantly acting upon, suggestions from schoolmasters and others who are in touch with educational work. If we have erred in the direction of too many new experiments recently, at any rate we cannot be accused of stagnation. And when we have made an experiment we do not hesitate to modify it in deference to a consensus of representative opinions. It is so much easier for critics to criticise than to offer really constructive suggestions. Some two years ago we sent out to persons who had recently entered candidates for our examination about 500 circulars on a point where the experience of actual teachers would have been simply invaluable. Of these circulars 400 were answered.

never

Few departments of the work of examining bodies are more difficult than the selection of examiners and the assignment of them to different

It would be impracticable to carry out the suggestion of "S. 25," that examiners should "only be selected from experienced and enlightened schoolmasters." So far as my knowledge goes, examining agencies are only too ready, wherever possible, to obtain the co-operation of those who have or have had definite schoolteaching experience. But it could hardly be expedient that only those who have retired from school-work should examine, and it is impossible that those at present engaged in it should, as a rule, find time and opportunity to examine other schools. Is it certain that the average schoolmaster would be always ready to accept with equanimity the criticisms of a member of the working staff of another school?

The criticisms on Responsions at Oxford as at present constituted are perfectly fair, but they hardly do justice to the actual position. It is a matter of common knowledge that an abstract resolution in favour of accepting French or German in lieu of one of the two classical languages for all purposes of Responsions was rejected by a small majority in Congregation last year. It is an open

secret that steps have been taken to draft a similar scheme in favour of candidates in certain Honour Schools. For all examinations in and after Michaelmas Term, 1904, a course of elementary geometry has recently been prescribed in lieu of the text of the first two books of Euclid. For the past two years set books in Latin and Greek have ceased to be necessary. They may still be offered, but the alternative of unprepared translation in either Latin or Greek or both languages is freely open.

I notice that the views expressed in the report are, as a rule, strongly in favour of unprepared translation as against set books. I quite agree with this view in all cases where a working knowledge of a language is being tested. On the other hand, whenever candidates are capable of studying and appreciating the literature of a language, it is a grievous pity that the study of a work of literature as a whole should be abandoned, as is too often the case, in favour of the study of isolated passages which are regarded as likely to be set in examinations.

F

THE EDUCATIONAL VALUE OF

SCIENCE.1

ROM the point of view of the schoolmaster these collected papers may not inaptly be styled "the gospel according to Armstrong." For the last twenty years Prof. Armstrong has been insisting that a radical change in English educational ideals is imperative, and in this book are to be found the most important of his contributions to educational science. The modern conditions of human intercourse are profoundly different from those in existence when current systems of public school and university education were formulated and stereotyped. The development of science during the nineteenth century has resulted in a complete transfiguration of our methods of thought and action, but so rigid has pedagogic conservatism been that, despite this growth, there has been little educational evolution, and our scholastic system is still, to all intents and purposes, medieval.

Those observers whose business it is periodically to diagnose the state of our national education are, however, of opinion that symptoms of improvement are evident, that a quickening of our educational forces has begun. It may be hoped that the near future has in store much that will gladden the educational reformer's heart and result in the production of intelligent and resourceful young citizens, no longer dominated by the tyranny. of antiquated authority, but alive with the spirit which demands personal experiment and individual research. The future historian who traces the history of the growth of English education will, it may be predicted with confidence, attribute much of the improvement during the twentieth century to the patriotic and self-denying efforts of a small

1 "The Teaching of Scientific Method and other Papers on Education." By Henry E. Armstrong, LL.D., Ph.D., F.R.S. xiii. 476 pp. (Macmillan.) 6s.

band of scientific pioneers, among whom Prof. Armstrong will be given a prominent place.

The main contention of these essays may be stated briefly in a few sentences. Hitherto English education has been too bookish, too much concerned with words instead of things. Boys and girls have been taught as if the only faculty worth serious cultivation was the verbal memory, and as if the only standard of truth was an appeal to precedent. The practical training of hands and eyes has been neglected and learning by rote has been glorified. Instead of being led to believe because they themselves have personally proved by experiment a given truth, they have been taught to accept statements on the authority of the teacher or the text-book. Prof. Armstrong urges that learning should take place by doing if it is to be of real value. The class-room must for the future become subsidiary to the workshop; and there pupils are not to practise scientific tricks in the way that poodles perform antics under the eyes of their trainers, but are to answer questions by experiments devised by themselves with that object in view. The attitude of the scientific detective, or of the keen scout, is to be developed at whatever cost. The facts of science are of second-rate importance; the matter of vital consequence is that scientific methods should become natural habits of the learners, so that they may always have trustworthy reasons for the faith that is in them. Such training will, it is claimed, we think rightly, endow boys and girls with initiative, resource, and general intelligence, and enable them to face new circumstances with confidence, because they have learnt already to trust their own natural powers.

Like many reformers, Dr. Armstrong is so dominated by his message that he is apt to lose sight of the good points in the procedure of the many who have not yet accepted the heuristic method as the way of educational salvation. The classical education given by our public schools and universities has, after all, produced great statesmen, great divines, great lawyers, great soldiers-many of them. As Huxley pointed out, the proper teaching of classics is, up to a certain point, instruction in the scientific method, and the classical instruction in our public schools is at least the best teaching to be found in the country-a fact which is not surprising in view of the years of experience classical masters have to draw upon. Moreover, public-school boys learn initiative, too, through their games and their systems of self-government; in fact, the best products of our public schools are youths of whom we can all, exponents of the heuristic method included, well be proud. It is conceivable that a more sympathetic disposition towards the believers in classical education would strengthen the advocacy, by Dr. Armstrong and others, of the introduction of the teaching of scientific method in all schools and colleges.

Some practical teachers who have acquainted themselves with the reforms urged by Prof. Armstrong, while admitting the truth of his generalisations, are unable to see how they can

satisfy him, please the advocates of commercial and other forms of education, and meet the demands of parents, when they have only something under thirty hours per week at their disposal, and yet must not-they are told-set their pupils any home work. The fundamental questions which have yet to be answered are: What subjects are essential to the curriculum of each grade of school, and how much of the available time should be given to each such subject? Once these questions are decided and entrance examinations to the professions and universities modified accordingly, and teachers will enter heartily enough on the work of reform.

Many of the minor points raised by Prof. Armstrong will not meet with general acquiescence. We think, for instance, that the good text-book will long play an important and useful part in the work of the school. Again, what is possible and right in the education of an individual alone must of necessity be modified when the education of a class is being dealt with, and to urge that boys and girls are not sufficiently treated as individuals in schools is much the same as saying the classes are too large-in other words, that as a nation we are unprepared to spend a sufficient amount on the education of our children. Similarly, to abuse examinations indiscriminately is to lose sight of the fact that, while many schoolmasters and schoolmistresses are very ordinary human beings, with very inadequate training and emoluments, the abolition of every form of examination might lead to a falling off in the present poor quality of our education.

To conclude, it must be said that no teacher can afford to neglect this book; it deserves careful study. The vigorous style and the enthusiasm of its author will probably convince every reader that the book is worth reading more than once.

THE TEACHING OF ARITHMETIC.'

ΤΗ

A REVIEW

By SIR OLIVER LODGE, F.R.S. Principal of the University of Birmingham. HESE two volumes consist of hints and instructions to teachers: they are not intended to be put into the hands of the pupils. They are quite elementary, but they contain occasional information some of which must be new to some teachers, and it would be a pleasure if we could unreservedly commend them: but unfortunately there is a good deal in them that we are constrained to consider pedantic, fidgeting, and over-laborious, and a few things that we think unsound.

These assertions we must make good by quotation, but meanwhile the scope of the volumes may be indicated.

1" The Teaching of Arithmetic" By W. P. Turnbull, M.A., formerly Fellow and Assistant Tutor of Trinity College, Cambridge, and sometime Fellow of St. Catherine's College, Cambridge. Vol 1., pp. VI. <- 225 Vol. II., pp. viii. 208. (London: O. Newmann & Co., 1903.)

Volume I. consists of first principles, the simple rules, a chapter on mental arithmetic, on dealing with concrete numbers, on G.C.M. and L.C.M., then a long treatment of fractions and decimals, concluding with "Practice;" then appendices on the use of Tillich bricks, on series, on a perpetual calendar, and on weights and measures.

The second volume consists of chapters on ratio and proportion, roots, mensuration, a chapter on negative numbers, and on some properties of numbers; with an appendix on remainder-tests.

That the author is well acquainted with his subject and delights in it may be taken as manifest. throughout, and that a teacher may find some useful hints in the book is also true; but there are serious divergences-differences of opinion-between what the author thinks true and sound and what the present reviewer is disposed to agree with. Accordingly most space must be given to criticism, because it is in some of these places that the book is likely to do harm if followed by

too assimilative and docile a teacher.

Very early in the first volume (on page 3) the author says:—

For a sighted child the means I would recommend for showing number is length. Why length?

Given a unit of length, a length which we agree to call "one," all other numbers, integral or fractional, can be represented by length. . .

Conscious exactness, of course, in representing even the number 2, by correctly doubling a given unit, is impossible. For man it is impossible, &c.

.

Length, or Line, is continuous; and, rightly understood, so is Number.

The last sentence we hold to be false, as exhibited in detail in THE SCHOOL WORLD for December, 1902. The former sentences are objected to as needlessly complicating a simple matter. Children, like savages, readily acquire the ideas two and three, &c., and by dealing with objects-say oranges-they get the idea exactly; there is no approximation about it. The idea of approximation is out of place.

On page 5, dealing with bricks, it is said that

The teacher can begin arithmetic by placing on the table a ene and a two, naming each. The children will soon know which is the one, which the two. And so on, up to the ten. At a later stage they will learn that two is greater than one, three greater than two, &c.

Why at a later stage? This sort of elaboration of the simple only worries children. Every child knows almost before he is out of the cradle that two is greater than one. But the author seems to think that the forming of the notion of abstract number is hard :—

The child sees three dogs, three nuts, three fingers, and so on; and from all these groups he extracts or abstracts-that which is common to them all, the number three. The child, in order to perform this abstraction, must get rid of the dog's head and tail, the shell of the nut, the joints and nail of the finger, and so on; which does not seem a very easy task. There must not be different kinds of objects for different No. 59, VOL. 5.]

numbers-three dogs for the number three, four geese for four, five cats for five, and so on. Better keep to dogs throughout than vary the animal. Better have the balls of a ball frame than such complex things as dogs. Better still are the simple Tillich bricks (p. 6).

The idea of six, for instance, is to be developed by showing him repeatedly the brick six. This is said to be much better than talking of a motley assemblage of things-six beans, six apples, six nuts, &c.

Perhaps some teachers may agree with this, but I do not. I hold that to form simple number conceptions, objects are right; and that later on, for the clear perception of fractions and the like, lengths and divided scales are right too, but that they are more difficult and do not come first. Moreover when they do come, they should come experimentally not didactically.

66

On page 8, the author appears willing to confuse digits "figures," "marks," or the children by discussing whether to call the digits." He emphasises the desirability of keeping children for a long time to the lower range before proceeding to numbers above ten; which is probably right in moderation, but it is rather strong to say :

Let the children become expert in dissection, addition, subtraction, multiplication, and sharing, in the range 1 to 10, before the word "eleven" is heard.

At the same time the following quotation from Kehr, on page 9, is surely sensible:

"In no subject of instruction," says Kehr, "is the punishment for haste and hurry so much felt and so lasting as in arithmetic. Is it not a humiliating thing that, in spite of three and four arithmetic lessons a week, many children, even in the upper classes of higher elementary schools, are so slow and inaccurate in the operations within the range I to 100 that they stick fast if asked 37 39, 91 — 46, 4 × 18, or 76 ÷ 4? And yet in practical life most calculations are within that narrow range. The fault lies in this, and in this alone-a rotten, yielding foundation; a foundation not deep and firm."

The author rightly advocates also that children should find out rules for themselves, and be assisted to formulate rules instead of being told them from the beginning; but he overpresses this when he says (on page 17): "Let them find out for themselves that twelve inches make a foot." This is hardly one of the laws of nature that can be ascertained by experiment.

At the same time the following are sensible remarks :-" Do not correct a child who says 'two and three is five'" (p. 18).

"Do not torture children by insisting on their saying 'twice three is six.' 'Two threes are six' is good enough" (p. 19).

"The word unit' is not easily intelligible to children" (p. 19).

In chapter II. the author quotes several curious methods for subtraction, and wisely advocates the "shop" or complementary method as in every way easier and more powerful than the old-fashioned and still ordinary method, whereby the child wastes time by saying or thinking, "six from

K K

three you can't," and then proceeds to mysterious operations of so-called borrowing and paying back, which the author rightly points out is really a method of equal additions:

Thus in taking 269 from 310 we add 110 to each number, and really take 379 from 420.

The author says that there is no logical fault in this common method, but that the method is somewhat unnatural.

It seems a strange thing, when we have to take 27 from 43, to alter the sum and take, instead, 37 from 53, while, if we had been asked to take 37 from 53 in the first instance, we should have altered this sum and taken 47 from 63 (p. 26).

It is indeed an extraordinary method when thus expressed; old-fashioned teachers may fail to recognise their ordinary procedure in this guise, and the author does not make it perfectly clear. But if they will take the trouble to go through the operation of taking 269 from 310 they will find themselves saying 9 from 10 (a ten which is not really there) leaves one, then 7 from 11 (a seven which is not there, from an eleven which is not there) leaves 4, and then 3 from 3 (the first three being not there) leaves o, so that the result is 41; but the course of procedure has been virtually to add a gratuitous digit 1 to every place except the unit places; that is really to add 110 to both numbers.

If any teacher does not believe this and upholds the habitual procedure as the best possible, I would ask him, or perhaps more especially her, to think it possible that he, or she, may be mistaken. On page 29 we are told that—

The sign may be used as an abbreviation either for "times

or for " multiplied by." In the early stages the teacher should

be very clear as to which meaning is intended.

As a reviewer I am bound to say that I do not consider the distinction in the least important. I believe, however, that many teachers will agree with the author rather than with me.

On page 31 a good deal of time and attention is given to this problem :

How many nuts must I have in order to give 5 to each boy in a class of 47 ?

We are told, after a page of discussion, that we must be careful to multiply five by forty-seven and not forty-seven by five, which appears to me an instance of fidgeting pedantry; the reason given being that the forty-seven refers to boys, and the answer is wanted in nuts. I should have thought a thing like that not worth discussing, because any child could see that the answer was 5 X 47.

I wish to maintain parenthetically that the complete statement is as follows:

the above form of statement essentially wrong. It is positively right, however, though I do not assert with any certainty that it is an appropriate mode of treatment for children. I would not be understood as denying even that, however; it is the method which has to be employed, sooner or later, when dealing with comparatively complicated sums in physics and mechanics.

Again, in division, a great deal of attention is paid to the difference between "measuring" and "sharing," and the children are to be able to say which it is that we are doing in any given case.

The answer to the question "What is a third part of twelve?" is "sharing" twelve by three. The answer to the question "How many three's make twelve?" is said to be "measuring" twelve by three.

This distinction is emphasised by the bulk, and even the title, of the chapter, and runs throughout it; but surely it must be regarded as needless? If not, I should welcome instruction on this point from practical teachers. It appears to be a distinction made by German writers. I do not deny the distinction, but I doubt both its emphatic and helpful character. So also a careful distinction is drawn between the factors of a multiplication. The following quotation from page 44 illustrates the author's point of view :

In every multiplication there is a multiplier and a multiplicand. The multiplier multiplies. The multiplicand is multiplied. The very name multiplier" indicates activity; the multiplier is the active factor. The very name "multiplicand," if we know a little Latin, indicates passivity; the multiplicand is the passive factor. When we measure 12 by 3 we are given the product and the multiplicand and we find the multiplier. We are given the product and the passive factor, and measuring may be called "passive" division. When we share 12 by 3 we are given the product and the multiplier and we find the multiplicand. We are given the product and the active facto, and sharing may be called "active" division.

All this is tedious and unnecessary, in my judg

ment.

The teacher is well advised to illustrate sharing and measuring in the sight of the children by such a thing as ribbon, which can be folded and creased; but one of the examples is the following:

Take a ribbon, say 3 feet 2 inches long mark the points 12 inches, 24 inches, and 36 inches on it, and show how you could easily share this ribbon into three equal pieces if it were not for the two inches over at the end.

An extraordinary notion to instil.

Of the two inches each can be cut into three equal pieces, and you find that of the ribbon is 12 inches plus of each of the two inches, or 12 inches. In giving this little lesson the word "measure" should be avoided (p. 51).

On the other hand, the author rightly says that sand and a tin cup are useful to exhibit a remainder; and further on, that a sheet of postage stamps is useful in dealing with area questions.

Concrete quantities the author calls "named numbers" and he has a whole chapter on "Ope rations with Named Numbers." With several