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Digitized by the Internet Archive 
 in 2011 with funding from 
 The Library of Congress 
 
 http://www.archive.org/details/mentaltestsOOball 
 
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 MENTAL TESTS 
 
MENTAL TESTS 
 
 BY 
 
 PHILIP BOSWOOD BALLARD 
 
 M.A., D.Lit. 
 
 AUTHOR OF " OBLIVISCENCE AND REMINISCENCE," AND "HANDWORK 
 AS AN EDUCATIONAL MEDIUM " 
 
 HODDER AND STOUGHTON, LTD. 
 
 LONDON NEW YORK TORONTO 
 1920 
 

 Ms% 
 
 'n 
 
 } 
 
^ 
 
 PREFACE 
 
 The aim of this little book (its achievement is 
 another matter) is to make the teacher his own 
 critic, and the teacher's critic a just and discriminat- 
 ing judge. By the teacher's critic I mean the 
 head master, the inspector or the examiner — whoever, 
 in fact, passes an authoritative judgment on his 
 work. The teacher and his judge do not always 
 see eye to eye ; and the judge, holding as he does 
 the position of authority, is prone to press his point 
 of view. If he cannot convince he commands. 
 And, indeed, if he is to justify his post what else 
 can he do ? A difference of opinion about the 
 temperature of the classroom may be composed 
 by an appeal to the thermometer ; a difference of 
 opinion about the average height of the pupils may 
 be settled by resort to the foot-rule. But in the 
 realm of mind there are, it is thought, no thermo- 
 meters and foot-rules : and we sorely need them. 
 We need objective measurements recognised by 
 all as final and unassailable. Indeed, we shall have 
 benefited but little from the new psychology if we 
 are not, critic and teacher alike, made aware of our 
 own complexes — our whims and grooves and fads — 
 
 v 
 
vi PREFACE 
 
 our prejudices masquerading as principles, and our 
 personal standards laying claim to universality. 
 Even if we cannot identify these complexes, to 
 know that they are there is something : it makes us 
 rigorous in judging ourselves, cautious in judging 
 others, grateful for a means of escape from the 
 precariousness of individual judgment. To provide 
 a few such avenues of escape is one of the purposes 
 of the book. 
 
 A common malady among teachers, especially 
 women teachers, is over-anxiety about their work. 
 They worry about the progress of their pupils, and 
 are peculiarly sensitive to the opinion of those in 
 authority. And those who worry the most are often 
 those who have the least cause for worry. The best 
 cure for this infirmity is knowledge ; knowledge of 
 the pupils, their aptitudes and attainments ; know- 
 ledge of the best means of measuring progress and 
 assessing results ; knowledge of what can be done 
 by other children, and other teachers. And it is 
 hoped that a little wholesome medicine of this kind 
 will be found in these pages. 
 
 The solution offered depends ultimately on 
 measurement. There are some who instinctively 
 dislike the idea of bringing measurement into educa- 
 tion. They urge that the highest products of 
 education, being spiritual, are outside the realm of 
 time and space to which measurements properly 
 belong. A partial reply to this argument will be 
 found in Chapter I. Here I will merely observe 
 
PREFACE vii 
 
 that it is possible to extend the notion of measure- 
 ment beyond the physical realm ; and that the 
 fact that some of the products of education cannot 
 be measured is no reason why we should measure 
 none. We do, in fact, measure, either well or ill, 
 whenever we examine. If we examine at all we 
 should examine well ; and to examine well is to 
 measure accurately. 
 
 No claim of novelty is made for the way in which 
 the subject is treated. Much space is devoted to 
 putting before the reader the attempts made in 
 England and abroad to arrive at a scientific system 
 of testing. The author's own modest contributions 
 to the science are to be found mainly in the chapters 
 on Reading and Arithmetic. 
 
 In a slightly different form some of the chapters 
 have already appeared in the Times Educational 
 Supplement and in the Journal of Experimental 
 Pedagogy ; and for permission to reprint them I 
 am indebted to the courtesy and kindness of the two 
 editors concerned. The chapter on the Develop- 
 ment of Mental Tests was read before the Educa- 
 tional Section of the British Psychological Society, 
 and the chapter on Practical Ability before the 
 Educational Handwork Association. 
 
 My personal obligations are many. To the 
 teachers who have so ungrudgingly helped me to 
 standardise the tests ; to Professor T. Percy Nunn for 
 his valuable criticism of the chapter on Distribution 
 and Dispersion ; to Dr. Emrys Jones for correcting 
 
viti PREFACE 
 
 the proofs — to all these I am deeply grateful. But 
 of all my debts of gratitude by far the biggest is due 
 to my friend Mr. Cyril Burt, who has not only let 
 me use his revision of Binet's Tests, and include his 
 tests of Reasoning and of Spelling, but has carefully 
 read through the whole of the manuscript and given 
 me the benefit of abundant criticisms and sugges- 
 tions. And all this did he do spontaneously : he 
 volunteered his help when he heard that I was 
 writing on Mental Tests — an act of generosity made 
 all the more striking by the fact that he himself 
 is about to bring out an important book on the same 
 subject. 
 
 P. B. Ballard. 
 
 Chiswick, 1920. 
 
CONTENTS 
 
 CHAP. 
 
 PREFACE . 
 
 I. THE DEVELOPMENT OF MENTAL TESTS 
 II. INTELLIGENCE AND KNOWLEDGE 
 
 III. THE MEASUREMENT OF INTELLIGENCE 
 
 IV. BINET'S TESTS OF INTELLIGENCE 
 V. BURT'S REASONING TESTS 
 
 VI. THE MEASUREMENT OF KNOWLEDGE . 
 
 VII. DISTRIBUTION AND DISPERSION 
 
 VIII. READING — 
 
 (a) AS A MECHANICAL ART . 
 
 (/;) AS A MEANS OF ACQUIRING IDEAS 
 
 IX. SPELLING ..... 
 
 X. ARITHMETIC — 
 
 (a) THE FUNDAMENTAL PROCESSES 
 {b) SIMPLE ORAL ARITHMETIC 
 (f) ARITHMETICAL DEVICES 
 (d) APPLIED ARITHMETIC . 
 
 XI. PRACTICAL ABILITY 
 
 XII. COMPOSITION 
 
 APPENDIX. SOCRATES ON INTELLIGENCE 
 
 INDEX ...... 
 
 PAGE 
 
 V 
 
 I 
 
 22 
 29 
 48 
 90 
 I06 
 115 
 
 134 
 145 
 
 155 
 
 l6o 
 186 
 I90 
 191 
 
 196 
 
 2IO 
 
 221 
 
 233 
 
 IX 
 
MENTAL TESTS 
 CHAPTER I 
 
 THE DEVELOPMENT OF MENTAL TESTS 
 
 It is a truism to say that advance in any branch 
 of physical science is largely dependent on improve- 
 ment in its mathematics. As the science develops 
 it gets more and more precise. It begins by being 
 qualitative only : it ends by being quantitative as 
 well. Indeed, no generalising idea, however illumin- 
 ating it may seem, can establish its validity and 
 become recognised as a law of nature, unless it can 
 be proved by the exact measurement of the facts 
 it is designed to unify and explain. Jevons, in his 
 Principles of Science, points out that Newton held 
 back his theory of Gravitation for fifteen years 
 because he found that it did not fit the accepted 
 facts about the orbit of the moon. When it was 
 possible to measure the orbit more exactly it was 
 found that the revised figures, instead of refuting 
 his theory, confirmed it to the full. Wisely or 
 foolishly he rejected the undulatory theory of light 
 in favour of the corpuscular because he had no 
 means of measuring with sufficient precision the 
 way in which, and the extent to which, a ray of 
 light is bent out of its course by the edge of an 
 
 B 
 
MENTAL TESTS 
 
 opaque body. A still more striking instance of the 
 importance of precise measurement is afforded by 
 the recent achievements of Einstein. Everybody, 
 indeed, admits the importance of measurement in 
 physical things, but when it comes to mental things 
 people become sceptical. They admit that measur- 
 ing would be admirable if it could be done ; but it 
 cannot be done. We can measure sticks and stones, 
 but we cannot measure ideas. We can fathom the 
 depth of a well, but we cannot fathom the depth of 
 an emotion. That is the opinion of the frank 
 opponents of mental measurements. The other 
 side is concisely put by Thorndike : " Everything that 
 exists exists in some amount, and if it exists in some 
 amount it can be measured." Here we have the 
 creed of the mental tester : the belief that in some 
 way or other, at some time or other, the most 
 subtle mental processes and the" most elusive mental 
 products will be made amenable to measurement. 
 It is not the test itself that is so difficult : it is the 
 evaluating of the product, giving to the result a 
 definite position in a graduated scale, assigning to it, 
 in fact, a number, a mark or a score ; and so 
 assigning it that it has objective value. It must 
 not be a guess, but a genuine measurement arrived 
 at by means of a technique which would in every- 
 body's hands yield, within assignable limits of error, 
 the same score. 
 
 Mental tests are as old as the human race. A 
 man never consciously and deliberately learns any- 
 thing without testing himself ; he never effectively 
 teaches anything without testing his pupils. All 
 competitive examinations and all school examina- 
 tions are series of mental tests. And we know that 
 
DEVELOPMENT OF MENTAL TESTS 3 
 
 competitive examinations began in China nearly 
 4000 years ago, and that school examinations are 
 as old as schools. Then there are the mental tests 
 that figure so largely in legend and story, the 
 riddles that baffle the learning of the learned and 
 are solved by the wisdom of the simple. (Edipus and 
 the Sphinx, Samson and the lion, are types of stories 
 where the test is of mental prowess as distinct from 
 bodily prowess. But these were mere pass-or-fail 
 tests : they were not designed to graduate, but 
 merely to select or sift. 
 
 The earliest attempts at real mental measurements 
 were of the nature of indirect measurements. Just 
 as we cannot measure electricity directly, but by 
 measuring something else whose size varies con- 
 comitantly with the strength of the electric current 
 can get a result which serves our purpose just as 
 well, so it was thought that some kind of vicarious 
 measurement might be found for the mind. And 
 the most plausible concomitant was the head. 
 This was the idea of Gall, the father of Phrenology. 
 At the close of the eighteenth century he and his 
 disciple, Spurzheim, taught that the head was an 
 index of the brain, and the brain an index of the 
 mind. They did not go so far as to say that a big 
 head meant a big mind, but they did assert that the 
 relative proportions of the skull and the configura- 
 tion of its surface, would, when exactly measured, 
 yield an exact indication of the mental powers. 
 The palmy days of phrenology were the early 
 decades of the nineteenth century. Nearly every- 
 body then believed in bumps. My readers will 
 recall an account of a certain dinner-party where 
 an unaccustomed guest solemnly asked the company 
 
MENTAL TESTS 
 
 whether they did not think Milton a great poet ; 
 and Charles Lamb, who was present, said he wanted 
 to feel the gentleman's bumps. Indeed, most of 
 us can remember the day when the cultured house- 
 hold was prone to lay great store by a china head 
 mapped out in plots. But we no longer display 
 these things in the home, nor use them in the study. 
 Phrenology has, in fact, failed to establish its claims. 
 If it is science at all it differs from all other sciences 
 by standing still. The charts that we see to-day 
 in O'Dell's window in Ludgate Circus are to all 
 intents and purposes the charts used by Gall and 
 Spurzheim a hundred years ago. 
 
 Older even than phrenology is physiognomy. 
 Nearly thirty years before Gall expounded his 
 theory of the skull Lavater put forward his theory 
 of the face. In the year 1772, when Gall was a 
 boy of fourteen, Lavater published his celebrated 
 essay on Physiognomy. His doctrine was that the 
 face, not the cranium, was the index of the mind. 
 A man's fighting qualities, for instance, resided in 
 his nose. A nose that protruded near the root like 
 a Roman nose meant an aggressive disposition. It 
 was the nose of attack. If it protruded in the 
 middle it meant a propensity to fight for others. 
 If it protruded at the point it meant an aptitude 
 for self-defence. The retrousse nose was neither 
 inquisitive nor self-assertive, but merely self- 
 defensive. 
 
 Shrewd as some of Lavater's observations were, he 
 made the fundamental mistake of confusing the 
 bony structure of the face with its fleshy covering. 
 He regarded the contours of the cheek-bone as 
 much an expression of character as the lines round 
 
DEVELOPMENT OF MENTAL TESTS 5 
 
 the mouth. Many years later, after the science 
 had emerged somewhat from the eclipse into which 
 it had been thrown by phrenology, the study of the 
 face was taken up afresh by scientists like Bell and 
 Darwin. They, however, definitely discarded the 
 osteology of the face in favour of its sarcology, and 
 devoted their attention to the mobile and plastic 
 covering, the changes in which seemed to betoken 
 the prevailing modes of thought and feeling. 
 Physiognomy became, in fact, the science of expres- 
 sion, and only indirectly and suggestively the science 
 of character and intellect. If a man, for instance, 
 has crow's-feet round his eyes before he is forty, 
 it seems no very wild conjecture to assume that he 
 smiles much and is of an amiable disposition. But 
 as weak eyes, as well as a kind heart, may cause 
 crow's-feet, the inference becomes somewhat pre- 
 carious. Indeed, Darwin never pretended that 
 physiognomy was an exact science. We cannot 
 measure a smile or a sneer or a look of surprise. 
 Heine states in his Florentine Nights that he 
 does not know whether the mouths of Parisian 
 women are large or small, because one can never 
 tell where the mouth leaves off and the smile 
 begins. 
 
 The next attempt to physiologise the mind was 
 Lombroso's. He was a criminologist who tried to 
 find the bodily peculiarities that went with con- 
 firmed evil-doing. He searched for certain marks 
 or malformations which he called stigmata, and 
 which he thought would distinguish the criminal 
 type. A lack of symmetry, for instance, in form 
 or feature was supposed to be one of the common 
 signs of degeneration. We admit its commonness, 
 
MENTAL TESTS 
 
 for we are all in some degree branded with it. 
 This line of research, however, has fallen into 
 discredit. It is now-a-days believed that if there 
 is a criminal type we must seek its characteristics 
 in the mind and its behaviour, rather than in the 
 body and its anatomy. 
 
 The man who gave the greatest impetus to mental 
 measurement in England was Sir Francis Galton. 
 But he was primarily an anthropologist, with a 
 bias towards physical measurements and com- 
 parative anatomy. He was imbued with a belief 
 that some sort of correspondence could be found 
 between intelligence and certain bodily traits, such 
 as the length of the middle finger, the character of 
 the finger-prints, and the span of the open arms as 
 compared with stature. And researches in this 
 direction have not proved altogether fruitless. If 
 they did nothing else they gave us the Bertillon 
 system of identification by finger-prints. But they 
 did not bring us appreciably nearer the object of 
 our quest. The physical correlate of intelligence 
 was still undiscovered. It was left to Professor 
 Karl Pearson to deliver the most crushing blow to 
 the belief that we can find a physical scale for 
 mental facts. In 1906 he published the result of 
 an elaborate investigation into the relationship 
 between intelligence and the size and shape of the 
 skull. And his verdict was that the connection 
 between them, if it existed at all, was so slight as 
 to be of no use for purposes of inference. Here 
 ends the first phase of the search for a scale to 
 measure mind. The conclusion reached was definite 
 enough, but entirely negative. We cannot tell 
 a criminal by looking at him ; we cannot tell a genius 
 
DEVELOPMENT OF MENTAL TESTS 7 
 
 by the shape of his skull ; and we cannot tell a fool 
 by the length of his ears. 
 
 But this does not dispose of physical measurements. 
 For it was next argued that although we cannot 
 measure the mind by measuring the body, we may 
 be able/ to do so by measuring the powers of the 
 body. /A static measurement failed, but a dynamic 
 measurement might succeed. For as soon as the 
 body does something, unless that something is 
 purely automatic, the mind co-operates in the work. 
 Volition, at least, is brought into play. This view 
 led to experiments with the various instruments 
 for measuring muscular strength and skill. The 
 dynamometer, for instance, measures the strength 
 of one's grip, and the ergograph the strength and 
 endurance of the middle finger. But valuable as 
 these instruments were for testing fatigue, they 
 revealed no sort of relationship between mental and 
 muscular traits. The tapping test was more promis- 
 ing. In its simplest form it consists in seeing how 
 many taps per second the subject can make with a 
 pencil on paper. It is found that one can tap 
 faster with the right hand than with the left, and 
 it is a conceivable hypothesis that a very stupid 
 person is, if I may use an Irishism, left-handed all 
 over his body. But although tapping afforded some 
 indication of motor ability it did not signify the 
 presence of any form of intellectual ability. 
 
 Reaction-time experiments ran on the same line. 
 It was found that people differed considerably in 
 the rapidity with which they responded to a 
 stimulus ; and a delicate apparatus was devised to 
 measure the time that elapsed between the hearing 
 of a sound and the pressing of a button ; or between 
 
8 MENTAL TESTS 
 
 some other signal and some other motor response. 
 This test is an excellent vocational test. Rapid 
 reaction is important to the boxer, whose aim is to 
 get his fist in first, and to the airman who needs, 
 at the sight of danger, to press the right lever at the 
 right time in response to the right signal. 
 
 It will be observed that the quest begins to lose 
 its singleness of purpose. The measurements began 
 by being physical, then they became psycho physical, 
 ultimately they became almost purely psychical. 
 As soon as the psychical element came in at all, 
 any measurement that was achieved was to a certain 
 extent a psychical measurement. But to measure 
 a particular mental function for its own sake is one 
 thing : to measure it in the hope of finding it an 
 index of general mental ability is quite another thing. 
 The latter has always been the bigger problem ; 
 but the former is by no means devoid of purpose and 
 value. To be able to measure any mental function 
 whatever, however limited its operation, is no mean 
 achievement, and in the types of experiments to 
 be now recounted definite measurements have been 
 attained which have proved valuable in develop- 
 ing psychological theory, and serviceable in their 
 application to various pursuits in life. It is only 
 in the larger quest that they have comparatively 
 failed. 
 
 In the nineteenth century attempts were made to 
 measure sensations. Weber put forward his cele- 
 brated law, which was afterwards interpreted and 
 elaborated by Fechner. It was supposed to establish 
 a relationship between the physical stimulus and the 
 sensation it produced, or, rather, between the way 
 in which an increase in the intensity of the stimulus 
 
DEVELOPMENT OF MENTAL TESTS 9 
 
 was accompanied by an increase in the intensity 
 of the sensation. In the sixties and seventies of 
 last century the Weber-Fechner law gave rise to 
 numerous discussions. While some thought that it 
 revealed the connecting-link between mind and 
 body and was of immense metaphysical import, 
 others held that it was merely an instance of the 
 general law of relativity : it merely illustrated the 
 fact that we judge things not absolutely but 
 relatively. But although the Weber-Fechner law 
 is regarded as of little importance now-a-days — of 
 little importance to the educationist at least — the 
 researches to which it led have considerably advanced 
 the science of mental measurements. Means were 
 devised, for instance, for measuring the acuity of 
 the various forms of sense-perception, particularly 
 of seeing and hearing. More important still, it led 
 to the measurement of sensory discrimination — of 
 the fineness with which we can detect differences 
 in things. For it was suspected that here lurked 
 the clue for which the intelligence-hunters were 
 searching. Indeed, the comparison of lines and the 
 comparison of weights are widely used to-day as 
 tests of intelligence. It was sensory discrimination 
 in the skin, however, that gave rise to the most 
 sanguine hopes. Early in this century an eminent 
 psychologist expressed the belief that he had found 
 a trustworthy instrument for measuring general 
 intelligence. That instrument was the Eesthesio- 
 meter. The sesthesiometer consists of a pair of 
 sharp points, like the points of a pair of compasses, 
 one of which can be shifted back and fore on a 
 graduated scale. When the points are applied to the 
 skin of a blindfolded subject they are felt as one 
 
io MENTAL TESTS 
 
 point unless they stand a certain distance apart. 
 The least distance apart at which they are felt as 
 two points is the discrimination threshold. It was 
 believed that the sensitivity of the skin, as indicated 
 by this threshold, was a key to the acuteness of the 
 mind ; that if a man was thick-skinned he was 
 thick-headed as well. But when the supporters of 
 this theory tried to prove it they found they 
 could not do so. It was found that if sensory dis- 
 crimination of the skin was an index of anything at 
 all, it was just as likely to be of stupidity as of 
 intelligence ; for McDougall and Rivers were able 
 to show that the savages on the shores of the Torres 
 Straits had more discriminative skins than Europeans. 
 So the sesthesiometer was, after all, merely an 
 sesthesiometer and not a phrenometer : it measured 
 sensitivity, but not sensibleness. 
 
 The scientific study of memory began with 
 Ebbinghaus, who was the first to measure memory 
 in its simplest form — in the form of retaining and 
 reproducing nonsense syllables — sounds devoid of 
 all sense and all associations. He laid the foundation 
 of modern laboratory methods of testing memory, 
 and of the distinction made in all pedagogical tests 
 between rote memory and substance memory. 
 Galton devised rough-and-ready means of estimating 
 the vividness of visual imagery. Later psychologists 
 have used ink-blots for measuring the rapidity with 
 which images emerge in the mind. A series of blots 
 are shown the subject, and a record made of the 
 time he takes to name the object suggested by 
 each. 
 
 It were both tedious and superfluous to take the 
 reader through the various means that have been 
 
DEVELOPMENT OF MENTAL TESTS n 
 
 invented for measuring the different mental faculties 
 — processes which, in fact, are neither simple nor 
 separate — processes such as attention, perception, 
 apperception, memory, imagination and reasoning. 
 And whenever an instrument or piece of apparatus 
 is used for any of these purposes it is always impossible 
 to claim that it singles out and tests one simple 
 and unitary mental function. One of the most 
 useful pieces of apparatus, for instance, in the 
 psychological laboratory is McDougall's dotting 
 machine. A strip of paper marked with an irregular 
 zig-zag row of small circles passes at a rate regulated 
 by clock-work behind a slot which enables only a 
 small number of circles to be exposed at a time. 
 The subject has to mark with a pencil the centre 
 of each circle as it passes before him. This machine 
 is used to test fatigue, to test attention and to test 
 accuracy of aim ; and there may be other kinds of 
 ability that it tests as well. 
 
 In the meantime, while specific tests were being 
 rapidly devised and improved, what progress took 
 place in the measurement of general intelligence ? 
 This can be best illustrated by reference to the 
 experiments of Mr. Cyril Burt, who has done more 
 to solve this particular problem than any other 
 British psychologist. Mr. Burt began his investiga- 
 tions among school-children in Oxford about the 
 time that Binet published his first series of tests in 
 1905. His method was to select the group of 
 children in a school who fell within certain age 
 limits (say from twelve and a half to thirteen and a 
 half years old), and to get the head teacher and class 
 teachers to arrange these children in order of intel- 
 ligence, relying partly on their empirical judgment, 
 
12 MENTAL TESTS 
 
 and partly on the results of the school examina- 
 tions. Then the children were given individually 
 twelve psychological tests, ranging from simple 
 sensory and motor tests to tests of voluntary atten- 
 tion, and it was calculated to what extent the 
 results tallied with the teachers' empirical estimate. 
 The higher the correlation between the two orders, 
 the more satisfactory was the test regarded as an 
 index of intelligence. Some five years later Mr. Burt 
 made a further investigation at Liverpool, using 
 tests of a higher and more complex kind — extending 
 them, in fact, so as to include various types of 
 reasoning. He was thus able to range in a sort of 
 hierarchy, on the basis of their value as criteria of 
 intelligence, a large series of tests involving mental 
 processes of widely varying levels. And the con- 
 clusion he arrived at was that when we have arranged 
 them in the order of their complexity we have already 
 roughly arranged them in their order as intelligence- 
 measurers. And of all the tests of intelligence those 
 that measure the power of thinking, that is, the 
 power to understand and to reason, are the best. 
 Thus is common sense vindicated by the psychologist- 
 Thus we have arrived at the conviction that if we 
 wish to test intelligence we must test it directly 
 and not indirectly : we must test those very mental 
 processes which the plain man regards as intelligent. 
 We must note whether the subject is " quick in the 
 uptake," whether he has " nous " or " gumption," 
 whether he can " see beyond his nose." And it 
 will be observed, too, that instruments and machines 
 have been relegated to the psychological laboratory, 
 where they are of inestimable value both to pure 
 psychology and to certain branches of applied 
 
DEVELOPMENT OF MENTAL TESTS 13 
 
 psychology. For educational purposes they are of 
 little use. At any rate, it is certain that no machine 
 has yet been invented which will measure intelli- 
 gence ; and faith in the possibility of such a machine 
 is growing fainter every day. We now regard 
 laboratory tests and school tests as distinct things — 
 a position which was taken up from the very first 
 by that pioneer of educational experiments, Mr. 
 Winch. 
 
 At this stage we have abandoned certain specious 
 by-paths which seemed to lead to the desired goal, 
 and we have found the true path, which has, after 
 all, proved to be the common high road which the 
 mass of humanity has been treading all along. But 
 in one sense we are as far from the goal as ever. We 
 know the kind of test to be applied, but we have no 
 scale. We can test, but we cannot measure. It 
 was left for Binet to discover the scale. And the 
 full significance of his discovery is rarely realised. 
 His critics — and they are very numerous — have bee a 
 so concerned in pointing out what he has not done 
 that they have neglected to give him credit for what 
 he has done. And Binet's crowning glory is, not 
 that he got together a medley of heterogeneous tests 
 for the detection of the feeble-minded, but that he 
 invented a scale. In this he resembles Saul, the 
 Son of Kish, who set out to look for asses and found 
 a kingdom. Binet's scale is his kingdom ; not the 
 individual tests — these may so change that there is 
 nothing recognisable left — but the scale itself. 
 Its principle is age-performance. He took a certain 
 test, such as, say, counting backwards from twenty to 
 nought, applied it to a large number of children, 
 found the lowest age at which between 60 and 70 per 
 
1 4 MENTAL TESTS 
 
 cent, of the children passed, and allocated the test 
 to that age. Thus he has a series of about five 
 tests for each age ; and if a child of five passes the 
 tests for seven, his mental age is recorded as two years 
 in advance of his chronological age. Thus the unit 
 of his scale was one year of mental age. It was a 
 plan so simple and obvious that one wonders that it 
 never was used before. But it is certain that it 
 never was. We came near it in the old Standards 
 of Examination that were issued by the Board of 
 Education in the days of payment by results. But 
 they just missed it through being an arbitrary scale, 
 based on opinion and not on actual age-performance. 
 And in modern standardised tests the standard is 
 always actually, or ideally, an age-performance. 
 
 Binet regarded intelligence as a complex process 
 whose main characteristics were threefold : its 
 purposefulness, its capacity for making adaptation, 
 and its power of self-criticism. He therefore made 
 his tests as heterogeneous as possible. He looked 
 everywhere for tests, and showed much sagacity in 
 finding those that were simple, practical and effective. 
 They involve such ordinary questions as : " Are you 
 a little boy or a little girl ? " and such unusual 
 problems as : Put the following words in such order 
 that they make sense — 
 
 To Asked Spelling 
 My I Master 
 Correct My. 
 
 And he used no apparatus. The only material 
 required, beyond what is found in an ordinary school- 
 room, is a series of five pill-boxes similar in size 
 and appearance, but differently loaded. 
 
DEVELOPMENT OF MENTAL TESTS 15 
 
 Binet's scheme led to abundant controversy. 
 Indeed, the literature of the controversy would fill a 
 small library. Everybody abused Binet, and every- 
 body used him. They said his tests were very bad, 
 but they were the best we had. If Binet had lived 
 he would have improved his tests, for he was con- 
 tinually revising them. He, indeed, issued three 
 series— the 1905, the 1908 and the 191 1 series — each 
 an improvement on the previous one ; and just 
 before he died in 191 3 he was engaged in making ^' 
 another revision. His line of research was en- 
 thusiastically taken up in America, where three 
 important revisions were issued, the Goddard 
 revision, the Yerkes point-scale revision (where the 
 method of marking was changed), and finally the 
 revision that should be best known in this country, 
 the Stanford revision, carried out by Terman. The 
 basis in each case was Binet, and the alterations 
 and extensions were matter of detail rather than of 
 principle. The tests applied to the recruits for 
 the American Army were partly based on Binet ; 
 the tests used for Matriculants at Columbia Uni- 
 versity were inspired by Binet's, and the tests used 
 in Berlin to select supernormal children are imitative 
 of Binet's. The only extension of principle is the 
 addition of group-tests. Binet's tests are indi- 
 vidual, and it takes from half-an-hour to an hour 
 to examine a single subject. A large number of 
 new tests have been devised, which may be applied 
 simultaneously to a large number of pupils ; but 
 they agree with Binet's in being age-performance 
 tests, and in being tests of intelligence rather than 
 of acquired knowledge. 
 
 The latest development of the Binet system is 
 
1 6 MENTAL TESTS 
 
 to be found in Burt's system of Reasoning Tests ; 
 or rather, it is the logical outcome of Burt's own 
 theories, for the only part of Binet's system that he 
 retains is the age-performance basis of selection. 
 The tests themselves he rejects. If intelligence, 
 which Burt defines as " inborn all-round mental 
 efficiency " is mainly manifested in the higher 
 mental processes, the best intelligence tests would 
 embody various forms of reasoning, and would omit 
 all reference or appeal to the lower mental processes. 
 Burt has, accordingly, recently published a series of 
 fifty reasoning tests, which are the best of an initial 
 list of 250 that were tried on miscellaneous groups 
 of children and adults. The questions are not the 
 usual syllogistic questions of traditional logic, but 
 involve the application of thought to the ordinary 
 affairs of life. Where the purpose of the test is to 
 pick out the brightest children rather than to pick 
 out the blockheads, these tests will, in my opinion, 
 prove far more satisfactory than Binet's. They are 
 new as yet and have not been extensively used ; 
 but I believe there is a great future for them. 
 They display much ingenuity, and the more difficult 
 tests are far more likely to pick out what Terman 
 calls the superior adult than Ter man's own tests. 
 
 So much for intelligence tests. But this is only 
 one of the fields in which the technique of mental 
 testing has been improved, and in which it has been 
 put to practical purposes. Laboratory apparatus 
 and laboratory methods have been rapidly improving 
 within recent years, and psychological tests have 
 been applied with great success in the realms of 
 medicine, business and industry. To describe these 
 developments here is outside my scope ; I must 
 
DEVELOPMENT OF MENTAL TESTS 17 
 
 limit myself to mental tests in the educational 
 realm, and so far I have not touched the measure- 
 ment of school attainments. 
 
 Our success in securing standardised tests and 
 standardised measurements depends mainly upon 
 three mathematical discoveries. One of these I 
 have already dealt with — that of age-performance. 
 Before Binet's day we tried to measure one unknown 
 by another unknown. We tried to test mental 
 processes by means of tests whose difficulty was 
 merely a matter of guess-work. We knew neither 
 their absolute nor their relative difficulty. Binet 
 gave us a method by which the difficulty of the tests 
 could be graded and standardised. But he himself 
 seems to have made no use of the other two mathe- 
 matical conceptions which have largely advanced 
 the science of mental measurements — the theory 
 of normal distribution, and the theory of correla- 
 tion. It was Quetelet, the Belgian mathematician, 
 who showed how widely applicable was the law 
 of normal distribution, what a large number of 
 social and physical phenomena were found to follow 
 the normal curve, and how the form of distribution 
 could be deduced from the laws of probability. But 
 it was Galton who suggested that mental traits 
 generally, and intelligence in particular, would be 
 found to follow the same law. And to-day this 
 curve is universally used to test tests and to certify 
 them. If the results do not conform to the normal 
 curve they at once become suspect. Goddard and 
 Terman have amply demonstrated that Binet's 
 tests triumphantly stand this criterion of validity. 
 To Galton, too, we are mainly indebted for the 
 doctrine of correlation, which has proved so valuable 
 c 
 
1 8 MENTAL TESTS 
 
 an instrument in determining the extent to which 
 two orders of measurements tally with each other — 
 or, in other words, the extent to which two functions 
 vary concomitantly. The doctrine of Correlation 
 was developed and elaborated by Professor Karl 
 Pearson, to whom we owe the formula most com- 
 monly used. Professor Spearman discovered a 
 formula of correlation which, although not so 
 strictly accurate as Karl Pearson's, is much simpler 
 to use, and is quite satisfactory when the rank only 
 of the subjects is known. This correlation formula 
 was extensively used by Burt, and has figured 
 largely in the exposition and proof of the doctrine 
 of Intelligence as conceived by Spearman and his 
 school. 
 
 Another device which has proved of great service 
 is that of " equal grasps," invented by Mr. Winch. 
 Each child in one group is paired with another 
 child of equal merit in the other group. Such an 
 arrangement enables the experimenter to estimate 
 the efficacy of a new method of teaching, or to 
 compare the efficacy of two rival methods ; for one 
 group may be taught by one method and the 
 other group by the other method. 
 
 It remains for me to deal with the development 
 of mental tests in the realm of school studies — a 
 realm where mental tests in the form of examina- 
 tions have from time immemorial been regarded 
 as an essential part of the school machinery. But 
 the newer system of school tests differs essentially 
 from examinations. An examination, however care- 
 fully it is conducted, is a test of comparative ability. 
 It enables the examiner to arrange his examinees 
 in order of proficiency. But it does not enable 
 
DEVELOPMENT OF MENTAL TESTS 19 
 
 him to compare the proficiency of the group as a 
 whole with the proficiency of any other group as 
 a whole, nor yet with the normal achievement of 
 other pupils under similar conditions of age and 
 schooling. For a public examination is like a 
 rocket : it can be used but once. It measures, it 
 is true ; but it measures the individuals of a group 
 one against the other : it does not measure them by 
 reference to a standard scale. The newer tests, 
 on the other hand, are standardised tests : they are 
 tests whose difficulty is already known in terms of 
 age-achievement. The separate tests, of which an 
 examination consists, are either regarded as carrying 
 equal marks, or as carrying marks which vary in 
 accordance with the examiner's opinion of their 
 difficulty or their importance. Standardised tests, 
 on the other hand, do not depend for the marks 
 they carry on anybody's mere opinion, but rather 
 on their difficulty as experimentally determined. 
 The tests are tested and standardised by a mathe- 
 matical analysis of the results obtained by applying 
 the tests to a large number of children. The sub- 
 jective element is reduced to a minimum, and the 
 objective element raised to a maximum. 
 
 The extent to which objective tests of school 
 studies are possible depends partly on the study 
 itself, and partly on what aspect of the study it is 
 desired to test. Proficiency in arithmetic, for 
 instance, is easier to test objectively than pro- 
 ficiency in English composition ; and proficiency in 
 the fundamental processes of arithmetic easier than 
 proficiency in the capacity to apply these processes. 
 This difference in the degrees of objectivity is still 
 more readily seen in the attempts that have been 
 
2 o MENTAL TESTS 
 
 made to measure the various aspects of reading. 
 For proficiency in reading depends upon at least 
 three distinct types of ability — ability to translate 
 symbols into sounds, ability to absorb meaning, 
 and ability to read aloud so as to make the meaning 
 intelligible to others. These are concerned with 
 the mechanical aspect, the intellectual aspect and 
 the elocutionary aspect respectively. The first 
 ability is easy to measure, the second difficult, the 
 third almost impossible. Apart from a few abortive 
 experiments with the dictaphone nobody has ever 
 attempted to invent standardised tests of elocu- 
 tionary power. 
 
 In America alone have educational tests received 
 the attention they deserve. There a number of 
 tests have been devised and norms established in 
 arithmetic, reading, spelling, grammar, geometry 
 and algebra. All these rest on the same basic 
 principle as Binet's Intelligence tests, except that 
 grade-performance is substituted for age-perform- 
 ance. The standardised tests in composition, and 
 handwriting and drawing, however, involve an 
 entirely new principle — a principle which, though 
 not invented by Professor Thorndike, is mainly 
 associated with his name. It consists in devising 
 a scale of typical specimens, a scale arrived at by 
 collating the opinions of a number of independent 
 judges. When it is wished to mark a particular 
 paper, it is compared with the specimens of the 
 standard scale with a view to discovering to which it 
 is most nearly equal in merit. If the variability in 
 the marking of the same set of papers by a number 
 of independent teachers is less when the scale is 
 used than when it is not used, it is claimed that 
 
DEVELOPMENT OF MENTAL TESTS 21 
 
 the use of the scale is justified. As a matter of fact 
 it is found that after some practice in the use of 
 the scale the variability is less ; but not so much 
 less as to give this type of measurement any very 
 high degree of objective validity. Even in America 
 the scales are not used much. In England they are 
 not used at all. But the other scales are to a certain 
 extent. We have not, in this country, gone far in 
 the invention of tests and the establishments of 
 norms ; but we have begun the work, and we are 
 slowly but steadily forging ahead. 
 
CHAPTER II 
 
 INTELLIGENCE AND KNOWLEDGE 
 
 All who have given serious thought to education 
 have been wont to exalt intelligence at the expense 
 of knowledge. " Wisdom," says an ancient writer, 
 " is the principal thing ; therefore get wisdom ; 
 and with all thy getting get understanding." And 
 although by wisdom he doubtless meant something 
 more than intelligence, he at least meant intelligence. 
 On the other hand, " he that increaseth knowledge 
 increaseth sorrow." Here in these far-off times we 
 see recognised a distinction which has much exer- 
 cised the mind of the modern educationist — the 
 distinction between wisdom and learning, intelli- 
 gence and knowledge, mental power and mental 
 content. 
 
 The cry for intelligence was acutely clamant 
 in the first decade of the twentieth century. The 
 primary schools had just recovered from the cramp- 
 ing effect of annual examinations and had begun to 
 breathe more freely. Intelligence became a cult 
 and a quest and a watchword. Teachers aimed at it ; 
 inspectors looked for it ; administrators encour- 
 aged it. There was a " slump " in accuracy and 
 a " boom " in intelligence. And the educational 
 psychologist, seeing herein a promising field for his 
 labours, began to investigate intelligence and to 
 
INTELLIGENCE AND KNOWLEDGE 23 
 
 cast about for means to measure it. Although 
 Binet's name was alone prominent before the public, 
 he was by no means the only investigator ; nor, 
 perhaps, the most original. Still, the work he 
 achieved was great. He had a genius for discerning 
 what was worthy in the work of others ; he cast his 
 net so wide that nothing valuable escaped him ; 
 and — most important point of all — he kept a steady 
 eye on practicability. 
 
 But while the teacher tried to cultivate intelli- 
 gence, and the psychologist tried to measure in- 
 telligence, nobody seemed to know precisely what 
 intelligence was. It was certain that the term 
 covered a wide field. When at a recent meeting 
 of an education committee a member asserted that 
 teachers as a body were highly trained and intelli- 
 gent, an opponent (advocatus diaboli) retorted that 
 the same was true of elephants. Clearly there was 
 need to sharpen and define the term. It is not 
 enough to say that it means ability as distinct from 
 knowledge, capacity as distinct from content, power 
 as distinct from product. For how can we gauge a 
 mind's capacity except by finding out what it can 
 contain ? But what it contains is knowledge. And 
 how can we measure a mind's power without 
 measuring its product ? But its product is, again, 
 in part at least, knowledge. Binet saw this diffi- 
 culty, and frankly accepted knowledge as one of the 
 many marks of intelligence. One of his earlier 
 intelligence tests, for instance, for a child of nine 
 is : name in order the days of the week. He would 
 probably argue that a child of nine who in his inter- 
 course with his fellow-creatures had not picked up 
 these names was necessarily somewhat stupid, 
 
24 MENTAL TESTS 
 
 Binet was inclined to adopt the easy-going attitude 
 of the artist, who does not mind a notion being 
 nebulous so long as it is workable, rather than that 
 of the scientist, who strives for precision and con- 
 sistency at all costs. 
 
 There are other psychologists, however, who 
 have taken up the question in a different spirit ; 
 most notably Professor Spearman in England and 
 Professor Thorndike in America. Their mode of 
 research was mathematical. They submitted specific 
 mental abilities — the ability to add numbers, to 
 memorise words, to discriminate lengths, to sort 
 cards, and so forth — to certain rigid tests, and care- 
 fully marked the results. Then they compared the 
 various scorings and found the correlation between 
 them ; that is, the degree of concomitant variation, 
 or the extent to which the compared abilities tend 
 to rise and fall together. And from similar statistics 
 the two investigators arrived at entirely different 
 conclusions. Thorndike concluded that the indi- 
 vidual abilities were entirely independent ; that 
 there was, in fact, no such thing as general intelli- 
 gence, but only particular intelligences. For may 
 not a man be intelligent at geometry and stupid 
 at history, or brilliant as a poet and hopelessly bad 
 at figures ? Spearman, on the other hand, con- 
 cluded that there was a certain dominant factor 
 common to all the specific abilities, a central fund 
 of intellective energy, to which the term general 
 intelligence or general ability might fitly be applied. 
 To put it in another way, Thorndike held that a 
 man's intellectual wealth consisted entirely of 
 coupons ; Spearman that it consisted partly of 
 coupons, each of which may be expended in one 
 
INTELLIGENCE AND KNOWLEDGE 25 
 
 direction only, and partly of cash, which could 
 be expended in any direction. Both views recog- 
 nised the obvious fact that individuals varied widely 
 in intellectual wealth ; the views clashed on the 
 question of the availability of that wealth. 
 
 Let us examine the ground of the belief in 
 general intelligence. It is a matter of common 
 observation that a man who is good at one thing is 
 good at most other things. At least it is so as a rule ; 
 cases of one-sided ability are very rare. Generally 
 speaking, a wise man is wise in all things, a fool is 
 a fool all round. Indeed, it can be proved mathe- 
 matically that there is a positive correlation between 
 all forms of native ability ; they always tend to 
 hang together ; the odds are always in favour of 
 high ability in any given function being accom- 
 panied by high ability in any other function. Why 
 should this be ? Why should mathematical ability 
 be positively correlated, as it is, with linguistic 
 ability ? Even if we make every allowance for 
 such operations as might be conceived to be common 
 to the two abilities, we still fail to account for the 
 whole relationship. There still remains an un- 
 explained nexus. We are forced, in fact, to assume 
 a general factor common to all the multifarious 
 operations of the mind, a factor with which each 
 specific ability is, in its own measure, charged and 
 energised. This common factor is intelligence. 
 Such is Spearman's reasoning ; and its cogency is 
 hard to dispute. But he further arrives at the dis- 
 concerting conclusion that this central factor cannot 
 be cultivated. It is born with one, and can neither 
 be improved by schooling nor dulled by neglect. 
 Intelligence is mother wit, and mother wit is a 
 
26 MENTAL TESTS 
 
 matter of heredity. The ancient writer already 
 quoted holds a more hopeful view. He believes in 
 the possibility of cultivating wisdom. But even he 
 admits that it is sometimes difficult : " Though thou 
 shouldest bray a fool in a mortar among wheat, 
 with a pestle, yet will not his foolishness depart 
 from him." 
 
 It follows from this that the only practical thing 
 a psychologist can do with general intelligence, if 
 there is such a thing, is to measure it. Hence the 
 assiduous pursuit of mental tests. It is clear that 
 general intelligence cannot be directly tested, for 
 it can never be found alone : it is always embedded, 
 as it were, in specific abilities. But can it not be 
 tested indirectly ? We have in the thermometer 
 an excellent example of indirect measurement. 
 There are no known means of measuring temperature 
 directly ; we have to make use of the fact that the 
 expansion of a thin column of mercury is almost 
 perfectly correlated with temperature. So instead 
 of measuring the temperature, we measure the 
 mercury ; which does quite as well. Now is there 
 not some simple function of mind or body which 
 when measured will give us in the same way an exact 
 valuation of intelligence ? The quest of this key- 
 ability resembled the quest of the philosopher's 
 stone. It sometimes led to the discovery of un- 
 expected treasure ; it often led to the discovery of 
 mare's nests ; it always, as far as the essential search 
 was concerned, ended in disappointment. Every 
 device failed that assumed an essential corre- 
 spondence of soul with sense and sought to measure 
 mind through matter. 
 
 There was no help for it. The hope of finding 
 
INTELLIGENCE AND KNOWLEDGE 27 
 
 a simple key-ability had to be abandoned ; and 
 investigators had to fall back on the laborious 
 expedient of testing as many abilities as possible and, 
 by a process of mathematical analysis, extracting 
 the common intellective element. Among the 
 pioneers in this particular field of research, Mr. 
 Cyril Burt takes the foremost place. After years 
 of patient labour he proved that while almost any 
 kind of ability was a presumptive sign of intelligence, 
 some abilities were much safer signs than others. 
 To use his own words : " Of all the tests proposed, 
 those involving higher mental processes, such as 
 reasoning, vary most closely with intelligence." 
 
 There are no tests of intelligence that are more 
 widely used than Binet's. And Binet's tests are 
 based on the principles I have just expounded. 
 Like Spearman and Burt, he discarded brass instru- 
 ments, and relied more on the higher mental pro- 
 cesses than on the lower/ His tests measure general 
 ability simply because they measure a large number 
 of specific abilities. So far as he is concerned, it 
 does not in the least matter whether Spearman is 
 right or Thorndike ; on either theory his tests are 
 a real, though rough, measure of individual mental 
 endowment. 
 
 William James, in advocating his pragmatic 
 method, contends that the best way to discover the 
 essential difference between two conflicting theories 
 is to find out the practical difference in the conse- 
 quences that flow from them. How, in fact, do 
 they affect practice ? We have seen that, whichever 
 of the rival theories of Spearman and Thorndike 
 be accepted, it makes no difference in the mode of 
 testing ; does it make any difference to the teacher ? 
 
28 MENTAL TESTS 
 
 Again the answer is " No." On either view the 
 only cultivable thing is the multifarious group of 
 special abilities. It must not, however, be thought 
 that all this theorising and researching has had no 
 effect on school practice. It most distinctly has. 
 Its effect has been to broaden the outlook, to 
 multiply the school pursuits, to vary and amplify 
 the methods of study. 
 
CHAPTER III 
 
 THE MEASUREMENT OF INTELLIGENCE 
 
 The British Press refers to mental tests as though 
 they were new things invented by Americans. In 
 point of fact they are neither new nor American. 
 They have been the common property of the race 
 since the dawn of history. They are no more 
 mysterious than the conundrums that delight 
 children at a Christmas party. They are, in fact, 
 merely questions or tasks that invite a trial of 
 intelligence. What is new is not the tests them- 
 selves, but the aptness with which they are chosen 
 and the scientific precision with which they are 
 applied. 
 
 A tacit distinction seems to be made between 
 examinations and mental tests. This distinction 
 is illegitimate ; for an examination is nothing but 
 a series of tests, which are just as mental or psycho- 
 logical as any that have ever been devised. They 
 are not non-mental tests, but simply a special kind 
 of mental test. The real distinction lies between 
 tests of knowledge and tests of ability ; tests of 
 school attainments and tests of natural intelligence ; 
 tests of book-learning and tests of mother-wit — a 
 distinction which is easy to make but difficult to 
 maintain. For it is impossible to devise a test of 
 ability which does not also test knowledge, and 
 
 29 
 
30 MENTAL TESTS 
 
 impossible to devise a test of knowledge which does 
 not also test ability. Let us, for example, take one 
 of the most characteristic of Binet's intelligence 
 tests. The child is asked to say what is absurd in 
 the following : " If I should ever grow desperate 
 and kill myself, I will not choose Friday, because 
 Friday is an unlucky day and will bring me unhappi- 
 ness." To answer this correctly he must know, 
 among other things, the meanings of the words, 
 and he must know that a dead man is, in this world 
 at least, neither happy nor unhappy. If the ques- 
 tion were put in these words to a unilingual China- 
 man he could never answer it, however intelligent 
 he might be ; and to a race of immortals it would 
 be meaningless. Now let us consider this peda- 
 gogical test : Which are the four largest towns in 
 Scotland ? A correct answer would at least involve 
 ability to grasp a fact and to remember it, to under- 
 stand a question and to respond to it. The differ- 
 ence between the two types is one of proportion. 
 To answer the second we must acquire a special bit 
 of knowledge which casual experience will not 
 necessarily force upon us ; to answer the first 
 involves the application of such knowledge as no 
 sane mortal can fail to pick up in the ordinary 
 course of life. 
 
 The distinction, however, so far as it goes, is 
 perfectly sound, and indeed is constantly cropping 
 up in the folk-lore and legends of all races. The 
 point of the old English ballad of King John and the 
 Abbot depends entirely on this distinction. The 
 king sets the abbot three mental tests. At the 
 risk of forfeiting his life in case of failure, the abbot 
 has to say what the king is worth, how long it 
 
MEASUREMENT OF INTELLIGENCE 31 
 
 would take him to ride round the world, and what 
 he is thinking of. A respite of three weeks is given. 
 The abbot cudgels his poor brains in vain. He rides 
 to " Cambridge and Oxenford, but never a doctor 
 there was so wise that could with his learning an 
 answer devise." In fact, the only man who could 
 rescue him from his plight was his own shepherd, 
 a man who could neither read nor write. The 
 shepherd, who happened to resemble his master in 
 appearance, disguised himself as the abbot, pre- 
 sented himself before the king, and spoke thus : 
 " How much are you worth ? Twenty-nine pieces 
 of silver, for you are worth at least one piece less 
 than our Saviour. How long will it take you to 
 ride round the world ? You must rise with the 
 sun, and ride with the sun, until he rises here again 
 next day ; then the journey will take you" exactly 
 twenty-four hours. What do you think ? You 
 think I'm the abbot ; but I'm not : I'm his shep- 
 herd." Here we have three tests, which all the 
 learning in the land could not satisfy, triumphantly 
 solved by simple mother-wit. And, indeed, all 
 through the records of folk-lore and mythology do 
 we find the learning of the learned put to confusion 
 by the wisdom of the simple. The supreme ordeal 
 which reveals the native nobility of the hero is just 
 as likely to be the solution of an enigma or the 
 interpretation of a dream as the slaying of a dragon 
 or a giant. While the dragon is the test of physical 
 prowess, the enigma is the test of intellectual 
 prowess. Perseus by his courage rescued Andro- 
 meda, but (Edipus by his intelligence rescued the 
 whole of Thebes. As the reader will remember, 
 the riddle of the Sphinx (" What animal walks in 
 
32 MENTAL TESTS 
 
 the morning on four legs, at noon on two, and in 
 the evening on three ? ") was solved by OEdipus 
 alone, a king's son reared by peasants, a man in whom 
 nature triumphed over nurture. 
 
 The whole family of riddles, puzzles, charades 
 and conundrums belongs to a larger group of ability 
 tests. They require for their solution no special 
 knowledge, but a general aptitude for applying 
 knowledge — for the discernment of subtle analogies 
 and contrasts. We must not, however, fall into 
 the error of thinking that the modern application 
 of mental tests consists in the mere asking of riddles. 
 The tests are, in a sense, riddles, but they are riddles 
 of a special kind : they must have diagnostic value. 
 Let me illustrate by comparing an old riddle with a 
 new test. The riddle is : What relation does a 
 loaf of bread bear to a steam-engine ? And the 
 test : Complete the analogy : As a loaf of bread 
 
 is to a glass of water, so is eating to . The 
 
 answer to the riddle is " mother " ; for a loaf of 
 bread is a necessity, a steam-engine an invention, 
 and necessity is the mother of invention. This is 
 not a test of intelligence, but of a perverted ingenuity. 
 It is not intended to gauge one's reasoning powers, 
 but to raise a laugh. As a means of diagnosis it is 
 quite useless, unless, indeed, one gives the result a 
 negative interpretation ; for success in its solution 
 is, as a mark of sanity, no more significant than 
 failure. It is sophistry rather than logic, a jest 
 rather than a test. Very different is the analogies 
 test given above. Failure to answer this would, in 
 an adult, mean a serious defect of intellect. For 
 its solution lies not in some crooked by-path of 
 sophistry, but on the great highway of human 
 
MEASUREMENT OF INTELLIGENCE 33 
 
 thought. That is why it serves for a diagnosis of 
 mental endowment and unfoldment. For there is 
 a certain stage of mental development below which 
 it cannot be answered, and above which it cannot 
 be mis-answered. Although, therefore, the enigmas 
 of the ancients and the catch-questions of to-day 
 are, in the broad sense of the term, mental tests, 
 they lack the special characteristics of those tests 
 which are now-a-days called mental or psychological. 
 The whole point and pungency of the riddle or the 
 catch lies in its being exceptional. To repeat it in 
 another form is to thwart its purpose. For its 
 purpose is to trip us up ; and once the trick of it is 
 known it ceases to trip us up. After we have got 
 the hang of such a sentence as " Pas de l'yeux Rhone 
 que nous," it is quite easy to read " Guy n'a beau 
 dit qui sabot dit nid a beau dit-elle ? " When 
 CEdipus, in pondering over the riddle of the Sphinx, 
 guessed that " the morning " meant " the morning 
 of life," the enigma was virtually solved ; and all 
 others based on the same metaphor. The riddle, 
 in fact, needs novelty for its success. The nut to 
 be cracked may be any nut but a chestnut. 
 
 As distinct from this spurious mental test, the 
 genuine mental test depends for its value upon its 
 universality. It is always a member of a family, 
 and the larger the family the better. The analogies 
 test given above may be multiplied indefinitely ; 
 indeed, as many as a hundred have been set at one 
 sitting. For example : As cat is to kitten, so is 
 
 dog to ? As sheep is to ox, so is flock to ? 
 
 As Paris is to France, so is London to ? In 
 
 testing ability, as in testing knowledge, it is always 
 best to set a fair number of questions. To base a 
 
34 MENTAL TESTS 
 
 judgment on one test, however good that test may 
 be, is extremely precarious ; when the test itself 
 is suspect, no verdict at all can be reached. Each 
 test must itself be tested, and the results inter- 
 preted in accordance with the laws of probability. 
 I have, for instance, tried the following test on young 
 and old : If you are given a corked bottle half full 
 of wine, how can you get the wine out without 
 taking out the cork or breaking either the cork or 
 the bottle ? Most adults proclaim the task im- 
 possible, but many a small boy, who has solved 
 certain difficulties with his bottle of ginger-beer 
 or liquorice water, can answer the question promptly. 
 The test, in fact, proves to be too dependent on 
 an accident of experience to be a real gauge of 
 practical ability. Nor is it necessary to fall back 
 on such doubtful tests when we have so many 
 that are of demonstrable validity. 
 
 Another element of prime importance in scientific 
 testing is speed — an element which is clearly ex- 
 emplified in the cancellation test. The subject is 
 required to cancel as rapidly as possible all the ah 
 or all the rs, or any other letters, separately or 
 concurrently, in a page of printed matter. A 
 limited time is allowed — say, two minutes. In 
 rating the results the marker has to take into account 
 the number of letters rightly erased, the number 
 wrongly erased, and the omissions. It is obvious 
 that with unlimited time all who could distinguish 
 the letters at all would score full marks. To ignore 
 the time element is to nullify the test. 
 
 If, however, there is one single feature which 
 essentially distinguishes the modern test from the 
 gncient, it is that the modern test h standardised, 
 
MEASUREMENT OF INTELLIGENCE 35 
 
 The man who first convinced the world of the 
 necessity for standardised tests, as distinct from 
 casual and haphazard tests, was Alfred Binet. And 
 he achieved it incidentally. What he really was 
 after was to find out which children in the schools 
 of Paris were mentally defective. To do this he 
 devised two carefully graduated scales, one to 
 measure school attainments and the other to 
 measure general intelligence. The first measured 
 roughly, the second more exactly ; the first sifted 
 out the suspects, the second found from among the 
 suspects the real blockheads. The assumption was 
 that all fools are dunces, but all dunces are not 
 fools — an assumption quite in accordance with 
 common sense. This general scheme, full of flaws 
 as it is in detail, has given birth to the whole modern 
 system of scientific testing. He has not only shown 
 us how to discover intellectual and moral weaklings, 
 but he has led us into a fertile land which it is 
 our duty to explore and subdue. 
 
 Binet avoided the mistake of trying to deduce a 
 scale from first principles. He based his scale on 
 fact. Before asserting what degree of intelligence a 
 child of ten ought to possess, he took the trouble 
 to ascertain what degree of intelligence a child of 
 ten actually does possess. Before testing children 
 with a test, he first tested the test with children. 
 By applying it to a large number of children of 
 different ages he was able to fix the lowest age at 
 which the majority were able to pass it. Let me 
 illustrate this with reference to a type of test which 
 was evidently a favourite of Binet's, for in his scale 
 of fifty-four intelligence tests it appears four times 
 — more frequently, in fact ? than any other. It 
 
36 MENTAL TESTS 
 
 consists in the repetition of a series of digits. The 
 examiner says : " I am going to say x numbers. 
 Listen and repeat them after me : 5, 8, 2, . . . 
 etc." The numbers are uttered steadilv at intervals 
 of half a second. Binet found that at three years 
 of age few could repeat three digits, but consider- 
 ably more than half could repeat two. Thus he 
 fixed the repetition of two digits as a three-year- 
 old test ; and acting on the same principle he 
 assigned three, five and seven digits to the ages of 
 four, eight and fifteen respectively. This innocent 
 little test is not, in its implications, so simple as it 
 seems. It measures the span of primary memory — 
 the number of things one can hold in the conscious 
 memory at the same time. It depends on the fact 
 that consciousness is not a point but a patch ; and 
 the assumption is, the bigger the patch the bigger 
 the mind. When the mind ceases to attend to A 
 and passes on to B, A does not suddenly vanish from 
 consciousness leaving B in sole possession, but 
 fades gradually away, forming in the process what 
 William James calls a " fringe " to B. If by the 
 time the last digit is uttered by the examiner the 
 first has quite disappeared from the child's mind, 
 the child will fail in the test. His psychic fringe is 
 too small. 
 
 The importance of primary memory is more 
 apparent in dealing with words than in dealing 
 with figures. For if all the essential parts of a 
 spoken sentence do not in some sense reverberate 
 together in the mind, the sentence has no chance 
 of being understood. Fortunately the words in 
 connected discourse have greater cohesion than a 
 string of digits, and the number of syllables that 
 
MEASUREMENT OF INTELLIGENCE 37 
 
 can, according to Binet, be repeated at the ages 
 of three, five and fifteen amount to six, ten and 
 twenty-six respectively. Roughly speaking, a child 
 should be able to repeat twice as many syllables as 
 the number of years he has lived. Binet's typical 
 example for fifteen is : " The other day I saw in 
 the street a pretty yellow dog. Little Maurice 
 has stained his nice new apron." 
 
 Much interest is attached to Binet's third test 
 for children of twelve years of age : " I am going 
 to allow you three minutes, and I want you to say 
 as many words as you can think of. Some children 
 have said more than two hundred ; let me hear 
 how many you can say. Ready ? Start." In 
 order to pass the child must say at least sixty words. 
 This is an ingenious way of finding the child's 
 association time — the time it takes one word to call 
 up another. The laboratory method is to deal 
 separately with each word and to measure precisely 
 by means of a specially constructed clock the interval 
 that elapses between the hearing of the word and 
 the emergence of an associated idea. And, indeed, 
 some such plan is necessary in scientific investigations 
 of the association process itself. But for measuring 
 mental activity in children, for finding roughly 
 the rate at which ideas march through the mind, 
 Binet's method is equally effective and much 
 simpler. Although he uses this test once only, it 
 has been found that the number of words a child 
 can utter in the given time increases steadily with 
 his age ; that norms or averages could consequently 
 be fixed, and the test used to mark different levels 
 of intelligence. It has also been found that one 
 minute will give results just as trustworthy as three 
 
38 MENTAL TESTS 
 
 minutes. All this serves to illustrate how Binet's 
 tests are constantly being criticised and refined 
 upon ; how tests themselves are not exempt from 
 the testing of time and experience. 
 
 Interesting, however, as these tests are, they are 
 probably inferior in diagnostic value to the absurdity 
 tests to which I have already referred . And although 
 Binet sets them at one point only — ten years of 
 age — they are appropriate to all ages except the 
 very lowest. The following test, which I devised 
 some years ago to arrange rapidly (and of course 
 roughly) in order of intelligence a group of children 
 of eleven years or over, was found to be suitable for 
 all children who could read fluently and were 
 advanced enough to express their ideas in writing — 
 
 John Carew lived in a small cottage which stood 
 on the top of a barren hill and faced the east. From 
 the foot of the hill a grassy plain stretched in every 
 direction as far as the eye could see. On the even- 
 ing of John's thirtieth birthday, while he was sitting 
 on the front door-step looking towards the setting 
 sun and watching his shortening shadow on the 
 gravel path, he suddenly became aware that a 
 horseman was riding down to the cottage. The 
 intervening trees and foliage made it difficult for 
 him to see clearly, but he was able to perceive 
 that the horseman had only one arm. When, 
 however, he got a closer view he recognised that the 
 visitor was his son William who had left home to 
 join the army twenty years before and had not 
 been heard of since. On seeing his father William 
 immediately dismounted, ran towards him, threw 
 his arms round his neck, and burst into tears. 
 
MEASUREMENT OF INTELLIGENCE 39 
 
 Each child in the class was given this passage in 
 print, and was allowed a quarter of an hour to read 
 it and to write out any absurdities he could find 
 therein. It contains about seven absurdities, and 
 it was found that it did actually differentiate the 
 children in close accordance with the teacher's 
 rating of their general intelligence. Elementary 
 school children of eleven years of age who discovered 
 at least five absurdities were, as a rule, those who 
 on other grounds had been selected as worthy of a 
 secondary school training. 
 
 It has been complained that most absurdity tests 
 are too easy for the older pupils. Given, however, 
 a time limit, it would not be difficult to devise a 
 test which would floor the majority of adults. 
 Let the reader, for instance, try to find within 
 fifteen seconds the absurdity (there is but one) in 
 the following : " John Jones, who had married his 
 widow's sister, used to say that if a man had a bad 
 sister it was his misfortune, but if he had a bad wife 
 it was his fault." 
 
 When Binet published his scale in 1908 he regarded 
 it as tentative. Indeed, he revised it himself three 
 years later ; and since his death many a patient 
 experimenter has laboured at separating still further 
 the gold from the dross. It has been found that 
 while some of the tests are almost worthless, others 
 are of no small value : they are reliable in practice 
 and suggestive in theory. Moreover, new tests 
 are daily being devised and put to the trial of rigid 
 experiment, so that we are gradually accumulating 
 a body of tests which bear the hall-mark of demon- 
 strated success. 
 
 One of the main defects of Binet's scale is its 
 
4 o MENTAL TESTS 
 
 bias in favour of language — of words rather than 
 things ; another defect is the paucity of tests (there 
 are but five) prescribed for adults. When therefore 
 adults have to be tested for intelligence — and 
 especially such illiterate adults as were plentiful in 
 the American Army — recourse has to be had to 
 tests of a new type. One of the most useful of 
 these is the " construction board," a variation of 
 the jig-saw puzzle. The sections, however, are 
 generally rectangular, and the time always restricted. 
 
 A test which has gained considerable vogue 
 during recent years consists merely in the giving of 
 instructions to be obeyed by the subject. These 
 instructions may possess any degree of complexity 
 and may be used to mark the rapidity with which 
 the meaning is grasped. For instance : " Print 
 your Christian name (or names) in small letters 
 and your surname in capitals unless there are more 
 than six letters in your surname, in which case you 
 should print your surname in small letters and your 
 Christian name (or names) in capitals." It is quite 
 easy to see how these tests may be indefinitely 
 complicated either by making the provisos more 
 puzzling or by simply increasing their number. 
 As a sample : " If your grandfather's only child was 
 your uncle draw a square ; if not, draw a circle." 
 Here, as always, a time limit is essential. 
 
 So much for intelligence tests. Binet's other 
 scale (his bar erne d' instruction) consisted of ordinary 
 examination questions, with the difference — a highly 
 important difference — that they have been carefully 
 sifted and standardised. The development of this 
 scale is quite another story. Nor must the intelli- 
 gence tests with which we have been dealing be 
 
MEASUREMENT OF INTELLIGENCE 41 
 
 confused with vocational tests, which are designed 
 to find out what sort of work a person is best fitted 
 for. These are just as often physical tests as mental 
 tests, and frequently involve the use of delicate and 
 complicated apparatus. 
 
 Having made a distinction between the two broad 
 types of mental tests (tests of knowledge and tests 
 of ability), and having shown that these types are 
 never quite pure, let us examine the bearing of this 
 theoretical distinction on the practical art of 
 examining. There are four possible methods of 
 procedure. First, we may dispense with the ordin- 
 ary examination altogether and substitute a series 
 of ability tests. This is no new proposal. It has 
 been made many a time before, but it has always 
 been rejected. And rightly so. For it cannot be 
 too strongly insisted on that education is directly 
 concerned not with natural ability but with culture. 
 For natural ability, as scientifically conceived, grows 
 with the growth of the brain, fluctuates with fresh- 
 ness and fatigue, and varies with varying states of 
 health and nutrition. The most that the school- 
 master can do is to take full advantage of what 
 natural ability his pupils may happen to possess. 
 His business is not to train intelligence but to use 
 it — to use it himself, and to see that his pupils 
 use it. And his success is measured by the degree 
 of culture he imparts. But culture means know- 
 ledge. True, it means other things as well ; but 
 it means knowledge at least. And the most effec- 
 tive way of testing knowledge is by examinations. 
 
 The second possibility is to leave things as they 
 are — to rely on examinations pure and simple, 
 examinations of the good old-fashioned sort. But 
 
42 MENTAL TESTS 
 
 this policy implies a wilful blindness to certain grave 
 defects which have been pointed out repeatedly and 
 persistently for the last half -century. 
 
 The third possibility is to hold two distinct 
 examinations, one a pedagogical examination, and 
 the other a psychological examination — one a test 
 of acquired knowledge, the other a test of natural 
 aptitude. This is virtually Binet's plan for detect- 
 ing the feeble-minded. The teacher sifts first, the 
 psychologist afterwards. It is also the scheme that is 
 reported to have been recently adopted at Columbia 
 University for selecting candidates for entrance. 
 Those who pass the ordinary matriculation ex- 
 amination are further submitted to a series of tests 
 for general intelligence. It is not quite clear 
 whether any are knocked out in the second round. 
 It is not indeed clear whether the second round 
 is intended to knock them out at all. The prob- 
 ability is that the second examination is not selective 
 but experimental. It is intended to reveal the 
 degree of correspondence between the results of 
 the two types of examination. Rash indeed would 
 be the examiner who would lightly brush aside the 
 evidence of combined scholarship and intelligence 
 which a wisely conducted examination affords. 
 Besides, the virtue of matriculation lies in the fact 
 that it guarantees a certain minimum of culture. 
 The university starts no course of study from the 
 beginning ; it takes up the tale at the point where 
 the secondary school left off. It demands of its 
 alumni a determinate measure of literacy, and by 
 means of a matriculation examination it assures 
 itself that its demand is met. And if this demand 
 is met — if the candidate has sufficient intelligence 
 
MEASUREMENT OF INTELLIGENCE 43 
 
 to carry him successfully to that point in the road 
 of learning — it would need more proof than our 
 modern mental tests can at present afford to demon- 
 strate that he can go no farther. If the purpose 
 of the second examination is to reduce the element 
 of chance, there seems to be more reason for re- 
 testing the failures than for re-testing the passes. 
 For failures may be due to illness or excessive 
 nervousness, or sheer bad luck. Moreover, a high 
 degree of intelligence in a candidate may well be 
 regarded as counterbalancing certain gaps in his 
 store of knowledge. 
 
 The last alternative is to combine both types 
 of test in one. examination. When this took place 
 in the past- it was mainly a matter of accident; 
 now it is done by design. It is the way in which 
 the new science of testing has affected English 
 examinations. The examiner is beginning to ask 
 himself what it is that he is really examining. Is it 
 parrot knowledge, or is it knowledge that has been 
 intelligently acquired and can be intelligently 
 applied ? Is it the application of common know- 
 ledge in an unfamiliar field, or is it the application 
 of exotic knowledge to familiar instances ? Is it 
 the capacity to acquire, or the capacity to express ? 
 In any case the wise examiner never neglects to test 
 the capacity of the candidate to apply knowledge 
 and to express it in new forms, for in so doing he 
 kills two birds with one stone : he tests both know- 
 ledge and intelligence. Speaking generally, the 
 younger the pupil the less the importance to be 
 attached to school attainments as distinct from 
 native ability. In other words, if intelligence tests 
 are important anywhere, they are important at that 
 
44 MENTAL TESTS 
 
 stage in the pupil's career when we decide upon 
 the type of education for which he is best fitted. 
 This principle is clearly observed in the selection 
 of mentally defective children at the age of seven ; 
 less obviously in the selection of supernormal 
 children at the age of eleven. It is customary at 
 examinations for junior scholarships to set two 
 papers only, one in English and the other in arith- 
 metic. And the questions are so devised as to 
 frustrate, as far as may be, the designs of the 
 crammer. That this examination will radically 
 change in the near future is highly improbable, 
 for it is difficult at present to conceive a better 
 practical device for testing annually the intelligence 
 of a large number of children. The fact that it is 
 conducted every year, or even twice a year, in the 
 same schools renders known and standardised tests 
 almost useless. If we are to remove entirely the 
 possibility of special coaching, the element of 
 novelty is essential. And the scope for variety in 
 the realm of English and mathematics is virtually 
 unbounded. Here intelligent anticipation on the 
 part of parents and teachers can readily be defeated. 
 Again, the 8000 children who sit every six months 
 for the London junior scholarship examination can 
 all be examined quite easily in one morning with 
 no superintendents besides the ordinary teachers. 
 Under the Binet scheme, where the testing is oral 
 and individual, it would take a trained examiner 
 nearly four years to get through one half-yearly 
 batch. To test the whole lot in one morning 
 would need the services of 1400 examiners specially 
 trained for the purpose. As a matter of fact samples 
 of the candidates have been tested by both written 
 
MEASUREMENT OF INTELLIGENCE 45 
 
 and oral methods, and the results obtained are so 
 similar that confidence in the present system is 
 amply justified. 
 
 There are two fairly distinct types of ability which 
 are tested by these junior examinations — mathe- 
 matical ability and literary ability. Proficiency in 
 problem arithmetic is in itself no poor criterion. 
 One of the most trustworthy of Binet's tests is the 
 second in his scale for eight-year-olds : Count 
 backwards from twenty to nothing in twenty seconds. 
 It is the departure from the beaten track that gives 
 it its value. The modern tendency, however, is to 
 attach more importance to the English paper than 
 to the arithmetic. Binet long ago remarked that 
 no child who could compose was mentally defective ; 
 and Mr. Cyril Burt, the psychologist to the London 
 County Council, has expressed the opinion that the 
 school subject most clearly symptomatic of intelli- 
 gence is composition, provided it is marked for its 
 power of thought. The only serious defect of the 
 present system is the absence of tests of the third 
 broad type of ability — manual ability. This defect 
 has been carefully considered by the London 
 authority, who have adopted the view that in 
 early years the ablest with their heads are also as 
 a general rule the ablest with their hands ; that it 
 is very difficult to discover at the age of eleven (that 
 is, before the children have begun to attend the 
 handicraft and . domestic centres) what practical 
 ability children actually do possess ; and, finally, 
 that those few children who have a special aptitude 
 for craftsmanship and escape the junior county 
 scholarship net are captured by the trade scholarships. 
 
 It were unwise to prophesy what developments 
 
46 MENTAL TESTS 
 
 will take place in English examinations in the near 
 future. Already one English authority has included 
 in its junior examination a test of the " instruc- 
 tions " type given above, and it is not impossible 
 that a third paper will become the general rule — a 
 paper corresponding to the obsolete general know- 
 ledge paper, except that it will aim at discovering 
 not whether the candidate is well-informed, but 
 whether he is sharp-witted. The secondary schools 
 and universities show as yet no alarming symptoms 
 of infection. 
 
 Thoughtful people have recently been asking : 
 Why is it that America has been moving so rapidly 
 in the matter of mental tests while England has 
 almost stood still ? The answer is simple : Speaking 
 generally, Americans believe in psychology but 
 Englishmen do not. When America entered the 
 war one of the first things she did was to mobilise 
 her psychologists. The war was nearly over before 
 England discovered that psychologists were of any 
 use. And the discovery was due partly to the 
 witnessing of what was achieved in the American 
 Army, and partly to an appreciation of the wonder- 
 ful results that followed the psychological treat- 
 ment of shell-shock and war-strain by those numerous 
 psychologists (medical and non-medical) who volun- 
 teered their services early in the war. The fault 
 did not lie with the British psychologists. In the 
 pursuit of their particular science and in the inven- 
 tion of new tests they were in no way behind their 
 neighbours. And the Americans knew this ; they 
 consulted our professors and freely used their tests. 
 There is no psychological instrument which is more 
 generally useful than the dotting machine, an 
 
MEASUREMENT OF INTELLIGENCE 47 
 
 invention of Mr. McDougall, of Oxford ; there is 
 no instrument more specifically useful than the 
 K tube, an invention of Dr. C. S. Myers, of Cam- 
 bridge. The new science of testing could never 
 have reached its present stage but for the discovery 
 of that potent means of mathematical analysis known 
 as " correlation." It was discovered by an English- 
 man, perfected by an Englishman, and simplified 
 for common use by an Englishman. In the investiga- 
 tion of general intelligence and in the critical 
 examination of the methods used nobody has done 
 better work than Mr. Cyril Burt. Like Binet, he 
 was concerned in testing tests as well as in testing 
 ability. But the methods he adopted were more 
 rigidly mathematical. He invented tests too ; among 
 others the analogies test mentioned above. Many 
 other Englishmen have successfully laboured in the 
 same field, such as Mr. W. H. Winch, Dr. W. Brown, 
 Dr. E. O. Lewis, Professor J. A. Green, Dr. J. L. 
 Mclntyre, Dr. N. Carey, Miss N. Taylor, Mr. 
 H. B. English, Miss May Smith, Dr. Bernard Hart, 
 and Dr. Edgar Schuster and other investigators in 
 the psychological laboratories of University College, 
 King's College and Oxford. Such records of their 
 work as have already been published may be found 
 distributed among the pages of the British Journal 
 of Psychology, the Journal of Experimental Pedagogy, 
 and the Annual Reports of the British Association. 
 
CHAPTER IV 
 
 binet's tests of intelligence 
 
 The translation of Binet's Tests given below 
 was made by Mr. Cyril Burt in consultation with 
 Dr. Simon, who was Binet's collaborator in de- 
 vising and standardising the scale. The tests, 
 originally standardised for Parisian children, have 
 been tried by Mr. Burt on a large number of 
 London children, and modified to suit their char- 
 acteristic rate of development. The tests, in fact, 
 are here rearranged in the order of their freshly 
 ascertained difficulty, and the age-assignments are 
 given as they were determined afresh for children 
 of London Elementary Schools. 
 
 Each child has to be tested individually, and 
 under conditions most favourable to the removal 
 of shyness and nervousness. The examiner must 
 use his discretion respecting the point of the scale 
 at which he should begin : the usual rule is to 
 start with the group of tests just below the child's 
 chronological age. If, however, there is a failure 
 in any of those tests it is expedient to go back and 
 try all the tests in the previous group. The ex- 
 amination should then be carried up the scale until 
 the child fails in four or five consecutive tests, 
 
 4 8 
 
BINET'S TESTS OF INTELLIGENCE 49 
 
 Terman gives as the lowest permissible limit of 
 thoroughness a range which starts at the year 
 which yields only one failure, and ends with the 
 year which yields only one success. To estimate 
 the child's mental age the examiner should regard 
 the age at which all tests are passed as the base 
 age, and should add one-fifth of a year for every 
 additional test belonging to any of the higher 
 ages ; or, where in the following revision there are 
 more or less than five tests in the higher year, the 
 corresponding reciprocal fraction. 
 
 It is now customary to state the final result in 
 the form of an Intelligence Quotient, a method 
 first suggested by the German psychologist, Stern. 
 The Intelligence Quotient is found by dividing the 
 mental age by the real age. If, for instance, a 
 child's real age is eight and his mental age six, 
 his intelligence quotient is '75. If his mental 
 age were ten his intelligence quotient would be 
 1-25. 
 
 Binet lays it down that the amount of retarda- 
 tion that determines a child as defective is two 
 years when he is under nine, and three years 
 when he is past his ninth birthday. Stated in 
 terms of the intelligence quotient the border-line 
 between normality and deficiency is somewhere 
 about '75. No cases, however, where the intelligence 
 quotient falls between "j and *8 are quite free from 
 doubt. 
 
50 MENTAL TESTS 
 
 BINET TESTS (BURT'S TRANSLATION 
 AND REVISION) 
 
 Age Three 
 
 1. Understanding Simple Commands. 
 
 Instructions. — " Show me (point to, put your 
 finger on) — 
 
 (i) your nose. 
 
 (2) your eyes. 
 
 (3) your mouth." 
 
 Evaluation. — All should be correctly performed ; 
 but free encouragement may first be given. 
 
 2. Repeating Numbers. 
 
 Instructions. — " I am going to say some numbers. 
 Will you listen, and say them after me ? " 
 
 (For use only after failure in first set.) 
 
 5 8 9 
 
 37 64 72 (Age 3) 
 
 714 286 539 (Age 4) 
 
 3681 5749 8526 (Age 5) 
 
 52947 63852 973i8 (Age 6) 
 
 250634 5739 16 495827 (Age 9) 
 
 9647518 4829653 5928136 (Age 11) 
 
 Note : rate should be two per second ; utter- 
 ance should be without rhythm, emphasis or in- 
 flection. Do not tell the child if he is wrong. 
 Do not repeat the same series. Merely give him 
 
BINET'S TESTS OF INTELLIGENCE 51 
 
 another chance with another series. Failure owing 
 to interruption does not count. (While uttering 
 the numbers or syllables, hold up the hand or 
 finger to prevent the child starting to repeat before 
 entire phrase or list has been completed. Drop 
 the hand as a signal to child that you have finished 
 and he is to repeat.) 
 
 Evaluation. — One correct repetition out of three 
 trials counts as success. Note, therefore, the largest 
 number the child can repeat. The age at which 
 series of different lengths can be repeated is given 
 in the last column above. The repetition of figures 
 in their natural order, e. g. 9645678, should be noted 
 as an instance of automatism. 
 
 3. Naming Own Sex. 
 
 Instructions. — " Are you a little boy or a little 
 girl ? " (for a boy). " Are you a little girl or a 
 little boy ? " (for a girl). 
 
 If child says " yes " or " no " or merely echoes 
 part of the phrase, ask the two questions separ- 
 ately : " Are you a little girl ? " " Are you a little 
 boy ? " 
 
 4. Giving Surname. 
 
 Instructions. — " What is your name ? " If child 
 merely gives Christian name, ask : " And what 
 else ? . . . Tommy what ? " 
 
 Evaluation. — If child gives surname he has some- 
 times been known by e.g. stepfather, or mother 
 (when illegitimate) record it as correct. 
 
52 MENTAL TESTS 
 
 5. Naming Simple Objects. 
 
 Materials. — A penny, a closed knife, and a 
 common kind of key. 
 
 Instructions. — " What is that ? " or " What is 
 this called ? " showing each object successively. 
 
 Evaluation. — All three must be named, but slight 
 errors, such as " money," " pennies," for " a 
 penny," are allowable. 
 
 6. Describing Pictures. 
 
 Materials. — Binet's three pictures — chosen as con- 
 taining people, and suggesting a story, and having 
 a certain standardised difficulty. 
 
 There can, I think, be little doubt that pictures 
 (1) better printed, (2) larger, (3) coloured, (4) re- 
 presenting actions in progress, (5) showing children, 
 would be much more appropriate than Binet's 
 original engravings. But these alone have been 
 standardised. 
 
 Instructions. — " Look at this picture and tell me 
 all about it." Binet's instructions are : " What is 
 this ? " and if the child says, " A picture," " Tell 
 what you see there." It is better, however, to 
 avoid leading phrases like " What can you see in 
 it ? " (which rather suggests enumeration) and 
 " What are they doing ? " (which suggests inter- 
 pretation). Repeat instruction once for each pic- 
 ture, if there is no answer. Words of praise or 
 encouragement alone may be added : " Isn't it a 
 pretty picture ? . . . Do you like it ? " Or even 
 
BINET'S TESTS OF INTELLIGENCE 53 
 
 " That's right ! " if the child is on the point of 
 saying something but is withheld by shyness. 
 
 Evaluation of replies. — 
 
 Record the type of response given to the first 
 picture ; if doubtful, use the second and third and 
 record the type of response most frequently given, 
 i. e. employed for two pictures out of the three. 
 Binet distinguishes three types of response corre- 
 sponding to three stages of development. 
 
 A. Enumeration (E.). (Age 3.) E.g. — 
 
 i. " A man, boy." 
 ii. " There's an old man and a lady," 
 
 etc. (mere list of objects or details), 
 iii. " I can see a room with a chair, a 
 
 table, and a looking-glass, and there's 
 
 a man and a sofa." 
 
 Two items at least should be enumerated. 
 If the child only gives one, do not ask, 
 " Anything else ? " but proceed to another 
 picture. 
 
 B. Description (D.). (Age 6.) (Phrases indicat- 
 
 ing actions or characteristics.) 
 
 i. " They're pulling a cart." 
 ii. "A man and a woman sitting on a 
 
 seat." " An old man asleep." 
 iii. " A man standing on a bed and trying 
 
 to look out of the window." " A 
 
 man looking at himself in the 
 
 glass." 
 
54 MENTAL TESTS 
 
 C. Interpretation (I.). (Age 12.) (Goes be- 
 yond what is actually visible in the picture 
 and mentions the situation or emotion it 
 suggests.)' 
 
 i. " They're moving," " they've a heavy 
 load," " they can't pay their rent." 
 ii. "Miserable," "poor," "have no 
 home," " the man is saying his 
 prayers," " his daughter " or 
 " wife " (looking after him, etc.). 
 iii. " A prisoner," " he wants to get out," 
 " he's trying to see what's in the 
 yard," " he is lonely " or " think- 
 ing," " a rag-picker," " a man in 
 trouble," " a man on board ship." 
 
 Age Four 
 
 7. Repeating Syllables. 
 
 Instructions. — " Listen again, and say this after 
 me." (The phrases should be pronounced deliber- 
 ately and with expression. Begin with no. iii. ; 
 but if the child remains silent the examiner may 
 give him first a shorter sentence (i. or ii.), and then 
 apparently try iii. again.) — 
 
 i. (2 syllables). " Father." 
 ii. (4 syllables). " My hat and shoes." 
 iii. (6 syllables). " I am cold and hungry." 
 
 (Age 4.) 
 iv. (8 syllables). "Here is the cloth ; my hands 
 
 are clean." 
 v. (10 syllables). " His name is Jack : he's 
 
 such a naughty dog." (Age 5.) 
 
BINET'S TESTS OF INTELLIGENCE 5$ 
 
 vi. (12 syllables). " It is raining outside ; but 
 
 we can stay indoors." 
 vii. (14 syllables). " While Jack was doing his 
 
 lessons, I caught a little mouse." 
 viii. (16 syllables). "We are going for a walk: 
 
 Mary, let me see your pretty hat." (Age 7.) 
 
 xiii. (26 syllables). " The other morning I saw 
 in the street a little yellow dog. Little 
 Maurice has spoilt his new apron." 
 (Age 14.) 
 
 Evaluation. — Allow no error at all, except mis- 
 pronunciations due to speech defects. (Binet's 
 sentences appear to have been deliberately com- 
 posed of two clauses. This seems unfortunate, as 
 even an intelligent child may forget one. In trans- 
 lating them I have endeavoured to keep the general 
 sense of the original, while making the phraseology 
 more natural for a child.) 
 
 8. Repeating Numbers. 
 
 Instructions. — " Listen. Say these numbers after 
 me"— 
 
 (For use only after failure in first set.) 
 714 286 539 
 
 Evaluation. — (See Test 2.) 
 
 9. Counting Pennies. 
 
 A. Four Pennies. (Age 4.) 
 
 Materials. — Four pennies placed in a row. 
 
 Instructions. — " Do you see these pennies ? 
 Count them, and tell me how many there are." 
 
56 MENTAL TESTS 
 
 If the child at first answers at random, add : 
 " Count them aloud, and point to each penny as 
 you count it " ; but do not demonstrate. (It may 
 be of interest to see if the child can do it when 
 
 shown : " Count like this : one, two " touching 
 
 the first two with the finger as each is counted. 
 But do not use his answer for strict comparisons.) 
 
 Evaluation. — The first random answer does not 
 count. 
 
 B. Thirteen Pennies. (Age 6.) 
 Instructions, etc., as before. 
 
 10. Comparing Two Lines. 
 
 Materials. — Two parallel horizontal lines, 5 cm. 
 and 6 cm. respectively, previously drawn in ink on 
 a card or paper, the longer 3 cm. below the shorter, 
 with its centre under that of the other. 
 
 Instructions. — " Do you see these lines ? Tell 
 me which is the longer ? " 
 
 Evaluation. — No hesitation is allowed. (Some 
 investigators allow the examiner to repeat the in- 
 struction : English children will often respond 
 more readily to the injunction : " Put your finger 
 on the long one." But Binet insists that the child 
 shall not only perceive the difference, but also 
 understand, without any further help, that the 
 phrase " the longer " implies making a comparison.) 
 
 11. Comparing Faces. 
 
 Materials. — Binet's six faces. Show only two at 
 a time. 
 
BINET'S TESTS OF INTELLIGENCE 57 
 
 -O 
 
 705 
 
 (Lo 
 
 Us "^ 
 
 r 
 
 
 % 
 
 %& 
 
 
58 MENTAL TESTS 
 
 Instructions. — " Which is the prettier of these 
 two faces ? " (If " prettier " seems not to be under- 
 stood, "prettiest" or "Which do you like the best 
 of these two ladies ? " "Which is the nice one ? " 
 may evoke correct answers. But these should not 
 be counted for purposes of strict comparisons.) 
 
 Method. — It is better to cover the lower pairs or 
 pair while dealing with the first or second. 
 
 Evaluation. — All three comparisons must be cor- 
 rectly made. Repeat the questions once if necessary. 
 
 Age Five 
 
 12. Performing Three Commissions. 
 
 Materials. — Key, book, etc. Arrange the room 
 while the child is carrying out one of the drawing 
 or writing tests. 
 
 Instructions. — "Do you see this key? Go and 
 put it on the table there. Then shut the door. 
 And after that bring me the book on the chair near 
 the door. Do you understand ? First, put the 
 key on the table, then shut the door, then bring 
 me the book." (Note repetition of instructions. 
 Do not let the child commence until this is com- 
 pleted.) 
 
 Evaluation. — All three commissions must be per- 
 formed spontaneously without any further instruc- 
 tion or hint (" Well, and now ? " " What have you 
 forgotten ? "). 
 
BINET'S TESTS OF INTELLIGENCE 59 
 
 13. Draws from Copy. 
 
 A. A Square. (Age 5.) 
 
 Materials. — A square, each side measuring about 
 3 to 4 cm., drawn beforehand in ink, preferably on 
 a card. Plain paper. Pen and ink (deliberately 
 advised by Binet, making the task more difficult. 
 Most American adapters recommend pencil.) 
 
 Instructions. — " I want you to copy this for me " 
 (pointing to square). " Draw it here " (handing 
 pen and paper). (If encouragement is needed : 
 " What do you think this shape (picture) is ? See if 
 you can draw it." Do not use the word " square " 
 yourself.) 
 
 Evaluation. — Passes if it can be recognised as an 
 attempt at a square. If one side is twice the other, 
 if the lines cross considerably at the corners or bend 
 round without any angles, the drawing fails. The 
 size does not matter. (Allow only one attempt.) 
 Should take about one minute. 
 
 B. A Rhombus or Diamond. (Age 6.) 
 
 Materials. — A " diamond," about 7 cm. long 
 and 4 cm. high, with sides 4 cm. long, drawn as 
 before on a card. Paper, pen and ink. 
 
 Instructions and Evaluation. — As before. Binet 
 apparently requires at least one pair of opposite 
 angles to be fairly equal, at least one pair of adjacent 
 sides to be fairly equal, and the vertical diameter to 
 be long. Absolute parallelism of the opposite sides 
 is not insisted upon. The pass-standard is thus con- 
 siderably below what an uninstructed teacher would 
 
6o MENTAL TESTS 
 
 be apt to accept as a satisfactory reproduction. 
 (Reference should be made to his samples.) 
 
 14. Repeating Syllables. 
 
 (10 syllables.) " His name is Jack : he's such a 
 naughty dog." 
 
 Instructions and Evaluation. — (See Test 7, no. v.) 
 
 15. Giving Age. 
 
 Instruction. — " How old are you ? " 
 
 Evaluation. — Child should give his age in years, 
 last birthday. Note : children very often say 
 " seven " when they mean " getting on for seven." 
 Hence, if the first answer is wrong, ask specifically 
 " How old were you last birthday ? " Parents also 
 often give an infant and a child about to leave 
 school an age above the true one : and dull children 
 (except when about to leave) an age below the real 
 one. The child's answer should be accepted if it 
 corresponds with what it has commonly or recently 
 been told. Do not, therefore, insist too rigidly on 
 the age given by the birth certificate or the register. 
 
 16. Distinguishing Morning and Afternoon. 
 
 Instructions. — " Is it morning or afternoon now ? " 
 (in the morning). Or, " Is it afternoon or morning 
 now ? " (in the afternoon). 
 
 Evaluation. — Repeat the question if there is any 
 possibility of the child having merely echoed one 
 of the words thoughtlessly. (Asking " Have you 
 had your dinner yet ? " elicits answers interesting 
 to compare with the above.) 
 
BINET'S TESTS OF INTELLIGENCE 61 
 
 17. Naming Four Primary Colours. 
 
 Materials. — Four oblong pieces of paper, 2x6 
 cm., coloured bright red, yellow, blue and green, 
 and gummed beneath one another on a card. 
 
 Instructions. — " What colour is this ? " pointing 
 to each in turn. 
 
 Evaluation. — No error is allowed. Should take 
 about 6 seconds. But the time limit does not appear 
 to be strictly enforced. 
 
 18. Repeating Numbers. 
 
 Instructions. — " Listen. Say these numbers after 
 me." 
 
 (For use only after failure in first set.) 
 3681 5749 8526 
 
 Evaluation. — (See Test 2.) 
 
 19. Comparing Two Weights. 
 
 Materials. — Four small similar boxes (about 
 1*5 x 2*5 x 3*5 cm.) weighing 3, 12, 6 and 15 grammes. 
 
 Instructions. — " You see these boxes (showing 
 first the pair weighing 3 and 12 grammes placed 5 or 
 6 cm. apart). Tell me which is the heavier." 
 
 If the child merely points, add, without any 
 gesture : " Take them in your hands and weigh 
 them." (English children respond better to the 
 instruction " Lift them " or " Feel them." " And 
 give me the heavy one." But do not use the 
 modification if strict comparability is required. 
 Kuhlman and the Stanford Revision allow a demon- 
 stration : Binet and Yerkes prohibit it.) In any 
 
62 MENTAL TESTS 
 
 case do not put them in his hands. If he merely 
 lifts one, or both together, do not correct him. If 
 there is any doubt with the first pair, repeat the 
 experiment with the second pair (6 and 15 grammes) ; 
 and then with the first pair again. (If the child 
 fails to understand, it is interesting to put them 
 successively into his hand, and ask, " Which is the 
 heavier ? " But his response in this case does not 
 count.) For the second and third trials use the 6 
 and 15 gramme weights and then the first pair again. 
 
 Evaluation. — All three trials must be correct : if 
 any doubt continue repetitions. 
 
 20. Giving Number of Fingers. 
 
 Instructions. — " How many fingers have you on 
 your right hand ? " " And how many on your left 
 hand ?"..." How many does that make on both 
 hands altogether ? " 
 
 Evaluation. — The replies must be made without 
 stopping to count : and all three questions must be 
 correctly answered. 
 
 Age Six 
 
 21. Counting Pennies. 
 
 A. Thirteen Pennies. 
 
 Materials. — Thirteen pennies placed in a row. 
 Instructions and Evaluation. — (See Test 9, B.) 
 
 22. Drawing from Copy. 
 
 B. A Rhombus or Diamond. 
 
 Instructions and Evaluation. — (See Test 13, B.) 
 
BINET'S TESTS OF INTELLIGENCE 63 
 
 23. Transcription. 
 
 Materials. — " See little Paul " written in a bold, 
 copy-book handwriting on a card or sheet of paper. 
 Paper, pen and ink. 
 
 Instructions. — " Will you copy that for me ? " 
 
 Evaluation. — The test is passed if the copy is 
 sufficiently legible to be read by a person who did 
 not know what was to be written. 
 
 24. Naming Days of the Week. 
 
 Instructions. — " Can you tell me what are the 
 days of the week ? " 
 
 Evaluation. — The days must be named in order 
 without error or hesitation, in 10 seconds. 
 
 25. Naming Coins. 
 
 Materials. — Nine coins, all placed in a row on the 
 table with the head upwards : similar coins should 
 not be adjacent. Order upon table : is., id., 6d., 
 Id., 2s., \d., £1, 2s. 6d., 10s. Order of difficulty : id., 
 Id., \d., is., 6d., 2s., £l, 10s., 2S. 6d. (3^., 5^., 4J.). 
 
 (One pound and ten-shilling notes must be allowed.) 
 
 Instructions. — Ask " What is this ? " pointing to 
 each in succession. Neither examiner nor child 
 should handle them or turn them over. 
 
 Evaluation. 
 
 A. Four Commonest Coins. (Age 6.) 
 (is., 6d., id., r^d.) No error allowed. 
 
 B. Nine Commonest Coins. (Age 9.) 
 
 All should be named correctly in 40 seconds. If an 
 error is attributable to passing confusion, Binet 
 
64 MENTAL TESTS 
 
 allows a second trial of the whole series after a few 
 minutes. (An interesting variant is to ask what 
 coins there are larger than a shilling, before passing 
 to B.) 
 
 26. Reconstructing Divided Oblong. 
 
 Materials. — Two cards (4*5 x 7*5 cm.), one in- 
 tact, the other divided along one diagonal into two 
 equal triangles. Place the triangles so that the 
 longest sides are at right angles, but do not face 
 towards each other. 
 
 Instructions. — " One of my cards has been cut 
 in two ; can you put the pieces together again, to 
 make a whole one, like this ? " 
 
 If the child merely looks at the cards without 
 touching them, say : " Move them about and see 
 if you can fit them together," and, if necessary, place 
 one in his hand. 
 
 See that the child does not turn one triangle over. 
 (Before cutting the card, black one side all over. 
 This does not appear to alter the difficulty of the 
 test, but prevents turning over.) If the child 
 makes a wrong combination and appeals for judg- 
 ment, give no opinion. Remain silent, or say 
 merely, " What do you think ? " 
 
 27. Defining Concrete Terms. 
 Instructions. — " What is — 
 
 (1) a fork ? 
 
 (2) a table ? 
 
 (3) a chair ? 
 
 (4) a horse ? 
 
 (5) a mother ? " 
 
BINET'S TESTS OF INTELLIGENCE 65 
 
 (A word commonly used by other investigators 
 is " kitten," or " cat " : " fork " is unfortunately 
 a difficult word to begin with.) For shy or silent 
 children : " You know what a fork is, don't you ? 
 Well, tell me what it is — what is a fork ? " " You 
 have seen a horse, haven't you ? Tell me what a 
 horse is." The instructions may be repeated, but 
 use no other form of words. (Give the child a 
 minute to reply in.) 
 
 Evaluation of Replies. — The character of three 
 replies out of five determines the value of the test. 
 The variations in the age assignments of definition 
 superior to use depend largely on the inclusion of 
 such replies as ii., (1), (3), (4) and (7) under i. 
 rather than under ii. 
 
 Note " U " or " G " according as child defines — 
 
 i. In terms of Use. (Age 6.) 
 
 (1) What you eat with. 
 
 (2) Something to have your dinner on : 
 
 where the plates are put. 
 
 (3) It draws a cart. 
 
 (4) She takes care of the babies. 
 
 ii. In terms superior to Use (by Genus with or 
 without Differentia, or by Description). 
 (Age 10.) 
 
 (1) A thing to sit on : something that you 
 
 eat with. (" Thing " and " some- 
 thing," however, are not accepted 
 for " horse " or " mother.") 
 
 (2) An instrument. 
 
 (3) It has four legs : it's silver. 
 
66 MENTAL TESTS 
 
 (4) A piece of wood, part of the furniture. 
 
 (5) An animal. 
 
 (6) A lady. 
 
 (7) One who cooks our dinners. 
 
 (Note : if a child uses " thing " or " some- 
 thing " for " chair," I then give " mother " and 
 "horse," otherwise even a bright child, having 
 given "thing" for "chair," "table" and "fork" 
 without correction is apt from sheer inertia to 
 offer " thing " as the genus of " horse.") 
 
 iii. Merely repeating the word, or pointing to 
 the object is marked a failure, without 
 (apparently) giving the child a further 
 chance. 
 
 28. Repeating Numbers. 
 
 Instructions. — " Listen. Say these numbers after 
 me." 
 
 (For use only after failure in first set.) 
 52947 63852 973 18 
 
 Evaluation. — (See Test 2.) 
 
 29. Describing Pictures. 
 
 Description (D.) (Phrases indicating actions and 
 characteristics.) 
 
 Instructions and Evaluation. — (See Test 6, B.) 
 
 30. Distinguishing Right and Left. 
 
 Instructions. — " Which is your right hand ? " 
 ..." Which is your left ear ? " 
 
 Evaluation. — The child must perform both cor- 
 rectly without any kind of help. Hesitation and 
 
BINET'S TESTS OF INTELLIGENCE 67 
 
 self-correction (without any hint) are allowed : if 
 by a slip the child shows his left hand or right ear, 
 the experimenter waits a moment for a spontaneous 
 correction, which is allowed to pass, but his manner 
 of waiting should not suggest that the first action 
 was wrong. 
 
 Age Seven 
 
 31. Recognising Missing Features. 
 
 Materials. — Binet's four pictures of faces without 
 mouth, nose, eye, and of body without arms. 
 Instructions. — " Look at this lady's face. Can 
 
68 MENTAL TESTS 
 
 you tell me what has been left out ? " (Begin with 
 face without mouth.) 
 
 If the child says, " Her body," reply, " Oh, I was 
 only trying to draw her face. What must I put in 
 to finish the drawing of her face ? " (" What have 
 I forgotten in drawing her face ? ") 
 
 Evaluation. — Three correct answers out of four 
 are required. 
 
 32. Adding Three Pennies and Three Halfpennies. 
 (Concrete.) 
 
 Materials. — Three pennies and three halfpennies 
 set out in a row. (American investigators commonly 
 use stamps, but to many children the value of these 
 is unfamiliar.) 
 
 Instructions. — " Will you count this money for 
 me, and tell me how much there is altogether ? " 
 
 Evaluation. — No error and no repetition of the 
 instruction is allowed. The test should be done 
 in 8 to 10 seconds. " It is useless to wait 15 
 seconds." 
 
 33. Stating Differences between Concrete Objects. 
 
 Instructions. — " You know what wood is, don't 
 you ? . . . And you know what glass is ? . . . They 
 are not the same, are they ? ... In what way are 
 they not the same ? " (I would add, if child 
 hesitates : " They are different, are they not ? 
 Well, do you think you can tell me what the dif- 
 ference is ? . . . How can you tell ' glass ' from 
 < wood ' ? ") 
 
BINET'S TESTS OF INTELLIGENCE 69 
 
 The following words are suggested by Binet — 
 
 i. fly, butterfly; 
 ii. wood, glass ; 
 iii. paper, cardboard. 
 
 Evaluation. — Two out of three statements must 
 be correct. Any true difference will pass, though 
 trivial. But if the child repeats the same differ- 
 ence, e. g. " It is larger," it is insufficient. (Ask, 
 " In what other way are they not the same ? ") 
 Often a child takes a minute : but if he takes 
 longer than 2 minutes for all he fails. 
 
 34. Repeating Syllables. 
 
 (16 syllables.) "We are going for a walk: Mary, 
 let me see your pretty hat." 
 
 Instructions and Evaluation. — (See Test 7, no. 
 viii.) 
 
 35. Writing from Dictation. 
 
 Materials. — Pen, ink, paper. 
 
 Instructions. — " Will you write this down for me 
 on this piece of paper ? " 
 
 " The pretty little girls." 
 
 Evaluation. — The writing ( ? and spelling) must 
 be sufficiently legible and accurate to be read by a 
 person who did not know what was to be written. 
 
jo MENTAL TESTS 
 
 Age Eight 
 
 36. Reading and Reproduction. 
 
 Material. — Translation of Binet's passage, printed 
 or typed, with English place-names and money- 
 values substituted for the French. 
 
 Three / Houses / on Fire./ 
 London, / September 5th. / A huge fire / last night/ 
 burnt down / three houses in the middle of the 
 city. / Seventeen families /now have no homes. /The 
 loss is more than 15,000 pounds. /A young barber,/ 
 who saved /a baby / in its cradle, / was badly / hurt/ 
 about the hands./ 
 
 Instructions. — " Will you read this for me, 
 please ? " Two seconds after reading is finished, 
 remove the passage, and say : " Tell me what you 
 have been reading about." 
 
 Evaluation. — Each correct phrase or word as 
 indicated above constituted one item. 
 
 A. Recalls two items. (Age 8.) 
 
 B. Recalls six items. (Age 9.) 
 
 37. Answering Easy Questions. 
 Instructions. — " Tell me this — 
 
 (1) Suppose you are going somewhere by train. 
 
 What must you do if you miss your train ? 
 
 (2) Suppose one of the other boys (girls) hit you 
 
 by accident — without meaning to. What 
 should you do ? 
 
 (3) Tell me what you ought to do if you broke 
 
 something that belonged to somebody else I " 
 
BINET'S TESTS OF INTELLIGENCE 71 
 
 If no answer is given, repeat the question as usual, 
 not sternly, but pleasantly, prefixing : " Did you 
 catch what I said ? " Do not vary the wording. 
 
 Evaluation. — Two out of three must be answered 
 satisfactorily. 
 
 (1) Satisfactory answers. — " Wait for another " — 
 
 " Take the next." 
 Unsatisfactory answers. — " Go home again " 
 — " Run after it " — " Try not to miss it." 
 
 (2) Satisfactory answers. — " Do nothing " — " For- 
 
 give him." 
 Unsatisfactory answers. — " Tell teacher " — 
 " Hit him back." 
 
 (3) Satisfactory Answers. — " Pay for it " — " Own 
 
 up "— " Buy another " — " Ask to be for- 
 given " — " Say I was sorry." 
 
 Unsatisfactory answers. — " I should cry " — 
 " Hide it." 
 
 38. Counting Backwards 20-0. 
 
 Instructions. — "You can count, can't you — 1, 2, 
 3, and so on ? Now do you think you could count 
 backwards ? Start at 20, and go on till you reach 
 I." (If the child does not understand :) " Count 
 like this : 20, 19, 18 " (proceed no further). 
 
 (Yerkes suggests that the experimenter always 
 count from 25 to 21, and then pause for the examinee 
 to continue.) 
 
 Evaluation. — One error (either of omission or 
 inversion) only is permitted (Binet allows 20 seconds). 
 The child who thinks out the numbers by counting 
 up from 1 each time fails. 
 
72 MENTAL TESTS 
 
 39. Giving Full Date. 
 
 Instructions. — " What is the date to-day ? " (If 
 the word " date " is not understood, ask in detail : 
 " What day of the week is it to-day ? " " What 
 month is it ? " " Do you know what day of the 
 month?" [ist, 2nd, 3rd, or] "what number?" 
 " And what is the year — nineteen what ? ") 
 
 Evaluation. — All four items must be correctly 
 given : but an error of three days either way is 
 allowable for the day of the month (unless that 
 involves an error in naming the month). 
 
 40. Giving Change. 
 
 Materials. — The current coins \d., \d., id., 6d., 
 2s., 2s. 6d., ios., £1 and is., and in addition three 
 pennies and the three halfpennies. The five 
 boxes used for the weights. 
 
 The shilling is kept by the experimenter to pay 
 for the box. 
 
 The rest, with the boxes, are placed near the child. 
 
 Instructions. — " Now, shall we play shop for a 
 change ? You shall be the shopkeeper. Here are 
 some boxes for you to sell ; and here is your money. 
 See how rich you are ! Now, will you sell me one of 
 your boxes, please ? How much are they each ? 
 Twopence, shall we say ? Well, here is a shilling. 
 Can you give me the right change, please ? " (The 
 examiner holds out his hand for the money.) 
 
 Evaluation. — The child must actually hand over 
 the right amount (sixpence and fourpence in pennies 
 or halfpennies) : merely stating it correctly does 
 not count. 
 
BINET'S TESTS OF INTELLIGENCE 73 
 
 Age Nine 
 
 41. Repeating Numbers. 
 
 Instructions. — " Listen. Say these numbers after 
 
 me"- 
 
 (For use only after failure in first set.) 
 250634 5 7 3 9 ! ^ 495827 
 
 Evaluation. — (See Test 2.) 
 
 42. Naming Months. 
 
 Instructions. — " Can you tell me what are the 
 months of the year ? " 
 
 Evaluation. — Binet allows 15 seconds, and one 
 error. 
 
 43. Naming Coins. 
 Nine Commonest Coins. 
 
 Instructions and Evaluation. — (See Test 25, B.) 
 
 44. Reading and Reproduction. 
 Recalls Six Items. 
 
 Instructions and Evaluation. — (See Test 36, B.) 
 
 45. Defining Concrete Terms. 
 Superior to Use (G.). 
 
 Instructions and Evaluation. — (See Test 27, no. ii.). 
 
 46. Arranging Five Weights in Order. 
 
 Materials. — Five boxes, identical in colour, shape 
 and size (about 1*5 x 2*5 x 3*5 cm.), and loaded 
 with shot and cotton wool to weigh 3, 6, 9 and 
 
74 MENTAL TESTS 
 
 15 grammes, without rattling. The key letters, B, I, 
 N, E, T, may be written in order on the bottom of 
 the boxes. 
 
 Instructions. — " Do you see these boxes ? They 
 all look the same, don't they ? But they don't 
 weigh the same. Some are heavy, and some are 
 light. I want you to find the heaviest of all, and 
 put it here. Then find the one which is nearly 
 as heavy, and place it next. Then the one which 
 is still less heavy ; then the one which is lighter still ; 
 and, last of all, the one which is lightest of all, here." 
 
 Allow three trials if necessary, mixing the boxes 
 up first. 
 
 Evaluation. — The arrangement must be abso- 
 lutely correct in two out of three trials, and the 
 whole accomplished in 3 minutes. It is of special 
 interest to record the subject's actual arrangement. 
 
 47. Sentence Building with Three Words. 
 
 Materials. — Paper, pen and ink: and a card 
 with " London, river, money " written on it. 
 
 Instructions. — " I want you to make up a sentence 
 for me with these three words in : London, river, 
 money." 
 
 Instead of " London " it is often customary to 
 employ the nearest town that is on a river. (Most 
 American investigators, following Goddard, conduct 
 this test orally.) 
 
 Evaluation. 
 
 A. Two distinct ideas or sentences given (indi- 
 cates mental age of 10). " London has 
 money and rivers." 
 
BINET'S TESTS OF INTELLIGENCE 75 
 
 B. One idea or sentence given (indicates mental 
 
 age of 1 1), e. g. " In the river at London 
 I found some money." A set of sen- 
 tences in which the thought is well 
 co-ordinated into a unitary story or 
 description passes. 
 
 C. Three distinct ideas or sentences consti- 
 
 tuted a failure. E. g. " London is a 
 town. There is a big river. Some people 
 have money." 
 
 Enter "1," "2" or "3" according to number 
 of sentences given, and note time. At least three- 
 quarters of the test should be written within a 
 minute. Binet states that this is one of the rare 
 cases in which a child may succeed by having heard 
 of the test from another child. If there is any 
 likelihood of this, ask at the outset : " What do you 
 think I have been asking the others to do with these 
 words ? " and substitute others, if necessary. The 
 child may guess the test from school exercises. 
 
 48. Drawing Two Designs from Memory. 
 
 Materials.— Binet's two designs, drawn pre- 
 viously on a single card or sheet, kept out of sight 
 until required. A pencil and plain paper. 
 
 Binet's list No.4*S. 
 
76 MENTAL TESTS 
 
 Instructions. — " I am going to show you two 
 easy drawings. I want you to look at them very 
 carefully until I take them away. Then, after I 
 have turned them over, see if you can draw them 
 both from memory on this paper. You will only 
 see them for a very few seconds. Now look at 
 them both carefully first of all. Ready ? Now ! " 
 The drawings are held steadily in front of the child, 
 the truncated prism on the left, for 10 seconds (see 
 that the child does not imagine he has to copy them 
 at once), and then taken away and turned face down- 
 wards. " Now try and draw them for me here." 
 
 Evaluation. — The whole of one and a half of the 
 other must be reproduced fairly exactly. No 
 second attempt is allowed. Neatness of drawing 
 does not count. The examiner must be careful 
 not to interpret " fair exactness " more strictly for 
 older than for younger children. The standard 
 accepted in the case of this test is thus far below 
 what the uninstructed teacher would accept as a 
 satisfactory reproduction. 
 
 Age Eleven 
 49. Explaining Absurdities. 
 
 Instructions. — " Listen carefully to what I am 
 going to say. There is something in it that is 
 really quite silly and impossible. See if you can 
 tell me what is wrong." 
 
 i. " ' One day, a man fell off his bicycle on to his 
 head and was killed instantly. He was taken 
 to the hospital and they say he will never 
 get better.' What is there silly in that ? " 
 
BINET'S TESTS OF INTELLIGENCE yj 
 
 ii. " ' Once the body of a poor girl was found 
 in a wood, cut into eighteen pieces. They 
 say that she killed herself.' What is silly 
 in that ? " 
 
 iii. " ' Yesterday there was a railway accident. 
 But the newspaper says it is not a serious 
 one, as only forty-eight people were killed.' 
 What is silly in that ? " 
 
 iv. " * I have three brothers — Jack, Tom and 
 myself.' What is silly in that ? " (Female 
 examiners must preface this with, " A boy 
 said to me, etc.," or else substitute, " I have 
 three sisters, Jane, Mary and myself.") 
 
 v. " ' A man once said, " If I should ever grow 
 desperate and kill myself, I shall not choose 
 a Friday to do it on, for Friday is an un- 
 lucky day, and would bring me bad luck." ' 
 What is foolish in what the man said ? " 
 
 Evaluation. — Three absurdities should be de- 
 tected out of five. If a child's first statement is 
 not clear (e. g. " myself is silly " in answer to iv.), 
 say, " Explain what you mean." Otherwise, give 
 him no second chance. 
 
 (i.) Correct : " He couldn't get well if he was 
 already dead." " First you said he was 
 dead, and then you said he wouldn't get 
 well again." 
 Incorrect ; " They ought to have taken him 
 to the mortuary." " If he fell off his 
 bicycle, he wouldn't fall on his head." 
 (ii.) Correct : " You can't cut yourself into 
 eighteen pieces." " If she killed herself 
 she couldn't cut herself up." 
 
78 MENTAL TESTS 
 
 (iii.) Correct : " It must have been serious if 
 forty-eight were killed, or if anybody was 
 killed." " If it wasn't serious only one 
 or two would have been killed." " Forty- 
 eight isn't serious in war-time." 
 
 Incorrect : " Forty-eight people couldn't be 
 killed in a railway accident." 
 (iv.) Correct : " You have only two." " You are 
 not your own brother." " You shouldn't 
 count yourself." 
 
 Incorrect : " You should put yourself last." 
 (v.) Correct : " If he killed himself, the day 
 wouldn't matter." " He couldn't have 
 bad luck if he was dead." " If he was 
 desperate, he wouldn't wait till Friday." 
 
 Incorrect : " He is silly to believe in bad luck." 
 " Friday isn't different -fee any other day." 
 
 50. Answering Difficult Questions. 
 Instructions. — " Can you tell me this ? " 
 
 (1) " What should you do if you found you were 
 
 late on your way to school ? " 
 
 (2) " Suppose a boy does something that is un- 
 
 kind : why do we forgive him more readily 
 if he was angry than if he was not angry ? " 
 
 (3) "If some one asked what you thought of a 
 
 boy (or girl) whom you did not know very 
 well, what should you say ? " 
 
 (4) " Why should we judge a person by what he 
 
 does, and not by what he says ? " 
 
 (5) " Suppose you were going to undertake some- 
 
 thing very important : what should you 
 do first of all ? " 
 
BINET'S TESTS OF INTELLIGENCE 79 
 
 Repeat a question once, if necessary, but do not 
 vary the wording. 
 
 Evaluation. — Allow 20 seconds for reflection on 
 each question. Three out of five must be answered 
 satisfactorily. 
 
 (1) Satisfactory: "Hurry" or "Run" ("Go 
 
 straight to school " may be accepted if it 
 appears that the child sometimes plays or 
 carries out errands on its way). 
 Unsatisfactory : " Get the stick." " Leave 
 earlier." " Get up sooner next time." 
 " Ring the bell." " Get a note to excuse 
 me." By convention, anything not em- 
 bodying the idea of hurrying. 
 
 (2) Satisfactory : " Because he didn't know what 
 
 he was doing." " Because he'd be sorry 
 afterwards." Anything suggesting that 
 anger may constitute an excuse, however 
 badly expressed. 
 Unsatisfactory : " He oughtn't to get angry." 
 Anything suggesting disapproval of anger. 
 
 (3) Satisfactory : " I could not say anything." 
 
 " I could not tell him without finding out." 
 " I should say, ' I do not know.' " 
 Unsatisfactory : " I should have to ask." 
 " Say I did not know his name." Usually 
 unintelligible. 
 
 (4) Satisfactory : " You can rely on his actions, 
 
 but not on what he says." " Because 
 he might not always speak the truth." 
 " Actions speak louder than words." 
 Unsatisfactory : Usually unintelligible. " Be- 
 cause you can't tell." " You ought to 
 speak the truth." 
 
80 MENTAL TESTS 
 
 (5) Satisfactory : " Think it over." " Ask some 
 one about it." " Prepare for it." 
 Unsatisfactory : Usually unintelligible. " Not 
 do it." 
 
 (Some say " Tidy myself," " Put on a clean collar ; " 
 in that case make it clear that you mean doing some- 
 thing important, not going somewhere important.) 
 
 51. Repeating Numbers. 
 
 Instructions. — " Listen. Say these numbers after 
 me." 
 
 (For use only after failure in first set.) 
 9647518 4829653 5928136 
 
 Evaluation. — (See Test 2.) 
 
 52. Giving Sixty Words in Three Minutes. 
 
 Instructions. — " I want you to give me as many 
 words as you possibly can in 3 minutes. Keep 
 saying words like this till I stop you : school, teacher, 
 board, boy, girl, and so on. Some children can 
 give more than 200. Are you ready ? Now start." 
 When he stops encourage him immediately by say- 
 ing : " Very good. Keep on." 
 
 Evaluation. — Sixty words must be given, ex- 
 clusive of repetitions. If the child gives sentences, 
 start him again, saying: "You must give separate 
 words." Be careful (1) to note the time, if possible 
 with a second hand (2) to count the words, entering 
 a stroke or other mark for each, and calculating the 
 total. It is interesting to record the key-words of 
 the child's various topics ; it is seldom possible to 
 put down all words. 
 
BINET'S TESTS OF INTELLIGENCE 81 
 
 53. Sentence Building with Three Words. 
 
 Materials. — Paper, pen and ink, and a card with 
 " London, river, money," written on it. 
 
 One Idea or Sentence. 
 
 Evaluation. — (See Test 47, B.) 
 
 Age Twelve 
 
 54. Giving Three Words to Rhyme. 
 
 Instructions. — " Do you know what a rhyme is ? 
 When two words end the same way, we call them 
 rhymes. ' Jill ' rhymes with ' hill ' because they 
 both end in ' ill.' Do you understand ? Now can 
 you give me three words which rhyme with 
 < obey ' ? " 
 
 Evaluation. — -The child must give three genuine 
 words that rhyme in 1 minute. Binet's instruc- 
 tions to the child ask for " other words " or " all 
 the words." It saves time to specify three to the 
 child. If the child gives nothing, or has not given 
 enough, urge him by saying " what (else) rhymes 
 with ' obey.' " Apparently " disobey " may be 
 accepted as one of the three. 
 
 55. Rearranging Mixed Sentences. 
 
 Materials. — Three cards containing the following 
 words — 
 
 i. a defends dog good his bravely master ; 
 ii. my have teacher I the correct asked paper to ; 
 iii. home we early our in country left visit the to 
 friends. 
 
 G 
 
82 MENTAL TESTS 
 
 Instructions. — " Put these words in order, and 
 find out the sentence which they make." 
 
 Evaluation. — Two correct solutions must be given 
 out of three. Only I minute is allowed for each. 
 
 Correct solutions are — 
 
 i. " A good dog defends his master bravely." 
 " A dog defends his good master bravely." 
 (" A master defends his good dog bravely," 
 is, according to Binet, " poor " and appar- 
 ently incorrect), 
 ii. " I have asked my (the) teacher to correct 
 the (my) paper." 
 (" I asked my teacher to have the paper 
 correct" is, presumably, incorrect.) 
 iii. " We left home early to visit our friends in 
 the country." 
 (" We left our friends in the country to visit 
 our home early," and other sensible variants 
 are presumably correct.) 
 
 56. Describing Pictures. 
 
 Interpretation. — (Goes beyond what is actually 
 visible in the picture, and mentions the situation or 
 emotion it suggests.) 
 
 (See Test 6, C.) 
 
 Age Thirteen 
 
 57. Resisting Suggestion. 
 
 Materials. — A book of six leaves with two lines 
 drawn in the same straight line on one page in 
 opening. The lengths must be as follows — 
 
BINET'S TESTS OF INTELLIGENCE 83 
 
 
 1st line. 
 
 2nd line. 
 
 
 1st page 
 
 4 cm. 
 
 5 cm. 
 
 
 2nd page 
 
 5 cm. 
 
 6 cm. 
 
 
 3rd page . . 
 
 6 cm. 
 
 7 cm. 
 
 
 4th page . . 
 
 7 cm. 
 
 7 cm. 
 
 
 5th page . . 
 
 . - . 7 cm. 
 
 7 cm. 
 
 * 
 
 6th page 
 
 7 cm. 
 
 7 cm. 
 
 
 Instructions. — For the first three pages : " Which 
 is the longer of those two lines ? " for the last three, 
 without changing the tone : " And these ? " 
 
 Evaluation.- — Note whether child's judgments 
 are right or wrong in each case, especially with 
 reference to the last three. The child succeeds 
 if he judges two out of three equal lines to be 
 equal. 
 
 58. Solving Circumstantial Problems. 
 
 Instructions. — " Can you guess the answer to this 
 riddle ? 
 
 i. " One day a woman, walking in Epping Forest, 
 stopped still, terribly frightened. Then she 
 hurried to the nearest police station, and 
 told the policeman she had just seen, hang- 
 ing from the branch of a tree, a well, 
 
 what do you think it was she saw ? " 
 ii. " My next-door neighbour has had three 
 visitors. First, a doctor called ; then a 
 lawyer ; and then a clergyman. What do 
 you think has been happening there ? " 
 
 Evaluation. — Both questions must be correctly 
 answered. 
 
84 MENTAL TESTS 
 
 i. Correct: Replies must contain the idea of 
 some one hanged. If the child answers 
 " a man," " a dead person," therefore, ask 
 " How did he get up in the tree ? " 
 Incorrect : " A bird." " Some one robbing a 
 nest." 
 
 ii. Correct: "Some one is dying," "is very 
 ill." (Severe illness can be inferred from 
 the visit of the doctor alone. But Binet 
 apparently accepts it, without inquiring 
 whether the child knows the object of the 
 other visitors.) 
 
 Age Fourteen 
 
 59. Repeating Syllables. 
 
 (26 syllables.) " The other morning I saw in the 
 street a little yellow dog." " Little Maurice has 
 spoilt his new apron." 
 
 Evaluation. — (See Test 7, no. xiii.) 
 
 60. Defining Abstract Terms. 
 
 Instructions. — " Can you tell me this ? What is 
 meant — 
 
 i. by kindness ? 
 ii. by justice ? 
 iii. by charity ? " 
 
 (For " charity " some investigators have substi- 
 tuted " obedience " : but this changes the difficulty 
 of the test.) 
 
BINETS TESTS OF INTELLIGENCE 85 
 
 Evaluation. — Two must be correctly defined out 
 of three. Correct definitions — 
 
 For (i) contain the idea of an instance of affec- 
 tion, tenderness, politeness or consideration to 
 others. (" Being polite or good to others " is 
 correct. " Being kind," " doing something good," 
 are inadequate.) 
 
 For (ii) contain the idea of treating people accord- 
 ing to their merits, or of protecting the innocent 
 and their interests, or of punishing the guilty. 
 E. g. " when you punish wicked people," " playing 
 fair." 
 
 For (iii) contain the ideas of (a) poor or un- 
 fortunate people, and (b) of showing kindness. 
 E. g. " when you give poor people some money," 
 " giving alms." 
 
 Age Fifteen 
 
 61. Drawing from Imagination the Cuts in a 
 Folded Paper. 
 
 Materials. — Two sheets of paper about 6 inches 
 square. A pencil. One sheet is folded in four like 
 a letter ready for an envelope. In the middle of 
 the edge which presents but a single fold, a small 
 triangular notch, about 1 cm. deep, is drawn. 
 
 Instructions. — " Here is a sheet of paper that has 
 been folded across and then folded again. Suppose 
 now Icut out a notch just here. When the paper 
 is unfolded again, what would it look like ? Will 
 you show me on this piece how and where it would 
 be cut ? " 
 
86 MENTAL TESTS 
 
 Evaluation. — Two diamond-shaped holes should 
 be drawn in a line with each other, each in the middle 
 of one half of the paper. 
 
 62. Giving Differences between Abstract Terms. 
 
 Instructions. — " What is the difference between — 
 
 i. pleasure and happiness ? 
 ii. poverty and misery ? 
 iii. evolution and revolution ? " 
 
 The words baggested by Binet {Bulletin) are — 
 
 i. paresse, oisivete ; 
 
 ii. evenement, avenement ; 
 
 iii. evolution, revolution : and in 1908 scale also — 
 iv. plaisir, bonheur ; 
 
 v. orgeuil, pretention. 
 
 Evaluation. — Two out of three must be cor- 
 rectly answered. Good replies should bring out 
 an opposition or antithesis between the differenti- 
 ating ideas. E. g. (i) " happiness " is superior to 
 or more general than " pleasure " ; (ii) should con- 
 trast having little money with being in misery or 
 pain ; (iii) should contrast slow change with sudden 
 change. But Binet admits mere differences ; e. g. 
 evolution is the movement of troops, revolution is 
 an insurrection. 
 
 63. Drawing the Displaced Triangle. 
 
 Materials. — Paper and pencil for drawing. A 
 card about 10 x 15 cm., cut across the diagonal, 
 as used for divided card test, The card is first laid 
 
BINET'S TESTS OF INTELLIGENCE 87 
 
 on the table before the subject with the cut edges 
 touching. 
 
 Instructions. — " Look carefully at the lower piece 
 of this card. Suppose I turn it over and lay this 
 edge (A-C) along this edge (A-B of the upper 
 triangle), and suppose that this corner (C) is placed 
 just at this point (B), what would it all look like ? 
 Now I am going to take the piece away (remove 
 lower triangle from view). Imagine it placed as 
 I told you, and draw its shape in the proper position. 
 Begin by drawing the outline of the top triangle." 
 
 Evaluation. — The essential points are : (i) A C B 
 must be preserved as a right angle ; (ii) A C must 
 be made shorter than A B. 
 
 64. Summarising Hervieifs Reflections on Life. 
 
 Instructions. — " Attend carefully to what I am 
 going to read you. When I have finished I shall 
 want you to tell me the meaning of what I read in 
 
88 MENTAL TESTS 
 
 your own words. The exact words that I use do 
 not matter. Listen — 
 
 ' Many opinions have been given on the value of 
 life. Some say it is good, others say it is bad. It 
 would be truer to say that it is just medium. For, 
 on the one hand, the happiness it brings us is never 
 so great as we ourselves should like, and, on the 
 other hand, the misfortunes it brings us are never 
 so great as our enemies would want us to have. 
 It is the intermediate nature of life that makes it 
 fair, or, at least, prevents it from being altogether 
 unfair.' 
 
 Now see if you can give me, in your own 
 words, the sense of what I have just read to you." 
 
 Evaluation. — The central thought must be under- 
 stood and these three ideas reproduced : (i) Life 
 is neither good nor bad, but medium, for (2) it is 
 not so good as we wish, but (3) better than what 
 others wish for us. The terms and expressions 
 matter little. 
 
 65. Giving the Differences between President and 
 King. 
 
 Instructions. — " There are three chief differences* 
 between a King and a President of a Republic. Can 
 you tell me what they are ? " " Can you think of 
 any of them ? " 
 
 Evaluation. — Two of the following differences, 
 apparently, must be given. (Some consider Binet 
 required all of the first three.) 
 
 i. A King inherits his crown : a President is 
 elected. 
 
BINET'S TESTS OF INTELLIGENCE 89 
 
 ii. A King is king for life : a President's term of 
 
 office is limited, 
 iii. The powers of a King are greater than those 
 
 of a President, 
 iv. A King is not directly responsible to the 
 
 people : a President is. (Added by Melville 
 
 in place of iii.) 
 
 (This test is obviously more suited to French and 
 American children than to English. The third 
 difference is hardly true of an English king.) 
 
CHAPTER V 
 
 burt's reasoning tests 
 
 A teacher who has studied Binet's tests will at 
 once perceive that they are unsuitable for the upper 
 standards. They were not devised for the discovery 
 of the bright children, but for the detection of the 
 dull. If the aim is to select supernormal children 
 to whom scholarships might be awarded, a more 
 difficult series of tests — a series that appeals more 
 exclusively to the higher mental functions — is 
 necessary. The tests recently published by Mr. 
 Cyril Burt and printed below were designed to meet 
 that need. A full description of the circumstances 
 under which the tests were drawn up and stan- 
 dardised, together with an account of the develop- 
 ment of reasoning in school-children, will be found 
 in an article by Mr. Burt in the Journal of Experi- 
 mental Pedagogy for June 191 9 and December 1919. 
 
 To quote from that article : " The test-questions 
 are intended to be given to each child individually 
 and orally. In my own experiments each problem 
 was type-written upon a separate card ; a fresh 
 statement commenced on a fresh line ; and by 
 means of indentation and spacing, question and 
 premises were distinguished from each other. A 
 card is handed to the child with the following 
 instructions ; ' Will you read this little puzzle ? 
 
 90 
 
BURT'S REASONING TESTS 91 
 
 There is an easy question at the end. When you 
 have read the question, read carefully again what 
 is printed above, and try whether you can think of 
 the answer.' The younger and duller children 
 should read the test-questions aloud ; and with 
 the youngest and dullest of all, the examiner should 
 read the questions with or to the child. Children 
 of higher levels (Standard III) need only read 
 aloud the first few questions. Any child who is 
 unable to read a particular word or to comprehend 
 its meaning should be freely helped. The graver 
 incongruities between difficulty of phrase and 
 difficulty of logic have been eliminated. In a per- 
 fectly revised list they should never occur. A bright 
 young child is occasionally puzzled by such words 
 as ' sub-tropical,' and ' emotion,' although com- 
 petent to follow the reasoning. When it is clear 
 that the child understands his task, he should be 
 left quietly with the card, forgetful, if possible, of 
 the examiner's presence. The emotional confusion, 
 the ' examination paralysis,' that so commonly 
 embarrasses an oral interview is by this means 
 largely avoided. When the child gives an answer, 
 it is invariably received with a word of praise, 
 whether right or wrong ; and the child is asked 
 to give his reason. 
 
 " One mark is given for each test correctly answered 
 and correctly reasoned. When necessary, the child 
 may be given additional trials, not exceeding three 
 in all for any one test. But for each unsuccessful 
 attempt a quarter of a mark is deducted. A frac- 
 tion — as a rule, a quarter, a half, or three-quarters 
 respectively — is also deducted for an ill-expressed 
 reason, an inadequate reason, or no reason at all, 
 
92 MENTAL TESTS 
 
 In the cross-examination as to reasons lies the most 
 valuable part of the test. The examiner gleans 
 considerable information, not only about the know- 
 ledge and intellectual procedure of the child, but 
 also about its temperament and disposition so far 
 as they affect his intellectual efficiency. In the 
 final estimate of the child he would take into account 
 both these broader observations, and in particular 
 the speed with which the child has worked. In 
 the actual marking no allowance is made for such 
 latter factors ; nor is any time-limit assigned. 
 Could scores be corrected on the basis of the general 
 impressions incidentally gained, the correlations 
 with ability, high as they are, would be still further 
 raised. 
 
 " For a child to work steadily through a series of 
 fifty reasoning tests until he breaks down would, 
 at any rate for the brighter and older children, be 
 a slow and fatiguing process. A short series has 
 therefore been constructed by selecting every third 
 test in the full series. The short list thus contains 
 only seventeen questions, two for each age except 
 the first, which has three. 
 
 " In the full list appended these selected questions 
 are marked with asterisks. They have been more 
 carefully chosen, more extensively used, and more 
 thoroughly revised. For practical purposes, indeed, 
 the short list will be sufficient, since this allows a 
 rough and rapid determination of mental age. 
 Where, however, it is required to obtain a more 
 exact estimate of a child whose mental level is 
 already approximately known — for example, in 
 testing children within the same school standard — 
 the full list is indispensable, since with the short 
 
BURT'S REASONING TESTS 93 
 
 list no member of a fairly homogeneous class could 
 be expected to differ from the others by more than 
 one or two marks. 
 
 " Children should be tested with the short list first. 
 Even the oldest and brightest should begin with 
 the easiest test. They should be carried through 
 the series until they have broken down with three 
 consecutive tests. The supplementary questions 
 should be given subsequently, and upon a different 
 day. Here it will be expedient to start, not at the 
 beginning of the series, but about four tests below 
 the level of the first serious failure made on the 
 short list ; and the child should be carried through 
 until he breaks down on at least six tests consecu- 
 tively." 
 
 BURT'S GRADED REASONING TESTS. 
 
 Seven Years 
 
 *i. Tom runs faster than Jim : Jack runs slower 
 than Jim. Who is the slowest — Jim, Jack or Tom ? 
 
 2. All wall-flowers have four petals : this flower 
 has three petals. Is this a wall-flower ? 
 
 3. It looks like rain : but I shall stay indoors. 
 Shall I want an umbrella to-day ? 
 
 *4. Kate is cleverer than May : May is cleverer 
 than Jane. Who is the cleverest — Jane, Kate or May ? 
 
 5. It is Sunday ; and on a Sunday afternoon Ada 
 usually takes the baby out, or goes by herself to the 
 pictures, or walks over to see her aunt, or else goes 
 by tram to the cemetery. To-day she has no 
 money with her : and the baby is asleep upstairs. 
 Where do you think she has probably gone ? 
 
 6. Tom said to his sisters : " Some of my flowers 
 
94 MENTAL TESTS 
 
 are buttercups." His sisters knew that all butter- 
 cups are yellow. So Mary said : " All your flowers 
 must be yellow." Grace said : " Some of your 
 flowers must be yellow." And Rose said : " None 
 of your flowers are yellow." Which girl was right ? 
 *7. I have bought the following Christmas pre- 
 sents : a pipe, a blouse, some music, a box of 
 cigarettes, a bracelet, a toy engine, a bat, a book, 
 a doll, a walking-stick and an umbrella. My 
 brother is eighteen : he does not smoke, nor play 
 cricket, nor play the piano. I want to give the 
 walking-stick to my father and the umbrella to my 
 mother. Which of the above shall I give to my 
 brother ? 
 
 Eight Years 
 
 8. All great men work hard and long every day : 
 Sir John Smith worked three hours a day. Was 
 Sir John Smith a great man ? 
 
 9. Peter has a half-holiday on Wednesdays and 
 Saturdays, and a whole holiday on Sunday. I am 
 at work all day, except on Monday, Wednesday, 
 Friday and Sunday. I want to take Peter to the 
 tailor's to buy a new suit. Which afternoon could 
 we go together ? 
 
 *io. I don't like sea voyages ; and I don't like 
 the seaside. I must spend Easter either in France, 
 or among the Scottish Hills, or on the South Coast. 
 Which shall it be ? 
 
 1 1 . Ethel has twice as many apples as John : 
 Lucy has half as many as John : Lucy has ten. 
 How many has Ethel ? 
 
 12. Edith is fairer than Olive, but she is darker 
 than Lily. Who is darker — Olive or Lily ? 
 
BURT'S REASONING TESTS 95 
 
 *I3« The person who stole Brown's purse was 
 neither dark, nor tall, nor clean-shaven. The only 
 persons in the room at the time were : (1) Jones, 
 who is short, dark and clean-shaven. (2) Smith, 
 who is fair, short and bearded. (3) Grant, who is 
 dark, tall, but not clean-shaven. Who stole Brown's 
 purse ? 
 
 Nine Years 
 
 14. C is smaller than B : B is smaller than A. 
 Is A greater than C ? 
 
 15. A burglar entered my room at the Hotel 
 Splendid last night. The windows were all securely 
 fastened on the inside, and the fastenings and the 
 window-panes are undisturbed. The opening up 
 the chimney is only nine inches square. The door 
 opening into the main corridor was locked and the 
 key left on the outside. The ceilings, walls and 
 floor have no other openings, either secret or forced, 
 through which he could have entered. How did 
 he get in ? 
 
 *l6. Three boys are sitting in a row : Harry is 
 to the left of Willie ; George is to the left of Harry. 
 Which boy is in the middle ? 
 
 17. If I have more than a shilling I shall either 
 go by taxi or by train : if it rains I shall either go 
 by train or by 'bus. It is raining, and I have half a 
 crown. How do you think I shall go ? 
 
 18. On one side of my street the houses all have 
 odd numbers, beginning with the grocer's, which 
 is No. 1. On the other side the numbers are even ; 
 No. 2, the baker's, being opposite No. 1. My 
 house is No. 16. Walter is my next-door neigh- 
 bour : you pass his house as you come up from the 
 
96 MENTAL TESTS 
 
 baker's just before you get to mine. What is the 
 number on his door ? 
 
 *I9« In cold, damp climates, root crops like 
 potatoes and turnips grow best ; in temperate climates 
 there are abundant pastures, and oats and barley 
 flourish ; in sub-tropical climates, wheat, olives 
 and vines flourish ; in tropical climates, date palms 
 and rice flourish. The ancient Greeks lived largely 
 on bread, with oil instead of butter : they had wine 
 to drink and raisins for fruit. Which climate do 
 you think they had ? 
 
 Ten Years 
 
 20. Some children were asked : " Why are towns 
 nearly always more unhealthy than the country ? " 
 They gave the following replies : (i) " Some country 
 places are by the seaside." (2) " There are more 
 doctors in the towns." (3) " The smoke of the 
 houses and the breath of the people prevent the 
 air from being fresh." (4) " The cottages in the 
 country are dark, tiny, and badly built." (5) 
 " Disease spreads where people are crowded to- 
 gether." Which two children gave the best 
 answers ? 
 
 21. " Drinking the sea dry." " Catching the 
 wind in a cabbage net." " Gathering grapes from 
 thistles." " Washing a blackamoor white." " Touch- 
 ing the end of a rainbow." All these sayings mean 
 
 something that is ? (Give the meanings of all 
 
 of them in one word.) 
 
 *22. The doctor thinks Violet has caught some 
 illness. If she has a rash, it is probably chicken-pox, 
 measles or scarlet fever. If she has been ailing with 
 
BURT'S REASONING TESTS 97 
 
 a cold or cough she may develop whooping-cough, 
 measles or mumps. She has been sneezing and 
 coughing for some days, and now spots are appearing 
 on her face and arms. What do you think is the 
 matter with Violet ? 
 
 23. "I sprang to the stirrup and Joris and he : 
 
 I galloped, Dirck galloped, we galloped 
 all three." 
 
 What was the name of the person referred to as 
 " he " in these lines of poetry ? 
 
 24. The Duchess of Dustiland's diamonds have 
 been stolen. After the ball at the palace she gave 
 them to her manservant to take home, with instruc- 
 tions to hand them over to her maid at once. When 
 he was half-way home he met a friend, and a few 
 minutes afterwards a man in blue uniform and helmet 
 came up to -them and said : " I arrest you for stealing 
 the Duchess of Dustiland's jewels." They were 
 taken to a large building outside which a blue lamp 
 was hanging with the words " Police Station " 
 printed on it. Here another man in uniform took 
 possession of the diamonds, and locked up both 
 the manservant and his friend in a small, bare room 
 for the night. When day dawned, hearing nobody 
 about they climbed out through the window, but 
 could see nothing of either the lamp or policemen. 
 The Duchess is still looking for her jewels. Who do 
 you think is the thief ? 
 
 *2$. There are four roads here. I have come 
 from the South and want to go to Melton. The 
 road to the right leads somewhere else : straight 
 ahead it leads only to a farm. In which direction 
 is Melton — North, South, East or West ? 
 
98 MENTAL TESTS 
 
 Eleven Years 
 
 26. A man was found nearly dead with his throat 
 cut, and on the back of his left arm there was a 
 blood-stained mark of a left hand. The policeman 
 says he tried to kill himself. Do you think the 
 policeman was right ? 
 
 27. C is West of B : B is West of A. Is A to the 
 North, South, East or West of C ? 
 
 *28. Father has just come home in a brand new 
 overcoat : there is clay on his boots, and flour on his 
 hat. The only places he can have been to are North- 
 gate, Southgate, Westgate or the City. He has 
 not had time to go to more than one of these. 
 There is no clay anywhere in the streets except 
 where the pavement is up for repair. There are 
 tailor shops only in Southgate, Westgate and the 
 City. There are flour mills only in Northgate, 
 Westgate and the City. I know the roads are not 
 being repaired in the City, though they may be in 
 the other places. Where has father been ? 
 
 29. The following are some of the occasions on 
 which people shed tears : People laugh till they 
 cry. When they are very unhappy they weep. 
 A fly in the eye makes the tears flow. Peeling 
 onions, scraping horseradish, going through smoke, 
 a cold wind in the face — all make the eyes water. 
 These instances suggest two general causes which 
 produce tears. What are they ? Choose your 
 answer from the following phrases : (1) Moderate 
 happiness. (2) Bright colours such as red and green. 
 (3) Germs. (4) Violent emotions. (5) Irritation of 
 the eye-ball. (6) A warm temperature. 
 
 30. In our school a third of the school play 
 
BURT'S REASONING TESTS 99 
 
 football, and a third play cricket. (1) Are there 
 any who play neither football nor cricket ? (2) Are 
 there any who play both ? (If it is impossible to 
 tell without asking further, say so.) 
 
 *3I. Where the climate is hot, aloes and rubber 
 will grow : heather and grass will only grow where 
 it is cold. Heather and rubber require plenty of 
 moisture : grass and aloes will grow only in fairly 
 dry regions. Near the river Amazon it is very hot 
 and very damp. Which of the above grows there ? 
 
 Twelve Years 
 
 32. My brother writes : " I have walked over 
 from Byford Wood to-day, where I had the mis- 
 fortune yesterday to break a limb." Can you guess 
 from this which he probably broke — his right arm, 
 left arm, right leg, or left leg ? 
 
 33. In the old world the most thickly-populated 
 parts have usually been India, China, and the South 
 and West of Europe. In India and China the 
 rainfall is high in the summer ; on the shores of the 
 Mediterranean it is high during the winter ; on the 
 shores of the Atlantic it is fairly high all the year 
 round. In the deserts of Russia, Persia and Africa, 
 it is dry all the year round. Africa is very hot ; 
 India and China are very warm ; South and West 
 Europe rather warm ; the deserts of Russia cold. 
 What kind of climate seems to have helped the 
 growth of civilisation most of all — cold and dry, 
 warm and dry, or hot and dry ? cold and wet, warm 
 and wet, or hot and wet ? 
 
 *34_. Field-mice devour the honey stored by the 
 humble-bees : the honey which they store is the 
 
ioo MENTAL TESTS 
 
 chief food of the humble-bees. Near towns there 
 are far more cats than in the open country. Cats 
 kill all kinds of mice. Where, then, do you think 
 there are most humble-bees — near towns or in the 
 open country ? 
 
 35. My birthday is on December 27, and I am 
 just four days older than Tom. This year Christmas 
 Day comes on a Tuesday. On what day of the 
 week is Tom's birthday ? 
 
 36. If the train is late he will miss his appoint- 
 ment : if the train is not late he will miss the train. 
 We do not know whether the train was late or not. 
 Can we tell whether he kept his appointment ? 
 
 *37. I started from the church and walked 100 
 yards ; I turned to the right and walked 50 yards ; 
 I turned to the right again and walked 100 yards. 
 How far am I from the church ? 
 
 Thirteen Years 
 
 38. Explain how the following code is worked : 
 Message (in code) . dpnf up Mpoepo bu podf. 
 The same (translated) come to London at once. 
 
 What is the secret letter for " x " in this code ? 
 
 39. Dismal Johnny said to Sunny Jim : "If I 
 marry I shall be miserable, because I shall be bothered 
 with looking after my wife ; if I don't marry I shall 
 still be miserable, because I shall have no wife to 
 look after me. So in either case I shall be miser- 
 able." Sunny Jim replied : " On the contrary, you 
 ought to be happy in either case ; for, if you do not 
 marry, you will be happy, because you will not be 
 
 bothered with looking after your wife, and " 
 
 How do you think he finished his argument ? 
 
BURT'S REASONING TESTS 101 
 
 *40. A pound of meat should roast for half-an- 
 hour ; two pounds of meat should roast for three- 
 quarters of an hour ; three pounds of meat should 
 roast for one hour ; eight pounds of meat should 
 roast for two hours and a quarter ; nine pounds of 
 meat should roast for two hours and a half. From 
 this can you discover a simple rule by which you 
 can tell from the weight of a joint how long it 
 should roast ? 
 
 41 . I walked 10 yards down High Street ; I turned 
 to the left and walked 15 yards down Thomas 
 Street ; I turned to the left again and walked 10 
 yards down James Street ; I turned to the left 
 again and walked 15 yards down another street; 
 I turned to the left again and walked 10 yards down 
 that street ; I turned to the left again and walked 
 5 yards. What street was I in ? 
 
 42. 1 is 1, that is, 1 times 1. 
 
 1 and 3 added together are 4, that is, 2 times 2. 
 1 and 3 and 5 added together are 9, that is, 
 
 3 times 3. 
 1 and 3 and 5 and 7 added together are 16, 
 
 that is, ? 
 
 Look at the above carefully. Can you see a simple 
 rule for guessing the answers without adding up the 
 figures ? Work the following sums yourself ; this 
 will help you to find the rule : (i) 1 and 3 and 5 and 
 
 7 and 9 added together are , because this is 
 
 times . (ii) What do the first seven odd 
 
 numbers (1, 3, 5, 7, 9, 11, 13) come to when added 
 
 together ? This is times . Use the rule 
 
 to find how much the first hundred odd numbers 
 would come to if added up. 
 
102 MENTAL TESTS 
 
 *43. What conclusions can you draw from the 
 following facts ? Iron nails will not float in a pool ; 
 a cup of pure gold dust weighs nearly twenty times 
 as much as a cup of water of the same size ; if you 
 drop a silver sixpence or a copper coin into a puddle, 
 it will sink to the bottom ; a cubic inch (about a 
 tablespoonful) of water weighs less than half an 
 ounce ; a cubic inch of brass weighs over two 
 ounces ; a leaden weight will drop to the bottom 
 of the ocean. Sum up all these observations in one 
 
 short sentence of the following form : " Most 
 
 are ." 
 
 Fourteen Years 
 
 44. When you enter my house you will find a 
 window on your right in the side wall of the passage. 
 When the sun sets it shines straight through this 
 window on to the wall opposite. What direction 
 are you facing when you stand in the doorway and 
 look across the street ? 
 
 45. If the A's have a bigger army than the B's 
 we ought first either to fight the B's, or attack the 
 C's by sea, but not attack the A's ; if their army 
 is smaller we should attack the A's first. If the C's 
 have a bigger navy than we, we ought to fight either 
 the B's or the A's, but not the C's. If their navy 
 is smaller, we should first attack the C's by sea. 
 The size of their armies and navies is as follows — 
 
 A. 
 
 Men 
 7,000,000 
 
 Ships 
 300 
 
 B. 
 C. 
 
 Ourselves. 
 
 5,000,000 
 4,000,000 
 6,000,000 
 
 400 
 500 
 200 
 
 Whom should we attack first ? 
 
BURT'S REASONING TESTS 103 
 
 */\6. John said : " I heard my clock strike yester- 
 day ten minutes before the first gun fired. I did 
 not count the strokes, but I am sure it struck more 
 than once, and I think it struck an odd number." 
 John was out all the morning, and his clock stopped 
 at five to five the same afternoon. When do you 
 think the first gun fired ? 
 
 47. Mary has just taken a penny ticket. The 
 trains from this station all stop at Euston, but after 
 that some go to Chalk Farm and Golders Green ; 
 others go to Kentish Town and Highgate. They 
 stop nowhere else. The fare to Euston, Chalk 
 Farm or Kentish Town is a penny : to Highgate or 
 Golders Green twopence. Mary did not get in 
 the Golders Green train. To what station do you 
 think she is travelling ? 
 
 48. They say that in Dodoland hundreds of years 
 ago all the kingfishers had legs about six inches 
 long, and beaks about two inches long, and they 
 used to wade in the water to catch fish for food. 
 The individual birds might differ from one another 
 in the length of their beaks and legs by about half 
 an inch or so—- not more. But the offspring of the 
 birds with the shortest legs or beaks would inherit 
 legs and beaks equally short, though again the 
 brothers would differ a little from each other ; and 
 similarly with the birds whose parents had longer 
 legs and longer beaks. And the same happened 
 with each succeeding generation. Now in those 
 days the pools were only four inches deep. But 
 they got gradually deeper and deeper ; and to-day, 
 where the fish swim, the water is always a foot 
 deep at the very least. Kingfishers of the ancient 
 kind would now-a-days either drown in the deep 
 
104 MENTAL TESTS 
 
 water, or starve for lack of food ; for they could 
 never learn to swim. What, then, do you think 
 has happened to these wading birds in the course 
 of centuries ? 
 
 *49« Captain Watts and his son James have been 
 found shot — the father in the chest, and the son in 
 the back. Both clearly died instantaneously. A 
 gun fired close to the person — as, for example, 
 when a man shoots himself — will blacken and even 
 burn the skin or clothes ; fired from a greater 
 distance it will leave no such mark. The two 
 bodies were found near the middle of a large hall 
 used as a rifle range. Its floor is covered with 
 damp sand, which shows every footprint distinctly. 
 Inside the room there are two pairs of footprints 
 only. A third man standing just outside the door 
 or window could aim at any part of the room, but 
 the pavement outside would show no footmarks. 
 Under Captain Watts's body was found a gun ; 
 no such weapon was found near James. In each 
 case the coat, where the bullet entered, was blackened 
 with gunpowder, and the cloth a little singed. 
 Captain Watts was devoted to his son, and would 
 have died sooner than harm him purposely ; hence 
 it is impossible to suppose that he killed him deliber- 
 ately, even in self-defence. But some think that 
 James secretly disliked his father, and hoped to inherit 
 his fortune at his death, (i) Was Captain Watts's 
 death due to murder, accident or suicide ? (-2) 
 Was James's death due to murder, accident or 
 suicide ? 
 
 50. The crust of the earth — that is, the outer 
 layer down to at least fifty miles below the top — 
 consists chiefly of rock and stone. Rock and stone 
 
BURT'S REASONING TESTS 105 
 
 weigh about three times as much as a bulk of water 
 of the same size. The heaviest materials found in 
 the crust of the earth are metals ; but in the outer 
 layer of the earth these are, of course, comparatively 
 rare. The earth as a whole weighs over five times as 
 heavy as a globe of water of the same size. What 
 does this suggest that the interior and middle of 
 the earth are mainly composed of — water, rock and 
 stone, metal or hot gas ? 
 
CHAPTER VI 
 
 THE MEASUREMENT OF KNOWLEDGE 
 
 The heart of the problem may best be made 
 manifest to the reader by supposing that a father 
 brings to him a boy of ten years of age with the 
 request that he should ascertain whether that boy, 
 who is, say, attending a dame's school, is up to the 
 average in his school studies. The father does not 
 want to know anything about the boy's intelligence 
 (no father ever doubts that), but he does want to 
 know whether the school is giving him value for 
 his money — a matter which all parents frequently 
 call into question. Have we any means of telling 
 with any degree of exactness whether the lad is of 
 average proficiency in such rudimentary branches of 
 instruction as reading, composition and arithmetic ? 
 Until quite recently we had not. We did not know 
 what the average child of that age could perform : 
 the most we could do was to make a rough guess ; 
 and the value of that guess depended purely upon 
 personal judgment, which again depended upon the 
 range and nature of personal experience. We had, 
 in fact, no stable standards of measurement. Each 
 man measured for himself, and each measured with 
 a private yard-stick. And even to-day the position 
 is not much better. We have only just begun to 
 standardise our tests, and have merely arrived at a 
 
 106 
 
MEASUREMENT OF KNOWLEDGE 107 
 
 few tentative standards of achievement in the 
 simplest of processes. There is an urgent call for 
 the extension of this work. 
 
 Many are the motives that urge us to make the 
 attempt. In France the aim has been to find the 
 child who fails to benefit by the ordinary instruc- 
 tion of the e coles primaires. Binet's motive in for- 
 mulating his Bareme d 'Instruction was the same as 
 his motive in establishing his scale of intelligence — 
 the quest of the subnormal child. But other motives 
 are constantly operative. There is a need for stan- 
 dards of comparison between the achievements of 
 children of different races, of different historic 
 periods, of different environments, and under 
 different types and modes of education. Pedagogic 
 records are no less useful than athletic records. It 
 is surely as profitable to know how long it would 
 take a nine-year-old child to add a given column 
 of figures as it is to know how long it would take 
 a two-year-old horse to run a mile. Yet we have 
 records in the one case and not in the other. 
 Finally, there is the need for placing in the hands 
 of the class teacher some means of protection against 
 arbitrary and unreasonable criticism by the head- 
 master or the inspector. 
 
 It is well to be quite clear as to the precise 
 nature of the standards we wish to establish ; for 
 there are three distinct possibilities. We may ascer- 
 tain what children of a given age actually do do, 
 or what they can do, or what they ought to do. 
 The first standard is actual, the second maximal, 
 and the third ideal. And none of them can be 
 either deduced from a priori principles or extracted 
 from the inner consciousness of a Board of Examiners. 
 
108 MENTAL TESTS 
 
 Our scale must rest on measurable facts, must be 
 built up by a careful investigation into the actual 
 achievement of children under clearly defined con- 
 ditions. What standard of proficiency in reading, 
 for instance, or in spelling, or in arithmetic, can be 
 expected of London children of a given age under 
 their present conditions of schooling ? The simplest 
 and most convenient means of ascertaining this is 
 to devise a suitable test (by no means an easy 
 matter), apply it to as large a number of children 
 as possible, and submit the results to statistical 
 analysis. The scale thus arrived at will afford what 
 may be called, by way of distinguishing it from the 
 other two types of standard, Norms of Performance. 
 These norms have a simple and definite meaning ; 
 they can be verified or modified by further testing, 
 and they have a definite range of usefulness. 
 
 Is it possible to establish either of the other two 
 standards ? And if possible, is it expedient ? Is 
 there any point, for instance, in trying to discover 
 what the result in arithmetic would be if all the 
 schools in London were to sacrifice for a time every 
 kind of intellectual activity in order to secure 
 maximal proficiency in this one direction ? There 
 evidently is not. Apart from the violence done to 
 the victims of the experiment, the results would 
 be of no value. Can we deduce from the norms 
 of actual performance some sort of ideal standard 
 which would serve as an index of what the children 
 ought to do as distinct from what they do ? I 
 myself see no scientific way of doing so. Where 
 ethics and aesthetics have failed, it does not seem 
 likely that pedagogics will succeed. We have there- 
 fore to fall back on norms of actual performance as 
 
MEASUREMENT OF KNOWLEDGE 109 
 
 constituting the only type of standard which proves 
 to be both practicable and useful. Of the other 
 two, one is practicable without being useful, and 
 the other useful without being practicable. 
 
 Let us now consider what attempts have actually 
 been made to arrive at standards or norms of 
 instruction. They first appear in the guise of 
 curricula issued by a central authority. In our own 
 country the Board of Education's standards of 
 examination are familiar to all those who remember 
 the days of payment by results. Indeed, they have 
 not yet quite disappeared from the Code of Regula- 
 tions : they appear in a modified form in the section 
 on certificates of proficiency. It may be said at 
 once that they do not represent any pure type of 
 standard, as the word is used in this book. They 
 are neither actual, maximal, nor ideal. Partaking 
 of some of the worst features of each, they are 
 hybrids of very doubtful pedigree. Based originally 
 on the opinion of what certain authorities at the 
 Education Department thought reasonable, moulded 
 to suit the exigencies of examination, they lacked a 
 solid foundation of objective fact. Moreover, the 
 scheme was used, and, indeed, intended to be used, 
 in such a way as to exemplify what Professor Adams 
 has pointed out to be the one great danger to which 
 all norms or standards are exposed : it was used as 
 a goal, and not merely as a test. Since preparation 
 for annual examinations was at that time virtually 
 the sole aim and purpose of the school, it was 
 inevitable that these standards of examination 
 should become syllabuses of work ; should form the 
 ground of the classification of scholars ; should, by 
 simple metonymy, give their name to the classes 
 
no MENTAL TESTS 
 
 preparing for the specific examinations ; and, finally, 
 be regarded as norms of performance for children 
 of various ages. Thus the word tried to do several 
 distinct pieces of work, and did none of them well. 
 
 As examination syllabuses and schemes of study, 
 the standards were marred by serious faults. In 
 the first place, they were often so vague as to be 
 almost useless. The reading requirement for Stan- 
 dard III, for example, was " To read a passage from 
 a reading-book " ; and for Standard IV, " To read 
 a passage from a reading-book or history of England." 
 Neither sentence tells us more than the first two 
 words alone. No indication is given of the mode 
 of judging whether a child has reached the specified 
 standard, nor any indication as to the amount of 
 progress in reading to be expected of a child between 
 the ages of ten and eleven, the normal ages for 
 " passing " these standards. Secondly, the scale 
 involved too high a standard of mechanical accuracy 
 — a standard which could not be reached without 
 an undue expenditure of time, and a consequent 
 narrowing of the curriculum and loss of interest. 
 With the present wide and generous scheme of 
 studies, so high a level of attainment in one direction 
 would be difficult, if not impossible. Finally, as 
 norms of achievement, the standards of examination 
 were woefully defective. Even supposing that some 
 objective means of testing were prescribed, so that 
 two independent examiners would inevitably arrive 
 at the same results (which was certainly not 'the 
 case), the standards themselves were arbitrary and 
 lacked the guarantee of a careful scientific study of 
 the normal capacities of children. 
 
 Nor did the schedule of standards represent a 
 
MEASUREMENT OF KNOWLEDGE in 
 
 real age scale. Although a normal pupil was sup- 
 posed to pass through each of the seven standards 
 before he reached fourteen years of age, he could 
 only pass one a year ; and while a stroke of bad 
 luck would put him back a whole year, no amount 
 of good luck could put him forward a day. The 
 consequence was that retardates were plentiful and 
 accelerates entirely absent. 
 
 A very different kind of standardisation is that 
 of Binet. His Bar erne & Instruction was based on 
 the mean performance of a large number of Parisian 
 children. It supplies, in fact, real norms in three 
 important branches of instruction — reading, number 
 and spelling. But although the aim is laudable, the 
 table published in Les idees modernes sur les Enfants 
 is of no great value. As the term " Bareme " 
 implies, it claims to be a ready reckoner — a rough- 
 and-ready means of finding out whether a child of 
 a given age has profited adequately by his schooling. 
 But its very roughness and readiness constitute its 
 main defect. It is supposed to take only ten minutes 
 to assess a child's scholarship — to fix his position in 
 the age scale ; and it is hard to believe that so 
 meagre and hurried an examination can gauge the 
 effect of years of teaching. 
 
 Binet's method of judging the reading is based 
 on the position of the pauses made by the reader. 
 If he pauses between the syllables, it is marked 
 " syllabic " ; if he pauses between the words, it is 
 marked " hesitant " ; and if he does not pause at 
 all, except where the sense of the passage demands 
 it, the reading is marked " current." In all, five 
 grades of proficiency are indicated — subsyllabic, 
 syllabic, hesitant, current and expressive. This 
 
ii2 MENTAL TESTS 
 
 seems a simple scheme, and if it were easy to apply, 
 its obvious lack of delicacy of gradation might be 
 overlooked. But, as a matter of fact, it is impos- 
 sible to apply it with any feeling of certainty. It 
 is very rare that any child's reading is found to fall 
 entirely within any one of the prescribed grades. 
 
 In arithmetic simplification is again aimed at. 
 Binet goes so far as to contend that it is unnecessary 
 to test both addition and subtraction, for a know- 
 ledge of the latter implies a knowledge of the former. 
 By parity of reasoning, a test in division is claimed 
 to render a test in multiplication unnecessary. 
 Indeed, three simple questions for each child seem 
 to be considered adequate ; but each question must 
 be given in concrete form. To illustrate the kind 
 of question he advocates, I will cite his typical 
 example for children between six and seven years 
 of age : " From 19 apples take away 6 apples : 
 how many remain ? " 
 
 The spelling test is of no value outside France ; 
 for it is a test of grammar as well as of spelling — 
 the two being inseparable in the French language. 
 This peculiarity is rendered obvious by the typical 
 sentence given in the Bareme : " Les jolies petites 
 filles etudient les plantes qu'elles on remasses hier " 
 — a sentence abounding in pitfalls. 
 
 Turning from France to America, we find there 
 the home of standardisation. A tremendous volume 
 of work has been done by Thorndike, Courtis, Ayres, 
 Terman, Munroe, Judd and others with a view to 
 reaching as much exactitude as the nature of the 
 subject will permit. But its usefulness for us is 
 marred by its insularity — by the fact that it is 
 American and not English. Their arithmetic tests 
 
MEASUREMENT OF KNOWLEDGE 113 
 
 abound in dollars and cents, their problems often 
 refer to customs and transactions peculiar to them- 
 selves, and the spelling is Websterian. The next 
 serious defect, however, is that the results are not 
 embodied in an age scale, but in a grade scale. We 
 are told what level the children in Grade IV, say, 
 of a certain American school, did, on an average, 
 attain in arithmetic, spelling and reading. But we 
 are not told the actual age of these children. Nor 
 can we infer it from the grade. We learn from 
 their educational papers that the ages in the grades 
 are not what they are theoretically supposed to be. 
 They vary from school to school, and from city to 
 city. Moreover, it makes a very great difference 
 whether the tests were given at the beginning, the 
 middle, or the end of the school year. Binet's 
 scales are of universal value because they are age 
 scales ; and if the American scales are to be used 
 in England they must be translated from grade 
 scales to age scales. They will then cease to be 
 national and become international. 
 
 I must emphasise the fact that the tests are 
 merely tests, and that their value diminishes in the 
 proportion that they deflect the general course of 
 study. Although in those rudimentary habits which 
 are the beginnings of school pursuits this danger 
 may be met by making the tests comprehensive, 
 that device is impossible in those higher and more 
 advanced branches of study where no test can cover 
 more than a small fraction of the whole field. We 
 have, in fact, ultimately to rely on the co-operation 
 and good faith of the teacher. And my experience 
 goes to show that such confidence is rarely misplaced. 
 
 It has been urged as an objection to the use of norms 
 1 
 
ii4 MENTAL TESTS 
 
 that they refer to the most measurable school sub- 
 jects, and the most measurable are the least valuable. 
 There is thus a danger that the teacher will con- 
 centrate his efforts on the more mechanical aspects 
 of school work, to the neglect of the higher and 
 more spiritual aspects. As a matter of fact, this 
 fear is groundless. Norms in the mechanical sub- 
 jects are just as much a protection as a menace. 
 They will probably show that in some schools the 
 mechanical work is too good : it is so far above the 
 normal that too much time and attention have been 
 devoted to it. When the norm is reached further 
 " drill " is for the time unnecessary. The teacher 
 would realise that he could with a clear conscience 
 reduce the drudgery and render the work more 
 recreational and more broadly cultural. What is 
 really aimed at in establishing the more mechanical 
 norms is the discovery of that degree of automatism 
 which best serves the interests of the higher pro- 
 cesses of thought. And in any given school it may 
 be just as necessary to slacken the standard as to 
 string it up. 
 
CHAPTER VII 
 
 DISTRIBUTION AND DISPERSION 1 
 
 When we measure a multitude of natural objects 
 belonging to the same genus or class we find that 
 the results tend to assume a determinate shape. 
 The magnitudes occur in accordance with a general 
 law. Let us suppose, for instance, that we start 
 measuring the heights of adult Englishmen by 
 making one after the other stand against a post and 
 marking each height with a horizontal stroke. If 
 we choose our specimens at random we shall soon 
 find our marks tending to crowd round a fixed 
 height. By the time we had measured ioo the 
 marks would appear somewhat as in Fig. I. The 
 largest number of marks would probably fall between 
 6j and 68 inches, and the numbers would tail off 
 as they diverged in either direction from this central 
 position. As the number of men increased we should 
 find our range of heights extending, for we are 
 much more likely to find a giant or a dwarf among 
 10,000 men than among fifty. By the time 8000 
 had been measured we should probably find our 
 range extending from 57 to 78 inches. Let us now 
 
 1 For a fuller treatment of this subject the reader is referred 
 to Nunn's Exercises in Algebra, Vol. II. , Sec. IX. (Longmans). 
 
 Some excellent diagrams illustrating distribution and dispersion 
 will be found in Burt's Educational Abilities (King and Son). 
 
 i J 5 
 
n6 
 
 MENTAL TESTS 
 
 take our ioo men, or, for statistical convenience, 
 let us say ninety-nine, and put them to stand in a 
 row in order of height so that the tallest stand at 
 one end of the row and the shortest at the other. 
 An unreflecting observer would expect the line 
 joining the tops of their heads to be a straight line. 
 
 Figs. land 2. Probable heights of 99 
 Englishmen- taken at 
 
 Quartile. 
 
 Inches 
 
 7+1 
 
 
 7 3 " 
 
 
 7* 
 
 — 
 
 V 
 
 70- 
 
 n 
 
 69- 
 
 - : 5^ UblwT 
 
 66- 
 
 6 7 - 
 
 ^ — Nedian 
 
 66- 
 
 ^52— Latter 
 =f Qvartik 
 
 65- 
 
 s 
 
 64- 
 
 = 
 
 63 
 
 ~ 
 
 61 
 
 t 
 
 6m 
 
 E 
 
 6o- 
 
 59 
 
 1 
 
 5$\ 
 
 
 f'a 
 
 99»ien standing in a row in. oraitr of height (£ou«si s6"tnniiu<l) 
 
 Ka.x 
 
 In fact, however, the line tends to take the forms 
 of an Ogive — the curve represented by Fig. 2. 
 This, indeed, could be deduced from the facts 
 recorded in Fig. 1. Let us arrange the results in 
 yet another way. If we erect a column, A (Fig. 3), 
 proportional to the number of measures that fall 
 between 6j and 68 inches, place to the right another 
 column, B, proportional to the number of measures 
 
DISTRIBUTION AND DISPERSION 117 
 
 that fall between 68 and 69, and so on for the 
 other groups of measures, we shall get what is 
 called a frequency-column-graph, or a surface of 
 frequencies. 
 
 It is clear that we have not been dealing with 
 discrete units like the abstract numbers 1, 2, 3, 4, 
 etc., but with continuous magnitudes. For there 
 is no limit, except those imposed by our instru- 
 ments and our sense-organs, to the number of 
 
 ZZ3 
 
 Inches 6/ Sz 65 6<J- 65 66 6f 6% 69 70 7/ ~]2- 73 74- 
 
 f^.3 frecucncy-ccJumn.- graph- . 
 
 different measurements that may be made between, 
 say, 6y and 68 inches. Nor is there any fixity 
 about the group-range. We have chosen one inch, 
 but we might just as well have chosen half an inch, 
 or a quarter of an inch, or, indeed, any range we 
 liked. It is obvious, however, that the smaller the 
 range of statures the smaller the number of men 
 whose statures fall within that range ; and to show 
 the general scheme of distribution it is most con- 
 venient to choose one's range in accordance with 
 
n8 
 
 MENTAL TESTS 
 
 the number of men measured. If the numbers are 
 very large we can conveniently make our columns 
 thinner ; and by increasing the numbers and 
 diminishing the range we find the zigzag formed 
 by the tops of the columns tending towards a 
 continuous curve, as in Fig. 4. This peculiar bell- 
 shaped curve is known as a frequency curve. The 
 particular type here illustrated, to which stature 
 closely conforms, is called the Curve of Normal 
 Distribution. 
 
 , > * — j — 1 
 
 Jnrfrraijmttl 
 
 TOTjige 
 
 i- fle a n 
 
 Variation | 
 " Dtytatioh.' 
 
 65 64. 6S 66 6J 68 69 70 7/ 
 
 %4-. Gitvs ofriormal dlslnhut 
 
 71 73 7+ 75- 76 
 
 ion. 
 
 If instead of taking the men's heights we had 
 taken their weights, we should have found the 
 measurements distributed in almost the same way. 
 
 Finally, when instead of a physical trait we 
 measure a mental trait we appear usually to get the 
 same type of result. A number of girls, say, of 
 eleven years of age exhibit degrees of educational 
 ability which, when carefully tested, prove to be 
 distributed in much the same way as their heights 
 or weights. In other words, examination marks 
 
DISTRIBUTION AND DISPERSION 119 
 
 should follow the same law as the measurements 
 of other natural features : they should roughly 
 conform to the Curve of Normal Distribution. 
 
 This curve is also called the Curve of Probability 
 and the Curve of Error. The term Curve of Prob- 
 ability derives from the fact that the curve shows 
 the frequency of a series of events composed of a 
 number of factors when the presence or absence of 
 a given factor is determined merely by chance. 
 Suppose, for example, I have two coins, toss them 
 up again and again, and make a record of the 
 number of times there is no head, the number of 
 times there is only one head, and the number 
 of times there are two heads. I shall find the 
 score for the three cases tending towards the pro- 
 portion of 1, 2 and 1. This, indeed, could be 
 deduced by the laws of probability from the fact 
 that there are but four possible ways in which the 
 coins can fall, viz. TT, TH, HT and HH ; and 
 out of these four " no head " appears once, one 
 head twice, and two heads once. If instead of the 
 presence of heads we had considered the absence 
 of heads, or the presence or absence of tails, we 
 should have got the same result. The same kind 
 of thing, too, will happen if we toss three coins a 
 large number of times, except that the proportion 
 would now be that of 1, 3, 3 and 1. The case of 
 no head (or three tails) would occur about once 
 every eight throws, one head about three times, 
 two heads about three times, and three heads about 
 once. With four coins the probable ratios would 
 be 1, 4, 6, 4 and 1. The reader will by this time 
 have observed that the proportions I have given 
 are the coefficients of the expansion of (x + i) 2 , 
 
i2o MENTAL TESTS 
 
 (x + i) 3 and (x + i) 4 ; and if he will proceed to 
 expand the higher powers of the binomial and 
 represent them by frequency-column-graphs, he 
 will find that the graphs gradually approximate the 
 curve in Fig. 4 — the curve of probability. 
 
 The term Curve of Error is a relic of an older 
 nomenclature. The curve was, in fact, first studied 
 in connection with errors of observation, particu- 
 larly in astronomy ; and a tendency arose to call 
 all divergences from a mean " errors." In gunnery, 
 too, it was natural to regard as errors all the shots 
 that missed the mark. 
 
 It should be strongly emphasised that the curve 
 is an ideal curve. It is seldom or never actually 
 reached : it merely marks a limit towards which 
 the values tend — an ideal arrangement to which 
 they approximate more and more as certain con- 
 ditions (those of pure chance) are fulfilled. Infer- 
 ences drawn from it, arguments based on it, are 
 never certain : they are only probable. For it is 
 the main characteristic of all inferences from statis- 
 tical uniformities, that as they increase in particu- 
 larity they diminish in certainty. They are whole- 
 sale truths, not retail truths. The smaller the 
 number of cases the less sure we feel that any 
 general statement will hold good. But the number 
 of children grouped in a class is rarely so small 
 that a central tendency is not observable ; and if 
 the results of examining them depart widely from 
 the normal type, it shows that the examination was 
 unsuitable. It was either a bad examination, or a 
 bad sample of children — bad in the sense of not 
 being representative. A picked sample, it is true, 
 always exhibits certain peculiarities ; but these. 
 
DISTRIBUTION AND DISPERSION 121 
 
 should be allowed for : they should not come as a 
 surprise to the examiner. The results of an 
 examination are, in fact, a standing criticism of the 
 examination : they search the suitability of the 
 questions and the correctness of the marking. 
 
 From what we have already said certain important 
 principles may be deduced — 
 
 (1) On an ideal examination mark-sheet, where 
 the candidates have been ranked in order of merit, 
 the degrees of difference between consecutive marks 
 are not equal. They are greatest at the extremes, 
 and gradually diminish as they approach the middle. 
 
 (2) If equal ranges of ability be taken, the number 
 of cases falling within the central range is large, and 
 the number within the extreme ranges small. If, 
 therefore, we arrange the examinees in three groups, 
 A, B and C, representing equal ranges of ability, 
 the B group should be the largest, and the A and C 
 groups should be about the same size. Similarly, 
 if we classify them in five groups, A, B, C, D and E, 
 the C should be the largest group, the B and D 
 the next, and the A and E the smallest. 
 
 (3) A series of tests of any mental quality or 
 attainment should be so devised, and the results so 
 marked, that nobody should gain full marks, nobody 
 gain none, and the average gain about half marks. 
 This is an ideal examination which is never in 
 practice attained. When the aim of the examina- 
 tion is to pick out the brightest intellects these 
 conditions do not hold good. 
 
 (4) The range of marks between the median, or 
 middle mark, and the quartile (the mark half-way 
 between the middle and the ends) is less than that 
 between the quartile and the extreme, 
 
122 
 
 MENTAL TESTS 
 
 It must not be thought that every test the 
 teacher sets his class can give results which accord 
 with these rules. It may be, for instance, that the 
 test is only intended to divide the class into passes 
 and failures, to find out those who can do a certain 
 simple thing and those who cannot. This sheep-and- 
 goat classification is extremely useful for teaching pur- 
 poses, and may involve any degree of inequality in 
 the sizes of the two groups. 
 
 Marks IS 
 
 10 IS 3C 35 40 ^5 SO SS <SO 65 JO JS SO 65 
 
 5 SteuuCuTve 
 
 % 
 
 Nor must it be assumed that the series is always 
 symmetrical. In fact, the curve is as often as not 
 skewed, as in Fig. 5 : the numbers crowd towards 
 the right or towards the left. There is a general 
 rise and a general fall, but one is often steeper than 
 the other. 
 
 The only way to describe "a series of measure- 
 ments fully is to state all the facts, either by giving 
 the actual measurements or by representing them 
 by a graph. But we rarely use all these facts : we 
 are generally content to know their central ten- 
 dency, and to take that value as representative of 
 
DISTRIBUTION AND DISPERSION 123 
 
 the whole series. When the series is normally dis- 
 tributed the central tendency is represented by the 
 average or arithmetical mean. If the terms of this 
 normally distributed series be arranged in order of 
 magnitude the mean is also the median or middle 
 term. But when the series is not symmetrical the 
 mean is not in the middle, and its right to repre- 
 sent the series has been disputed. It is claimed 
 that the median represents it better. Take, for 
 example, the series (a) 1, 2, 3, 3, 3, 4, 19. The 
 average here is 5, but it is clear that the median, 3, 
 is a better index of the central tendency than 5. 
 It may, in fact, be stated generally that when 
 erratic items disturb the tenor of the series, the 
 median is better than the mean as a measure of 
 the central tendency. But there are, on the other 
 hand, other abnormal occasions when the average 
 is the better measure. Take, for instance, the 
 series (b) o, 1, 1, 7, 7, 8, 11. The median, 7, is 
 clearly too high. The average, 5, is better. And 
 in the series (c) o, o, o, 8, 9, the median, o, would 
 be entirely misleading. 
 
 It is sometimes suggested that the mode — the 
 most frequent value (e. g. 3 in series (a), and o in 
 series (c)) — be taken as the representative value. 
 But in some series no value occurs more than once ; 
 in others it is impossible to decide between rival 
 claims (the 1 and the 7, for instance, occur with 
 equal frequency in series (b)) ; in others, again, the 
 mode occurs at the beginning or end of the series, 
 as in series (c), and is a bad representative. 
 
 It may be argued that the series of marks we 
 have been citing violate the very rules we have 
 already laid down : they depart widely from the 
 
124 MENTAL TESTS 
 
 normal, and indicate either very bad testing or very 
 bad sampling. The charge of bad sampling may 
 be admitted, for the class teacher cannot always 
 pick his samples : he has to test what children he 
 has. Moreover, he has to measure the success of 
 his teaching — to find out the extent to which he 
 has imparted knowledge or fostered understanding ; 
 and here irregular results may reasonably be 
 expected, especially if the numbers are small. I 
 admit, therefore, that for the purposes of emphasis 
 I have taken extreme cases — possible cases rather 
 than probable cases. But these infrequent cases 
 illustrate conditions which are by no means infre- 
 quent. They magnify peculiarities that are nearly 
 always present. 
 
 When the series is of normal distribution, it does 
 not matter whether we take the mean, the median 
 or the mode ; for they all three coincide. When, 
 however, the distribution is not normal we have to 
 choose between them. The mode we may dismiss 
 at once as never quite suitable, and often quite 
 inapplicable. Of the other two sometimes one is 
 more suitable, sometimes the other ; and rarely is 
 either a really bad representative value. For sim- 
 plicity of calculation the median is undoubtedly the 
 better. 
 
 When we have learnt the average or central ten- 
 dency of a series we have learnt the most significant 
 thing about it. But there are other things we want 
 to know ; and the most important of these other 
 things is the degree of scatter — the closenes's or 
 looseness with which the various values cluster round 
 the average. In series (d) 4, 5, 5, 6, 6, 6, 7, 7, 8, 
 for instance, there is very little scatter ; no value 
 
DISTRIBUTION AND DISPERSION 125 
 
 deviates from either the mean or the median by- 
 more than 2. But in the series (e) 1, I, 2, 3, 3, 5, 
 8, 14, 17, which has the same average as {d), the 
 deviations are very much greater. To evaluate these 
 deviations the obvious plan is to treat them as we 
 treat the original series, that is, find their average. 
 In series (d) the deviations are respectively 2, 1, 1, 
 o, o, o, 1, 1, 2, and their average is *8. This is their 
 mean deviation from the mean, or, more briefly, their 
 mean deviation or mean variation. The mean devia- 
 tion of series (e) is 4*6, that is, more than five times 
 as great as that of the first series. 
 
 In the same way we can calculate the mean 
 deviation from the median, another index of dis- 
 persion. 
 
 The simplest and quickest way, however, to 
 measure the general degree of deviation is to extend 
 the principle of the median, and after finding the 
 median, which divides the series into halves, to find 
 the median of each of the halves. In other words, 
 we arrange the series in order of magnitude, and 
 divide it into four equal parts. The value one 
 quarter of the .way up is the lower quartile, the 
 value half the way up is the median, and the value 
 three-quarters of the way up is the upper quartile. 
 The difference in value between the upper and 
 lower quartile is known as the interquartile range. 
 Since this range is an index of dispersion both 
 above and below the median, it is usual to halve 
 it, and thus get the semi-interquartile range, or 
 quartile deviation. This is, in fact, a convenient 
 way of averaging the deviations of the two quartiles 
 from the median. In the series (J) 1, 2, 3, 3, 4, 4, 
 5, 5, 6, 6, 7, 8, 8, 9, 10, for instance, 3 is the lower 
 
126 MENTAL TESTS 
 
 quartile, 5 the median, 8 the upper quartile, 5 the 
 interquartile range, and 2\ the quartile deviation. 
 Sometimes the lower quartile is called the 25 per- 
 centile, the median the 50 percentile, and the upper 
 quartile the 75 percentile. The semi-interquartile 
 range is practically the same as the -probable error. 
 It is so-called on what seems to be a lucus a non 
 lucendo principle ; for it is neither an error, nor is 
 it probable. Error means deviation, as in the phrase 
 " curve of error " ; and it is only a probable devia- 
 tion in the sense that since twice its amount includes 
 half the number of values, any particular value is 
 just as likely to fall without that amount as within it. 
 We have one other means of measuring the degree 
 of variation from the central tendency — standard 
 deviation, or root-mean-square-deviation. Instead 
 of taking the mean of the individual variations from 
 the mean, we take the mean of their squares and 
 then find its square root. This takes a longer time 
 to calculate than any of the others, but it has 
 certain advantages. In calculating it we have not 
 to commit the algebraical solecism of adding terms 
 of opposite signs as if they were signless, as in 
 estimating the other measures of deviation ; for the 
 squares of all numbers are necessarily positive. 
 Moreover, by squaring, extreme deviations are mag- 
 nified, and given their due weight as indications of 
 individual ability. The very items that cause us 
 trouble when we try to find the central tendency 
 are of supreme service in calculating the correlation 
 of abilities. The best-known method of finding the 
 correlation coefficient involves the finding of the 
 standard deviation. Those, therefore, who wish to 
 make further calculations from an array of values 
 
DISTRIBUTION AND DISPERSION 127 
 
 are prone to use the standard deviation as a measure 
 of variation instead of the simpler measures, or of 
 the mental age. Mr. Burt does so. He suggests 
 that for strictly scientific purposes it should be used 
 in the schools as a unit of measurement. 
 
 In a normally distributed series the quartile de- 
 viation is less than the mean deviation, and the 
 mean deviation less than the standard deviation — 
 a fact illustrated graphically in Figs. 4 and 5. 
 
 I have described various means of finding the 
 central tendency of a list of examination marks, 
 and various means of finding the deviation from 
 that central tendency. From among these there is 
 in actual use in the schools only one way of record- 
 ing the central tendency, and none of recording 
 the deviation. The average, or arithmetical mean, 
 is the only statistical device in common use. The 
 result of a test in arithmetic is supposed to be 
 adequately reported and recorded when the average 
 number of sums right is given. And as I have 
 already shown, the way of the average is quite a 
 good way : it is at least as good as any other. But 
 it is not enough. Some mode of expressing the 
 degree of dispersion is also necessary — the mean 
 deviation, for instance. As a matter of simplicity 
 in working, however, and completeness of statement, 
 I would commend the method of the median and 
 quartile deviation. To record a result it is only 
 necessary to give five values — the lowest, the lower 
 quartile, the median, the upper quartile and the 
 highest. This will give more information in a small 
 compass than any other method. The mean devia- 
 tion affords no clue to the symmetry of the series, 
 for it does not differentiate the deviations below 
 
128 MENTAL TESTS 
 
 the average from the deviations above the average. 
 But the quartiles reveal to us at a glance both how 
 and how much the several values are dispersed (see 
 Fig. 5). In fact, we learn from the five items men- 
 tioned above the range of the series, its central 
 tendency, its degree of dispersion, and its mode of 
 dispersion. 
 
 The teacher unfamiliar with statistical terminol- 
 ogy will no doubt consider these distinctions irri- 
 tating and useless. Irritating perhaps they are, but 
 not useless. For different investigators affect dif- 
 ferent systems. Some find it more convenient to 
 reject the average and use the median, others cling 
 to the older scheme. Those who wish to base 
 elaborate calculations on their data prefer to 
 measure dispersion by the standard deviation ; 
 while those who desire quick practical results prefer 
 the simpler measures, the mean variation or the 
 quartile deviation. The few explanations I have 
 given should enable the reader to adjust his mind 
 to these varying usages. 
 
 I will try to illustrate some of the ways in which 
 a broad knowledge of the principles of distribution 
 may be useful to the teacher. Let us suppose that 
 he has to mark forty composition exercises written 
 by the boys in his class. It is doubtful whether he 
 can arrange them with any degree of confidence 
 into more than ten groups. Although a teacher 
 sometimes tries to mark on a scale of 1 00, awarding 
 one boy, say, 73 marks and another 74, it is idle to 
 pretend that he can make such fine discriminations. 
 Generally speaking, ten grades are as many as he 
 can manage ; and on a ten-grade basis it is clear 
 that the forty papers in question cannot all receive 
 
DISTRIBUTION AND DISPERSION 129 
 
 different marks. To examine his distribution the 
 teacher should, after marking, draw up a frequency 
 graph as in Figs. 3, 5, 6 and 7. He will then see 
 at once whether he has judiciously apportioned his 
 scores. If the bulk of the marks are somewhere 
 near the middle it is presumptive evidence of careful 
 marking. As an example of bad marking I will 
 take an instance that occurred some years ago in 
 the top standard of an elementary girls' school. At 
 the terminal examination the thirty-five girls in the 
 class were examined by the head mistress in com- 
 position, 20 being the maximum marks allowed. 
 Twelve girls got full marks, five got 19, twelve got 
 18, and six got 15. If the reader will plot this 
 result either as an ogive or as a frequency graph, 
 he will note that the principles I have tried to 
 expound are flagrantly violated. In point of fact 
 the twelve papers that were awarded full marks 
 were of very unequal merit, and it is doubtful 
 whether the best of them deserved more than 14 
 marks out of 20. 
 
 Both composition and reading are quite frequently 
 marked in this haphazard fashion. If more than 
 one pupil receive full marks it generally means that 
 the best of these pupils is getting less than justice. 
 Towards the middle of the scale " ties " are in the 
 natural order of things, but the further from the 
 middle we get the more unlikely is equality to be 
 found. A test, therefore, that fails to differentiate, 
 and spread out the pupils at the higher and lower 
 ends of the list, is either bad in itself or badly 
 marked. 
 
 Let us now consider a subject in which it is 
 possible to calibrate more finely. Mathematics, for 
 
 K 
 
130 
 
 MENTAL TESTS 
 
 instance. Here, with a sufficiently searching exami- 
 nation, it is quite possible to find ioo distinct grades 
 of proficiency. If the base line of a frequency graph 
 be spaced out in equal ranges of from o to 5 per cent., 
 from 5 to 10 per cent., from 10 to 15 per cent., 
 and so forth, and columns raised proportional to 
 the number of pupils whose marks fall within these 
 ranges, the result will be a graph or curve of which 
 Figs. 5 and 6 are possible varieties. The skew shown 
 in Fig. 5 may be due to an imperfect grading in 
 
 Ma-rks XO IS 30 3S 4o ^S So SS 60 6S lo IS Co SS 9a 3S 
 
 H^. 6 Curve cuilK tuJo cresls 
 
 the difficulty of the questions, or to some peculiarity 
 in the class itself. When there are two distinct 
 crests, as in Fig. 6 — and especially if this duality 
 reappears in other examinations — it points to a 
 serious lack of homogeneity in the class. These are 
 really two central tendencies due to the presence 
 of two natural groups. We get this kind of curve 
 when we plot the heights of a mixed group of men 
 and women. One crest will indicate the central 
 tendency of the men, and the other the central 
 tendency of the women. A double summit that 
 
DISTRIBUTION AND DISPERSION 131 
 
 sometimes appears in the plotted results of a com- 
 petitive examination probably indicates two distinct 
 types of candidates — those who work for the exami- 
 nation and those who do not. Peculiarities in the 
 curve of distribution, although they fall short of 
 proof, always suggest points for investigation. 
 
 nJ 
 
 75* 
 
 £20- 
 
 r 
 
 % 7 
 
 Surface of freousncu of marks 
 obtained by £40 girls o{ 9-3i -years 
 old in }he Tnechqnical Teading test 
 
 . ■ ■ ■ ■,.,> !~l I" ) 
 
 S 10 is 20 is la as <%> *s So is 60 &s -jo js so es m m /» at iu us m 11s is* as iv u* uz> «cr 
 
 /larks 
 
 I would particularly warn the reader not to 
 expect a smooth curve from so small a number of 
 cases as a single class provides. Rather should he 
 expect something like what is seen in Fig. 7, where 
 I have plotted some of the results obtained in the 
 reading test described in Chapter VIII. Although 
 there are 540 cases dealt with, yet there is much 
 irregularity in the rise and fall of the frequencies. 
 Indeed, so conspicuous is the fall at 90-95, or 
 rather the rise at 100-105, tnat an explanation 
 
132 MENTAL TESTS 
 
 seems to be called for. As, however, these features 
 do not reappear in the corresponding frequency 
 surface for boys, I conclude that the causes are 
 accidental, and not due to any peculiarity in the 
 test. 
 
 Another way of using the notion of normal dis- 
 tribution in ordinary class work may be indicated. 
 Suppose the teacher has to mark forty drawings. 
 Their absolute merit is beyond his, or indeed any- 
 body's, power to determine : his concern is to 
 appraise them relatively to one another. He will 
 find it a good plan to spread the drawings out on 
 a large table, and proceed thus : If there is one 
 copy which is manifestly the best, mark it io ; and 
 if there is a copy which is manifestly the worst, 
 mark it I. Then look for the second best — there 
 may be two or more. Mark each of these 9. Then 
 look for the next to the worst, and mark these 2. 
 Work thus towards the middle, making the groups 
 larger and larger as the middle is approached. 
 Here we have a working conception which will be 
 found serviceable as a guiding principle, but dan- 
 gerous as a hard-and-fast rule. It is, indeed, very 
 improbable that a set of papers if rightly marked 
 will tamely fall in with a preconceived scheme, for 
 each set will have peculiarities of its own which 
 must be recognised ; but it is equally improbable 
 that the drawings will depart widely from the 
 general scheme I have outlined above. In the final 
 issue the marks should fit, not the scheme, but the 
 papers. 
 
 In Chapters VIII and X, I give two standardised 
 tests in reading and seven in arithmetic. The norms 
 appended represent the central tendency (the average 
 
DISTRIBUTION AND DISPERSION 133 
 
 or the median) of the results obtained by applying 
 the tests to several thousands of children in a large 
 variety of schools. They indicate the normal 
 achievement at the exact age mentioned ; and the 
 way to use them is simple. If, for instance, a 
 teacher gives the silent reading test to his pupils, 
 whose average age is ten years three months, he 
 should expect an average score of 11 ; for the table 
 of norms gives 10 for ten years of age, and 14 for 
 eleven years of age, and his boys are a quarter of the 
 way between ten and eleven. 
 
 Judging from the score made in certain individual 
 schools, the mean variation for the written arith- 
 metic tests is on the whole nearly 50 per cent, of 
 the average reached. If, for instance, the norm is 
 6, the mean variation is nearly 3. It is larger even 
 than this for the younger children, but consider- 
 ably smaller for the older. It should be borne in 
 mind, however, that in collating my results it was 
 not children of the same class or grade or standard 
 that were grouped together, but children of the 
 same age. And unless the degree of dispersion in 
 the class is less than the degree of dispersion in the 
 age group, the school is no better organised (for that 
 particular subject at least) than if the classification 
 of scholars were based strictly upon age. The smaller 
 the mean deviation the more homogeneous is the 
 class. 
 
CHAPTER VIII 
 
 READING 
 
 A. — As a Mechanical Art 
 
 What is the fundamental and essential factoi 
 in the ability to read ? Binet seems to assume il 
 to be fluency ; for the scale for marking reading in 
 his Bareme ^Instruction is based upon the frequency 
 of such pauses as are not necessary to elucidate the 
 meaning of the passage read. The examinees an 
 classified according as they pause after the letters, 
 the syllables, the words or the phrases. More 
 recent investigators, discriminating between the 
 silent reading we do for our own use and pleasure 
 and the oral reading we do for the benefit of others, 
 claim the former to be the more important, anc 
 select the comprehension of the material read as 
 the first essential, and speed of reading as the second. 
 Compared with these, intonation, expression and 
 pauses are regarded as unimportant. For this 
 point of view there is much to be said. It is signifi- 
 cant of that happy change which is taking place 
 in our schools — the change from reading as an 
 elocutionary display (a very indifferent one at best) 
 to reading as a pleasurable pursuit. But compre- 
 hension is a difficult thing to measure ; and it pre- 
 supposes a more rudimentary ability which is quite 
 easy to measure — the ability to translate certain 
 
 134 
 
READING 135 
 
 visual symbols into sounds, whether those sounds 
 are actually produced or are merely imagined. This 
 is the basal ability — the sine qua non of reading — ■ 
 the step which no amount of intelligence would 
 enable the learner to dispense with. His intelligence 
 will, of course, eke it out ; it will enable him to 
 anticipate coming words, to respond to slighter 
 cues ; but ultimately his power to read is rooted 
 in his ability to translate symbols into sounds, and 
 this fundamental ability is what I here set out to 
 measure. It is not the whole of reading ; but it 
 is the basal and indispensable part, and it is the part 
 which best lends itself to exact measurement. 
 
 The test I adopted after some preliminary experi- 
 ments is given on the following page : — 
 
 The pupil was given a paper on which the test 
 was printed as shown, and was asked to read as fast 
 and as carefully as he could until he was told to 
 stop. The number of words correctly read in a 
 minute — that is, the total number read minus the 
 number misread — gave the score. If the examinee 
 hesitated for more than five seconds over a word 
 and did not seem to be on the point of saying it, he 
 was prompted and told to pass on, that particular 
 word counting as an error. He was thus prevented 
 from being too heavily penalised by his inability 
 to recognise one or two particular words. 
 
 It is quite clear that the test does not take intelli- 
 gence into account ; it is designed to measure the 
 bare mechanical art of reading — the degree of 
 facility with which a pupil can translate the symbols 
 of the simplest and commonest words of the mother 
 tongue into the words themselves. Sense material 
 was discarded as tending to confuse the issue. If 
 
136 MENTAL TESTS 
 
 One Minute Reading Test 
 
 is me on at by so us an it or be 
 to as he of in go up am if no we 
 my ox do the and for but him 
 are can she dog let you not was 
 out try see mix cat now boy saw 
 bit met top run man pet lot get 
 did van bad red cup bee lit pin 
 had ran pen nut big old yet rob 
 gun leg fun lip new fog has sit 
 sly wig mud box ink sat end cut 
 pay fed who six lad wet dry cow 
 his peg tin say eat any far set bud 
 kid pup fox ask egg cab ill use jam 
 all pit got sad tea sky one yes fur 
 act toe her our ten arm rock gone feel 
 that rich till long flat this part foot 
 made upon came mile back sand time 
 said then wall into were done walk 
 much loss seem went with come 
 
READING 137 
 
 an intelligent lad, for instance, starts reading a 
 fairy tale which begins " Once upon a time," the 
 recognition of the first word brings inference into 
 play, and the rest of the phrase is largely a matter 
 of memory. But no such intelligent anticipation 
 is possible in the test used ; each word, standing 
 isolated in meaning, has to be read without any help 
 from the context. It has to be read, not inferred. 
 
 Much scorn has been levelled at this type of 
 reading. It has even been denied that it is reading 
 at all, and has been contemptuously called " barking 
 at print." But my investigation tends to show that 
 this mechanical response to the seen word, this bark- 
 ing at print — call it what you will — is not only the 
 basis of all reading, good as well as bad, but is also 
 a trustworthy criterion of the interest with which 
 reading is followed as a pursuit. 
 
 As a test common to children of different schools 
 and different ages, it possesses many points of 
 advantage. Familiarity with subject-matter, which 
 must always be a variable and disturbing factor 
 where sense material is used, does not enter into 
 the question ; there is no subject-matter. A 
 peculiar knowledge of uncommon words avails 
 nothing : there are no uncommon words. How- 
 ever young a child may be, however rudimentary 
 his knowledge, if he can read at all, he can read some 
 of the words in the first three lines ; for all the 
 common two-letter words in the language are to 
 be found there. And however proficient a child 
 may be he will find the task of reading the whole 
 of the 158 words in one minute quite as much as he 
 can accomplish. 
 
 But these a 'priori reasons in favour of the test 
 
138 MENTAL TESTS 
 
 do not dispense with the necessity of testing the 
 test — of comparing, for instance, the results obtained 
 by using this test with those obtained by using sense 
 material, such as an " unseen " passage in the ordinary 
 school reader. Such a comparison I carefully made 
 with ten boys of about eight years of age. The 
 mode of scoring was in each case the same — the 
 number of words correctly read in one minute. 
 The first point to be noted is that although 32 per 
 cent, more words were read per minute in the con- 
 tinuous prose than in my test, the order of merit 
 was, with one trifling exception, the same in both 
 cases. To test one kind of reading is virtually to 
 test the other. The second point to be noted is 
 that the discrete material gives a higher degree of 
 reliability or steadiness ; for when the children were 
 put to read the same passages again after five minutes 
 interval, they improved but 7 per cent, with the 
 discrete words as compared with an improvement 
 of 22 per cent, with the continuous prose. The 
 7 per cent, improvement was perhaps entirely due 
 to a loss of nervousness ; but most of the improve- 
 ment in the other case was doubtless due to the 
 acquired familiarity with the meaning. As a test, 
 therefore, the discrete words are better suited for 
 repeated use. 
 
 In estimating the speed of reading, it is well to 
 be clear what precisely we are measuring. For 
 there are four possibilities. We may measure the 
 normal or the maximal speed of either oral or silent 
 reading. The speed measured in this test is the 
 maximal for oral reading. 
 
 The question may be raised : how far is the 
 recorded speed a real index of the speed of reading 
 
READING 139 
 
 as distinct from speed of articulation ? There 
 is little doubt that adults can read silently very 
 much faster than they can read aloud — very much 
 faster than they can articulate the words. But 
 this is not true of a young child. I found by testing 
 a number of children of 7 years of age that they 
 could speak or recite at the rate of 170 words per 
 minute while they read the test words at the rate 
 of 40 per minute. Again, girls of 9I years old who 
 read 80 words per minute were able to recite 220 
 words per minute. 
 
 The following norms were obtained by applying 
 the test to the children of 49 schools : — 
 
 Age. 6 yrs. 7 yrs. 8 yrs. 9 yrs. 10 yrs. 14 yrs. 
 
 Boy's Score. 13 33 53 72 85 115 
 Girl's Score. 15 38 58 j6 88 122 
 
 The original experiment stopped at 10 years 
 of age ; for I did not regard the test as suitable 
 for older children, with whom the mastery of the 
 mechanical factor may as a rule be taken for granted ; 
 but as an afterthought I extended it so as to include 
 children of 14. The results show a considerable 
 flattening of the curve after 10. 
 
 Among the 49 schools I included 10 which were 
 reputed to be attended by the poorest children 
 in London, and 9 situated in good residential 
 areas. The results show that both boys and girls 
 in good neighbourhoods are about 6 months (10 
 marks) in advance of the average ; and in poor neigh- 
 bourhoods the boys are 3 months behind, and the 
 girls 6 months. Thus for the extreme types of 
 home we find a difference of 9 months for boys 
 
140 MENTAL TESTS 
 
 and 12 months for girls. A girl of 8 in Dulwich 
 can read as well as a girl of 9 in Bermondsey. 
 
 Through the courtesy of a friend, I was enabled 
 to secure results from 6 elementary schools in Lan- 
 cashire. In general tendency they tallied with the 
 London results ; but the Lancashire boys were 3 
 months ahead of London boys, and the girls 4 months 
 ahead. The 6 schools, however, included no poor 
 schools, and there is reason to believe that the social 
 conditions were above the average. 
 
 There is nothing to indicate whether the superi- 
 ority of the children from good homes is due to 
 heredity or environment — to higher native ability 
 or to better opportunities. Both probably con- 
 tribute. 
 
 The statistics obtained lend support to the popular 
 belief that girls read better than boys. Generally 
 speaking, they are 5 marks or 3 months ahead. But 
 it is a curious fact that this difference does not 
 obtain in slum neighbourhoods. There the boys 
 read quite as well as the girls. This is not merely 
 true of the ten schools taken in a lump ; but, with 
 one exception, of each of the 10 schools individually. 
 Whatever the reason may be, whether it is due to 
 the girls being more fully employed minding the 
 baby — there generally is a baby — or doing domestic 
 work, or whether this intrinsic sex difference does 
 not hold good generally, the fact itself seems to 
 admit of little doubt. 
 
 Occasionally a reader rushed through the test 
 with little regard to accuracy, and thus made a 
 fairly high score in spite of many blunders ; whilst 
 another reader would proceed more cautiously 
 and secure a lower score although he made no 
 
READING 141 
 
 blunders at all. The majority, however, maintained 
 a steady level of cautiousness ; and on an average 
 about three mistakes were made by children of all 
 ages. This means that accuracy improved with 
 age, and was roughly proportional to speed ; for 
 to get three mistakes out of 88 words read (see score 
 for girls of 10) was nearly six times as creditable as 
 to get three mistakes out of 15 words read (score 
 for girls of 6). 
 
 The method of teaching reading in all the schools 
 tested was some form of the phonic. The alpha- 
 betical method pure and simple may be said to be 
 obsolete in London, although the children are 
 generally taught the conventional names of the letters 
 either at the same time as their phonic values or 
 after the art of reading has been at least partly 
 acquired. The look-and-say mode of reading into 
 which all other forms ultimately merge, is to a 
 greater or lesser degree incorporated in the other 
 systems. In fact, the system in vogue is mixed, 
 with the phonic element predominating. There 
 are, however, various forms of the phonic method 
 current, some simple and some complex. Perhaps 
 the most systematic and complex of all is the Dale 
 method ; and in 19 out of the 49 schools this method 
 is followed. Do the scores at these 19 schools afford 
 evidence of the superiority of this system ? How 
 do they compare with the scores at the 30 non- 
 Dale schools ? Taken as a whole the Dale boys 
 are 1 month behind when they are under 7 years 
 of age, and 2 months in advance after 7 ; while 
 the girls are 2 months behind when under 7, and 
 2 months ahead after 7. But 5 of the 19 Dale 
 schools are included in the 9 schools above referred 
 
142 
 
 MENTAL TESTS 
 
 to as situated in the wealthier neighbourhoods. 
 And if the influence of home and district be elimin- 
 ated it is doubtful whether the Dale results are as 
 good as the non-Dale. It is certain that they are 
 no better. Here is a system of high repute, regarded 
 indeed by some as the mark of up-to-dateness in 
 infant teaching — a system requiring special training 
 on the part of the teacher, and involving the use 
 of special apparatus and special books ; but judging 
 from the results achieved, it is no better as a means 
 of teaching reading than the ordinary phonic system 
 in common use. It is true that it has other merits. 
 It includes other things besides reading proper, 
 such as printing, drawing, and phonetic analysis — 
 things in themselves valuable ; but taken purely 
 from the reading point of view, it fails to substantiate 
 the high claim generally made on its behalf. 
 
 What then is the salient characteristic of method 
 in the schools where the test shows reading to be 
 exceptionally good ? It is this. In the good schools 
 reading is encouraged as a pursuit, and not merely 
 taught in a series of lessons. The children read 
 for the sake of the story, not for the sake of reading. 
 It is a pleasurable occupation, and not a tiresome 
 phonetic drill, nor yet an elocutionary display. 
 Phonetic drill and elocution have their place in 
 school routine, but the root of proficient reading 
 grows in other soil. In the school where the reading 
 is best of all, even children of six read small fairy 
 tale books for pleasure. 
 
 There is one arresting exception to the above 
 generalisation. In a certain infants' school where 
 no private reading takes place, but a large amount 
 of word-building is taken on the blackboard, the 
 
READING 143 
 
 result reaches high-water mark ; but in the senior 
 school the curve sinks to the normal : the proficiency 
 is not maintained. It will thus be seen that the 
 same apparent results may be obtained in the earlier 
 period by opposed methods ; but while the momen- 
 tum is kept up by the one method, it is lost by the 
 other. As ever, it is a question of interest. 
 
 It should be clearly understood that this test, 
 consisting as it does of words of no connected mean- 
 ing, is intended to be used as a test only, and never 
 as material for practice, nor even as suggesting 
 the type of material for practice ; for I strongly 
 hold the view that in selecting reading-books for 
 children, subject matter is a consideration of supreme 
 importance. If the subject is of no interest to 
 the child, if it would not grip his attention when read 
 to him instead of by him, then we must regard it to 
 be of the wrong sort ; unless, indeed, we reject the 
 view that the main aim and purpose of the teacher 
 of reading should be to hasten the coming of the 
 time when the child will spontaneously take up 
 a book and read it for the sake of what it has to 
 tell him. 
 
 Although the test is oral, it must not be inferred 
 that practice should be entirely oral, or indeed 
 mainly oral. For the out-of-school reading, for 
 which the school reading is a preparation and a 
 training, is almost entirely silent : it is reading as a 
 device for getting ideas. And the training of any 
 specific activity should always, as far as possible, 
 take the form of that activity. It is not always 
 possible. At the earliest stage of reading, for instance, 
 much drudgery in associating symbols with sounds 
 is necessary before the process is sufficiently mechan- 
 
144 MENTAL TESTS 
 
 ised for the sense of what is read to stand out clearly 
 and predominantly in the mind. Indeed, for some 
 time, the child, unless he reads aloud — unless there 
 is somebody for whom he feels he is doing something 
 — will not read at all. But the sooner this stage 
 is passed the better. 
 
 Again, fluent reading, regarded merely from the 
 mechanical point of view, is mainly a matter of 
 practice, and the amount of practice given in school, 
 especially where individual class reading — reading 
 in turns — is adopted, is so small that many years 
 pass before a fair degree of fluency is attained. 
 
 The reasons are now clear why I regard this test 
 as useful for the early stages of reading only. As 
 the child grows older the aspect of reading which 
 becomes increasingly important is the extent to 
 which it can be employed as a thought-getting 
 device — the accuracy and rapidity with which the 
 child absorbs the meaning of what he reads privately. 
 
 It has often been pointed out that to read 
 mechanically is one thing ; to understand what is 
 read, another. And although it will be granted 
 that a child may do the former without the latter, 
 it is equally certain that he can never do the latter 
 without the former. Until, indeed, a child can 
 read about loo of the test words per minute, the 
 mechanical art of reading cannot be said to have 
 been completely mastered ; and the utilisation 
 of the test is profitable as a means of measuring 
 his fluency ; which is roughly a measure of the 
 practice he has had ; which, again, is roughly a 
 measure of the interest he takes in reading. Beyond 
 that stage other tests overshadow the mechanical 
 one. Reading, indeed, cannot in any sense be 
 
READING 145 
 
 regarded as a simple process, nor can the same means 
 be adopted for measuring proficiency in the earlier 
 and later stages of acquiring the art. 
 
 B. — As a Means of Acquiring Ideas 
 
 At the age of nine most children have acquired 
 a fair degree of facility in the mechanical art of 
 reading. Henceforth reading is to them either 
 an elocutionary exercise (reading aloud), or a means 
 of getting ideas (silent reading). And of these 
 two the more important is the latter. It is no 
 exaggeration to say that in adult life ninety-nine 
 out of every hundred books are read silently. The 
 essential aim, therefore, in the teaching of reading, 
 should be to give the pupil the power to absorb 
 meaning from the printed page. If he is to gain 
 either pleasure or profit he must understand what 
 he reads. And the measure of his progress in under- 
 standing is virtually the measure of his progress 
 in reading. But how are we to measure understand- 
 ing ? It is clear that the time-element cannot be 
 ignored. What we have to determine is the rate 
 at which the pupil can master the meaning of a given 
 piece of prose or poetry. 
 
 There are in use, in the United States, at least 
 eight different types of silent reading tests. They 
 generally consist in allowing the pupil a fixed time 
 to read a given passage, and then ascertaining how 
 much of the meaning can be reproduced. But 
 here we encounter the difficulty that makes com- 
 position so hard to assess. How can we weigh 
 ideas ? How can we measure meaning ? Daniel 
 Starch, in his silent reading tests, tries to get over 
 
 L 
 
146 MENTAL TESTS 
 
 the difficulty by getting the pupil to write out 
 what he remembers of the passage read, and by 
 counting the number of words written which cor- 
 rectly express the thought. This is equivalent 
 to marking a piece of composition by its length. 
 Some of the other systems require a complicated 
 key by which the reproductions may be scored. 
 The scheme, however, which seems to be most 
 widely used in America, is the Kansas Silent Reading 
 Scale. It comprises a series of sixteen exercises 
 which carry marks proportional to their difficulty. 
 Exercise 6, for instance, which is valued at 2*3, 
 runs as follows : " In going to school James has to 
 pass John's house, but does not pass Frank's. If 
 Harry goes to school with James, whose house 
 will Harry pass, John's or Frank's ? . . . " The 
 examinee has to fill in the blank at the end. This 
 question is typical of the series — a series which 
 admittedly tests reasoning : but does it test reading ? 
 The pupil's mind is required not merely to follow 
 the meaning of the sentence, but to go beyond it ; 
 and it is quite conceivable that a child may be able 
 to follow a plain narrative with ease and rapidity, 
 and yet be very slow at dealing with puzzles of 
 the Kansas kind. In any case the exercises differ 
 in toto from the kind of matter people generally 
 read. The last book one thinks of reading is a book 
 of conundrums. 
 
 Another peculiarity common to the American 
 silent reading tests, is that more than one series 
 is used. There is generally one for the lower grades, 
 one for the middle grades, and one for the higher 
 grades. And although the several series are supposed 
 to be so adjusted in the matter of difficulty, that 
 
READING 14- 
 
 the norms for the various school grades increase 
 regularly, the adjustment is in point of fact never 
 perfect. In the Kansas tests, for instance, the norms 
 for Grade V and Grade VI are nearly the same. 
 
 There is, further, the outstanding disadvantage 
 to the Englishman, that the tests and results are 
 arranged by grades and not by ages. The scale is 
 never, except by precarious inference, an age scale. 
 
 The test I have devised for my own use is as 
 follows : — 
 
 Silent Reading Test 
 (3 Minutes) 
 
 One fine morning in spring a robin flew down 
 to the brink of a stream to quench his thirst. See- 
 ing a trout in the water he began to talk to him. 
 " I have often wondered," said he, " how you manage 
 to keep alive. If I tried to stay under water like 
 you I should be dead in a few minutes. And even 
 supposing I could remain alive I should feel miserably 
 cold in the chilly water without either fur or feathers. 
 Please tell me why you are not drowned, and why 
 you do not perish with cold." " You should never 
 ask two questions at once," said the trout. " Quite 
 right ! " croaked an old crow who had heard their 
 conversation and had alighted on the bank beside 
 the robin. He was very old and very wise and very 
 inquisitive. Some thought that it was because he 
 was inquisitive that he was so wise, others thought 
 that his wisdom came from age and experience. 
 Certain it was that he was regarded as the most 
 learned of all the birds of his time, and that he 
 used such long words that the little birds, beasts 
 and fishes could rarely understand what he was 
 
148 MENTAL TESTS 
 
 talking about. To return to the robin's questions, 
 the trout replied : " Why don't I get drowned ? 
 Why, one does not drown in the water : one drowns 
 in the air." " Nonsense ! " said the robin. But the 
 crow looked so severely at him that he trembled, 
 and drooped his tail by way of apology. " As for 
 feeling cold," continued the trout, " I don't know 
 what you mean." The robin was about to say 
 " Liar ! " when he caught the crow's eye and 
 restrained himself. Then the crow, having held up 
 his right foot to enjoin silence and attention, delivered 
 himself thus : " It was held by Aristotle, and his 
 opinion is confirmed by modern scientific theory, 
 that there is no living creature that can exist in 
 any and every environment : each requires sur- 
 roundings suitable to its bodily structure and its 
 bodily functions. To secure a supply of oxygen, 
 which is necessary to maintain the purity and tem- 
 perature of the blood, each animal is provided with 
 organs which are adapted for extracting this element 
 from the atmosphere, where it is present in great 
 abundance. In land animals lungs serve that 
 purpose ; in fishes, gills. Gills are so constructed 
 that they can only take up the oxygen that is dis- 
 solved in water. In the air the gills adhere together 
 and the poor fish dies of asphyxiation. Our friend 
 the trout was therefore quite justified in asserting 
 that the atmosphere drowns fishes. As for his 
 avowed ignorance of the distinction between heat 
 and cold, we must not rashly accuse him of false- 
 hood. It is a well-known psychological fact that 
 sensitiveness to heat and cold is dependent on certain 
 specialised nerve endings in the skin." He paused 
 here to see the effect of his oration on his audience. 
 
READING 149 
 
 While speaking he had been gradually closing his 
 eyes in order to think better ; but at this point he 
 opened them wide and found to his disgust that the 
 trout had disappeared and that the robin was strug- 
 gling with a big fat worm about twenty yards away. 
 
 A double sheet, with the story printed inside, is 
 distributed, and the children told that they will be 
 given three minutes to read it, and that they will 
 afterwards be tested to see how much they can 
 remember. On the word of command the children 
 must open the papers and read silently. At the 
 end of three minutes the papers are collected and 
 the following completion test given out to each 
 child, with instructions to supply the missing words 
 except those marked (x). 
 
 Completion Test 
 (Unlimited Time) 
 
 One fine morning in (1) a (2) flew down to 
 the brink of a ( 3 ) to quench his thirst. Seeing a 
 ( 4 ) in the water he began to talk to him. " I 
 have often wondered," said he, " how you manage 
 to (5) (6). If I tried to stay under water like 
 you I should be dead in a few minutes. And even 
 supposing I could remain ( x ) I should feel miserably 
 ( 7 ) in the ( x ) water without either ( 8 ) or ( 9 ). 
 Please tell me why you are not ( 10 ), and why you 
 do not perish with (x)." "You should never 
 ask ( 11 ) questions at once," said the ( x ). " Quite 
 right ! " (12) an old ( 13 ) who had heard their 
 conversation and had alighted on the bank beside 
 the ( x). He wg§ very ( 14) and very ( 15 ) and 
 
150 
 
 MENTAL TESTS 
 
 very ( 16.) Some thought that it was because he 
 was ( x ) that he was so ( x ) ; others thought that 
 his (17) came from (18) and (19). Certain 
 it was that he was regarded as the most ( 20 ) of 
 all the birds of his time, and that he used such ( 21 ) 
 ( 22 ) that the little birds, beasts and fishes could 
 ( 23 ) understand what he was talking about. To 
 return to the ( x ) questions, the ( x ) replied : 
 " Why don't I get drowned ? Why, one does not 
 drown in the ( 24 ) : one drowns in the ( 25 )." 
 "(26)" said the (x). But the (x) looked so 
 ( 27 ) at him that he ( 28 ), and drooped his tail by 
 way of ( 29 ). " As for feeling ( x )," continued the 
 ( x ), "I don't know what you mean." The ( x ) 
 was about to say " ( 30 )," when he caught the 
 ( x ) eye and ( 31 ) himself. Then the ( x ), having 
 held up his right foot to enjoin ( 32 ) and ( 33 ), 
 delivered himself thus : " It was held by ( 34 ), 
 and his opinion is (35) by (36) scientific theory, 
 that there is no living creature that can exist in 
 any and every ( 37) : each requires (38) suitable 
 to its bodily ( 39 ) and its bodily ( 40 ). To secure 
 a supply of ( 41 ), which is necessary to maintain 
 the ( 42 ) and ( 43 ) of the ( 44 ), each animal is 
 provided with ( 45 ) which are adapted for extracting 
 this ( 46 ) from the ( 47 ), where it is present in 
 great ( 48 ). In land animals (49) serve that pur- 
 pose ; in fishes, ( 50 ). ( x ) are so constructed 
 that they can only take up the ( x) that is ( 51 ) in 
 water. In the air the ( x) adhere together and the 
 poor fish dies of ( 52 ). Our friend the trout was 
 therefore quite ( 53 ) in asserting that the atmosphere 
 (54) fishes. As for his avowed (55) of the dis- 
 tinction between (56) and (57), we must not 
 
READING 151 
 
 rashly accuse him of ( 58 ). It is a well-known ( 59 ) 
 fact that ( 60 ) to ( x ) and ( x ) is dependent on 
 certain ( 61 ) nerve endings in the skin." He paused 
 here to see the ( 62 ) of his ( 63 ) on his ( 64 ). While 
 speaking he had been gradually closing his eyes 
 in order to think better ; but at this point he opened 
 them wide and found to his ( 65 ) that the ( x ) had 
 (66) and that the ( x ) was struggling with a big 
 fat worm about (6j) yards away. 
 
 The most convenient way to administer the com- 
 pletion test, is to distribute strips of paper upon 
 which the missing words are to be written. If the 
 lines on the paper are numbered from 1 to 67 it will 
 facilitate marking. One mark is awarded for each 
 word correctly given. As it is a test of substance 
 memory, and not rote memory, synonymous words 
 are accepted. General terms, however, must not 
 be regarded as substitutes for particular terms. 
 
 The following synonyms and variations are per- 
 missible : 3, brook, river ; 5, remain ; 5 and 6, 
 exist; 8 and 9, in either order; 12, said; 14, 15 
 and 16, in any order; 18 and 19 in either order; 
 21, big; 23, hardly, scarcely; 25, atmosphere; 27, 
 sharply, crossly; 31 checked, stopped; 35, upheld; 
 38, conditions ; 39 and 40, in either order ; 42 
 and 43, in either order ; 43, heat ; 46, oxygen ; 
 47, air ; 48, quantities ; 52, asphyxia, suffocation ; 
 53, right, correct ; 56 and 57, in either order ; 58, 
 lying, untruth; 61, special, particular; 63, speech, 
 words ; 64, listeners, hearers ; 66, gone, vanished. 
 In every other case the exact word must be given. 
 
 This test has the merit of being simple and work- 
 able, of being applicable to all readers from the ages 
 of nine to ninety, and of being objective in the 
 
152 
 
 MENTAL TESTS 
 
 sense that two independent examiners will, if they 
 follow the instructions, inevitably give the same 
 mark for the same achievement. The examiner may, 
 if he wishes, examine himself. It will be seen that 
 the narrative is easy to begin with, and gradually 
 increases in difficulty, so that the dullest reader 
 will be able to remember some, and the brightest 
 fail to remember all. I have tried as far as possible 
 to select, as missing words, those which indicate 
 that the meaning of the text has been understood, 
 and yet are not such as an intelligent pupil would 
 infer from the context. The first blank, for instance, 
 cannot be filled by reasoning, for there are many 
 possibilities. The missing word may be " Summer," 
 or " April," or any other season or month. And 
 the second word may be any one of the numerous 
 species of birds or insects. In fact, the missing 
 words are not inevitable words : they really test 
 whether the pupil has read the piece, has understood 
 it, and has remembered it. 
 
 To prevent the examinee from inferring the 
 missing words at the beginning of the piece from 
 what is said later on, I have omitted the words 
 that afford a ground for retrospective inference 
 and substituted ( x ). If, for instance, I had printed 
 " trout " instead of ( x ) in the twelfth line, a shrewd 
 lad would at once know that the fourth missing 
 word was " trout." In order to ascertain experi- 
 mentally, to what extent inference could supply 
 the place of direct knowledge acquired from actually 
 reading the piece, I submitted the second paper 
 to a number of intelligent children who had not 
 read the first. In no instance were more than three 
 words guessed correctly. 
 
READING 153 
 
 By applying the test to about 5000 children from 
 nine to fifteen years of age, I arrived at the following 
 norms : — 
 
 Age. 9 yrs. 10 yrs. n yrs. 12 yrs. 13 yrs. 14 yrs. 
 
 Score. 6 10 14 17 19 21 
 
 Through the courtesy of Miss Lloyd Evans, the 
 Principal of the Furzedown Training College, I 
 was able to test the students in training. They 
 made an average score of 41. 
 
 The mean variations for the various ages from 
 nine to fourteen were successively 3*5,' 5*3, 6"l, 
 6, 6-i, 6-3. 
 
 For the training college students it was 6. 
 
 It has been urged in criticism of the test that it 
 measures not understanding but memory. My 
 reply is that it measures both ; and in measuring 
 both it measures the actual intellectual gain got 
 from the exercise. Indeed, the two factors are 
 both inseparable and indispensable. If a reader 
 forgets the meaning of the earlier sentences he cannot 
 possibly grasp the meaning of the later sentences. 
 Any word he reads may turn out to be key-word 
 on which the significance of all that follows depends ; 
 and if the key-word, or at least its meaning, be 
 forgotten, his reading becomes vain. Sometimes 
 the key-word comes late and modifies the sense 
 of all that precedes it ; and if what precedes is 
 forgotten, the point and significance of the whole 
 piece is missed. Browning affords many instances 
 of this kind. The key to " My Last Duchess," 
 for example, is to be found a few lines from the 
 end. The hint that the Duke contemplates a 
 second marriage illumines all that he has previously 
 
154 MENTAL TESTS 
 
 said, giving it point and purpose, and turning the 
 poem into an intelligible whole. 
 
 Again, if the reader will refer to my absurdity 
 test on p. 38, he will see that the absurdities all 
 occur in the latter half, and their detection depends 
 on an exact remembrance of what is said in the first 
 half. Not a single sentence is absurd in itself : 
 it is only absurd when brought into relation with 
 the rest ; and if the incompatibility is to be seen, 
 the rest must be remembered. 
 
 Admitting, however, that it is impossible to 
 understand the piece without also to a large extent 
 remembering it, is it not possible to remember it 
 without understanding it ? It is possible, but so 
 highly improbable that the possibility need not be 
 seriously considered. It is only necessary to imagine 
 a similar test given in Latin to an intelligent lad 
 who knows no Latin, but can only read the words 
 as though they were English, to see the futility of 
 supposing a mere verbal memory to be of much 
 service in a three minutes' test of this kind. For 
 all practical purposes, if the subject understands 
 the narrative, he will be able to supply the missing 
 words ; and, conversely, if he remembers the missing 
 words, it will be due to the fact that he has under- 
 stood the narrative. 
 
CHAPTER IX 
 
 SPELLING 
 
 The usual mode of testing spelling in school is 
 by means of an " unseen " piece of dictation. 
 The main objection to this procedure is that the 
 piece given is not standardised : its difficulty is 
 unknown. And passages of prose vary so enor- 
 mously in difficulty that to lay down any general 
 rule regarding the number of mistakes per line 
 that might reasonably be allowed at different ages 
 is clearly impossible. 
 
 Opinions differ respecting the range of words 
 which a child should be expected to spell. Some 
 think that he should never be required to spell 
 words outside his own vocabulary, and that his 
 written composition should be the only basis on 
 which his ability to spell should be estimated. To 
 this view it may be objected that a child's vocabu- 
 lary is a growing thing, and it would be well to 
 anticipate a little and to teach him to spell words 
 which he will probably want to use in the near 
 future. Moreover, it is sometimes necessary to 
 write from dictation, or to record in notes the 
 sayings of others ; and if the writer's own vocabulary 
 is very limited, or restricted to certain favourite 
 words (as in fact most people's vocabulary is), the 
 range of his spelling vocabulary should be extended 
 
 *53 
 
156 MENTAL TESTS 
 
 so as to include the words that are in most common 
 use. Thus we have two overlapping groups of 
 words whose spelling should be known : first, those 
 which constitute the pupil's speaking and writing 
 vocabulary ; secondly, those most frequently used 
 by the nation as a whole. But which are the words 
 most frequently used ? And how many of them 
 are we to include ? 
 
 In America these questions have been answered 
 by Dr. L. P. Ayres, who has compiled a list of the 
 thousand commonest words in the English language, 
 or rather the American variety of the English 
 language. The method employed was to examine 
 written material of various types, such as letters, 
 newspapers, and children's compositions, and to 
 make a list of the words used and the number of 
 times each word occurred. Ayres combined the 
 results of four such studies, which comprised 368,000 
 words written by 2500 different persons. Some 
 interesting facts emerged. It was found, for in- 
 stance, that fifty of the words were used so fre- 
 quently that they made up about half of the 
 material examined. In order to secure a thousand 
 words it was necessary to include words which only 
 occurred once every 8000 words. 
 
 By testing a large number of children with this 
 list Ayres was able to divide the words into twenty- 
 six groups, named after the letters of the alphabet. 
 The words in each group (the groups vary con- 
 siderably in size) are supposed to be of equal diffi- 
 culty. The following list comprises the words in 
 Group N. The percentages of these words that 
 should, according to Ayres, be spelt correctly in 
 the grades from III to VIII are 58, 79, 88, 94, 
 
SPELLING 157 
 
 98 and 100 respectively. Translated into English 
 terminology it means roughly that Standard II 
 children should be able to spell 58 per cent, of the 
 words, Standard III 79 per cent., and so forth. 
 
 Ayres' Spelling Test 
 
 Group N. — Except, aunt, capture, wrote, else, 
 bridge, offer, suffer, built, centre, front, rule, carry, 
 chain, death, learn, wonder, tire, pair, check, prove, 
 heard, inspect, itself, always, something, write, 
 expect, need, thus, woman, young, fair, dollar, 
 evening, plan, broke, feel, sure, least, sorry, press, 
 God, teacher, November, subject, April, history, 
 cause, study, himself, matter, use, thought, person, 
 nor, January, mean, vote, court, copy, act, been, 
 yesterday, among, question, doctor, hear, size, 
 December, dozen, there, tax, number, October, 
 reason, fifth. 
 
 The most useful list for English schools is Mr. 
 Burt's, which I append — 
 
 Burt's Graded Spelling Test 
 
 Age. 
 
 5.— a it cat to and the on up if box 
 6. — run bad but will pin cap men got 
 
 to-day this. 
 7. — table even fill black only coming sorry 
 
 done lesson smoke. 
 8. — money sugar number bright ticket speak 
 
 yellow doctor sometimes already. 
 9.— rough raise scrape manner publish touch 
 
 feel answer several towel. 
 
i 5 8 
 
 MENTAL TESTS 
 
 10. — surface pleasant saucer whistle razor 
 vegetable improvement succeed begin- 
 ning accident. 
 
 ii. — decide business carriage rogue receive 
 usually pigeon practical quantity 
 knuckle. 
 
 12. — distinguish experience disease sympathy 
 illegal responsible agriculture intelligent 
 artificial peculiar. 
 
 13. — luxurious conceited leopard barbarian 
 occasion disappoint necessary treacher- 
 ous descendant precipice. 
 
 14. — virtuous memoranda glazier circuit de- 
 cision mosquito promiscuous assassinate 
 embarrassing tyrannous. 
 
 Note. — " The words assigned to any given age are 
 those answered correctly by 40 to 60 per cent, of the 
 age-group specified. Thus, approximately, 50 per 
 cent, aged 10 last birthday can spell ' surface ' . . . 
 ' accident.' Therefore, to attain a mental age of 
 ioi a child should spell fifty-five words, *". e. all to 
 ' vegetable ' inclusive (or the equivalent). 
 
 " It is not necessary that all the children should 
 be given all the words : twenty or thirty from the 
 appropriate consecutive ages are usually sufficient. 
 The mental ages assigned to the earlier words are 
 somewhat arbitrary owing to wide differences in 
 infants' schools." 
 
 A protest should be made against the frequency 
 with which unseen pieces of dictation are given in 
 the higher standards of English elementary schools. 
 Sometimes two lessons per week are devoted to it 
 in the top class. The defence generally made is 
 
SPELLING 159 
 
 that the children are backward in spelling ; to 
 which it may be replied that dictation is primarily 
 a test, a means of measurement, and not a means, 
 except indirectly, of teaching spelling. At any rate 
 it is not the most economical means. When a child 
 suffers from malnutrition we do not try to fatten 
 him by weighing him twice a week. 
 
CHAPTER X 
 
 ARITHMETIC 
 
 (a) The Fundamental Processes 
 
 Several attempts have been made in America to 
 standardise tests in Arithmetic. The most widely 
 used, the Courtis Tests, share with all the rest the 
 defect of insularity : they constitute a grade-scale 
 and not an age-scale, and the monetary units are 
 dollars and cents and not pounds, shillings and pence. 
 
 Little has been done to establish norms suitable 
 for England. In 191 3 and 1914 I carried out an 
 extensive research into the ability of London children 
 to perform the simple fundamental processes of 
 adding, subtracting, multiplying and dividing. The 
 results of this research were published in the 
 Journal of Experimental Pedagogy for December 
 1914 and March 1915. The tests were repeated 
 and the standards broadly confirmed by Mr. P. L. 
 Gray, H.M.I., in the schools of Leeds. The copy 
 of the Journal (June 191 5) which contained Mr. 
 Gray's account of his experiment also contained a 
 criticism of my tests by the editor, Professor J. A. 
 Green. At the meeting of the British Association 
 at Newcastle in 191 6 the Report of the Committee 
 on the Mental and Physical Factors involved in 
 Education dealt with Norms in Mechanical Arith- 
 metic and gave an account of investigations in 
 
 160 
 
ARITHMETIC 161 
 
 London and Sheffield on similar lines to my own. 
 The tests used (they were devised by Mr. Cyril 
 Burt) were better than mine. Mine suffered from 
 the defect of being too brief. Five minutes were 
 allowed for working twenty-four sums, and in nearly 
 every school tested some of the older children finished 
 the paper before the time was up. If the paper had 
 been longer their score would have been higher. 
 
 In the autumn of 191 9 I revised my original tests 
 and administered them to a large number of London 
 children. They differ in important respects from 
 the 1914 tests. They are both simpler and more 
 searching. The time allowed is three minutes 
 instead of five, and none of the children tested were 
 able to complete the papers within the time. A 
 yearly age-scale is substituted for a half-yearly 
 age-scale. Finally, the numbers have been so 
 selected as to secure the greatest variety compatible 
 with leaving all the sums of approximately equal 
 difficulty. If a multiplication table be constructed 
 up to 9 times 9, and a similar table for each of 
 the other processes, every item in those tables will 
 be found represented somewhere in the examples 
 set ; generally twice, once in the first half and once 
 in the second. 
 
 Addition : Three Minutes 
 
 64 
 
 35 
 
 82 
 
 78 
 
 46 
 
 27 
 
 3 
 
 16 
 
 29 
 
 63 
 
 92 
 
 58 
 
 56 
 
 98 
 
 31 
 
 40 
 
 9 
 
 5o 
 
 7i 
 
 93 
 
 5i 
 
 98 
 
 78 
 
 H 
 
 63 
 
 42 
 
 16 
 
 43 
 
 2 
 
 5i 
 
 23 
 
 17 
 
 39 
 
 72 
 
 19 
 
 75 
 
 47 
 
 65 
 
 89 
 
 4 
 
 80 
 
 65 
 
 M 
 
1 62 MENTAL TESTS 
 
 70 
 
 44 
 
 86 
 
 39 
 
 81 
 
 24 
 
 16 
 
 28 
 
 8 
 
 97 
 
 85 
 
 5o 
 
 69 
 
 92 
 
 76 
 
 57 
 
 42 
 
 16 
 
 72 
 
 92 
 
 35 
 
 52 
 
 26 
 
 5o 
 
 46 
 
 24 
 
 5 
 
 48 
 
 13 
 
 4 1 
 
 13 
 
 9 
 
 68 
 
 74 
 
 70 
 
 89 
 
 93 
 
 72 
 
 53 
 
 73 
 
 38 
 
 13 
 
 29 
 
 36 
 
 7 
 
 5i 
 
 89 
 
 40 
 
 21 
 
 81 
 
 90 
 
 24 
 
 85 
 
 73 
 
 49 
 
 5 
 
 6 
 
 54 
 
 19 
 
 24 
 
 15 
 
 58 
 
 18 
 
 47 
 
 18 
 
 57 
 
 39 
 
 24 
 
 24 
 
 58 
 
 58 
 
 63 
 
 26 
 
 66 
 
 16 
 
 79 
 
 73 
 
 72 
 
 59 
 
 38 
 
 70 
 
 3 
 
 63 
 
 64 
 
 92 
 
 16 
 
 27 
 
 34 
 
 53 
 
 69 
 
 75 
 
 15 
 
 37 
 
 3i 
 
 16 
 
 27 
 
 92 
 
 43 
 
 70 
 
 4 
 
 96 
 
 52 
 
 69 
 
 28 
 
 82 
 
 48 
 
 48 
 
 80 
 
 79 
 
 15 
 
 15 
 
 68 
 
 29 
 
 95 
 
 58 
 
 48 
 
 34 
 
 73 
 
 7 
 
 36 
 
 24 
 
 27 
 
 8 
 
 78 
 
 40 
 
 94 
 
 Subtraction : Three Minutes 
 
 69152 80031 68703 54218 
 48729 63175 37956 49221 
 
 17690 91435 62098 761 12 
 7948 23256 34089 57346 
 

 ARITHMETIC 
 
 163 
 
 85694 
 
 2787 
 
 60321 
 H359 
 
 70592 
 26819 
 
 80941 
 53437 
 
 78580 
 
 29395 
 
 6021 1 
 437 l6 
 
 81427 
 42078 
 
 93505 
 16693 
 
 74816 
 53 6l 7 
 
 92240 
 59830 
 
 80134 
 46965 
 
 75702 
 28139 
 
 78265 
 2495 
 
 70124 
 65139 
 
 80367 
 20548 
 
 94521 
 16973 
 
 35172 
 19438 
 
 59203 
 47689 
 
 69375 
 
 7089 
 
 49315 
 19782 
 
 
 Multiplication : 
 
 Three Minutes 
 
 
 273905 
 4 
 
 360197 
 
 7 
 
 59H7 2 
 5 
 
 465239 
 6 
 
 629175 
 2 
 
 196704 
 9 
 
 297836 
 3 
 
 519824 
 8 
 
 148637 
 4 
 
 254879 
 
 7 
 
 368051 
 
 5 
 
 780147 
 6 
 
164 
 
 MENTAL TESTS 
 
 308465 328547 541783 736582 
 2938 
 
 612549 598162 561923 726493 
 7465 
 
 598263 
 9 
 
 793428 439716 
 
 625097 
 3 
 
 180493 
 
 641857 
 5 
 
 834729 
 4 
 
 582736 
 7 
 
 Division : Three Mitiutes 
 4/26930 7/ 66 759 5/4 8l 75 6/44957 
 
 2/365H 9/534 12 3/28103 8/58849 
 
 4/5779 2 7/ r 3°26 5/82947 6/33802 
 
 2/12978 9/16743 3/24861 8/85390 
 
 7/59304 4/21 1 59 6/52298 5/63772 
 
ARITHMETIC 165 
 
 9/24419 2/18758 8/39857 3/55378 
 
 5/19238 7/ 8 9 2 9 2 9/34 26 3 4/7 82 95 
 
 The examples were graphed or cyclostyled and 
 distributed face downwards, one process at a time. 
 Three minutes were allowed for working, and one 
 mark allowed for each sum that was absolutely 
 correct. 
 
 The following norms were arrived at — 
 
 L b 
 
 Number of Sums right in Three Minutes 
 Age. 9yrs. 10 yrs. nyrs. 12 yrs. 13 yrs. i4yrs. 
 
 Addition ... 3 4 5 6 7 8 
 
 Subtraction . . 2 3i 4i 5i 6J 7 
 
 Multiplication 1^ 3 \\ 5I 6f 7I 
 
 Division . . . 1 2f 4 5i 6J 7 
 
 If we mark the papers in another way and 
 instead of counting the number of sums right 
 count the number of operations right, we shall get 
 a more exact score, for examples partly correct 
 would score marks. By operations I mean pro- 
 cesses of the kind tested. For instance, in the first 
 addition example there are ten addition operations, 
 in the first subtraction example five subtraction 
 operations. For multiplication and division the 
 corresponding numbers are six and four. The 
 advantage of giving the norms in operations per 
 minute, as in the following table, is that in applying 
 a rough test any examples may be set by the teacher, 
 provided he makes a little allowance for the size of 
 
1 66 MENTAL TESTS 
 
 the sums, and the time taken in writing the figures 
 and in passing from one sum to another. 
 
 Number oj Operations per Minute 
 
 Age. 9yrs. ioyrs. nyrs. 12 yrs. I3yrs, i4yrs. 
 
 Addition ... 12 16 20 24 27 30 
 
 Subtraction .. 4 6 8 10 12 13 
 
 Multiplication. . 4 7 10 12 14 16 
 
 Division ... 2 4 6 8 9 10 
 
 When reduced thus to operations per minute the 
 results of my 191 9 investigation confirm the results 
 I obtained in 191 4. 
 
 Comments on the Addition Test. — The improve- 
 ment with age is only partly due to a more facile 
 application of the same method : it is mainly due 
 to a change of method, to a gradual supersession of 
 habits of a lower order by habits of a higher order. 
 The lowest habit of all is that of adding by units ; 
 the highest, that of adding en bloc. For example, 
 in adding the series 8 + 5 + 9 + 2 + 7+1 the pupil 
 working by the former method would start 8 + I + 
 1 + 1 + 1 + I, etc., while the pupil working by the 
 latter would say 8 + 5 =13 as a mere matter of rote 
 memory. Between these two extremes there are 
 various intermediary stages. Some, for instance, 
 decompose the addends in order to form tens. 
 Thus 8 + 5 = 8 + 2+3 = 10 + 3 = 13. Adding the 
 next item, 13 + 9= 13 + 7 + 2 = 20 + 2 = 22, etc. 
 Some other devices used to avoid counting by units 
 are also based upon the decomposition of the 
 addends into groups that can be added without 
 further reduction. Then there is the method of 
 arriving at the result by noting how far it falls 
 
ARITHMETIC 167 
 
 short of a readily ascertained sum. For instance, 
 13 + 9=13 + 10 — 1 ; and 8 + 7 = 8 + 8 — 1. Lastly, 
 there is the method advocated in some schools of 
 searching along the column for numbers which 
 form tens. Thus in the series given above the 8 
 and the 2 would be coupled, and also the 9 and the 
 I. This is a useful device when the paired numbers 
 come together ; but to link them when widely 
 separated is to increase unnecessarily the mental 
 strain, and to run the risk of omitting or duplicating 
 some of the addends. 
 
 There can be little doubt therefore that the 
 most efficient method is that of adding the items 
 seriatim and memoriter — as they come and by the 
 addition table. Advantage should, of course, be 
 taken of any obvious ten-group that would appear, 
 but there should be no hunting for it. It has been 
 maintained by some that to add 4 + 9 as 4+ 10— 1 
 is more " intelligent " than to say straight off 
 4 + 9 = 13. But why should it be so ? There is 
 an assumption that 4 + 10 is known, while 4 + 9 is 
 not. Logically the proposition 4 + 9 = 13 rests on 
 the number system, 1, 2, 3, 4, etc., and counting by 
 units is, in a sense, the one and only " intelligent " 
 method — the one and only method that lays bare 
 the ultimate ground of the proposition. But it is 
 assumed that the rationale of adding is clearly 
 understood by the pupils ; and the question under 
 discussion is not the most explicitly logical but the 
 most expeditious mode of adding. As a step 
 towards memorising 4 + 9 = 13, the operation 
 4 + 10 — I may be permitted ; but the process is 
 not complete from the point of view of practical 
 efficiency till it is short-circuited into 4 + 9 = 13. 
 
1 68 MENTAL TESTS 
 
 The number of items to be thus memorised is not 
 great. For if 4 + 9 = 13 be learnt, the sums of all 
 such combinations as 14 and 9, 29 and 4, etc., are 
 easily inferred therefrom. 
 
 The time taken to work the addition paper gives 
 a clue to the method used. I have applied the test 
 to a few children without imposing a time limit. 
 The children handed in their papers as soon as 
 they were finished, and the time taken was recorded 
 thereon. Later on each child was privately asked 
 to work through one of the sums orally, in order 
 that the method adopted might be ascertained. 
 The results confirmed the view that both speed 
 and accuracy depend upon the grade of habit upon 
 which the process of adding is based. 
 
 The danger of forming bad habits of computation 
 is far greater in addition than in multiplication. 
 In working the latter there is little temptation to 
 count. The veriest tyro cannot fail to perceive 
 the enormous labour-saving advantage of remem- 
 bering that 6 X 8 = 48 over the counting of six 
 eights ; but the advantage of memorising 6 + 8 = 14 
 is not so obvious when the result can readily be 
 arrived at by a mechanical drumming with the 
 fingers. It is indeed a notorious fact that a certain 
 percentage of educated adults count on the fingers 
 ■ — when nobody is watching them. 
 
 Comments on the Subtraction Test. — The most 
 salient feature of the subtraction results is the 
 evidence afforded of the superiority from a prac- 
 tical point of view of the method of equal addition 
 over the method of decomposition. In my account 
 of the 1 91 4 investigation I gave abundant evidence 
 to this effect, evidence which is further strengthened 
 
ARITHMETIC 169 
 
 by 1117 recent investigation. When the subtraction 
 score was in any school markedly below the scores 
 for the other three processes 1 guessed that the 
 method of decomposition was taught at that school ; 
 and my guess was always right. Let me take as an 
 example one of the best schools tested. Situated 
 in a very good residential district, it is attended 
 by children of exceptional advantages. The girls' 
 school is noted for the general thoroughness of the 
 work. Now observe the difference in the results 
 obtained in the two departments both at the lowest 
 age and the highest age tested. 
 
 + - x -=- 
 
 9 ^ rs -\Girls 7-3 3-8 & 3 47 
 
 i4.vni B °y s 6 " 8 7 * 6 7 " 8 7 ' 2 
 
 * 7 '\Girls io - 2 87 li"4 io - 3 
 
 An examination of these figures will show that 
 the girls' school, where the method of decomposi- 
 tion is adopted, is, in spite of the excellent teaching 
 labouring under a heavy disadvantage as compared 
 with the boys' school, where the method of equal 
 additions is taught. The figures also illustrate the 
 fact that although the advantage of one system 
 over the other tends to diminish with the age of 
 the children, the advantage is never lost — not at 
 any rate during the elementary school period. 
 
 But the disparity in the practical efficacy of the 
 two methods is really greater than would appear 
 from the above account ; for the examples set having 
 few or no noughts in the minuends failed to bring 
 out the more glaring disadvantages of the decom- 
 position method. When, however, such an example 
 
i jo MENTAL TESTS 
 
 as 40,000 — 197 is set, the ineptitude of the method 
 is more strikingly revealed. Even in the highest 
 classes of the decomposition schools the time taken 
 to work such an example is excessive, and the degree 
 of accuracy abnormally low. And yet it is examples 
 of this type (where the minuend is a round number) 
 that are of most frequent occurrence in everyday 
 life. This is obviously so in the case of money. 
 We want change from a five-pound note, a sovereign, 
 a half-sovereign, or a shilling, and not from such a 
 collection of coins as is represented in ^4 13J. J%d. 
 The reason for the inferiority of the decomposi- 
 tion method is not far to seek. In the equal 
 addition method the compensation is made — 
 accounts are squared — at the very first number 
 dealt with after the minuend has been disturbed. 
 In subtracting 37 from 85, after taking 7 from 15 
 the disturbed relationship of difference between 
 minuend and subtrahend is immediately restored 
 by increasing the 3 tens to 4 tens. In the method 
 of decomposition, however, it is the 8, the second 
 figure dealt with, that has to be changed to restore 
 the balance. If the minuend figure is zero the 
 balancing of accounts is still longer deferred. In a 
 phrase, the main secret of the difference lies in the 
 dispatch with which accounts are settled. One is 
 " cash payment," the other " credit." And the 
 postponement of the compensating act increases the 
 chances of its fulfilment being forgotten. But this 
 is not the only point of difference between the two 
 methods, for there is a further disparity in the area 
 of disturbance. When the figure in the minuend 
 represents a smaller number than the corresponding 
 figure in the subtrahend it is necessary to disturb 
 
ARITHMETIC 171 
 
 the minuend (method of decomposition) or both 
 minuend and subtrahend (method of equal addition). 
 In the latter case it is never necessary to disturb 
 more than two figures ; in the former it is always 
 necessary to disturb two, and sometimes many more ; 
 and for a young child to bear the many changes in 
 mind is no easy task. 
 
 The disadvantage of the decomposition method is 
 not of course limited to pure subtraction sums : it 
 vitiates all exercises into which subtraction enters. 
 Long division, for instance, is, as I have abundantly 
 tested, performed in decomposition schools with 
 difficulty and with dubious accuracy. 
 
 And yet the decomposition method is apparently 
 taught in about two-thirds of the London schools. 
 What is the reason for its popularity ? It is not 
 the method we learnt in our youth ; it does not 
 seem to be the method adopted by the adult, even 
 when he has learnt that method at school. The 
 reason is to be found in its greater intelligibility. 
 It is easier for a child to understand the decom- 
 position of numbers than to grasp and apply the 
 principle that the difference between two numbers 
 remains unchanged if the same number be added 
 to both. It is therefore the favourite method in 
 the infant school, and the senior school follows the 
 lead. But granted its greater intelligibility, its 
 practical efficiency is not encouraging. The younger 
 the child the more is he shackled by the inferior 
 method. Unless, indeed, we assume that some of 
 the older children in the decomposition schools 
 discover in some indirect way the equal addition 
 method and use it in preference. It is not often 
 that one finds a class of older children all of whom 
 
172 MENTAL TESTS 
 
 practise the decomposition method. Do we not 
 in any case pay too great a price for a doubtful 
 boon ? If at first the child sees the rationale of 
 the process of decomposing the minuend, he soon 
 gets to perform it automatically. The " intelli- 
 gence " supposed to be concerned is a temporary 
 illumination only. Indeed for pure practical effi- 
 cacy it is better that the rationale should not, at 
 the actual time of working, be thought of at all. 
 The pupil should confine his efforts to a rigid 
 application of the rule. I have frequently observed 
 that when teachers in training are asked to work a 
 subtraction sum and explain the steps, they fre- 
 quently give the right reason but the wrong answer. 
 It may be pointed out that an intelligent appli- 
 cation of an arithmetic rule does not necessarily 
 mean a scientific knowledge of the underlying prin- 
 ciples. A child may learn to walk and to put the 
 power to intelligent uses without knowing anything 
 about the mechanism by which walking is achieved. 
 So may he learn to work subtraction by rule of 
 thumb, and be able to apply it quite intelligently 
 to the practical purposes of life. He may later on 
 study the physiology of walking, or the logical basis 
 of the rule ; but there is no more reason to think 
 that he will compute better in the latter case than 
 there is for thinking that he will walk better in the 
 former. This is not a plea for the mechanical 
 teaching of subtraction ; but it is a plea for regarding 
 subtraction as primarily an instrument to be placed 
 in the hands of the young pupil for the purpose of 
 solving certain problems of actual life. If he can 
 understand, the reasons for the steps taken, well and 
 good. If not, he should for the present use it 
 
ARITHMETIC 173 
 
 without understanding it. Indeed I have long 
 contended that during the last year or so of an 
 elementary pupil's schooling he should be taught 
 the underlying principles of all the rules he has 
 learnt. Attempts should, of course, be made to 
 render the rules intelligible at the time of learning ; 
 but the teacher should be in the main content if 
 the pupil can use these rules in concrete cases. A 
 critical examination of " long division," for instance, 
 is a valuable exercise for a lad of 13 — far more 
 valuable than the senseless manipulation of symbols 
 which often passes for algebra. The mathematics 
 for the last year of the school life of an elementary 
 pupil should include the assimilation of all the 
 undigested material in the whole arithmetic course, 
 if that course is, as it should be, regarded as a 
 systematic study of the principles of numbers. 
 
 It has frequently been asserted that there is a 
 third method of teaching subtraction — the method 
 of complementary addition. But this is not, like 
 the two methods just dealt with, a device for 
 meeting the difficulty of " borrowing " : it is an 
 alternative way of looking at the process of sub- 
 traction itself. 16—7 may mean either : (a) what 
 is left when 7 is taken away from 16? or (b) what 
 must be added to 7 to make 16 ? If the latter view 
 be adopted then subtraction is regarded as com- 
 plementary addition — as a solution of the equation 
 a -+- x — b. 
 
 It may be remarked about this form of subtrac- 
 tion that it is not taught as a general process in any 
 of our schools, at least not to my knowledge. It 
 is true that complementary addition sometimes 
 appears in a hybrid form. Thus 43 — 26 is some- 
 
i 7 4 MENTAL TESTS 
 
 times worked in this way : 6 from 10 leaves 4, 
 4 and 3 are 7, etc. But such roundabout methods, 
 in which two steps are taken where only one is 
 necessary, are not to be commended. 
 
 Complementary addition pure and simple, com- 
 bined with equal addition as a " borrowing " device, 
 is advocated at some of the Universities, especially 
 where much work in logarithms has to be done. 
 Instances are known where greater speed and 
 accuracy have resulted from a change from the 
 subtractive to the additive attitude. 
 
 The additive view is strongly urged by the few 
 head teachers who have tried it. They think that 
 the subtraction method should be discovered by 
 the child : the steps being indicated by the following 
 examples — 
 
 Step I. 4x1 Step II. xx\ Step III. 
 
 xc^Vadd. 4 7/ add. r 43 
 
 86 J 4 7] add. 
 
 H3 \ 
 
 159 xx] 
 
 The " carrying " or compensating step is naturally 
 adopted, with no need for more explanation than 
 the " carrying " in simple addition. 
 
 It is not for me to judge this method on a priori 
 grounds, but its advantages are sufficiently obvious 
 for us to declare a true bill in its favour and give it 
 at least an experimental chance. 
 
 On the Importance of Tables. — It has already been 
 shown that the facility in working addition and 
 subtraction mainly depends upon a ready knowledge 
 of the addition table. 
 
ARITHMETIC 175 
 
 The complete table may be written in this form — 
 
 1+1= 2 
 
 2+1= 3 2+2= 4. 
 
 3 + 1= 4 3 + 2= 5 3+3= 6 
 
 4 + 1= 5 4+2= 6 4+3= 7 4+4= 8 
 
 5 + 1= 6 5+2= 7 5+3= 8 5+4= 9 5+5=io 
 
 6+1= 7 6 + 2= 8 6+4= 9 6+4=10 6 + 5=11 6+6=12 
 
 7+1= 8 7+2= 9 7+3 = 1° 7+4=ii 7+5 = 12 7+6=13 7+7=14 
 
 8+1= 9 8-t 2=10 8+3 = 11 8+4=12 8+5=13 8+6=14 8 + 7=15 8+8=16 
 
 9 + 1 = 10 9+2=11 9 + 3=12 9+4=13 9+5=14 9+6=15 9 + 7=i6 9+8 = 17 9+9 = 18 
 
 It will thus be seen that there are 45 results to be 
 memorised — 45 habits to be fixed — it being under- 
 stood that each of the above items represents four 
 processes. Thus 8 + 4=12 should also be memor- 
 ised as 4+8=12, 12 — 8 = 4 and 12 — 4=8; 
 not of course as independent processes, but as 
 necessarily implied in the one formula 8 + 4= 12. 
 
 The same remarks apply to the multiplication table, 
 except that there are only 36 items to be learnt. 
 
 There are some educationists who contend that 
 the tables should not be memorised. In so saying 
 they do not mean that they should not ultimately 
 be memorised ; but rather that no conscious effort 
 should be made to memorise them. The results 
 should be arrived at either — 
 
 (a) By building them up afresh each time, or 
 
 (b) By referring to a table book. 
 
 If they are continually being built up afresh, any 
 intellectual value such a process may originally 
 possess soon disappears. It sinks to the level of 
 the merest mechanical work. And if this method 
 is to be applied to the multiplication table, logic- 
 ally it should be applied to the addition table as 
 well, and counting by units should always be 
 encouraged. 
 
 If, on the other hand, it is merelv meant that the 
 
176 MENTAL TESTS 
 
 results should be calculated ab initio each time until 
 they are fixed in the memory, experience shows that 
 the mere habit of doing so tends to form a stronger 
 tendency to start the process than to recall the 
 result. Older children, for instance, who count on 
 their fingers delay indefinitely the counting by 
 groups. No effort is made to memorise the results, 
 and in consequence they elude the memory. Indeed 
 a far shorter way of reaching the goal is afforded 
 by the second alternative, that of using a table- 
 book — assuming, of course, that the construction 
 of the tables is understood. Whenever, for in- 
 stance, the product of 7 and 8 is needed the table 
 is looked at. Here the mind attends exclusively to 
 the result, 56, and is not absorbed in attending to 
 the process. Mr. Winch has experimental evidence 
 to show that if a large number of examples involving 
 the use of a specific table are worked rapidly by the 
 pupils who have this table in front of them, it is 
 actually memorised better than if a conscious effort 
 is made to memorise it without working examples. 1 
 
 It seems clear that progress in mathematics is 
 made possible by assuming the results of previous 
 processes and using these results as stepping-stones 
 to still higher results. 
 
 On the Best Method of Memorising the Tables. — 
 The addition table has generally been left to look 
 after itself, but the multiplication table has always 
 received a certain amount of attention. In bygone 
 days it was systematically memorised by frequent 
 simultaneous repetition ; and even at present the 
 chanting of the tables, although less widely adopted, 
 
 1 See also Kirkpatrick : " Memorising versus Incidental Learn- 
 ing," J. of E due. Psychol, v. 7, 405-412. 
 
ARITHMETIC 177 
 
 is almost the only means that is employed. But 
 this chanting of the tables is open to several 
 objections. 
 
 Memorising of all kinds depends upon the fixation 
 of a habit-series ; and the limits of the series should 
 be clearly defined. Each formula, such as 4 x 7 = 
 28, constitutes a self-contained system, and it 
 should be so memorised as to be completely usable 
 without reference to preceding formulae. In other 
 words no unnecessary associations should be set up. 
 To associate by rote memory 4x5 with 4x6, and 
 4x6 with 4 x 7, etc., is a superfluous, if not an 
 injurious, bit of mental mechanisation. Chanting 
 tends to establish these useless associations. 
 
 Another objection is that the speed of this simul- 
 taneous repetition is far too slow for the economic 
 fixation of habit. The effect of speed upon 
 mechanisation, although not generally recognised, 
 is considerable. If, for instance, a passage of 
 poetry has to be memorised so as to render its 
 repetition automatic, the repetition of the lines at 
 maximum speed has been found, in my own case 
 at least, to diminish the number of repetitions 
 necessary. It has probably something to do with 
 the span of attention. 
 
 A third objection to the simultaneous chanting of 
 tables is based upon the liability of the attention to 
 wander during the repetition. Attentive repetition 
 is far more efficacious than the inattentive kind. 
 
 Finally, there is the objection that may be urged 
 against all kinds of simultaneous class work ; that is, 
 that it makes no allowance for individual differences 
 in the mode and rate of learning. 
 
 There are experimental grounds for believing 
 
 N 
 
178 MENTAL TESTS 
 
 that the method of individual muttering — a method 
 which unfortunately seems to " get on the nerves " 
 of some teachers — is considerably more efficacious 
 than the method of concerted repetition. 
 
 There are two methods of memorising the tables 
 which I have reason to think would prove effective 
 — methods which are not exclusive but supple- 
 mentary. Both might be tried. 
 
 (1) Take, say, two items per diem in the addition 
 table, such as 7 + 8 = 15 and 4 + 6 = 10 ; and two 
 per diem in the multiplication table, such as 
 7x8=56 and 4x6= 24. If this be systematic- 
 ally done, and past work frequently revised, the 
 whole will be learnt in less than five weeks. If 
 only one of each be taken per day the whole can 
 be mastered in less than three months. 
 
 (2) Learn by applying. Put, for example, the 
 7 times table before the boys and let them work 
 very rapidly a large number of sums involving 
 multiplication by 7. Of the two methods this is 
 probably the better. 
 
 On the Importance of Practice, and the Claim of 
 the Individual. — That the principles of number 
 should be intelligently taught ; that they should be 
 recognised by the pupil as rooted in the experiences 
 of everyday life ; that they should be learnt and 
 applied with understanding ; that they should fre- 
 quently be presented in novel combinations — these 
 are matters upon which there is now no divergence 
 of opinion. But when we ask the questions : 
 Should every exercise be given in concrete form ? 
 Should the problem dominate the arithmetic 
 lesson ? we get a variety of answers. 
 
 There are many who believe — there are more 
 
ARITHMETIC 179 
 
 who wish, to believe — that sufficient practice in the 
 mechanism of computation is gained by working 
 problems and problems only. But whatever opinion 
 one may have held ten years ago on this matter, if 
 one has followed the recent development of mathe- 
 matics in the elementary schools one cannot help 
 being forced to the conclusion that such practice is 
 insufficient. Ciphering, in its rudimentary forms, 
 is so useful an art that proficiency therein is justly 
 regarded as one of the essential aims of an ele- 
 mentary school, and to discover the most economical 
 means of achieving that aim, without doing violence 
 to the pupils' instincts and interests, will ever be 
 one of the central and vital problems of teaching. 
 
 It is not fair to argue that since the excessive and 
 exclusive grind at mechanical arithmetic which 
 characterised the period of payment by results was 
 distasteful to the pupils, mechanical arithmetic is 
 in itself distasteful. Indeed, many children share 
 the opinion of the little girl of my acquaintance 
 who says that she likes sums but does not like 
 sums about John. 
 
 A noticeable feature of the present arithmetic 
 course is the absence — or at least the infrequence — ■ 
 of the pure practice or drill lesson. From having 
 all the lessons practice lessons we have come down 
 to none. The custom of wrapping up numbers in 
 abundant verbiage has become so inveterate that 
 the mere sight of a naked number gives some of us 
 a sort of shock. Some time ago I was reproached 
 by a teacher for asking a little girl in an infant 
 school to add 2 and 3. All departure from the 
 concrete has come to be regarded as wicked. We 
 have in consequence an ounce of arithmetic to a 
 
180 MENTAL TESTS 
 
 pound of padding. I have seen a teacher spend 
 ten minutes over this little question in mental 
 arithmetic : " If 80 birds sat on a tree, and 30 
 of them flew away, how many would be left sitting 
 on the tree ? " Laboriously she wrote it on the 
 board, and persistently she checked all attempts at 
 answering until she had explained the situation to 
 the point of boredom. 
 
 Another factor unfavourable to progress is the 
 non-recognition of the essential heterogeneity of 
 any collection of children, however carefully chosen. 
 Any seeming homogeneity in a class is both super- 
 ficial and temporary. However much the units 
 may resemble one another in their present attain- 
 ments they will differ enormously in their capacity 
 for work, and consequently in their rate of improve- 
 ment. If they appear like one another to-day, they 
 will appear unlike one another to-morrow. Al- 
 though this fact has been clearly demonstrated by 
 others, 1 I have taken steps to verify it for myself. 
 Three classes in a girls' school were allowed to work 
 through the exercises in their arithmetic text-books 
 at their own pace for half-an-hour per day. The 
 results were as follows — 
 
 Number in Class ..... 
 Approximate age of Children 
 Number of half-hour Lessons 
 Average total number of sums worked 
 correctly ..... 
 
 Highest Score ..... 
 Lowest Score ..... 
 Mean Variation ..... 
 
 1 See, for instance, Search's Ideal School, pp. 29 and 33. 
 
 
 -Class , 
 
 A 
 
 B C 
 
 5° 
 
 46 42 
 
 10 
 
 12 13 
 
 27 
 
 26 23 
 
 206 
 
 145 181 
 
 39° 
 
 250 514 
 
 95 
 
 70 24 
 
 57 
 
 34 87 
 
ARITHMETIC 181 
 
 It would be difficult to find a school more care- 
 fully organised — a school where the children in a 
 class were nearer the same level — and yet the varia- 
 bility in their rates of working is seen to be enormous. 
 In the highest class the best girl was able to work 
 more than 21 times as fast as the worst ; and although 
 this amount of disparity is exceptional, rarely will 
 it be found that the fastest in the class does not 
 work at least three times as rapidly as the slowest. 
 
 It will be seen that, taking the three classes to- 
 gether, on an average 7 sums per child were worked 
 correctly in half-an-hour. Five girls in the top 
 class were able to do more than double this average. 
 It must not be thought that the exercises worked 
 were of an easy type, or were of a merely mechanical 
 nature ; they were continuous examples from 
 McDougall's Suggestive Arithmetics ; and these 
 books are above, rather than below, the average 
 in difficulty. 
 
 A careful investigation of the methods of teaching 
 arithmetic at present in vogue in elementary schools 
 has convinced me that the most serious and preva- 
 lent defect is the excessive use of the blackboard, 
 both for setting exercises to be worked by the class, 
 and for exposition — for explaining, and exempli- 
 fying, and correcting. 
 
 When we consider that it is rare for a class working 
 from examples written on a blackboard to get 
 through more than four sums during a lesson of 
 forty-five minutes (that is, half as long again as the 
 lessons referred to above) it becomes obvious that 
 the individual scholar is not working at anything 
 like his normal pace. I do not go so far as to urge 
 that a child should always work at the highest 
 
1 82 MENTAL TESTS 
 
 pressure, but I do submit that he should sometimes 
 do so. 
 
 It is often the practice of the teacher to write 
 an example on the board, and set the whole class 
 to work it on paper. After all have finished (note 
 the waste of time on the part of the brighter chil- 
 dren) the sum is marked. If about one-third of 
 the class gets it wrong, the teacher, as a rule, works 
 it himself on the blackboard, or gets the class to 
 work (or to seem to work) it with him. This is idle 
 time for two-thirds of the class ; and it is not the 
 best method of correction for the other third. 
 More often than not the mistakes are due to care- 
 lessness on the part of the pupil, or to an imperfect 
 knowledge of the tables ; and effective correction 
 depends on individual effort rather than on black- 
 board explanation. 
 
 An arithmetic lesson is occasionally taken up by 
 the teacher working one or two examples on the 
 blackboard with the class, the children afterwards 
 copying them out in their exercise books. The 
 concerted appearance of this work is illusory. The 
 work is really done by the teacher and a few of the 
 more alert pupils. The copying out is of little 
 value except as a relaxation from the boredom of 
 watching other people work. 
 
 These practices are by no means universal, nor 
 do they imply that the instruction is mechanical 
 and perfunctory. In making the criticisms it is but 
 fair to record my conviction that earnest efforts are 
 almost universally being made to vivify the instruc- 
 tion and to bring it into line with modern educa- 
 tional ideals, and that whatever faults exist are due 
 not to lowness of aim, but rgther to a misconception 
 
ARITHMETIC 183 
 
 of how a high ideal may best be approached. The 
 spirit of the Suggestions to Teachers and of the 
 Report of the L.C.C. Conference on Arithmetic has 
 permeated the majority of schools, and is doing 
 incalculable good ; but at the same time many 
 sound practices of the past have sometimes been 
 forgotten, and the new conditions that are develop- 
 ing with the gradually diminishing class and the 
 more rapid movement of pupils have not been met 
 by a corresponding change of method. That 
 change may briefly be described as a progress from 
 class teaching to sectional teaching, and from 
 sectional teaching to individual teaching — in fact 
 from larger to smaller units. The ideal teaching is, 
 of course, individual teaching, and Rousseau, in his 
 Emile, assumes as a principle : one teacher, one pupil. 
 It will be seen that " blackboarditis " (if I may 
 be permitted to call it so) arises from too ardent 
 and sanguine a desire to preserve the unity of the 
 class — from the belief that the individuals forming 
 this unity should work at the same rate, and progress 
 at the same rate. One teacher with whom this 
 matter was discussed not only held this doctrine, 
 but strictly maintained that the pace should be 
 that of the slowest pupil. This indeed seems to 
 be the only logical form of the doctrine. It is 
 clear that the average pupil (if there be such) 
 cannot set the pace, as that would leave about half 
 the class in the lurch. In actual practice a small 
 number is recognised as forming no real part of the 
 body of the class, and is labelled the " tail end." 
 The " tail end " is left out of account, and the 
 pace is virtually fixed by the slowest pupil among 
 the remainder. 
 
1 84 MENTAL TESTS 
 
 But it is clear from what has already been said 
 that the doctrine of the homogeneous class ought 
 to be abandoned, and the teachers should devise 
 means of securing the maximum of healthy effect 
 from each individual child. 
 
 That it is necessary to devise such means is obvious 
 when we consider the size of the class and the limited 
 time and energy at the disposal of the teacher. He 
 cannot possibly devote the necessary amount of 
 personal attention to each child. The solution of 
 the difficulty lies in the delegation of his powers, 
 and in fostering in his pupils a sense of responsi- 
 bility. We have not yet discovered the extent to 
 which we can trust the pupils. By adopting a 
 general policy of mistrust, by never allowing a child 
 to mark his own, or even another child's, exercises, 
 by making no child responsible for anybody's 
 conduct or progress but his own, by retaining all 
 corrective and coercive powers in the teacher's 
 hands, we gain certain advantages : we simplify 
 matters, we minimise the likelihood of abuse of 
 authority, and we cultivate in the pupils the virtue 
 of obedience. But we lose much more than we 
 gain. We fail to secure normal and healthy 
 progress, we fail to foster respect for an internal 
 as distinct from an external authority, we fail to 
 cultivate the power to rule wisely as a balance to 
 the correlative virtue of obeying wisely, and we 
 sacrifice the brilliant and the stupid to the mediocre. 
 The surprise with which we view the success of the 
 prefect system among elementary school children 
 is itself a mark of our traditional mistrust. The 
 possibilities of self-government and self-culture 
 among school children will, I believe, when fully 
 
ARITHMETIC 185 
 
 realised, provide the key to the solution of a large 
 number of the difficulties which press upon the 
 teacher at the present time, and which seem to 
 put an abnormal strain upon his nervous system. 
 I am not here concerned with showing how precisely 
 this delegation of work and responsibility may be 
 effected in the arithmetic lesson (each teacher can 
 best discover this for himself), but with suggesting 
 the direction in which the ideal of individual 
 development probably lies. 
 
 Recommendations. — In view of the facts and 
 arguments set forth above, I venture to make the 
 following definite recommendations — 
 
 (1) That the tables, both addition and multi- 
 plication, be by some means or other fixed in the 
 memory early in the arithmetic course. 
 
 (2) That the simultaneous repetition of the 
 tables be superseded by individual learning, or 
 better still, by their application to examples to be 
 worked rapidly. 
 
 (3) That seriatim repetition be discarded after 
 the structure of the tables is understood. 
 
 (4) That adding by tables be the final objective 
 in practising addition, and that adding by units, 
 or by partial groups, or through any roundabout 
 device, be regarded as a habit of a lower order, to 
 be abandoned as soon as habits of a higher order 
 can be engendered. 
 
 (5) That speed of adding be insisted on as a 
 means of pressing forward towards the higher 
 habits. 
 
 (6) That the method of equal addition be uni- 
 versally taught as the practical method of working 
 subtraction, 
 
1 86 MENTAL TESTS 
 
 (7) That the method of decomposition be re- 
 garded, if taught at all, as a means of showing the 
 correctness of the result arrived at by the usual 
 method. 
 
 (8) That at least one pure practice lesson be 
 given per week. 
 
 (9) That speed as well as accuracy be aimed at 
 in the practice lesson. 
 
 (10) That the terminal examination in arithmetic 
 contain at least one straightforward abstract sum. 
 
 (11) That each class be frequently practised in 
 the work of all the lower classes. 
 
 (12) That means be adopted to secure the progress 
 of each pupil at his own natural rate. 
 
 (13) That the blackboard be not used for setting 
 out examples when text-books are available for 
 that purpose ; nor for working sums which could 
 easily be worked by the majority of the class ; nor 
 for correcting errors due to mere carelessness. 
 (The blackboard has, of course, its legitimate use 
 for class and sectional teaching ; it is only when it 
 becomes a means of preventing individual effort 
 that its use is open to objection.) 
 
 (14) That the practice of copying in the exercise 
 books examples worked out on the board be 
 discarded. 
 
 (15) That much of the responsibility of marking 
 exercises be, with due reservations and precautions, 
 delegated to the pupils. 
 
 (b) Simple Oral Arithmetic 
 
 Many a teacher has felt the need of some simple 
 means of estimating, with a reasonable degree of 
 
ARITHMETIC 
 
 187 
 
 precision, the arithmetical attainments of young 
 children. The tests that have hitherto been 
 published are intended for older children, for 
 children who are able to work sums on paper. 
 They cannot measure the beginnings, and are 
 consequently of no use in dealing with children in 
 infant schools. 
 
 To meet this need I have used the following tests 
 in addition and subtraction — 
 
 One Minute Oral Addition Test 
 
 (1) I + 2 
 
 (11) 4 + 4 
 
 (21) 7 + 5 
 
 (2) 4 + 1 
 
 (12) 5 + 2 
 
 (22) 8 + 3 
 
 (3) 2 + 2 
 
 (13) 6 + 4 
 
 (23) 4 + 9 
 
 (4) 2 + 4 
 
 (14) 1 + 8 
 
 (24) 6 + 8 
 
 (5) 3 + 2 
 
 (i5) 3 + 7 
 
 (25) 7 + 6 
 
 (6) 4 + 3 
 
 (16) 6 + 3 
 
 (26) 9 + 8 
 
 (7) 2 + 5 
 
 (17) 2 + 6 
 
 (27) 9 + 6 
 
 (8) 5 + 4 
 
 (18) 5 + 5 
 
 (28) 8 + 7 
 
 (9) 3 + 5 
 
 (19) 7+2 
 
 (29) 5 + 9 
 
 (10) 8 + 2 
 
 (20) 4+6 
 
 (30) 7 + 9 
 
 One Minute Oral Subtrt 
 
 iction Test 
 
 (i) 2- I 
 
 (11) 8 — 2 
 
 (21) 11 — 2 
 
 (2) 3 - 2 
 
 (12) 7-5 
 
 (22) 10 — 6 
 
 (3) 5 - 1 
 
 (13) 8-3 
 
 (23) 12 — 3 
 
 (4) 6 - 2 
 
 (H) 7-4 
 
 (24) 1 1 — 6 
 
 (5) 5 - 3 
 
 (15) 9-3 
 
 (25) 12 - s 
 
 (6) 2-2 
 
 (16) 8-5 
 
 (26) 13—4 
 
 (7) 7-2 
 
 (17) 10-4 
 
 (27) i5-9 
 
 (8) 6 - 4 
 
 (18) 9-5 
 
 (28) 14 — 6 
 
 (9) 7 - 3 
 
 (19) 10 - 3 
 
 (29) 17 - 8 
 
 (10) 6 - 3 
 
 (20) 9-4 
 
 (30) 16-7 
 
MENTAL TESTS 
 
 Each child is tested individually and in isolation. 
 He is asked the question, " One and two ? " and as 
 soon as he answers it he is asked the next, " Four 
 and one ? " and so on. He is not allowed to proceed 
 until he has given the right answer. The number 
 of questions correctly answered in one minute 
 gives the score. 
 
 The same method is adopted for administering 
 the subtraction test. 
 
 A little preliminary questioning is desirable to 
 put a child at his ease, and to see that he knows 
 exactly what is required of him. 
 
 The following norms are based on the results 
 obtained by myself and others in the application 
 of the tests to about ten thousand boys and girls 
 within the last six years. 
 
 Age. 
 
 6 yrs. 
 
 7 yrs. 
 
 8 yrs. 
 
 9 yrs. 
 
 ioyrs 
 
 Addition Score 
 
 6 
 
 10 
 
 H 
 
 18 
 
 22 
 
 Subtraction Score 
 
 4 
 
 7* 
 
 II 
 
 Hi 
 
 18 
 
 The mean variation seems to be nearly the same 
 for each age group and for each process, and amounts 
 to between three and four. 
 
 The girls are able to add a trifle better than the 
 boys, but in subtraction there is no appreciable 
 difference between them. 
 
 With the very youngest children the score is low, 
 not merely because they are slow in computing, 
 but because their knowledge is limited to the first 
 few numbers in the scale. They cannot answer 
 the whole of the questions even if they are given 
 unlimited time. When, however, older children 
 score few marks it is because they add by units. 
 This points to the expediency of memorising the 
 
ARITHMETIC 189 
 
 addition table early. The answering in a few 
 schools, however, convince me that there is a danger 
 of premature memorising. 2 + 5 = 10, for instance, 
 is a type of answer by no means infrequent. This 
 confusion between the addition and the multipli- 
 cation tables is scarcely possible if the child is 
 familiar with the make-up of the first ten natural 
 numbers. 
 
 In subtraction the question that seems to present 
 the greatest difficulty is the sixth (2 — 2). 
 
 As the oral examination of a large number of 
 pupils took a considerable time it was hoped that 
 a saving might be effected by setting the same test 
 in written form. It was found however on actual 
 trial that even with the older children the written 
 test was a less delicate measure of arithmetical 
 ability. The questions were typed and set to a 
 number of children between nine and ten years 
 of age, in the form given above with a blank space 
 for the answer. The children between nine and a 
 half and ten did 20 per cent, worse than at the oral 
 examination, and the children between nine and 
 nine and a half did 30 per cent, worse. The differ- 
 ence would, it is reasonable to assume, be increasingly 
 great as we went down the scale of age. It was 
 therefore considered wiser, in dealing with such 
 rudimentary work, to adhere to the oral form 
 throughout. 
 
 I have endeavoured to find the difference between 
 the achievements in good and poor schools, the 
 terms good and poor being used in a social sense 
 only. Instead of comparing two schools, the best and 
 the worst — a plan accompanied by obvious risk — a 
 group of very good schools was compared with a 
 
190 MENTAL TESTS 
 
 group of very poor schools. The difference proved 
 to be greater than I had anticipated. In both 
 addition and subtraction the good schools were at 
 least one year in advance of the age-norms, and the 
 poor schools at least one year behind. There was, 
 in fact, a difference of more than two years between 
 the achievements of the two social classes. 
 
 I also found distinct evidence in support of what 
 seems to be a general rule : the higher the social 
 status the more favourably do the girls compare 
 with the boys. In good neighbourhoods the girls 
 compute a little better than the boys, in poor 
 neighbourhoods a little worse. 
 
 (c) Arithmetical Devices 
 
 This test aims at discovering how many of the 
 " rules " commonly taught in the elementary 
 schools have been mastered. If the pupil shows 
 that he knows the rule and has merely made a slip 
 in computation the sum is counted right. Each 
 correct sum scores one mark. 
 
 Arithmetical Devices {unlimited time). 
 
 (i) 658 x 204. 
 
 (2) 95567 ^ 53. 
 
 (3) & 14J. 5J x 26. 
 
 (4) £ 2 3 "*■ 9\ d -+ I 7- 
 
 (5) Calculate the cost of 15 tons 3 cwt. 2 qrs. at 
 
 f\ $s. 6d. per ton. 
 
 (6) i + f . 
 
 (7) *» - f • 
 
 (8) !xi 
 
 (9) * ■*■ I- 
 
ARITHMETIC 191 
 
 (10) -i x *i. 
 
 (n) -6-^ -003. 
 
 (12) 5 : 12 : : 9 : x. 
 
 (13) Find the average of 5, 11, 7, 2, o, 19. 
 
 (14) What is the value of £0-168 ? 
 
 (15) Find the simple interest on £650 f° r 2 years 
 
 It will be observed that where a simple example 
 will suffice to indicate whether the pupil knows the 
 rule the simple example is adopted. No. 5 and No. 
 12 proved the most difficult ; due no doubt to the 
 fact that within recent years " practice " has fallen 
 into discredit, and proportion has given place to 
 the method of unity. 
 
 ■Ai e - 9Y rs - 10 yrs. 11 yrs. 12 yrs. 13 yrs. 14 yrs. 
 
 Score . . . \ 3 5 61 8 9J 
 
 (d) Applied Arithmetic (Problems) 
 
 To develop the capacity to apply the principles 
 of numbers is after all the final aim of the teaching 
 of arithmetic ; and the extent to which the pupil 
 can bring his knowledge to bear upon the common 
 affairs of life is the real measure of his understanding. 
 Hence the importance which we now-a-days attach, 
 and rightly attach, to " problems." It is regarded 
 as questionable wisdom to reduce all problems to 
 types and to teach them under the old system of 
 rule and example. The root objection to this 
 plan is that the pupil, recognising a particular 
 problem (often by illegitimate signs) as belonging 
 to a certain group, is liable to work it by rule of 
 thumb rather than the direct application of basal 
 
192 MENTAL TESTS 
 
 principles. It prevents him, in fact, from reasoning 
 the thing out. If, however, pupils are to be trained 
 at all in the solution of problems, it is necessary 
 to call their attention to the underlying principles ; 
 directly or indirectly they must be taught to recog- 
 nise a certain sameness in the examples, and to 
 do this is to systematise and classify. Take for 
 example the 19th problem in the test given below. 
 This is the same as asking : " What are the two 
 numbers whose sum is 5 and whose difference is 
 2 ? " Or again, " A bottle and a cork cost z\& ; 
 the bottle cost 2d. more than the cork ; what did 
 the cork cost ? " This, too, is cousin german to 
 No. 10. The real danger lies not in the recognition 
 of the type, but in working successively so many 
 examples of the same type that the work becomes 
 mechanical — a danger not difficult to avoid. 
 
 At any rate, whatever objections there may be 
 to the teacher's classifying problems for his pupils, 
 there is a distinct advantage in his classifying them 
 for himself. He should be familiar with the common 
 applications of arithmetic, and should be careful 
 both in teaching and testing to vary his types. 
 He can never perhaps exhaust the types ; but he 
 can readily make a catalogue of the commonest 
 of them. The test below is, in fact, just such 
 catalogue. It comprises twenty fundamental types 
 of problems reduced to their simplest forms. It 
 will be observed that the actual calculations are 
 extremely easy ; for it is not computation that is 
 being tested, but merely the capacity to applj 
 principles. Hence a slip in counting is overlooked 
 when the papers are marked, and every problem 
 solved by the right method is allowed to score one. 
 
ARITHMETIC 193 
 
 The problems are arranged in order of increasing 
 difficulty — an order which differs from my precon- 
 ceived notion of their difficulty, and which was 
 discovered by actually applying them to a large 
 number of children. 
 
 Applied Arithmetic Test (unlimited time) 
 
 1. If there are 100 apples on a tree and the wind 
 blows down 1 7, how many are left on the tree ? 
 
 2. Two hundred oranges are put into 5 baskets so 
 that each basket has the same number of oranges. 
 How many are there in each basket ? 
 
 3. If a man earns .£5 y. 6d. in a week, how much 
 will he have earned at the end of a month ? 
 
 4. I want to buy a book which costs js. 6d., 
 but I have only is. S^d. in my pocket. How much 
 more money do I need ? 
 
 5. John pays 8s. \d. for 5 lbs. of butter. What 
 would Henry have to pay for 7 lbs. of the same 
 butter ? 
 
 6. If eggs sell at 3 for 2d., what will 2 dozen cost ? 
 
 7. One day two boys earn ten shillings between 
 them by carrying trunks from an hotel to a railway 
 station. One boy carries 5 trunks during the day 
 and the other 7. How ought they to share the 
 money ? 
 
 8. What is the least number that must be added to 
 1483 to make it exactly divisible by 16 ? 
 
 9. After spending a third of my money I find I 
 have 3 j - . \d. left. How much had I at first ? 
 
 10. Two girls had tea at a tea-shop. The waitress 
 charged for both on one bill, which came to is. 6d. 
 One girl had a threepenny cake more than the other. 
 How much of the half-crown ought each to pay ? 
 
 o 
 
i 9 4 MENTAL TESTS 
 
 ii. A certain man can dig a garden in 3 days, 
 and his son can do it in 6 days. If they both work 
 together how long will they take ? 
 
 12. Nine soldiers eat their food in one hut and 
 15 in another. Seven loaves of bread are allowed 
 for each hut. If the 9 soldiers in the first hut eat 
 their bread in 4 days, how long will it take the 15 
 soldiers to eat theirs, assuming that all soldiers eat 
 the same amount ? 
 
 13. A bankrupt pays 5.5". in the £. What did he 
 owe to a creditor to whom he pays £16 10s? 
 
 14. After the population of a town has decreased 
 by 10 per cent, the number of people left is 18,000. 
 How many were there at first ? 
 
 15. A shopkeeper wishes to sell a blend of tea at 
 is. 3d. a pound by mixing tea at 2s. a pound with tea 
 at 3-f. a pound. In what proportion should he mix 
 them ? 
 
 16. If I lose 5 per cent, by selling an article for 
 £9 ioj., what should I lose or gain per cent, by selling 
 it for .£10 5-f. ? 
 
 17. A, B and C cycle continuously round a 
 circular track. A takes 8 minutes to go round, 
 B 9 minutes, and C 12 minutes. If they all start 
 together, how long will it be before they are all 
 together again at the starting-point ? 
 
 18. P and Q are two towns 210 miles apart. A 
 train which travels at the rate of 30 miles an hour 
 starts at 9 a.m. to go from P to Q. At the same 
 time a train which travels at 40 miles an hour starts 
 going from Q to P. When will these trains meet ? 
 
 19. A man rows at the rate of 5 miles an hour 
 with the stream, and 2 miles an hour against the 
 stream. What is the rate of the stream ? 
 
ARITHMETIC 195 
 
 20. A cyclist who rides at the rate of 12 miles 
 an hour chases a man who walks at the rate of 3 miles 
 an hour and who has had 2 hours' start. How long 
 will it take the cyclist to catch the walker ? 
 
 The norms are as follows — 
 
 Age. 
 
 9 yrs. 
 
 10 yrs. 
 
 n yrs. 
 
 12 yrs. 
 
 13 yrs. 
 
 14 yrs 
 
 Score 
 
 2 
 
 3i 
 
 5 
 
 61 
 
 8 
 
 9* 
 
 The lowness of the level of achievement will 
 probably surprise those who have not had a wide 
 experience in setting arithmetical problems to chil- 
 dren. It is possible that the results I obtained were 
 somewhat vitiated by war conditions, and that it is 
 desirable to revise the norms later on when the 
 schools have completely recovered. Indeed, it is 
 always expedient to make a periodical revision of 
 scholastic standards, for these standards are the 
 resultant of native intelligence, courses of study, 
 and efficiency of teaching ; and two at least of these 
 factors vary with time. 
 
 The boys do better than the girls in applied 
 arithmetic, but the difference in these simple 
 problems is too slight to justify separate norms for 
 the two sexes. 
 
CHAPTER XI 
 
 PRACTICAL ABILITY 
 
 We cannot test the mind as a whole : we can only- 
 test it piecemeal. And in testing it piecemeal, it is 
 found that certain specific abilities manifest a sort 
 of kinship. They not only seem on the surface to 
 be kindred abilities, but when tested they give 
 results which are highly correlated. They form a 
 natural group, clearly separated from other natural 
 groups. Of the three such groups which are most 
 readily discernible, literary ability seems to be the 
 factor common to one, mathematical ability to 
 another, and motor ability to the third. It is 
 this third factor, the factor that underlies success in 
 clrawing, handwriting and handwork, that here 
 demands our attention. 
 
 It seems reasonable to assume that success in all 
 sorts of manual work depends on the general efficiency 
 of one's motor apparatus. A man's body is many 
 things at once. To the food-faddist it is a digestive 
 tube, to the bacteriologist it is a happy hunting- 
 ground for bacilli, to the boxer a fighting machine, 
 to the philosopher a thinking machine, and to the 
 craftsman a wonderfully complex and delicate 
 instrument for making things. And the important 
 point of application of the instrument is the hand. 
 The hand is in fact taken as representing the whole 
 
 196 
 
PRACTICAL ABILITY 197 
 
 neuro-muscular system. And if we test the dexterity 
 of the hand we are supposed to test motor ability 
 as a whole. We must distinguish, however, between 
 innate ability and acquired ability ; for it is the 
 former that mainly interests the psychologist. The 
 primary and basal test of motor ability has for its 
 aim the discovery, not of the amount of motor 
 skill that has been acquired by practice, but of the 
 amount of aptitude for acquiring skill. It is the 
 potentiality we wish to measure, not the actuality ; 
 the original capital, not the interest that has accumu- 
 lated through careful investment. Just as the aim of 
 Binet's tests is to measure that general intellectual 
 ability which islndependent of schooling, so the aim 
 of a motor test is to measure that general motor 
 ability that is independent of training. And the only 
 test of this kind that has crept into general use among 
 psychologists is the tapping test. 
 
 Essentially the test consists in discovering the 
 number of taps the unpractised subject can make per 
 second. A pencil and a piece of paper roughly serves 
 this purpose. It has, however, two disadvantages : 
 the marks made are difficult to count, and the subject 
 cannot be allowed to tap more than once on the 
 same spot. For careful work a piece of apparatus 
 is necessary which records automatically the number 
 of taps made, whether made with a stylus on a flat 
 surface, or by merely pressing a small lever after 
 the manner of the telegraph operator. The claim 
 of tapping to be regarded as a test of general motor 
 ability is considerably strengthened if the results 
 resemble in a broad way the results of intelligence 
 tests — if they show a gradual improvement with age, 
 if the maximum is reached during adolescence, 
 
198 MENTAL TESTS 
 
 and if the effect of special training is negligible. The 
 first two conditions are satisfied in the outcome of 
 a research conducted by Miss Bickersteth at Oxford, 
 and recorded in Vol. IX of the British Journal of 
 Psychology. She tested girls from five to fifteen 
 years of age and found that as they got older they 
 gradually improved, from 3 taps per second at 
 five years of age, to 5 taps per second at fourteen. 
 Here the maximum was reached : girls of fifteen 
 did no better than girls of fourteen. The third 
 condition, that the score should be unaffected by 
 practice, is fairly well satisfied. Miss Bickersteth 
 found that the improvement produced by practice 
 was very slight. Unfortunately, however, there is a 
 marked disparity among the results obtained by 
 different investigators. This is largely due to the 
 fact that they use different instruments. The 
 instrument I have myself used gives a higher score 
 than that used by Miss Bickersteth. My score at 
 the first trial was 7*4 taps per second. With a 
 pencil, however, on a piece of paper my rate is 5*4. 
 Several adults whom I have tested with the lever 
 instrument score about 6-5, and girls of fifteen give 
 on an average the same score as adults. It is a 
 curious fact that the few expert pianists whom I 
 tested did not tap any faster than the average. 
 Neither did expert typists. 
 
 Let us now consider a different kind of motor 
 test, which is carried out with a piece of apparatus 
 invented by Mr. McDougall of Oxford. The 
 apparatus consists of a heavy brass plate with 24 raised 
 sockets 2 centimetres high arranged in a circle. The 
 subject has to insert a small steel plunger with a 
 wooden handle into each socket as fast as he can ; 
 
PRACTICAL ABILITY 199 
 
 and the time taken to go completely round gives 
 the score. As the plunger exactly fits the socket, 
 the skill required is the same as that involved in 
 putting a key into a lock. Miss Bickersteth, who 
 has experimented with this instrument, found that 
 children of five took on an average 28 seconds, 
 and children of twelve took 20 seconds. Beyond 
 that age there was no improvement. Here again 
 we have results following the same laws as those 
 obtained by tapping. 
 
 When, however, we compare the tapping scores 
 with the plunger scores, we come against the amazing 
 fact that there is virtually no connection between the 
 two series. What slight correlation there is gradually 
 decreases with age. In other words, a child who 
 does well at the tapping test is just as likely to do 
 ill at the plunger test as to do well. So that if one 
 of these tests is a test of motor ability, the other is 
 not ; for they give contradictory results. Looking 
 closely at the two tests, however, we see that the 
 plunger test introduces a new element. Tapping 
 measures speed of movement only : the plunger 
 test measures precision as well. In tapping we may 
 aim as carelessly as we like, but with the plunger 
 we must aim precisely. Moreover, tapping can be 
 done blindfold, but the plunger test needs the co- 
 ordination and co-operation of eye and hand. 
 Motor ability, in fact, in any profitable sense of the 
 term, is not a simple thing : it comprises at least 
 three elements — strength, speed and precision. Any- 
 body who goes to a fair can roughly test his strength 
 at a machine and his accuracy of aim at a shooting 
 booth ; but if he wants it done scientifically he 
 must go to a psychological laboratory. There he 
 
zoo MENTAL TESTS 
 
 will find a dynamometer and an ergogograph for 
 testing his strength, and a dotting machine for testing 
 his precision. 
 
 Another simple motor test similar to the tapping 
 test consists in the dealing of cards. The score is 
 given by the number of cards dealt in a fixed time. 
 Mr. Burt has used this test extensively, and has shown 
 that it is positively correlated with other motor 
 tests. It is found, too, as any one who has watched 
 an old whist player dealing cards will readily believe, 
 that practice affects the rapidity with winch it is 
 done. 
 
 There is one important point upon which all 
 those who have carefully investigated these simple 
 motor processes are agreed ; and that is that the 
 connection between the simpler forms of motor 
 ability and intelligence is much smaller than that 
 shown by more complex motor processes. It is 
 true that certain American investigators have 
 arrived at different conclusions — have found a 
 marked direct correspondence between mental and 
 motor efficiency. But then they obtained their 
 data from non-experimental sources. The only 
 American who has investigated this matter by rigor- 
 ous experiment is Bagley, and he found an inverse 
 correspondence. The most careful researches of 
 all have been made in England by Mr. Burt, Mr. 
 Moore, Dr. Carey and Miss Bickersteth, and they 
 all found a comparatively small amount of positive 
 correlation between the two types of ability — an 
 amount which got smaller and smaller as the subjects 
 grew older, and more intelligent. With the older 
 defective children the correlation is still high. 
 This is not very surprising when we discover that 
 
PRACTICAL ABILITY 201 
 
 the kind of ability revealed by these instruments — 
 the tapping apparatus in particular — has apparently 
 little connection even with skill in craftsmanship. 
 From the few experiments that I have made (they 
 are far too few to be conclusive) the children who 
 are regarded as " clever with their fingers " cannot 
 as a rule tap more rapidly than those whose " fingers 
 are all thumbs." The only inference we can 
 legitimately draw from these facts is that the simple 
 motor tests I have described measure some specific 
 ability which is not an index either of fine powers of 
 craftsmanship or of high intellectuality. We cer- 
 tainly have no right to infer that the ability in 
 question is worthless. For the same line of reasoning 
 would force us to admit that memory too was 
 worthless. The correlation between rote memory 
 and intelligence is not high : a fool sometimes has 
 a good memory, and a genius a bad one. Yet we 
 are bound to concede that the fool would have been 
 a bigger fool if his memory had been worse, and the 
 genius would have been a greater genius if his memory 
 had been better. So with natural motor capacity, 
 in however narrow a field it may work. There may 
 be other things that are more serviceable even for 
 technical skill ; but in itself it is good : it is better 
 to have it than not to have it. 
 
 The only use of tapping that cannot be impugned 
 is as a means of determining whether a pupil is 
 congenitally right-handed or left-handed. I myself 
 am an inveterate dextral : I tap 7*4 to the second 
 with the right hand, and 5*5 with the left. 
 
 In experimenting with this instrument one cannot 
 fail to be struck by the evenness of the scores. I 
 dealt with five adults in succession who made 
 
202 MENTAL TESTS 
 
 precisely the same score — 200 in half a minute. In 
 Miss Bickersteth's experiments the mean variation 
 for both the tapping and the plunger scores was 
 surprisingly low as compared with the variation in 
 the other abilities tested. In fact, we here seem to 
 be testing a gift which among civilised races nature 
 has distributed with rare impartiality. People 
 differ very little in their basal motor endowment : 
 it is in the use to which they put this endowment 
 in the interests of the higher intellectual powers 
 that wide differences appear. 
 
 We cannot help feeling that we have not yet 
 reached the root of the matter — that we have failed 
 to put our finger on the essential thing in the making 
 of a craftsman. And if native hand-skill is not the 
 essential thing, what is the essential thing ? Let 
 us examine a few significant instances. Vierge, a 
 celebrated black-and-white artist, had the misfortune 
 to lose the use of his right arm. In a short time he 
 was producing drawings indistinguishable in execu- 
 tive skill from those which he had formerly produced 
 with his right. Mr. H. Weaver Hawkins, a young 
 student at the Camberwell School of Arts and Crafts, 
 was severely wounded during the war by shrapnel 
 passing through his right arm-pit and penetrating 
 his shoulder-blade. Pyaemia set in and attacked 
 both shoulder-blades and both elbows. Surgical 
 operations became necessary : the two elbow-joints 
 were removed and artificial ones put in their place. 
 The result was that when he got up from his bed of 
 sickness he found his arm movements woefully 
 restricted. He had little power in his shoulders, 
 little control over his elbows, not much more over 
 his wrists and fingers. He seemed like a man with 
 
PRACTICAL ABILITY 203 
 
 two paralysed arms. But he soon found that he 
 could move his left hand in one series of directions, 
 and his right hand in another series of directions. 
 So when he returned to school eighteen months 
 ago, and took up his art studies again under Mr. 
 Walter Bayes, he held his pencil in his less crippled 
 hand — his left — and by eking out its movements with 
 his right was able to make a start in re-learning the 
 art of drawing. Now he can draw as well as he 
 ever could. Indeed, his work, recently exhibited 
 at the Goupil Gallery, was highly praised by critics 
 who knew nothing of his infirmity. Requiring two 
 hands to do imperfectly the work of one, and drawing 
 as it were with his whole body, he manifests a strength 
 and precision to be found only in the accomplished 
 artist. Here we have a notable instance of the 
 triumph of mind over matter. To thwart the 
 creative impulse in such a man is impossible — unless 
 you kill him. If his hands are gone, he will draw 
 with his feet ; if his feet, too, are gone, he will draw 
 with his elbow, his chin, his teeth — with any part 
 of his person to which he can attach a pencil or a 
 brush. If the essential spirit is within him it seems 
 to create the machinery with which it works. In 
 the long run it is brain that counts, not muscle. 
 It is in the mind of man that artistry and craftsman- 
 ship reside : they depend on a form of psychic or 
 cerebral energy which flows out through the hand, 
 the hand being the most permeable outlet ; but if 
 this outlet is blocked the imprisoned energy will 
 force open some other channel of escape. 
 
 If, therefore, we try to gauge a person's capacity 
 for making things by getting him to wag his finger, 
 we must not be surprised to discover that we are 
 
204 MENTAL TESTS 
 
 merely touching the fringe of a great matter. And 
 whatever name we may give the primary essential 
 we may be sure it is not a simple thing. For we 
 shall find motor elements inextricably mixed up 
 with intellectual elements of the highest order, and 
 emotional elements of the subtlest form. To call 
 the central aptitude constructive ability is certainly 
 to connect it with one of the great instincts of 
 humanity, but at the same time it masses under 
 one name a number of distinct abilities which we 
 have neither analysed nor measured ; and until we 
 have measured them individually there is little 
 hope of our being able to estimate them collectively, 
 or, indeed, lay hold of that single factor (if there is 
 such a factor) which may be supposed to be common 
 to all these units. It has, however, been argued 
 that as all construction in the handicrafts consists 
 in adapting and arranging objects in space, a capacity 
 to conceive and to picture those arrangements in 
 the mind is at least part of the general constructive 
 ability. One of Binet's intelligence tests for adults 
 consists in folding a square of paper twice, cutting a 
 triangular notch in one of the sides, and asking the 
 subject to draw what it would look like if it were 
 opened. 
 
 A more complex construction test is that of the 
 dissected cube. The subject is asked to imagine a 
 painted cube of three-inch side cut into cubic 
 inches, and is required to say how many of these 
 little cubes are painted on three sides, how many 
 on two, how many on one, and how many on none. 
 Another way of administering the test is to present 
 the twenty-seven small cubes all mixed up and ask the 
 subject to put them together so as to form one large 
 
PRACTICAL ABILITY 205 
 
 cube painted all over. A record is made of the plan 
 adopted and the time taken. The subject who 
 works in accordance with a premeditated plan is 
 regarded as superior to the subject who works by trial 
 and error. It is a difficult test, which can only be 
 done with facility by what Terman calls " superior 
 adults." 
 
 The commonest type of construction test is the 
 form board, of which there are many varieties. The 
 essence of the problem is the same as that of the 
 jig-saw puzzle : how to put things together to form 
 a whole. The time taken gives the score. 
 
 Mr. T. L. Kelly of Texas University has devised a 
 construction ability test on the meccano principle. 
 A quantity of material consisting of strips of wood of 
 different shapes and sizes, and a variety of blocks 
 and wheels, is placed before the pupil and he is 
 asked to build the best thing he can out of them. 
 Here initiative and inventiveness are brought into 
 play. The test is reasonable enough and simple 
 enough ; the difficulty lies in assessing the result — the 
 same difficulty in fact that we have in working the 
 models made in the handicraft centre. It is hard 
 enough to mark them when all the things are the 
 same : it is harder still when they are all different. 
 In America they try to get over the difficulty by 
 forming a standardised scale of specimens which 
 have already been marked in accordance with the 
 average judgment of a number of independent 
 examiners. Any particular object to be marked 
 has to be compared with the standard specimens 
 until its equal is found. But it is not easy to find 
 its equal. It is not easy to say whether an indiffer- 
 ently made toy table is equal to. better than, or 
 
2o6 MENTAL TESTS 
 
 worse than, a badly made parquetry mat. The 
 specimen scale, in fact, does not do away with indi- 
 vidual judgment, nor does it appreciably lessen the 
 variability of marking. 
 
 The test that seems to give the best evaluation of 
 the factors which make up practical ability is the 
 maze test. Mr. S. D. Porteus, the Director of 
 Research at the Training School, Vineland, New 
 Jersey, has invented a series of these tests, has stand- 
 ardised them, and has compared the results with 
 those obtained by using other types of tests. The 
 correlation coefficients show that the Porteus tests, 
 while yielding as a whole the same type of develop- 
 mental curve as Binet's, differ widely from them in 
 the estimates they afford of certain individuals who 
 are mentally unstable and are temperamentally 
 unfit to make their way in the world. Mr. Porteus, 
 in fact, contends that the Binet tests are too ex- 
 clusively intellectual, and that they generally fail 
 to detect the children who have brains but no grit, 
 who have linguistic ability but little common sense, 
 who show a superficial brightness but have little 
 capacity for forethought and planning. 
 
 The accompanying diagram represents the Porteus 
 test for children of 14 years and 6 months. It 
 is one of the series of eleven standardised for the 
 years from 3^ to 14^, no test being given for 13^. 
 The problem is to trace with a pencil the most 
 direct route of threading the maze by entering at 
 S and getting out again by some other exit. The 
 following are Mr. Porteus's instructions : " Show 
 child starting-point at S, and tell him to find his way 
 through the test form without going along any 
 blocked path. As soon as a mistake is made, stop 
 
PRACTICAL ABILITY 
 
 207 
 
 the child and bring him back to the starting-point for 
 his second trial. Never allow the child to retrace 
 his course." Half-year credit is allowed if the test 
 is passed on the second trial. If he passes on the first 
 
 Porteus Test 
 
 Year XIV 
 
 trial his mental age is regarded as at least 14!, if 
 on the second at least 14. 
 
 A new line of investigation has recently been 
 opened up in America, mainly by F. B., and 
 
208 MENTAL TESTS 
 
 L. M. Gilbreth. It is technically termed " motion- 
 study." Mr. Gilbreth made a systematic study of 
 brick-laying, and found that a big reduction could 
 be made in the number of separate movements 
 involved. From eighteen they could be reduced to 
 five ; with the result that 30 men could by the new 
 method lay as many bricks as 1 00 men by the old 
 method, and would be less fatigued at the end of 
 the day. A brief account of this research will be 
 found in Dr. Myers's Present-Day Applications 
 of Psychology. This little book also describes the 
 chronocyclegraph, an instrument for photographing 
 a movement so that it can be examined in all its 
 details, and the extent and speed of each part scien- 
 tifically measured. By means of it an awkward 
 action may be compared with a skilled action, so 
 that the needless and harmful elements may be 
 brought to light and eliminated. It bids fair to 
 reveal to us in due time how we may learn to work 
 efficiently and to play efficiently ; and perhaps 
 allows us to indulge in the Utopian hope that the 
 distinction between work and play may disappear 
 altogether. With the drudgery part reduced and 
 the creative part increased work will become the 
 joy and delight we all feel it ought to be. 
 
 The conclusion at which we arrive is that skill in 
 carrying out any piece of practical work, needing as 
 it does the thinking mind as well as the creating 
 hand, involves a large number of special aptitudes 
 and a large number of special habits ; and that mere 
 motor ability, in the barest sense of that term, is only 
 a part, and that not the most important part, of the 
 whole process. Attempts to measure innate dex- 
 terity have not so far proved of any help to the 
 
PRACTICAL ABILITY 209 
 
 teacher ; nor have the methods of measuring the 
 higher functions involved in constructive work 
 developed sufficiently to give the young craftsman 
 any guidance in pursuing his craft. We have not 
 yet discovered a good indirect means of testing 
 practical ability : we must test it directly. We must 
 measure it as we have always measured it, by getting 
 the pupil to do a piece of work and forming our 
 estimate of it by standards which knowledge and 
 experience have fixed in our minds. 
 
CHAPTER XII 
 
 COMPOSITION 
 
 There is no branch of study more important 
 than English Composition, and there is none so 
 hard to mark. So heavy, indeed, is the task, that 
 teachers have been known to bargain with their 
 chiefs about the minimum amount of marking to 
 be done. In London Elementary Schools the mark- 
 ing of one set of composition exercises per week is 
 generally regarded as all that can be reasonably 
 demanded of the class master. Some teachers do 
 more, but this is looked upon as a work of superero- 
 gation. Marking involves a twofold task — correct- 
 ing the imperfections and appraising the result ; 
 and of these, one seems endless and the other hope- 
 less. And the corrections do not help us much in 
 aiming at an estimate of the merit of the exercise. 
 For to appraise a piece of writing by counting the 
 blunders is itself a blunder. On this basis Shake- 
 speare would fare badly, and Lamb would come 
 off worse than if he had placed himself in the 
 hands of the schoolmaster who wanted to teach 
 him how to write essays. A pretentious piece of 
 writing may have nothing in it — not even blunders ; 
 and another piece may be full of good things, and 
 at the same time full of faults. Not that faults 
 do not matter, but that value is to be judged 
 
 2IO 
 
COMPOSITION 211 
 
 positively, not negatively — not by subtracting marks 
 for each fault, but by adding marks for each 
 merit. 
 
 And the worst of the business is that the marker, 
 after spending weary hours in toiling through a 
 pile of papers, cannot rid himself of the suspicion 
 that his labours are vain. He knows that the 
 pupil, ignoring the emendations in red ink, will 
 simply glance at the final mark and cast the paper 
 aside. The corrections are made in the wrong 
 place. The mistakes are removed from the paper, 
 whereas they should be removed from the pupil's 
 mind. The corrections are not made in the right 
 place, because they are not made by the right 
 person. For the right person is the pupil himself. 
 
 How, then, can we make the task of correcting 
 fall more upon the shoulders of the pupil who is 
 benefited by it, and less upon the shoulders of the 
 teacher who is bored by it ? To begin with, the 
 pupil must have ideas. He should be put to write 
 on those topics only which really occupy his mind. 
 Every child thinks about something — constantly 
 thinks about something — and that something, if 
 it can be discovered, is the theme upon which he 
 is best fitted to write. His ideas are best put 
 when they come warm from his brain. Then 
 only does writing become a means of self-expression. 
 But since his ideas are often meagre and trivial, 
 and the composition exercise is a means of en- 
 larging both his circle of thought and his store of 
 words, as well as of improving his control of what 
 words he already has, he should constantly be 
 encouraged to venture on new topics. And for 
 this an opportunity for preparation is essential. 
 
212 MENTAL TESTS 
 
 Then, again, when he has finished the exercise 
 he should be given a chance to revise it. Many of 
 the mistakes which we point out to him he could 
 quite well with a little trouble find out for himself. 
 When you or I write anything, rarely do we leave 
 it as it first flowed from the pen. We set it aside 
 and read it again later ; we score out superfluous 
 words, change awkward phrases, rearrange the 
 ideas, and sometimes, indeed, write the whole 
 thing over and over again. All careful writers do 
 this. If they do not actually do it on paper, they 
 do it in their heads before committing it to paper. 
 To revise and to remodel, to reflect upon what is 
 written, and to reject even the good in favour of 
 the better — that is at least part of the secret of 
 clear and vigorous prose. We do this ourselves, 
 but do not allow our pupils to do it. Often do we 
 expect them to write without preparation ; always 
 do we expect them to write without revision. 
 Second thoughts are discouraged ; for erasures are 
 discouraged. The pupil must try to present a 
 fair page of writing without blot or blemish. So 
 chary are the children of crossing anything out 
 that if they make a mistake in phraseology or in 
 spelling, they enclose the peccant word in brackets 
 and leave it there. Let the teacher countenance, 
 nay praise, the untidy page (provided the untidi- 
 ness is due to careful thinking, not to careless writ- 
 ing), and he will find his pupils falling into a habit of 
 self-criticism. If the writing has become illegible 
 the piece should, of course, be re-written. The 
 stages of a composition exercise are, therefore, 
 three : preparation, rough draft and final copy. 
 And they may require three distinct lessons, or 
 
COMPOSITION 213 
 
 any two sequent stages may occupy one lesson, or 
 any one stage may spread over many lessons. 
 
 So much for correcting. The marking proper, 
 the measuring of the achievement, still remains to 
 be done. And in that lies the crux of the difficulty. 
 So complex is the thing to be measured, so numerous 
 the criteria of merit, so diverse the points of view, 
 that it is almost impossible to find different ex- 
 aminers of the same scripts arriving at the same 
 marks. They form different estimates because they 
 attach different values to the component factors. 
 Some think highly of quantity, others of quality ; 
 some of ideas, others of style ; some of wealth of 
 words, others of clearness of diction ; some of 
 logical arrangement, others of sound and rhythm. 
 Indeed, there is no end to the qualities which may 
 be exalted by some and belittled by others. In 
 measuring the achievement we are measuring a 
 medley. It is as though we were trying to repre- 
 sent the value of a room by a number which should 
 sum up the size of the room, its shape, the lighting, 
 the ventilation, the convenience of the fittings, 
 the pattern of the wall-paper, the state of the floor, 
 and a host of other qualities and quantities. The 
 consequence is that in appraising a piece of writing 
 we rely on the general impression left on our minds 
 after reading it. In fine, we do not measure at 
 all : we guess. True, it is not a pure guess : but 
 neither is it a pure guess when we guess the height 
 of a building by looking at it. We have data to go 
 upon, but our mode of estimating is purely sub- 
 jective. The standard by which we judge is our 
 own standard and nobody else's. And the aim of 
 the modern movement of reform in testing is to 
 
2i 4 MENTAL TESTS 
 
 provide objective standards — standards that are 
 everybody's standards. 
 
 In America they try to objectify the standard in 
 composition by means of a scale of specimens. 
 Certain pieces are standardised by a number of 
 reputable examiners ; they are arranged in order 
 of merit, and assigned definite marks. This is 
 then used as a scale by reference to which com- 
 position exercises are measured. Five such scales 
 are in general use, of which the Hillegas-Thorndike 
 is apparently the most popular. This scale has 
 15 grades of merit, ranging in marks from o to 95 — 
 presumably out of a maximum of 100. The sixth 
 specimen from the bottom reads as follows — 
 
 " De Quincy. 
 
 " First : De Quincy's mother was a beautiful 
 women and through her De Quincy inhereted 
 much of his genius. 
 
 " His running away from school enfluenced him 
 much as he roamed through the woods, valleys and 
 his mind became very meditative. 
 
 " The greatest enfluence of De Quincy's life was the 
 opium habit. If it was not for this habit it is doubt- 
 ful whether we would now be reading his writings. 
 
 " His companions during his college course and 
 even before that time were great enfluences. The 
 surroundings of De Quincy were enfluences. Not 
 only De Quincy's habit of opium but other habits 
 which were peculiar to his life. 
 
 " His marriage to the woman which he did not 
 especially care for. 
 
 " The many well educated and noteworthy 
 friends of De Quincy," 
 
COMPOSITION 215 
 
 This specimen is labelled Quality 47. What are 
 we to think of it ? It reads as though the writer 
 had been put to read something about De Quincey, 
 had ill-digested it, and had tried to reproduce it ; 
 not because he wanted to but because he had to. 
 It may be typically American ; it certainly is not 
 typically English. As it stands half-way up the 
 scale we are, I presume, to regard it a"s an average 
 performance. But the average performance in our 
 English schools bears so slight a resemblance to 
 this specimen that the two are in no way com- 
 parable. The bulk of the children's writings strike 
 a more even and a more genuine note. We never 
 find a pupil using such booky words and showing 
 at the same time so feeble a grasp of the structure 
 of the sentence. If he can use the colon (he rarely 
 can, by the way) he will not bungle at the apos- 
 trophe. If he uses long words he generally knows 
 how to spell them. Indeed, it would be difficult 
 to pick up in our schools a piece of composition 
 which, exhibiting the same combination of merits 
 and defects, could be confidently judged as equal 
 to the standard sample, and therefore deserving 
 of forty-seven marks out of a hundred. 
 
 There is the further difficulty of comparing dis- 
 parate types of composition. To equate an essay 
 with a story is by no means easy. A realisation of 
 this difficulty led to the formulation of the Harvard- 
 Newton scale, which comprises four distinct series 
 of samples, one for each of the four common forms 
 of discourse : narration, description, argumentation 
 and exposition. But the whole question of the 
 value of a scale of samples is still open. It is certain 
 that its worth has never been clearly demonstrated, 
 
2i 6 MENTAL TESTS 
 
 In one group of investigations upon one particular 
 scale, indeed, it was actually found that teachers 
 who used a scale of this kind showed greater vari- 
 ability in their marking than those who adopted the 
 usual plan of relying on general impression. In 
 fact, they measured better without the scale than 
 with it. On the other hand, it is claimed that 
 with practice this variability decreases, so that after 
 a time the advantage in steadiness will lie on the 
 side of the scale. Be that as it may, its merits 
 are not so obvious as to lead to its adoption in 
 other countries. If it ever comes to England it must 
 put on English garb. The sample pieces must be 
 taken from English schools and standardised afresh. 
 
 A promising line of inquiry has been opened up 
 by Dr. Kimmins in his inquiry into the methods 
 of expression used by London children in essay 
 writing at different ages. (The Journal of Experi- 
 mental Pedagogy, III, 289.) The criterion used 
 by Dr. Kimmins is the type of sentence employed. 
 From this point of view the most significant change 
 with increasing age seems to be the less frequent 
 use of the simple unrelated sentence, and the more 
 frequent use of the complex sentence. But im- 
 portant as is this way of looking at children's writ- 
 ings, it is not the only way : it merely marks one 
 point of merit out of many. 
 
 There is, in fact, no help for it : we must, for 
 the present at least, fall back upon the method of 
 personal impression. And, indeed, when we re- 
 member that in addition to the more tangible 
 features of a piece of writing, there is always that 
 peculiar appeal to our aesthetic sense which defies 
 $11 measurements and all standards — when, in fact, 
 
COMPOSITION 217 
 
 we remember that it is an artistic product as well 
 as an intellectual product — we find it hard to see 
 how the subjective standpoint can ever be out- 
 grown. There are, however, certain definite things 
 we can do to bring our individual judgments into 
 closer unison. 
 
 First, we must realise the roughness of the scale 
 we are capable of using, and give up trying to 
 calibrate more finely than the conditions warrant. 
 To pretend to find 100 degrees of difference in 
 however huge a number of papers, is to expose 
 oneself to ridicule. Who can say, with any measure 
 of confidence, that one paper merits 58 marks 
 exactly and another 59 ? — unless, indeed, he works 
 on some mechanical system of adding sentences, 
 of deducting for errors, and of ignoring all the 
 broader and more spiritual issues. The most finely 
 graded scale in America, the Hillegas-Thorndike, 
 has only 15 degrees of merit ; the others have 
 respectively 10, 9, 8 and 6. At our universities it 
 has ever been the custom to grade essays in four 
 groups, assigning to each one of the first four 
 letters of the Greek alphabet, with an occasional 
 plus or minus to indicate finer shades ; and even 
 this broad classification inspires in the under- 
 graduate no great degree of confidence, main- 
 taining, as he often does, that — 
 
 " 'Twixt right and wrong the difference is dim, 
 'Tis settled by the moderator's whim ; 
 Perchance the delta on your paper marked 
 Means that his lunch has disagreed with him." 
 
 Having fixed upon the number of grades of merit 
 (five is probably enough tQ stajt with) we must 
 
2i 8 MENTAL TESTS 
 
 criticise the efficiency of our marking by observing 
 the way in which our scores are distributed. If, 
 for instance, we use five grades the coefficients in 
 the expansion of (x + i) 4 , that is, i, 4, 6, 4 and 1 
 give the probable or normal distribution. Generally 
 speaking, out of every 16 papers 1 should receive 
 one mark, 4 two, 6 three, 4 four and 1 five. If ten 
 grades are used, the expansion of (1 + x) 9 , that is, 
 1, 9, 36, 84, 126, 126, 84, 36, 9 and 1, apportions 
 the number of papers that should, in a reasonable 
 system of marking, receive the scores from 1 to 10 
 consecutively. This, however, is a guiding principle, 
 not a compelling principle. It helps the teacher in 
 cases of doubt, it shows up the defects of a faulty 
 system, but it cannot decide what marks are actually 
 merited. The real starting-point is neither the best 
 paper nor the worst, but the middle or average. 
 The marks should crowd round this middle, but at 
 each end there should be elbow-room. This aver- 
 age is the standard which the marker should have 
 fixed in his mind, and with which he should mentally 
 compare the individual papers. There must be 
 much provisional marking before this standard is 
 fairly established. And in the case of the class 
 teacher it is a standard which should be constantly 
 rising, and should be assigned a constantly increasing 
 value. 
 
 Having developed for himself a sensible system 
 of marking, the teacher should now impart it to his 
 pupils. He should teach them how to mark. It 
 will save him hours of useless toil, will alter the 
 pupils' attitude towards his judgments, and will 
 evoke in them a healthy spirit of self-criticism. 
 At present the schoolboy never thinks of challenging 
 
COMPOSITION 219 
 
 the teacher's verdict. He regards it not as a 
 valuation but as a gift. He asks himself, " What 
 mark has he given me ? " He should learn to ask, 
 " What mark have I earned ? " And he should be 
 able to say approximately whether his wage is 
 correct, and have the right to challenge the figure. 
 One of the pupils should occasionally read his 
 composition to the class, and the rest be required 
 to record individually and independently their 
 estimate of its merit. After a little practice it is 
 surprising how close together the estimates become. 
 The scholars tend more and more to agree with 
 one another and to agree with the teacher ; and 
 soon the marking of a complete set of papers may 
 safely be delegated to one of the scholars. He may 
 be trusted to take pains over the task, knowing as 
 he does that his marks will be carefully scrutinised 
 by the writers, that his corrections and his findings 
 will in some cases at least be challenged, and that 
 he is to-day judging the work of one who to-morrow 
 may become his judge. When the marked papers 
 are distributed there will probably be much com- 
 motion in the class. There will be a simmering of 
 indignation and protest. And if the teacher has 
 " nerves " he had better not try the system. With 
 patience and tact, however, all the troubles will 
 disappear. The teacher becomes the umpire be- 
 tween the plaintiff, who states his grievance, and 
 the marker, who has to defend both his corrections 
 and his assessment. And the discussion that arises 
 will be of more value to both pupils than much 
 red ink and much blue pencil. In course of time 
 the class will become educated to this sort of thing, 
 and the members will take kindly and calmly the 
 
220 MENTAL TESTS 
 
 criticisms of their fellows. It affords the same sort 
 of moral training as boxing : it teaches them to 
 take hard knocks without losing their tempers. 
 Moreover, they are really learning to write English. 
 No claim of novelty or of originality is made for 
 this system. In modified form it has been used 
 by others, and used with signal success. Nor must 
 the teacher think that it entirely relieves him of 
 the burden of marking : it only reduces the burden. 
 In all cases he is the final arbiter : in important 
 examinations he is the sole arbiter. And when he 
 does mark he should mark very carefully; for his 
 papers will now go back to trained critics. 
 
APPENDIX 
 
 SOCRATES ON INTELLIGENCE 
 
 There is little doubt that the dream itself was 
 due to the lunch ; but the content of the dream 
 was determined by other things. It was holiday 
 time. In the morning I had taken a long and 
 solitary walk ; and, pondering over the question 
 of the discipline of the mind, had followed trains 
 of thought which led to flatly contradictory issues. 
 After a somewhat hearty lunch I retired to my 
 study and took down from the shelves a volume 
 of Jowett's translation of Plato. The book rested 
 on the broad arm of my reading-chair, and as I 
 turned over the leaves I was overcome with drowsi- 
 ness and fell into a profound sleep. And as I slept 
 I dreamed a dream. And I thought I stood in 
 the streets of a strange city, which by some obscure 
 process of reasoning or intuition I knew to be the 
 ancient city of Athens. And of those who passed 
 along the sunlit street two men specially arrested 
 my attention. One of them was short and un- 
 gainly, with a snub nose and protuberant eyeballs. 
 His feet were bare and his simple cloak old and 
 weather-stained. Indeed, his unattractive aspect 
 formed a marked contrast with that of his com- 
 panion, who, although a somewhat older man, 
 suggested by his dress and general bearing the 
 
222 APPENDIX 
 
 old Greek ideal of a gentleman — xaloxayaBoq. 
 Yet was the ill-favoured one not devoid of a certain 
 native dignity ; and I had no difficulty in recognising 
 him as Socrates. Who the other was I could merely 
 surmise. I followed them for some distance until 
 they turned into a porch and knocked at a door 
 of finely chased bronze. Presently the door was 
 opened by a slave, and passing along a narrow hall 
 we abruptly entered a room equipped with book- 
 shelves, a pedestal desk and oak furniture of modern 
 design. A severe-looking person in spectacles who 
 was sitting at the desk rose to greet his visitors and 
 bade them be seated. 
 
 The anachronisms of the dream are glaring and 
 palpable ; but during the dream itself they not 
 only failed to astonish me : they entirely escaped 
 my notice. It seemed quite right and fitting that 
 Socrates should be conversing in English with a 
 black-coated gentleman who quoted Tennyson. 
 There appeared no historical inconsistency in the 
 reference to prospectuses, school examinations and 
 medical inspection. Nor did the fact in the least 
 surprise me, that although I was present the whole 
 time nobody seemed to take the slightest notice 
 of me. Of the conversation that took place in that 
 strange-familiar room my recollection is clear and 
 vivid, and a faithful record thereof is herewith 
 given — 
 
 Soc. Hearing of your fame as a schoolmaster, 
 Sophisticus, I have come to consult you about 
 my two sons, one of whom is nine and the 
 other ten years of age. I have brought with 
 me my old friend Crito, who also takes much 
 
APPENDIX 223 
 
 interest in the lads. We wish to know how 
 best they may be trained in wisdom and virtue. 
 
 Soph. Well, Socrates, I do not think you could do 
 better than send them to my school. 
 
 Soc. Many of my friends say the same thing ; and 
 that, indeed, is why I came to you. You will, 
 I am sure, put it down to pardonable anxiety 
 on the part of a father if I seek, by asking you 
 questions, to assure myself that my sons will 
 get at your school a sound education. 
 
 Soph. You may ask me as many questions as you 
 like, Socrates, and I will do my best to answer 
 you. 
 
 Soc. Tell me, then, Sophisticus, what will my boys 
 learn in your school ? 
 
 Soph. They will learn everything that an educated 
 man should know. There is my prospectus. 
 You will see therein the full list of subjects. 
 
 Soc. But I see nothing here about the teaching of 
 virtue. Is not that one of the subjects ? 
 
 Soph. We do not put that down, Socrates ; but 
 we do teach our pupils to be good. We explain 
 to them the sacred writings, and we look very 
 carefully after their morals. 
 
 Soc. And I see nothing here about wisdom. You 
 will admit that a boy may know a large number 
 of things and yet not be truly wise. 
 
 Soph. I readily admit that. Although it is not 
 put down in my prospectus, that is really the 
 supreme aim and purpose of my school. We 
 have discarded the old-fashioned word " wis- 
 dom," and use the word "intelligence" in- 
 stead ; but it means the same thing. My boys 
 get a good training ; their intelligence is 
 
224 APPENDIX 
 
 awakened. That is in fact the chief way in 
 which my school differs from most other 
 schools. It is not a place where " knowledge 
 comes but wisdom lingers." Our aim is not 
 merely to prepare boys for examinations ; 
 what we really pride ourselves on doing is in 
 producing general intelligence. 
 
 Soc. I begin to understand. But it is a pity you 
 do not put this down in your prospectus, 
 Sophisticus, for I have for years been looking 
 for a school where they train intelligence, as 
 you call it, and have never found one. I see, 
 however, that you advertise the fact that pupils 
 are prepared for certain examinations. 
 
 Sopb. If I did not put that down, Socrates, I fear 
 I should get no pupils at all. But what I really 
 try to cultivate is general intelligence. 
 
 Crito. Don't you see, Socrates, that that is the 
 explanation he reserves for the parents of 
 children who fail at the examinations. 
 
 Soc. That suspicion, Crito, is unworthy of you, 
 and does injustice to a great schoolmaster like 
 Sophisticus. I indeed prefer to believe that 
 he seeks to produce general intelligence, and 
 that success at examinations is a sort of by- 
 product. 
 
 Sopb. You state the case truly, Socrates. 
 
 Soc. But tell me what you mean by giving the boys 
 a good training. 
 
 Sopb. I mean that we cultivate their mental 
 powers. We teach them not only to know, 
 but to do. We make them remember better, 
 observe better, and reason better, and, to put 
 it generally, we make them better thinkers. 
 
APPENDIX 225 
 
 Soc. That, indeed, is a great achievement. But 
 you must not bewilder me by telling me so 
 much at once, for I have a bad memory, and 
 can only deal with one thing at a time. Tell 
 me how you make a boy more observant. 
 
 Soph. By giving him practice in observation, of 
 course. 
 
 Soc. By practice, you mean that he repeats the 
 same act over and over again ? 
 
 Soph. Just so. 
 
 Soc. And he does it better the second time than 
 the first ? 
 
 Soph. Yes. 
 
 Soc. And the third time better than the second ? 
 
 Soph. Precisely. 
 
 Soc. But is not this what we call forming a habit ? 
 
 Soph. I suppose it is. 
 
 Soc. Observation, then, is a habit ? 
 
 Soph. I have never thought of it in that light, 
 Socrates, but I think you are right. 
 
 Soc. I do not say that I am right : I am trying to 
 find out what you can tell me about the matter. 
 You do not mind my putting these questions ? 
 
 Soph. Of course not, Socrates. I have heard of 
 your custom of questioning people, and I am 
 glad to have an opportunity of hearing you. 
 
 Soc. Tell me, then, does training consist in any- 
 thing else but the formation of habits ? 
 
 Soph. It depends on what you mean by habits. 
 
 Soc. Does not an act tend to become easier by 
 repetition ? 
 
 Soph. Yes. 
 
 Soc. And it is true of an act of thought, of feeling, 
 or of will, as well as of a physical act ? 
 Q 
 
226 APPENDIX 
 
 Soph. Certainly. 
 
 Soc. Shall we agree to call any act that has been 
 improved by practice a habit ? 
 
 Soph. It seems to be a suitable name for it. 
 
 Soc. Then training consists in forming habits ? 
 
 Soph. Yes. 
 
 Soc. And nothing else ? 
 
 Soph. And nothing else. 
 
 Soc. And is intelligence a habit ? 
 
 Soph. Well, I should not be disposed to call in- 
 telligence a habit. It seems to me to be less 
 a habit than observation even. 
 
 Soc. And yet you said that you could train in- 
 telligence. 
 
 Soph. There does seem to be a contradiction some- 
 where. And yet I am sure I can train intelligence. 
 
 Soc. Let us try again. What is intelligence ? 
 
 Soph. Now you have asked me a very difficult 
 question. I can pick you out my most in- 
 telligent pupils, but I cannot tell you off-hand 
 precisely in what this intelligence consists. 
 
 Soc. Are they necessarily intelligent if they can 
 read well ? 
 
 Soph. No. 
 
 Soc. Or write, or draw, or sing well ? 
 
 Soph. No. 
 
 Soc . Or repeat poetry, or remember history ? 
 
 Soph. No. 
 
 Soc. Or do arithmetic ? 
 
 Soph. It depends upon the kind of arithmetic. 
 
 Soc. What kind of arithmetic can an unintelligent 
 boy do ? 
 
 Soph. Simple straightforward sums, such as the 
 common rules which he has been taught. 
 
APPENDIX 227 
 
 Soc. And what kind can an intelligent boy alone do ? 
 
 Soph. Problems. 
 
 Soc. And what is the essential difference between 
 the two ? 
 
 Soph. The unintelligent boy can do sums which 
 he has previously practised, or has at least 
 been shown how to do. The intelligent boy 
 can do sums which are not quite the same as 
 any others which he has done or been shown 
 how to do. 
 
 Soc. And is intelligence shown in any other subject 
 besides arithmetic ? 
 
 Soph. Certainly, a boy may show intelligence in 
 geography, or history, or science, or hand- 
 work, or indeed in any subject which is not 
 purely mechanical. 
 
 Soc. And is it the novel part that requires intelli- 
 gence in other subjects as in arithmetic ? 
 
 Soph. That is right, Socrates, you have made it 
 quite clear. It is the new, the unfamiliar part 
 of any given situation that calls for intelligence 
 on the part of a boy. 
 
 Soc. I am glad to hear you say that, Sophisticus, 
 for that simplifies the case. Tell me, does 
 training have to do with the familiar, or with 
 the unfamiliar ? With the old or with the new ? 
 
 Soph. I do not see what you mean. 
 
 Soc. Does not training involve doing the same 
 thing over again ? 
 
 Soph. Yes, we agreed that it was based on practice. 
 
 Soc. And when you are trained to deal with any 
 kind of situation that situation is no longer 
 new ? it is no longer unfamiliar ? 
 
 Soph. Quite so. 
 
 Q2 
 
228 APPENDIX 
 
 Soc. Then a trained faculty has to do with familiar 
 
 material ? 
 Soph. Yes. 
 
 Soc. And intelligence deals with the unfamiliar ? 
 Soph. Yes. 
 
 Soc. Then intelligence cannot be trained ? 
 Soph. No, Socrates, I will never admit that. 
 
 There must be some flaw in the argument. 
 
 I think I see what it is. The situation which 
 
 you call new or unfamiliar is never wholly new. 
 
 There is always much that is old, and rarely 
 
 more than a little that is new. 
 Soc. But the unintelligent pupil can deal with the 
 
 old part of the situation if he has been trained 
 
 to it ? 
 Soph. Yes. 
 
 Soc. And if the new part is not dealt with, intelli- 
 gence is not shown ? 
 Soph. Quite so. 
 Soc. Then it is only intelligence that can deal with 
 
 the new part ? 
 Soph. 
 
 Soc. And no training can enable us to deal with 
 the new ? 
 
 Soph. It seems so. 
 
 Soc. Then we are again back in the same position. 
 Intelligence cannot be trained. 
 
 Soph. Although I cannot refute your argument, 
 Socrates, in your own way, I can do it in 
 another way. If you will send your boys to 
 me you will find that at the end of a year 
 they will be much more intelligent than when 
 they came ; and I call that a much stronger 
 argument than even you can devise. 
 
APPENDIX 229 
 
 Soc. If you can do that I will believe that our 
 discussion has somehow strayed from the 
 truth. I will think over what you say. Come, 
 Crito, let us depart, for I see that Sophisticus 
 is impatient of all this talk about things which 
 he can do but cannot explain. 
 (After the usual greetings they take their leave.) 
 
 Crito. Tell me, Socrates, do you really think that 
 intelligence cannot be cultivated ? 
 
 Soc. I should be glad to be convinced to the con- 
 trary. I fear there were many errors in our 
 discussion with Sophisticus, but not of the 
 nature that you imagine. You noticed that 
 we seemed to agree to call observation a 
 habit ? 
 
 Crito. I noticed that, Socrates. 
 
 Soc. And do you think it is a habit ? 
 
 Crito. I thought so at the time, but I don't feel so 
 sure about it now. 
 
 Soc. Tell me, Crito, is breathing a habit ? 
 
 Crito. We never call it a habit. 
 
 Soc. But is it not an act which we are continually 
 repeating ? 
 
 Crito. Certainly. 
 
 Soc. How, then, does it differ from an act which 
 everybody calls a habit, such as the trick which 
 some people have of frequently stroking the 
 beard ? 
 
 Crito. Only some people stroke their beards, but 
 everybody breathes. 
 
 Soc. And why does everybody breathe ? 
 
 Crito. He cannot help it, Socrates. It is a natural 
 power which he brings with him when he comes 
 into the world. 
 
230 APPENDIX 
 
 Soc. And why does not everybody who has a beard 
 
 stroke it ? 
 Crito. Because it is a habit which some acquire, 
 
 and some do not. 
 Soc. A habit, then, is a personal acquisition ? 
 Crito. Yes. 
 Soc. And in that sense breathing is not a habit, 
 
 but a natural power ? 
 Crito. Yes. 
 Soc. Can a natural power be improved, do you 
 
 think ? 
 Crito. I think it can, Socrates. My grandchildren 
 
 who are now at school have breathing exercises 
 
 every day. And the physician visits the school, 
 
 and examines the children's noses and air 
 
 passages, so that obstructions may be removed. 
 
 People, too, who have their voices trained say 
 
 that attention is paid not to their throats 
 
 where the sound is produced, but to the 
 
 mechanism for breathing. They are in fact 
 
 taught to breathe better. 
 Soc. Tell me any way in which children at school 
 
 are taught to breathe better. 
 Crito. They are taught to use handkerchiefs, and 
 
 to breathe through the nose, and to breathe 
 
 deeply. 
 Soc. And is not the proper use of a handkerchief a 
 
 habit ? 
 Crito. Certainly. 
 Soc. And breathing through the nose, rather than 
 
 the mouth, is that a habit, too ? * 
 
 Crito. It is a habit. 
 Soc. And what shall we say for breathing deeply ? 
 
 cannot that become a habit ? 
 
APPENDIX 231 
 
 Crito. It can. 
 
 Soc. Then, shall we be right in saying that a 
 natural power like breathing can be improved 
 by forming certain habits which render that 
 power more effective ? 
 
 Crito. We shall be right in saying that. 
 
 Soc. And is not the same thing true of observation, 
 which we have agreed to regard as a natural 
 power ? 
 
 Crito. Yes. 
 
 Soc. And is not intelligence a natural power inas- 
 much as everybody possesses it in some degree ? 
 
 Crito. Yes. 
 
 Soc. Then intelligence can be improved in the 
 same way as breathing and observation can be 
 improved ? 
 
 Crito. It seems so. 
 
 Soc. Then Sophisticus is right after all, and in- 
 telligence can be trained. 
 
 Crito. And yet, Socrates, it seemed to me while 
 you were arguing with Sophisticus that the 
 opposite was true. 
 
 Soc. May not both conclusions be true ? 
 
 Crito. How is that possible, Socrates ? 
 
 Soc. I fear, Crito, that we have been confusing 
 ourselves and obscuring the argument by using 
 the same words in different senses. When we 
 talked about observation we at one time 
 assumed it to be a simple power which could 
 either be trained or not be trained ; at another 
 time we spoke of it as though it were a group 
 of distinct and separate powers, some, if not 
 all, of which could be trained. And in the 
 same way we have been deceived by different 
 
232 APPENDIX 
 
 meanings of the word intelligence. I think, 
 Crito, that you and I had better go to school 
 again to learn the right use of words. 
 Crito. I am quite willing to go with you, Socrates, 
 provided you can find somebody to teach us. 
 
 Meanwhile we were walking along narrow streets 
 whose bare and windowless walls were relieved here 
 and there by doors that opened outwards into the 
 street. One of these doors, more pretentious than 
 the rest, was protected by a porch, near the entrance 
 of which stood one of those images of Hermes which 
 Alcibiades was supposed to have mutilated. As we 
 passed this porch, which we did just as Crito had 
 finished speaking, I touched the image with my 
 hand and it fell to the ground with a loud crash. 
 So loud indeed was it that I woke up with a start, 
 and looking down I saw the volume of Jowett's 
 Plato lying flat upon the floor. 
 
INDEX 
 
 Absurdity tests, 30, 38, 39, 76, 
 
 154 
 
 Adams, J., 109 
 
 Addition, 161 ff. 
 
 jEsthesiometer, 9-10 
 
 Age-performance, 13-14 
 
 Age test, 60 
 
 Alcibiades, 232 
 
 American tests, 15, 20, 29, 40, 
 
 46, 145, 214, 215 
 Analogies test, 32, 33 
 Applied arithmetic, 191 ff. 
 Arithmetic, 19, 112, 160 ff., 226 
 Arithmetical devices, 190 
 Association test, 37, 80 
 Average, 123 ff. 
 Ayres, L. P., 112, 156-7 
 
 Bagley, W. C, 200 
 
 Bareme d' instruction, 40, 107, 
 
 "I, 134 
 Bayes, W., 203 
 Bickersteth, M. E., 198-9, 200, 
 
 202 
 Binet, Alfred, 11, 13 ff., 17, 20, 
 
 23. 27, 30, 35 ff., 48 ff., 107, 
 
 in, 197 
 Blackboarditis, 182-3 
 Bottle test, 34 
 Breathing, 229-30 
 British Association, 47, 160 
 Brown, W., 47 
 Browning, R., 153 
 Burt, Cyril, viii, 11-12, 16, 18, 
 
 27, 45, 47, 48 ff., 90 ff., 115, 
 
 127, 157-8, 161, 200 
 
 Cancellation, 34 
 
 Carey, N., 47, 200 
 Central tendency, 122 ff. 
 Coin tests, 63, 68, 72, 73 
 
 Colour test, 61 
 
 Columbia University, 15, 42 
 
 Complexes, v 
 
 Complimentary addition, 173-4 
 
 Composition, 19, 45, 87, 128-9, 
 
 210 ff. 
 Correlation, 17, 18, 25, 26 
 Counting test, 55, 62, 71 
 Courtis, S. A., 112, 160 
 Criminology, 5 
 Crito, 222 ff . 
 Cube test, 204-5 
 
 Dale system of reading, 141 ff. 
 Darwin, C, 5 
 Date test, 72 
 Day of week test, 63 
 Decomposition method of sub- 
 traction, 168 ff. 
 Definitions test, 64, 73, 84 
 De Quincey, 215 
 Dictation, 158-9 
 Dictation test, 69 
 Differences test, 68, 86, 88 
 Digits test, 36, 50, 55, 61, 73, 80 
 Distribution, 115 ff. 
 Dotting machine, 11, 46 
 Drawing, 132 
 
 Drawing tests, 13, 62, 75, 85, 86 
 Dynamometer, 7 
 
 Einstein, 2 
 
 English, H. B., 47 
 
 Equal addition method of sub- 
 traction, 168 ff. 
 
 Ergograph, 7 
 
 Error, Curve of, 120 
 
 Evans, Miss Lloyd, 153 
 
 Examinations, 2, 14, 18, 19, 27, 
 29, 41 ff., no, 121 ff., 127, 
 131 
 
 233 
 
234 
 
 INDEX 
 
 Finger test, 62 
 French test, 33 
 Frequency-column-graph, 117 
 
 Gall, F. J., 3, 4 
 Galton, F., 6, 10, 17 
 Gilbreth, F. B. and L. M., 207-8 
 Goddard's revision of Binet's 
 
 tests, 15 
 Gray, P. L., 160 
 Green, J. A., 47, 160 
 
 Hart, Bernard, 47 
 Harvard-Newton scale, 215 
 Hawkins, H. W., 202 
 Heights of Englishmen, 115 ff. 
 Heine, H., 5 
 Hillegas-Thorndike scale, 214 
 
 Images, 10 
 
 Indirect measurement, 3 ff., 26 
 Individual work, 142 ff., 178 ff. 
 Instructions tests, 40, 50, 59 
 Intelligence, 6,11 ff., 21 ff., 29 ff ., 
 
 48 ff., 221 ff. 
 Intelligence quotient, 49 
 Interquartile range, 125 ff. 
 
 James, Wm., 27, 36 
 Jevons, S., 1 
 Jones, Emrys, vii 
 Judd, C. H., 112 
 
 Kansas silent reading tests, 
 
 146-7 
 Kelly, T. L., 205 
 Kimmins, C. W., 216 
 King John, Ballad of, 30-31 
 Knowledge, 22 ff ., 106 ff . 
 
 Lamb, C., 4, 210 
 Lancashire, Reading in, 140 
 Lavater, J. K., 4 
 Lewis, E. O., 47 
 Lines tests, 56, 82 
 Lombroso, C., 5 
 
 Manual ability, 45, 196 ff. 
 Mathematics, i, 17, 130 
 McDougall, W., 10, 11, 47, 198 
 Mclntyre, J. L., 47 
 Mean deviation, 125 ff. 
 
 Measurements, v, vi, 2, 3 
 
 Median, 123 ff. 
 
 Memory, 10, 36-7, 176 ff. 
 
 Milton, J., 4 
 
 Months test, 73 
 
 Moore, R. C, 200 
 
 Morning and afternoon test 
 
 60 
 Motion study, 208 
 Motor ability, 196 ff. 
 Munroe, W. S., 112 
 Myers, C. S., 47, 208 
 
 Name test, 51 
 
 Newton, I., 1 
 
 Normal distribution, 17, 118 ff. 
 
 Norms, 21, 108 ff., 139, 153, 160. 
 
 165, 166, 188, 191, 195 
 Nunn, T. P., viii, 115 
 
 Objects tests, 52, 68 
 Oblong test, 64 
 Observation, 225 ff. 
 CEdipus, 3, 31, 33 
 Ogive, 116 
 Oral arithmetic, 186 ff. 
 
 Pearson, K., 6, 18 
 
 Perseus, 31 
 
 Phrenology, 3-4 
 
 Physiognomy, 4-5 
 
 Pictures tests, 52, 56, 57, 66, 67, 
 
 82 
 Plato, 221, 232 
 Plunger apparatus, 198 ff. 
 Porteus, S. D., 206 
 Porteus test, 206-7 
 Poverty and attainments, 139- 
 
 40, 189-90 
 Practical ability, 196 ff. 
 Practice in arithmetic, 1 79 
 Probable error, 126 
 Probability curve, 119 
 Problems test, 83 # 
 
 Quetelet, L. A. J., 17 
 Quartile, 125 ff . 
 
 Reaction-time, 7, 8 
 
 Reading, 70, 73, no, in, 134 ff. 
 
 Reading-books, 143 
 Reasoning tests, 16, 90 ff. 
 
 
INDEX 
 
 235 
 
 Recommendations for improving 
 
 arithmetic, 185-6 
 Repetition test, 54, 60, 66, 69, 84 
 Rhyme test, 81 
 Riddles, 3, 29, 31. 33 
 Right and left test, 66 
 Rivers, W. H. R., 10 
 
 Samson, 3 
 
 S avoir j aire tests, 70-1, 78 
 
 Scale of samples, 20-1 
 
 Scholarships, 44 
 
 Schuster, E., 47 
 
 Sensory discrimination, 9-10 
 
 Sentence tests, 74, 81 
 
 Sex differences, 140 
 
 Sex -naming test, 51 
 
 Shakespeare, W., 210 
 
 Simon, Th., 48 
 
 Skew curve, 122 
 
 Smith, M., 47 
 
 Socrates, 221 ff. 
 
 Spearman, C, 18, 24, 25, 27 
 
 Spelling, 112, 155 ff. 
 
 Sphinx, 3, 31, 33 
 
 Spurzheim, J. G., 3, 4 
 Standard deviation, 126 ff . 
 Standardisation, 19, 34 ff ., 106 ff . 
 Stanford Revision of Binet's 
 
 tests, 15 
 Stern, W., 49 
 Subtraction, 162-3, ID 8 ff-. 187 
 
 Tables in arithmetic, 174 ff. 
 
 Tapping, 7, 197 ff. 
 
 Taylor, N., 47 
 
 Tennyson, A., 222 
 
 Terman, L. M., 15, 17, 49, 112 
 
 Thorndike, E. L., 2, 20, 24, 27, 
 
 112 
 Tossing coins, 119 
 Transcription test, 63 
 
 Vocational tests, 8 
 
 Weber-Fechner law, 8-9 
 
 Weights tests, 61, 73 
 
 Winch, W. H., 13, 18, 47, 176 
 
 Yerkes' point-scale, 15 
 
Printed in Great Britain by 
 
 Richard Clay & Sons, Limited, 
 
 brunswick st., stamford st., s.e. i, 
 
 and bungay, suffolk, 
 

 
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