BF 456 .P8 B3 Copy 1 Some Phases of the Psychology of Puzzle Learning J. HUDSON BALLARD SOME PHASES OF THE PSYCHOLOGY OF PUZZLE LEARNING *£ J. HUDSON BALLARD & Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at New York University ", A ^ Digitized by the, Internet Archive in 2011 with funding from The Library of Congress http://www.archive.org/details/somephasesofpsycOOball Contents 8 Chapter I PAGE INTRODUCTORY 5 Definition of a puzzle Classification of puzzles Value of puzzles General discussion of method Reasons for this study Chapter II. HISTORICAL and CRITICAL I0 i. General 2. Examination of Dr. Ruger's Monograph (A) Objective Report (B) Subjective Report Chapter III. FIRST EXPERIMENTAL SERIES 2 7 The Correlation Between Puzzle Learning and School In- telligence 1. Introductory and Explanatory 2. Reagents 3. Apparatus 4. Conduct of the Experiments 5. Method of Obtaining School Rating 6. Method of Calculating Results 7. Description of Results 8. Summary of Results 0. Conclusions Chapter IV. PAGE SECOND EXPERIMENTAL SERIES 56 An Intensive Study of Puzzle Learning with Special Ref- erence to Individual Differences and Methods of Learning 1. Apparatus 2. Reagents 3. Procedure (A) In General (B) In Particular 4. Discussion of Results (A) Preliminary (B) Individual Differences Among Reagents (C) Methods of Learning (D) Report of Supplementary Tests (E) Individual Differences Among Puzzles (F) Discussion of Results in Control Experiments Chapter V. CONCLUDING DISCUSSION 86 Conclusions Comparisons Suggestions BIBLIOGRAPHY Q2 CHAPTER I. INTRODUCTORY. I. It is a little difficult to define the word "puzzle," especially to define it in such a way as to include all puzzles worthy of the name without at the same time making the definition so very wide that there remain no descriptive features, and consequently no real in- formation is conveyed. One authority 1 defines a puzzle as "a mechan- ical toy or other device involving some constructional problem, to be solved by the exercise of patience and ingenuity." A somewhat more inclusive definition is to the effect that a puzzle is "a thing difficult to understand or solve — especially something purposely ar- ranged so as to require time, patience and ingenuity to arrive at the solution of its intricacies." 2 Lindley 3 defines a puzzle as "a problem which is apart from the usual experience of the given individual either in subject matter or method." Of these two items the relatively more im- portant is method. Lindley further says : "Any problem which fulfills these conditions and which is tried chiefly for the sake of the reaction, and for the solution as such, may be a puzzle." 4 For our present purposes we need to associate with the word "puzzle" at least the following characteristics: (a) a situation with a difficult and unknown solution, (b) a situation with an assuredly possible solution, (c) a situation all the factors of whose solution are en- tirely in the control of the one seeking to solve the problem presented thereby. The fact that a solution is possible has a certain stimulus effect upon the person endeavoring to solve the puzzle (this person we shall call the subject, or reagent). Knowing that the thing can cer- tainly be done he attacks the problem in a confident and expectant frame of mind which would not be regularly possible if he doubted the possibility of a solution. The unknown nature of the correct pro- (1) Bncyc. Brittanica. (2) Standard Dictionary. (3) A Study of Puzzles, Am. Jour. Psvch. VIII, 1S97. (4) ibid, p. 443. cedure in solving the puzzle makes room for the elements of time and ingenuity. The fact that all the factors of solution are to be completely in the control of the subject calls generally for small, easily handled mechanical or geometrical contrivances, and renders both the time taken in finding a solution and the procedure adopted for this purpose direct and valuable data representing the individual subject concerned. 2. The many puzzles coming in a general way within these require- ments may be variously classified. They may be classified for instance (a), as to whether they involve motion in two dimensions (the Maltese cross puzzle 1 ) or in three (the twisled nail puzzle) ; (b) as to the number of correct moves necessary for the solution, after the proper starting ; position has been found, from one move (the horse-shoe puzzle) to eight (the key puzzle) or more; (c) as to what might be called their flexibility, i. e., while some puzzles require the relation of their various parts one to another to be changed (the nail puzzle), others permit no shifting of parts but only the direct removal of some parts leaving the other parts unmoved (the match puzzles), while still other puzzles are not to be moved in any part but something is to be done with the puzzle as a whole (the tracing puzzles) ; (d) as to the number of choices possible at each or any stage of the solution : in this respect the same puzzle may at different stages offer varying degrees of complexity (as in the second maze puzzle, where some stages offer but one choice out of two while other stages offer one out of four) ; (e) and then, puzzles may be further classified at length on the basis of the combination of any two or more of these four more fundamental features. Lindley," including under the word some puzzles which would not meet the con- ditions imposed above, has rather popularly divided puzzles into the following groups: (a) Language and word puzzles, including riddles, connundrums, charades, acrostics, etc. ; (b) mechanical puzzles, includ- ing some dependent on dexterity and perseverance, some dependent on a trick or secret, dissected and combination puzzles, physical puzzles which involve unique applications of well known physical laws, and other puzzles more complicated; (c) mathematical puzzles, including numerical, geometrical and unicursal or tracing puzzles. 3. In using puzzles for the study of children and adults there are the following advantages, not all of them, however, unique: (a) This (1) These puzzle names refer to puzzles used in the second series of •iginal experiments herein reported. (2) A Study of Puzzles. Am. Jour. Psych. VIII, 1897. particular field is largely unworked. Outside the extensive research of Dr. Ruger 1 there is nothing yet printed which makes elaborate or de- tailed scientific use of the puzzle method for investigating the human mind, (h) The results of work on puzzles are such as lend themselves readily to exact record and tabulation, (c) Puzzles are sufficiently dif- ferent from the commonly accepted standards of intelligence, such as "book-learning" to furnish a new and independent set of investigating standards, (d) Puzzles such ag are used and described hereafter can be applied' to the young and old alike, (e) These puzzles demand for their solution some kind of motor reaction, (f) But this reaction rep- presents something far more complex than the reflex arc; it depends upon the functioning of a directly mental element, and this gives considerable purely psychic value to puzzle results. (g) Puzzles lie very largely outside the realm of daily or common experience, and their use is thus almost entirely free from the irrelevant factor of previous practice or familiarity. 4. The methods used in studying puzzles or in studying the human mind through the use of puzzles should be varied. To confine an entire research to one single method, as Dr. Ruger does, is to invite incom- plete or unbalanced results. The best scientific method calls for the intensive study of a problem by what we might almost designate the extensive method. That is, the problem is to be attacked from all di- rections and investigated from a fairly comprehensive set of points of view. One method may give true results as far as they go ; but in the light of the results which would have been obtained from the other side of the problem, to to speak, when tested by a different method, these first results may be not only partial but non-representative. Few untruths are so deceptive as half-truths. What is perfectly true in its place, may, without itself being changed, become an untruth when con- sidered by itself with no reference to its normal relations. For such reasons a variety of methods should be used with the study of puzzles, and in the original investigations reported later herein several methods were used. The question as to which way found to be most economical and exact, consequently most scientific, will be discussed in its place. In using a variety of methods, however, there is the necessity of making all these fully comparable. If, for example, the auditory method and the visual method and the motor-experience method are all used, everything else should be the same — the same reagents, the same puzzles, (1) Archives of Psychology. No. 15, June 1910. 7 the same directions, the same formula of solution for each puzzle, and a general standardizing of all other conditions. This eliminates ir- relevant factors, greatly reduces the liability of errors creeping in, renders the consequent tables of data fully comparable, and in such ways con- duces most directly to scientific results. Results in the work with puzzles find their highest value in being truly representative results. This kind of results we should earnestly strive for — results which represent the human mind in general. No one cares particularly to know what kind of psychic equipment is possessed by a handful of individuals ; but if we have good reason to believe that the mental traits discovered in tlrs particular group of individuals hold true of men in general, then these individual records and the conclusions based on them immediately take on immense value : our particular re- sults rise to the significance of representative results. Now in order to obtain results of this wide-reaching significance attention must be given to the selection of reagents, to the selection of individual tests, and to the general methods of the entire procedure. Enough has already been said, at this point, about such methods as lead to fully comparable results. As to tests, there should be several of them, all different, yet all proceeding on the same general principle. The differences in these tests should be governed by the principle of representative value, which will result in the entire series of tests covering all the chief lines of ap- proach to the mental powers under investigation. If the work is to be chiefly extensive the group of reagents should be large and homogeneous ; if the work is to be chiefly intensive the reagent group need not be so large but may well be made up of members varying between themselves as much as possible. By observing such guiding principles as these the results obtained will be increasingly representative, which means they will be possessed of increasingly general value. 5. This present investigation is undertaken in the belief that puzzles provide a relatively unknown but a very promising means of studying certain phases of the human intelligence. The investigation has been pursued in the further belief that the observance of such principles as have been briefly outlined above will lead to scientific and fundamentally valuable results. After a historical and critical review of work already done in this field, two series of puzzle tests are presented. The first series, which is somewhat preliminary, deals with the problem of the correlation be- tween puzzle learning and school intelligence. The second series is an intensive study by means of puzzles of a small but carefully selected group of subjects, with special attention to individual differences and methods of learning. CHAPTER II. HISTORICAL AND CRITICAL. i. GENERAL. There is exceedingly little to be said in a general historical survey of the use of puzzles as mental tests. And this for the good reason that puzzles have not been used to any considerable extent for this purpose. Outside the early but quite general discussion of Lindley and the later and careful research of Ruger, both to be noted below, we have nothing more than very brief references, in a few books on mental tests, to the possibility of using puzzles for this purpose. Chronologically Lindley antedates all others, but it may be well to glance at a few scattered references before noting Lindley more particularly. In the Binet-Simon tests, which first appeared in full in L'annee Psychologique in 1905, there are at least two tests closely approximat- ing if not including the puzzle situation. In test No. V for 5 year olds the child is so to place two separated right angle triangles as to form a square like the one shown him at the same time. 1 Again, in the second test for adults the two parts of a calling card cut diagonally are to be mentally pictured in an unusual given position. 2 These two tests remind us of the geometrical puzzles described hereafter. Partridge barely refers to the possible use of puzzles as tests but gives no particulars. 3 In his volume on Educational Psychology Thorndike places a figure looking like a maze puzzle. 4 This is but a single crooked path r however, (1) A Method of Measuring the Development of young children. Trans, by C. H. Towne, 1912, p. 24. (2) ibid, p. 60. (3) An Outline of Individual Study, 1910, p. 191. (4) Educational Psychology, 1910, p. 240. 10 within the two side lines of which the subject is to trace with a pencil a line of his own. The test here has no direct relation to the puzzle consciousness, but centers on steadiness of muscular control. The ir- regularity of the figure, however, suggests a maze puzzle, and may be taken as a harbinger of such. Several writers speak of the value of the ink-spot test — among them Plye. 1 The perceptual interpretation of these ink spots approaches certain types of puzzles ; but this is as much as can be said. Breitwieser refers to puzzle pictures but gives no details. 2 The method he recommends calls for a time record of how long it first takes the subject to recognize the hidden forms in the pictures, and for a further record of the time it takes to recognize these forms again after a space of 5 or 10 minutes. We find a bare mention of the jig-saw and other puzzles in Groszmann, for the purpose of testing judgment in the intermediate period. To this is added a reference to geometrical puzzles for the purpose of testing judgment in the advanced period. 3 The form board approaches the puzzle idea. This test is mentioned by several, including Whipple. 4 The first use of the form board as test- ing device is credited to Naomi Norsworthy, 5 and this particular piece of apparatus has recently been made the subject of an extended monograph by Sylvester. 6 The form board, however, can hardly be classified as a regular puzzle although it strongly suggests the puzzle form. An advance is registered by Healy and Fernald in their use of the com- bination form boards and picture puzzles, and of both round and square construction puzzles. 7 These latter are true puzzles, but are limited in that they are all built on the conception of form. These investigators (1) The Examination of School Children, 1913, p. 33. (2) Psychological Experiments, 1914, p. 113. (3) The Study of Individual Children, 1912, pp. 60, 64. (4) Manual of Mental and Physical Tests: Simpler Processes, 1914, p. 299. (5) The Psych, of Mentally Defective Children, Archives Psych. No. 1, 1906, pp. 25, 26. (6) The Form Board Test. Psych. Monographs Vol. XV, No. 4, 1913. (7) Tests for Practical Mental Classification. Psych. Monographs Vol. XIII, No. 2., 1911, pp. 11, 13, 14, 16. II made use of the puzzle box in testing children, 1 as Thorndike did in test- ing animals." The puzzle box used with children by Healy and Fernald could be opened only by a definite sequence of 5 or 6 steps. Here, of course, we again have a true puzzle. Without question the most suggestive work involving puzzles before the appearance of Ruger's monograph is that given at length by E. H. Lindley. 3 After an effort to define a puzzle and to classify puzzles (referred to above) Lindley reports the results from a rather elaborate questionnaire to which 556 replies had been received. By this method Lindley had sought information about the puzzle interest in children and adults. He concludes that there is in human nature "instinctive sub- strata of puzzle interest." The persons replying to the questionnaire revealed greatest interest in language and word puzzles, next in mechan- ical puzzles, and least interest in arithmetical puzzles. This order- of interest changes, Lindley concludes, with age, the more complex gradually driving the more simple puzzles from first place in interest. 4 Lindley exhibits his results by several tables and curves, and expresses himself as impressed' by the "persistence and tenacity with which a puzzle bids for attention and holds it." In addition to the questionnaire, Lindley put through a fairly ex- tensive experimental test. Using a unicursive or tracing puzzle of moderate difficulty he tested 500 school children and 300 adults. He found, among other things, that the average number of trials necessary in order to succeed did not vary greatly with the varying ages of the school children, 5 although there was an observable, tendency in the older children to analyze the situation and profit by errors. The objective record of the adults was supplemented by an introspective report. Lindley concluded that adults stud}'- the figure before proceeding as children do not. He attempted a gradation of methods of solving his puzzle, and adopted a threefold grouping. The children, he said, used almost entirely the sense-trial and error method, as animals. The most thoughtful adults, on the other hand, used what Lindley calls the con- (1) Ibid, p. IS. (2) Animal Intelligence, 1911. (3) A Study of Puzzles with special reference to the Psychology of Mental Adaptation. Am. Jour. Psych. VIII, 189' 7. (4) Ibid, p. 446; 453. (5) Ibid, p. 463. 12 ceptual method, 1 — that is, a deliberate search for underlying principles, with an attempt at analysis. Between these two extremes many used what Lindley calls the perceptual method : this is somewhat of a mixture of the other two, being an advance upon the sense-trial and error method but not making use of reason as in the conceptual method and attaining only a hazy idea of the relation. All told, Lindley's work deserves much praise. It broke the path for other investigations in an unworked but very promising field. Ruger acknowledges his indebtedness to Lindley, and evidence of the first writer's influence abound in the later investigator's monograph. To a care- ful consideration of this piece of painstaking research we now turn. 2. EXAMINATION OF DR. RUGER'S MONOGRAPH. The only serious attempt to work out the psychology of the puzzle is that recorded by Dr. H. A. Ruger in his monograph entitled "The Psychology of Sufficiency," 2 and to this we must give some attention. A. Objective Report. Dr. Ruger's aim in his investigation is to show by the use of puzzles how the human mind meets and masters a new situation. This general aim includes the testing of such mental powers as "the ability to size up a -situation, to eliminate the irrelevant, and to use independent judg- ment in that selection." It also covers the investigation of "the great role played by more or less explicitly conscious assumptions as to the nature of the problem" facing the subject in puzzle form. 3 His problem he sketches somewhat as follows : "The present study is an attempt, under simplified conditions and with special emphasis upon the motor type of process, to analyze human methods of meeting relatively novel situations and of reducing their control to acts of skill. It differs from previous studies in the learning process "in that the original situa- tion is distinctly of the problem type, and in that the acquisition of skill in the succeeding manipulations also involves the problem type of (1) Ibid, p. 471. (2) Archives of Psychology. No. 15, June 1910. (3) p. 4. 13 consciousness to a very considerable degree . . . the interest in the present study is dynamic rather than structural. It deals with the part which different sorts of thought processes actually play in the meet- ing of novel situations, and, as far as possible, with the conditions favoring the development of variations. The problem as thus treated may have lost somewhat in precision on account of the breadth of pro- cesses entailed, but it is hoped that there has been a corresponding gain in continuity and in the exhibition of organic relationships." 1 Ruger's method consisted in experimental work with twenty-seven subjects on a number of different puzzles, thirty-seven in all. Records were kept of the time taken to solve each puzzle at each separate trial, of the subject's oral or written introspective account as to how he solved the puzzle, of the experimenter's observation of the number and kind of moves made by the subject while working on each puzzle, and of all exclamations made by the subject during the course of each trial. These various records are presented in the form of tables, charts and graphs, and in the latter portion of the monograph many of their features are discussed somewhat in detail. Of the twenty-seven subjects thirteen were graduate students, seven had professional training in psychology, two were instructors in related fields, one was the laboratory mechanician and four were grammar and high school boys. All but the latter five had some special interest in psychology. Five of these in- terested subjects were women. 2 The procedure in these experiments is designated as "very simple." "The subject was seated comfortably at a table, on which the puzzle was placed. The puzzle was covered by a screen. After the warning signal, a starting signal was given, and the screen removed. When the manipulation for the given trial had been completed, the puzzle was im- mediately removed by the operator and prepared for the following trial. The subject was given no opportunity to examine the puzzle except during the actual trial. The number of trials for a given subject with a given puzzle varied from i to 1440. The standard number was 50 ... . The number of trials at a given sitting varied with the subject and the puzzle. The sittings were usually of an hour and a half in length. In some cases an entire series of 50 trials was completed in this interval. In others several periods were consumed in gaining the first solution." 3 (1) pp. 1, 2. (2) p. 6. (3) p. 3. 14 Most of the records are for one-way solutions, the puzzles being put together again out of sight of the subject. The instructions to subjects were very brief and general. In most cases the subjects were told no more than that some part of the puzzle was to be removed. They were, how- ever, asked to solve the puzzles as rapidly as possible. As a general rule a subject continued working on a given puzzle until complete skill was attained in its solution. Dr. Ruger's results are gathered under five heads, viz., Methods of Learning, Conditions of Efficiency, Transfer, Memory and Plateaus. (i) In summing up those results of his work which bear on methods of learning Dr. Ruger places chief emphasis on the discovery that there is no such clean-cut distinction between what have been called "animal" and "human" methods of learning. By the animal method has generally been meant the "trial and success" method in which success has been achieved by the mechanical stamping in of random or instinctively de- termined movements. The human method, on the other hand, has been described as one of "reasoning"— an understanding of the principles involved which results in learning by a single successful experience. To this Dr. Ruger replies that he finds frequent cases of the "trial and success" method well along in the course of a given subject's experi- ments with a given puzzle. There are various points of resemblance between the methods of these human reagents and the methods sup- posed by many to be confined to animals. These two methods, there- fore, do not come near exhausting the different forms of learning, but are best considered "as limiting members of a series of methods in which different types of analysis play an important if not a determining role." 1 (2) The conditions of efficiency center on the rise of variations in the methods of detailed procedure. Ruger finds, as others before him, that a sudden drop in the curve of learning follows a variation of method. Most of these variations first came unpremeditatively, but suc- cess then depended upon "the extent to which they were treated as hypotheses to be systematically tested with subsequent adoption or re- jection." 2 Physical condition was found to influence the occurrence of variations. Likewise attitude. Here Ruger points out that those reagents (1) P. 8. (2) p. 15. IS who were embarrassed by the presence of the observer, who "knew the an- swer," and those who were laboring under the notion that their self was being tested, were so self-conscious that, instead of centering attention on the puzzle, it was centered on themselves, with a consequent loss of successful variations of method. Moreover, variations were inhibited by false assumptions as to the method of solving a puzzle. The most successful way of breaking up these fixed assumptions was to analyze them out, criticize them, and then to reject them in search of new points of view. The shifting of assumptions, whether occurring by accident or purpose, often resulted directly in the solution." 1 Ruger concludes here that "efficiency was found to be directly dependent upon success in getting the most appropriate method or technique." 2 (3) Dr. Ruger uses the term "transfer" in a broad sense, including the general as well as the specific effects of an experience on subsequent experience. He found that "the value of specific habits under a change of conditions depended directly on the presence of a general idea which would serve for their control." 3 This general idea depended in turn upon precision of analysis. Often when two experiences had objective ele- ments in common there was no beneficial transfer because this similarity failed to be recognized. It was especially noted that previous mathemat- ical training exercised no observable effect on the dynamic constructive- ness called for by the puzzles. The greatest transfer was between simi- lar puzzles. Yet even here, an act of analysis was necessary in addition to the vivid image of the related puzzle. 4 (4) Memory was found to sustain a striking relation to continued analysis. In most instances "memory cues were promptly substituted for continued perception of relations." 5 If these memory cues were cor- rect much time was saved, but if, as frequently happened, the cues were erroneous much confusion resulted — the subject sometimes being in this way held for an indefinite period on the wrong line of procedure. The best success came to those subjects "who held their memories flexibly as hypotheses subject to rejection or revision as the case might be." fl (1) p. 18. (2) p. 14. (3) p. 19. (4) p. 20. (5) p. 87. (6) p. 20. 16 (5) As to plateaus, the experiments confirmed the generally accepted opinion that these are stages of stagnation due to the non-appearance of variations. Ruger finds plateaus due to several somewhat similar causes : (a) where there is a shifting back and forth between rival methods, (b) where "some feature remained intractable to control," or (c) where a method not efficient was nevertheless clung to. To get off a plateau a variation in method was necessary accompanied by its conscious use as an hypothesis. (6) In a later section of his monograph Dr. Ruger discusses results bearing on "Puzzle Material and Tests of Intelligence." He found th* ratio between the first and second working of puzzles by his subjects to average 7:1. Similar ratios for monkeys had been found to be 2:i, 3 and for raccoons 3 :2. 2 After discussing various possible methods of comparing intelligence, each of them subject to rather serious objections, he concludes that members of a group working with a single puzzle might be compared if the following factors could be either equated or controlled, viz., physical condition, degree of de- velopment of the fundamental function, concrete related knowledge, general methods, and mental attitudes. To Dr. Ruger one of the best ways of making such a comparison would be to train the subjects with a puzzle of a certain type and then to make a study of their ability to use this training in dealing with "a more or less thoroughgoing transforma- tion of the principle involved." 3 Dr. Ruger' s conclusions can probably be briefly stated in two divisions. The first has to do with the obtaining of efficiency. He gives it as his view that "the course of efficiency in the practice curve is largely a mat- ter of securing the appropriate variations and their conscious control." 4 He finds that "the drops in the curve depended. very largely on variations in method and their conscious use as hypotheses." 5 The rise of these needful variations was favored by such factors as a high attention level and the problem-attitude rather than the self-conscious attitude ; and the use of these variations as conscious hypotheses was obtained by a full control of all assumptions, which led to the constant trying out of all suggested steps of procedure and the continual search for new points (1) Comp. Neur. and Psvch. Vol. XVII, p. 211, L. W. Cole. (2) Am. Jour Psvch. Vol. XIII. pp. 126, 127, A. J. Kinnaman. (3) p. 47. (4) p. 86. (5) p. 20. 17 of view. The obtaining of skill was greatly facilitated by analysis, under which word Ruger includes the preeminently important power of getting "some mental grasp of the process as a unity." 1 The second division of Dr. Ruger's conclusions is related to subjective methods of learning and is to the effect that no one method of mental process predominates, nor can the processes of the problem-consciousness be reduced to two general methods, "trial and success" and "reasoning," but wide and at present irreducible variety characterizes the methods of mind by which different persons attack novel situations. B. Subjective Report. In discussing the quality and value of the work of Dr. Ruger it must first be said that if the form of his report had been somewhat different greater clearness might have resulted. For instance, his general con- clusions are difficult to locate. While the last chapter, that on Transfer, heads its final section as "General Discussion and Summary" a reading of this passage shows that almost the entire subject matter has to do with Transfer, which is only one of his several groups of results. One searches in vain for a succinct but comprehensive statement of general conclusions on the work as a whole. The nearest approach is Chapter II, General Statement of Results, but this is too lengthy for a statement of conclusions, besides it makes prominent several topics (Methods of Learning, Memory, Plateaus) which are either slighted in the general body of the book or are passed over in all but complete silence, and, further, it contains no reference to a topic to which he later devotes the whole of one of the six chapters of the book, viz., Tests of Intelligence. To mention these things, is, of course, but formal criticism ; nevertheless it represents a genuine reaction to the structure of the monograph as a whole. Can it be that the author in this particular case expects the reader to attack the monograph as a "novel situation" calling for the vigorous use of the reader's "problem-consciousness"? When, on the other hand, we take into consideration the amount of work done in obtaining data for the monograph there is abundant ground for admiration. The author speaks of 7000 different cases, and the records show that at least a few of these cases ran into the thousands of seconds and called for repeated sittings. All this represents an im- mense amount of energy concentrated on one very limited line of pro- CD p. 20. 18 cedure. Our only disappointment arises from the paucity of definite conclusions out of such an overwhelming amount of labor. Dr. Ruger's general method and procedure seem open to question at a number of points. As to the number of subjects used and their respective participation in the investigation, several things need to be pointed out. From twenty-seven subjects one can unquestionably discover much concerning the workings of the human mind if the work of these subjects is quite comparable. But there is no sufficient ground to be- lieve that this important condition was obtained in the investigation be- fore us. If this criticism is in error it is due in large part to the failure of Dr. Ruger to give anywhere a complete statement of just how many puzzles and what particular puzzles each subject worked with. Nor does he anywhere give complete tables of results. His discussion abounds with facts and figures, but we are given to understand that all these are selected. In many tables only a very few of the twenty-seven subjects have their records given, and in no table are more than nine of the entire twenty-seven shown at once. Moreover, none of the larger tables gives comparative records with an equal number of trials in each. Some of the subjects may show say fifty trials, others only half as many or less than half. Further indications are not wanting to sug- gest the partial incomparableness of these records. For instance, from some subjects the observer screened himself, but not from all. This necessarily affected both the subject's personal attitude and the experi- mentor's facility for observing. Moreover we are told that "in some cases the shift of assumptions was due to instructions given by the operator to the subject to critically define the assumption under which he was working, to seek out other assumptions, and to test them either in turn or in accordance with their probability." 1 Why was this ex- tremely valuable instruction given to some subjects at a critical moment but not to all? It surely produced decided differences in results. For such reasons as these we are unable to accept the records of the twenty- seven subjects as comparable. They did not all do the same puzzles, nor sit through an equal number of trials, nor were they all subjected to the same procedure. This being the case there seems to be good grounds for questioning the general representative value of the results outlined in the monograph under discussion. Twenty-seven reagents with records seriously incom- (1) p. IS. 19 parable can hardly furnish sufficient basis for results standing as rep- resentative of the human mind in general. This very point seems to be implicit in many of the author's statements. With commendable care- fulness he hesitates to make very definite statements, but tells us that such and such is "generally the case," "frequently found," holds "for the most part," and is "chiefly the explanation," etc. Such conclusions may truly help us on our way, but they disappoint our expectations from such a laborious and detailed investigation. In one sense the best sup- ported conclusion of all seems to be that which declares that the mental processes under investigation appear to be extremely varied. This is surely the direction in which the definite data the author has chosen to give us point. Might it not be, however, that even this conclusion does not represent the actual facts of the case? Would not a more repre- sentative or, on the other hand, a more homogeneous group of reagents, handled in such a way as to make all their records thoroughly comparable, have put us on the trail of some underlying mental unity in the problem- consciousness, or at least have brought us up to a few great types of problem-functioning? Such seems most reasonable to suppose. Such kind of a study would be greatly facilitated by a series of preliminary cests to free the problem from excrescences and to block out the main line of work. The results of such a study would be most admirably made secure by a careful set of control-experiments. The possibilities of valua- ble discovery from such a study would, moreover, be decidedly increased if, instead of having all the work done by one method, such as the no- instruction procedure by which alone all of Dr. Ruger's subjects worked, there should be given a careful selection of differing methods, all other circumstances involved being rigidly kept the same. As to Dr. Ruger's plan of keeping a record of false moves it is ex- tremely improbable that it amounted to anything definite. With some very simple puzzle forms a correct record of this nature might be kept, but it seems practically impossible to record all false moves when the puzzles are complex and when many of them are in three dimensions. This matter is dealt with in the report of original investigations found later in this book. It may be sufficient here to say that to know by watching what are truly false moves, to know when to count a partial move false, to know when to make allowance for moves inhibited al- most as soon as begun, to know how to divide up a series of connected motions into a definite number of moves, to know just when to count a move false which, if having other antecedents would not be false, to be able to act promptly and unerringly along all these and similar lines, and then to be able to keep an accurate record and for all sub- jects a full and complete record of such observations, giving the same value to the same form of move among all subjects alike, this is surely expecting the impossible. If, on the other hand, the record of moves is not kept as carefully and fully as here suggested it becomes merely a jotting of selected and partial observations and has no substantial scientific value. Here again Dr. Ruger seems implicitly to deny the value of his own method, for in discussing the experiments he almost never makes any reference to this record of false moves. Another item is the record of remarks or exclamations made by the subject in the course of his work on a puzzle. There is no doubt that occasionally a gleam of light may come to the observer through such remarks, that, is, if they are made. Here we are dealing with a matter in which personal differences function most directly. Some persons will work long in absolute silence, others will be saying things most of the time. This feature of course makes such a set of records entirely in- comparable. It we overlook this objection and take the record of each separate subject as quite complete in itself, it is extremely question- able whether few remarks made by a subject will convey any informa- tion, not immediately obtainable also from an observation of his move- ments made in handling the puzzle. For instance, when we see a subject with sudden eagerness make two or three swift, correct moves which solve the puzzle, we do not gain any information by hearing him exclaim at the beginning of this spurt, "Ah, now I have it!" We could tell that from h's face, from the swiftness and directness of his moves and from his immediate success. In short it is exceedingly ques- tionable if the explanations from those few subjects who made them re- veal anything more than states of mind — not mental processes. But it is processes we desire to study, and, furthermore, the states of mind are about as fully disclosed in other ways. Along with the two foregoing records Dr. Ruger used as a basis of his discussion a written record of each subject's introspective report of his mental activities in solving the puzzle. This was either written by the subject himself at the conclusion of the sitting or was dictated by him. This record ought to prove the most valuable of the three. It is not, however, free from serious objections. If in order to obtain a full record the observer urged the subject to watch his own mental activities and report thereon in detail either during the course of the 21 sitting or at its close, this could not fail to divide the attention of the subject. What time and energy he spent in trying to catch his mental processes was just so much attention taken from the puzzle. This of course would affect his solution of the puzzle. In tead of having an un- broken puzzle-consciousness, upon the need of which Dr. Ruger rightly lays much emphasis, the reagent would alternate with his puzzle-conscious- ness an introspective-consciousness or a report-consciousness. This would seriously interfere with the mental attack on the puzzle, the nature of which mental attack the experiments were aimed to disclose. On the other hand, if nothing was said to the subject about a forthcoming in- trospective report but he was allowed to lose himself completely in the problem of the puzzle in his hand (which is without doubt the better way), then how complete or correct an introspective account can we look for when it is unexpectedly called for at the close of the sitting? As is generally acknowledged, the so-called introspective report would be noth- ing more than a memory report. If the process of solving the puzzle had been long, being made up of an immense variety of moves, hypotheses and trials, some correct, some false, could we expect the sub- ject to remember enough of all this process to make his report any- thing like complete or even comprehensive? Assuredly not. Pure in- trospection is a self-contradictory notion. Memory of mental states and experiences is likely to be weak and incomplete in direct proportion to the degree to which the object of attention with which these particular states and experiences are associated is objective. Now few things could be more objective than a concrete puzzle, made of wire or wood, held in one's fingers, and to be taken apart by the fingers. To the degree to which the subject gave his genMm^ and undivided attention to attacking the puzzle, which was what h#^as desired to do, to that degree was he rendered incapable of giving a correct or complete introspective re- port. In other words these two parts of the method are mutually de- structive: if the subject gives that kind of attention to his puzzle which is necessary in order to make his attack upon it of any scientific value, he loses his grip on his inner processes and cannot report them satisfac- torily; if, on the other hand, the subject is able to give a full and de- tailed introspective report it shows that he was watching his subjective conditions instead of attacking the puzzle, and consequently his report has no value as a record of the puzzle-consciousness. We may wonder if once more the author of the monograph does not give implicit recognition of the reduced value of his own methods — 22 this time as to the introspective records. For at several important points in his discussion he abandons the introspections of his subjects and with a sense of decidedly greater certainty he records his own introspections. For instance, we read : "As stated above, the writer finds the process of analysis, so far as his introspections have gone, to be of the same sort whether occurring in the field of perception or of imagery. He found great difficulty in the attempt to image tridimensional transformations in advance of any movement, but, on the other hand, he found at certain stages a decided help in withdrawing the puzzle from sight or in clos- ing his eyes and then attempting to work out the relations involved." 1 Again we read : "These suggestions are based directly on the writer's introspections, but are supported by occasional remarks of subjects to the effect that they seemed to see the relations involved in solution directly, and without the use of imagery." 2 Here we have the studied introspections of the author given — one who was not a subject, one who could not very perfectly bring himself to the puzzle-consciousness which the monograph studies because he knew how to solve the puzzles and was therefore unable to attack them as were those to whom they were puzzles indeed. This does not mean that Dr. Ruger's own introspections have no value, nor that they are entirely out of place in a discussion of the work of other subjects, but the injection of his own introspections makes easier, to say the least, the suggestion that he realized to a certain degree the inadequateness of the introspective reports of his subjects. These reports from subjects are by no means to be disregarded. Many of them are suggestive and some of them enlightening. Yet the value of all introspection must be assigned in full light of the above remarks upon the difficulty of obtaining such records anywhere near complete, comprehensive or representative. If introspection is ever to be given a high value it is under circumstances when the mental condition can be caught on the wing, so to speak, when, by a sudden change of attention- focus, the mind can catch a glimpse of the fleeting form of its ante- cedent state. Of course even this after all is but memory, but it is ex- ceedingly recent and fresh and is therefore likely to be vivid and correct. This practice requires some experience and skill. Now it is obvious that when one is pondering hard over a puzzle he cannot swing his attention suddenly upon himself every few seconds. This would fatally interfere with the normal process of attacking and solving the puzzle. While (1) p. 35. (2) p. 13. 23 it may be granted, then, that under certain especially favorable conditions introspection may yield highly valuable results, it ought to be acknowl- edged that these favorable conditions are emphatically precluded by all genuine states of puzzle-consciousness. This criticism of introspection deals of course only with free or uncontrolled introspection, for this is the kind of which Dr. Ruger endeavors to make use. In his outline of method Dr. Ruger places almost all his emphasis up- on the results to be obtained from the three records above discussed. His practice, however, seems better than his theory, and we find throughout the book many tables and graphs based entirely on another factor, viz., the time-element. In giving such a large place to records of time in his discussion the author may tacitly be admitting the final insufficiency and unsatisfactoriness of his records of exclamations, moves and introspections. As a matter of fact the time record of these twenty-seven subjects appears to be the only record of their puzzle- working which is equally applicable to all, which is objective and there- fore complete, and which, at the same time, is to the last detail com- olete. It is wise therefore to make this record the basis of considerable discussion. In fact it is doubtful if very exact knowledge of the pro- cesses of the mind can be obtained by any form of subjective record. The very purpose of puzzle tests is to seek for satisfactory objective tests and evidences of subjective conditions. The chief value arising from the introspective reports in this mono- graph is to provide an explanation in mental terms of a successful work- ins: of the puzzle. This use of the introspective method is valuable in Dr. Ruger's work, providing we are ready to take the risk of accepting as reasonably complete and correct the subjective reports made by the reagents at the conclusion of each sitting. Dr. Ruger's numerous quota- tions from these reports seem to justify one of his main conclusions, namely, that efficiency arises in connection with the adoption of new as- sumptions and their use as working hypotheses. Another valuable and well substantiated point is that having to do with the distributing effect of the self-consciousness rather than the problem-consciousness. This result was reached through observation on the part of the experimentor, compared with the time records, and has nothing to do with introspection. There remains what is in some respects the most fundamental ques- tion of all. It has to do with the author's aim. As previously stated, these experiments were devised and put through with the purpose of dis- covering how the human mind attacks and masters a novel situation. 24 From this we understand that Dr. Ruger uses puzzles as representing novel situations in general, of all sorts and particular conditions, just so long as they are novel and must be attacked by the human mind. Now the question arises, is this a safe assumption? In other words does the method, in this case, agree with the aim? Before one can accept this general representative value of mechanical puzzles he must first clear up several perplexing phases of the situation. For instance, while puzzles unquestionably present novel situations, these are artificial situations, and are from the first recognized as such. How close does this come to the novel situations of ordinary life, which are never artificial? Again, puzzles admit for the most part of only one way of solution, while to many of the problematic situations of life there is more than one way out. Does this feature affect the representative value of the method? Further, with puzzles one is dealing with dead matter, which is ever the same, which will not yield nor change its form. But in the novel situations of life one almost always finds other human personalities as part of the factors of his problem, and these factors need to be handled in quite a different way from unresponsive, unyielding material things. The right kind of dealing with the personal factors opposing a given individual's freedom will result in their dis- appearing as parts of his problem, but the wrong way of dealing with such personal factors will only increase the seriousness of their opposi- tion and thereby render the individual's problem all the more complex. There is nothing in mental puzzles which presents such a delicate prob- lem as this. Again, when one handles a puzzle his problem is to change the puzzle to fit him, the person ; but when one meets a novel situation m life it is quite frequently a situation of such proportions that he can- not alter it materially but must on the other hand change himself to fit the situation, and by thus doing he solves his problem. And onc e more, the subject knows in advance that to every puzzle placed in his hands there is a complete solution, and he knows that the experimentor is fully acquainted w : th this solution. But many of the novel situations in life cannot be faced or attacked with such certainty. We often question whether there is any satisfactory solution to many of them ; rather they threaten to crush us, and we attack them in quite a different frame of mind than that with which we sit down to work out a harmless puzzle which a friend has already solved before us. Does not this affect the mental processes involved? Now, before one can accept what seems to be Dr. Ruger's underlying 25 assumption in this puzzle test the above questions must at least be taken into careful consideration. There is, to be sure, the element of novelty common to both the puzzle and the problem-situation in general life. This is quite fundamental to both, psychologically speaking, and is good as far as it goes. But in the light of such considerations as those just outlined, and of other similar ones that might be urged, there is difficulty in finding oneself ready to agree to the proposition that the way the human mind attacks a mechanical puzzle is representative of the way it meets and masters any life situation which is conceived as presenting some sort of problem. If this objection to Dr. Ruger's assumption were found to be well grounded it would not follow by any means that the value of his mono- graph was therebv destroyed. There still remains suggestive results, quite probably true. The damage wrought by the self-consciousness, the great gain resulting from a deliberate analysis of a novel situation, the advantage of being able to see a complex situation as a unity, the in- creased probability of a successful solving in proportion to the rise of the attention-level, and the widespread variety of mental activities among individuals —these and other results previously indicated give positive worth to the monograph and help make it a valuable piece of what after all must be called pioneer work in this promising field of investi- gating the actual processes of human intelligence. 26 CHAPTER III. First Experimental Series. THE CORRELATION BETWEEN PUZZLE LEARNING and SCHOOL INTELLIGENCE. i. INTRODUCTORY STATEMENT. As stated in the General Introduction, the purpose of this investigation is not to study intelligence in general, nor even a test of intelligence in general. Our problem lies in the field of the tests of intelligence, but is narrowed down to the one particular inquiry, viz., is there any determin- able correlation between what is called school intelligence in children, and their ability to solve simple mechanical puzzles ? All other purposes have been disregarded and every effort has been centered on this one definite point. The term "Mechanical Puzzles" is used to distinguish the puzzles ex- perimented with from mathematical puzzles, verbal puzzles, or various other forms, of which there are many. The puzzles here used belong to the class of simpler mechanical puzzles, chosen thus for the reasons given below. In view of the preceding historical and critical section, it may be well at the outset of this report of new work to indicate in brief form a number of the particulars in which the present investigation has sought to avoid errors or weaknesses appearing in previous work of the same nature and has endeavored to make the results herein recorded safe and 27 sure. Let it be said, then, that the present investigation has aimed at cer- tainty and value in the following ways, among others : (i) There has been no changing of experimentors during any series; all the tests in a series being given by the same experimentor. (2) All the tests have been applied individually, and not to children in groups or roomfuls. (3) All the tests have been given in private. (4) During the course of every test the experimentor has allowed himself to be taken up with no other matter which would in any degree distract his watchful attention from the reagent. (5) Even the room in which the tests have been given has been stripped as bare as possible of all possible sources of distraction. (6) Every test has been given to all students in precisely the same manner, down even to the directions given for working the test. (7) The children have all been of the same social status. (8) The children have all been students in the same school. (9) The children have been students in this school at the same time and were tested at the same time. (10) All features of sex and age have been carefully worked out as will appear below. (11) Both Spearman and Burt make something of the value of zeal in connection with such experiments. In the tests herein recorded, the zeal was good throughout. The students tested were, among other things, given exemption from a decidedly unpopular Study Hall. The students tested were, moreover, permitted, within certain limits, to choose their own time of day for taking the test and obtaining this ex- emption. In such ways as the above the reagents were all as nearly alike as possible, except in the factors investigated. (12) Tests given were all new, never being used before by others in this way. (13) The tests were few, four in number, and were all of the same nature. (14) The apparatus was simple and uncomplicated, attracting no at- tention to itself. (15) No previous practice was given in any instance, thus excluding this feature which often introduces personal differences that would not otherwise function in this kind of experiments. (16) Very careful mathematical procedure has been observed through- 28 out, not only are all results worked down to a definite figure by the most approved methods, but in every case mean variation or probable error has been given. (17) While the tests have involved of necessity sensori-motor ele- ments, they have been of such nature as to place the emphasis upon the purely intellectual factors involved. This will appear more particular- ly in the detailed descriptions which follow. 2. REAGENTS. The tests herein described were made on students. These naturally fall, by reason of differences in age and mental maturity, into several large groups. Group I, the smallest group, consisted of nine adults (five men and four women), all near thirty years of age and all engaged in advanced study of one kind or another. Very little use was made of this group, but it was of service in determining averages in the preliminary results. Group II, was composed of thirty-eight persons, twenty-eight young men and ten young women, all students whose educational progress had been arrested, and who, at ages averaging about twenty-two, were en- deavoring to supplement their early schooling by two or three years of special study, part of it Biblical and looking toward some modest form of religious work. These students were in no sense below the normal in the development of general mental functions ; there were no cases of abnormal retardation ; only they had not had thorough earlv training. This group also was used only in results having to do with averages. Group III, was the largest and by far the most important group for our purposes. It was made up of fifty-eight boys and forty-eight girls, one hundred and six in all, being students in the seventh and eiehth grades Grammar and the following years of High School. Some of the members of this group did not take all the tests, although many of them did. In calculating results in terms of correlation coefficients members of this group were divided, selected and rearranged in smaller companies to meet the conditions involved. In stating the results the number of reagents involved is always given. It will be noticed that a number of the recorded results are based on smaller grouos taken out of this large company on a basis of uniformity in age or sex or both. 29 Group IV, is a little-used grouping of sixteen college students, eleven boys and five girls. This group appears only in the results in averages, which are only preliminary to the chief results of these experiments. Concerning all the subjects of these tests, it may be said that they were attending the same group of institutions, were all personally known to the writer and were all tested at practically the same time. 3. APPARATUS. All the tests were made with extremely simple apparatus. This method represented a conclusion reached after a number of preliminary ex- periments. At first six or eight mechanical puzzles of varying degrees of difficulty were presented to about twenty high school students. But it required so much time to solve these, when they were solved at all, that it soon became evident that the result sought by this particular series of tests could not satisfactorily be reached in this way. For the same reason fairly complicated samples of geometrical puzzles were abandoned, and it was finally decided to use puzzles which practically every student could solve in a reasonable time (say fifteen minutes), but which none could solve without some degree of diligent mental application. The puzzles used were as follows : 1. The Bird Puzzle. Cardboard pictures of two birds, a vulture, S l A x 6 inches, and a peacock, 5^4 x &/ 2 inches, were cut into five and seven cross-wise strips respectively, all the strips being of equal width. These twelve strips from the two pictures were then mixed, placed face downward, in a single pile and handed to the reagent to be matched. To insure the greatest uniformity of conditions the twelve strips were always piled in the same order — that indicated by the left hand figures on accompanying illustration (see Plate I, No. 1), number one was at the bottom of the pile and number twelve at the top, all face down. The reagents' task was to piece together in as short a time as possible the complete pictures of the two birds. The fact that there were two birds instead of one complicated the task somewhat. Nevertheless this was by far the simplest puzzle. 2. The Match Puzzle. Seventeen matches were arranged in six con- tiguous squares (see Plate II, No. 1). The problem was to remove only five matches and leave intact three of the original squares. 3. The Geometrical Puzzle. A piece of heavy plain cardboard 4^4 30 inches square was cut as indicated in Plate II so that the pieces could be readjusted in the form of a cross with arms 6^ inches across (see Plate II, No. 2). The parts were first placed in a cross form and the reagent was required to rearrange them into a square. One side of the cardboard was slightly tinted to keep the reagent from turning any piece wrong- side up. 4. The Maze Puzzle. A maze was marked out in heavy black lines and placed under a ground glass cover in a wooden frame (see Plate I, No. 2). Starting from the arrow the reagent was to trace a continuous line through the open spaces to the dot in the center of the maze. It will be seen that very frequent choices have to be made, the number of choices depending upon the route taken. This particular maze was adopted after experiments with more complicated mazes as well as with simpler ones. Recent experimental psychology is demonstrating the fact that in most cases the most significant and trustworthy records of the deepest mental processes can be obtained by extremely simple apparatus just as well as by complicated apparatus. In fact the simple apparatus has an advantage over the more complex in that irrelevant but disturbing factors, some chiefly mechanical and some chieflv psychological are eliminated and the mental processes are thus allowed "to function all the more naturally. 4. CONDUCT OF THE EXPERIMENTS. All the tests involving correlation were given in the same room and all within the limit of the same three or four days, with the exception of the repeated tests mentioned below. The room was of small size but fight, a pleasant corner room on an upper floor of the school building The room was unfurnished except for several tables and chairs All the tests were in private; the reagents were admitted to the room one at a time. No one was in the room with the reagent except the ex- perimenter. Silence was carefully observed as soon as each experiment was begun. While the reagent was at work the experimentor was generally busying himself figuring at a separate table or standing with his back to the reagent looking out of the window. The tests were taken voluntarily, and all the reagents were particularly requested to say nothing at all to anyone else about the experiments 31 until the sittings were all over. There is reason to helieve that this request was carefully honored. Reagents were frequently asked, for instance, before undertaking their work, whether any other student had said anything to them about the tests. Moreover it was observed that those coming later were not able to do the tests any more rapidly than those who first undertook them. When a reagent entered the room he was asked to seat himself at a table. He was told in a few words what was expected of him, em- phasis being placed upon the necessity of working the puzzle in as short a time as possible. The material was then put into his hand and his time was taken with a stop-watch. When he had worked the puzzle he said "Done" and his record was closed on the stop-watch. He was then, after a moment, moved to another table and started in the same general manner on the next puzzle. The puzzles were given in the following order: Bird Puzzle, Match Puzzle and Geometrical Puzzle. The Maze Puzzle was given on a later day. Instructions to reagents were practically as follows : Bird Puzzle. "I have here two pictures of animals cut up into strips. I wish you to take the strips and piece together both pictures as soon as possible. Just as soon as you have finished, say 'Done.' The point here is to have you do this just as quickly as possible." The reagent was then handed the twelve strips of the bird puzzle piled together face down- wards, and always arranged in the order indicated above. Match Puzzle. "Under this paper you will find seventeen matches arranged in six squares. I want you to remove five of these matches, without touching the other ones, so that you will have left three of the squares unbroken, but not more than three. When you finish, say 'Done.' You are to do this just as quickly as possible." A paper was then re- moved showing the seventeen matches arranged on the table. Geometrical Puzzle. "Under this paper you will find several pieces of cardboard arranged in the form of a cross. I want you to rearrange these pieces so as to form a perfect square, using every piece. Do it just as quickly as you can, and say 'Done' when you are through." The puzzle was then uncovered and the time taken. Maze Puzzle. "Here is a maze. You are to start your pencil here (showing him) and trace an unbroken line through the maze until you reach this center. As soon as you have found your way clear into the 32 center from the beginning, say 'Done.' Now do this just as rapidly as you can." The reagent's time was taken when the puzzle was handed him. In such ways as these an effort was made to standardize all condi- tions and to avoid the influence of irrelevant factors. Occasionally reagents would ask a question before proceeding with their work, but not often. ! ; ! Records were kept in a card-filing system, one card to each reagent. On each card was entered the name, sex, age, and general grouping of the reagent, and his time on every test he took. On the same card was also entered by number his rank or position in the General School, the Mathematical and the English rating. When anything went wrong in such way as to make questionable the value of the record, that particular record was cast out. On these record cards all lists and computations were based. 5. METHOD OF OBTAINING SCHOOL RATING. " Since for the larger part of the tests the school rating of each reagent or group of reagents was one of the two terms between which correla- tion was sought, it was evident that care needed to be taken in procuring the figures representing this rating. The members of Groups I and II and IV were not given a school rating, but with the principle group (III) the rating was carefully worked out by combining several sets of data. First of all the monthly grades of all studies of every student for seven months of the same school year, the year during which these tests were made, were obtained from the regular school records, and these were averaged for each separate student. With this result was averaged, at a value of one-fourth, the average of all grades made by these students in the January term examinations. The studies thus counted in were, Foreign Languages, English Literature and Composition, Mathematics, Science and History. At the same time the teachers were asked to make lists of the students, graded as to general intellectual acuteness. The teachers were warned against basing their classification upon the students' general knowledge, which might have been accumulated in some cases only by very long and persistent study. The teachers particularly were asked to list the students as to their ability to see a point, to apprehend, their readiness to understand and to master new intellectual forms or content. The 33 teachers were asked to turn in their lists after working them over care- fully and regularly and in absolute independence. They were requested not to discuss this matter with one another in any form until the lists were all ready. These lists the Principal went over carefully, here and there, yet only in a very few instances, feeling obliged to alter the position of a student in any of the lists. After this a composite list was constructed which represented the average teacher-judgment as to the relative standing of each pupil in mental acuteness. There now were two general lists — one showing the grades of all the students as based on daily work, monthly tests, and one half-year examination; the other showing the consensus of judgment among the teachers as to the relative intelligence of the students. The remaining step was to combine these two listings of the same students. This resulted in one list, representing the average of these two, and in this list every factor used for determining the rating of a student played its part. This final list was designated School Rating, and is used as one term of the correlation in all comparisons making use of a student's intelligence as shown by his standing in his studies in general. It will be noticed that in a number of instances experiment results were correlated, not with the student's school rating in general, but with his school standing in a particular subject, mathematics or English. In such cases the school rating listing was of course not used, but a special listing which was made up of the student's record in that particular sub- ject, as indicated by an average of his daily work and monthly grades for seven months with one term examination. In these instances teach- ers' est : mates were not ascertained. 6. METHOD OF CALCULATING RESULTS. Nearly all of the results in this paper are expressed in the form of the correlation between two sets of measurements, the measurement of school ability on one side and the measurement of speed in working out a par- ticular puzzle on the other. The resulting figure expresses the degree of correlation in a given group of students between these two measure- ments; jt shows to what extent the two abilities tend to agree. This figure is called the correlation coefficient. The particular formula used in obtaining this correlation is the one 34 first suggested by Spearman in 1904, 1 later simplified by him and sup- ported by abundant mathematical proof, 2 and a few years later carefully tested with satisfactory results by Burt. 3 That some such precise method of ascertaining the exact relation be- tween two series of figures is a great improvement on the older ways is apparent almost without proof. Before a method of calculating cor- relation was worked out investigators in the field of psychological and related research could do little more than scan carefully the two series and endeavor to form some general impression of their relation to each other. Such lack of scientific method in securing results undoubtedly contributed much to the slow progress and frequent contradiction in the published results of research in psychology, not to speak of other de- partments of investigation. It has been demonstrated repeatedly that no amount of scrutiny of two series of figures can assuredly bring to light the presence or absence of definite correlation between them. Many times an array of statistics has been made the basis for a claim of overwhelming proof of correlation when a little actual figuring showed none to exist whatever. And on the other side correlation has frequently been altogether denied between two series which were found, upon calculation, to be very closely related. The crude method of dealing in general averages and the scarcely less crude method of arbitrarily dividing a series of results into such general groups as high, medium, low, or as good, fair, bad, and then comparing these artificial groups from one series with similarly determined groups from another series, have been able to give only approximate results in the most fortunate cases and misleading if not false results in the less fortunate cases. It was the realization of the utter unscientific character of such methods that led Bravais, Galton, and Pearson to devise what came to be general- ly called the "Standard Method" of obtaining a correlation result. This method, while it gave the desired preciseness, yet entailed such involved and laborious calculations, that it was highly desirable to work out some simpler though equally efficient formula. This was done by Spear- man. Spearman's method possesses the valuable features of being scientific, mathematical, simple of computation, of furnishing a formula applicable to many different kinds of results, of having a definite expression for (1) Amer. Jour. Psych. XV, pp. 72, 252. (2) British Jour. Psych. 1906, p. 89. (3) British Jour. Psych. 1909, p. 106 ff. 35 perfect correlation and a definite expression for the complete absence of correlation, of providing adequately for a valuation of probable error, and, finally, of being easily convertible into the coefficient of the "Stand- ard Method." A fundamental feature of Spearman's "foot-rule" for measuring cor- relation is the arranging of each series of values in a rank. One series may display results in special terms, another in time terms. Ordinarily these two would be incommensurable. By arranging each in a rank, however, it immediately becomes possible to compare one with the other. Absolute incommensurable quantities are converted into perfectly com- parable ranks. The highest result in the series is placed at one end of the list, the lowest at the other end, and each of the others in its proper rank between these two extremes. A given figure thereby loses, for purposes of correlation, its absolute quantitative value and takes on a relative value expressing its position in the rank. This procedure of course sacrifices for the time being a certain precision of quantitative information, but it makes possible the finding of an exact coefficient of correlation between two series otherwise mathematically unrelated. The possibility of exhibiting a precise relation between two such series is of immense value to experimental psychology. Since Spearman's method is the method by which the chief results in this investigation have been calculated, it will be well to explain the process, and in doing this, to make use of a simple example. Let us suppose that it is desired to measure the relation between keenness of hearing and tactual sensitiveness in a group of fifteen persons, A, B, C. . . .0. After experiment has determined the figures which represent each one's keenness in these two respects, a table is arranged as follows : 36 Example of Spearman's Foot-Rule 1 11 REAGENTS RANK FOR RANK FOR GAIN OF HEARING TACTUAL II SENSITIVENESS OVER I A 10 II B II 9 2 C 3 2 I D 12 12 E 1 I F 4 6 G 9 10 H 2 3 I 8 8 J 14 15 K 6 7 L 15 13 2 M 7 5 2 N 13 14 O 5 4 I 15 8 Here A, B, C, etc., represent the different persons tested. In column I the figures represent the position of each person as arranged in a rank based on the results of the measurement of keenness in hearing; the best stands at 1, the poorest at 15. Column II represents by figures the position of these same reagents when arranged in a rank based on meas- urements of ability to distinguish two points placed near each other on the skin. Here the person showing the greatest discrimination (short- est distance between points) stands at 1, the reagent at the other extreme is listed as 15. In the last column the figures indicate how many points in rank any reagent gained in touch over hearing. Spearman's formula is R=i — — 2. . R=;correlation coefficient. 2p- M s ' the sum of the gains of one rank over the other — in our example, 8. M denotes the sum of the gains to be expected by mere chance. This ?,7 equals where n is the number of cases in the double series, in our example, 15. Applying this formula to the above example we find U=37-33 which gives us R = i— -— =—— = 0.71 +. Now 1.00 would show perfect correlation, while 0.50 is considered a high correla- tion. Such a result as 0.71 therefore would be unusually high. But this result as it stands cannot be accepted as certain and final. The process must be tested for probable error. Spearman has demon- 0.43, strated 1 that the probable error may be taken as being — = n again \ n being the number of cases. Working this out from our example we have 0.43 0.43 n ,' . vl! = wr = - 114 Now as to the value of the coefficient of correlation and probable error, as found by this method, Spearman declares that when a high correlation (R=o.5o or over) exists between two series, about a dozen cases are quite sufficient to prove this existence. The lower the correlation the greater the number of cases necessary ; as low a coefficient as R=o.20 could not be proved with less than about one hundred cases. The value of even a few cases when the correlation is 0.5 or above to be borne in mind when the results of the present investigation are ex- amined below. As to the probable error, Spearman shows that it must be no larger than one-half as great as the correlation coefficient if the latter is to have any scientific value. Good evidence of the correlation calls for a probable error of only one-third or less. When it becomes one-fifth or less of R we reach a perfectly satisfactory demonstration. In view of these values our sample case is unusually strong, as it shows R=o.7i with a probable error of only 0.114. The coefficient results given for the investigations reported in this paper are all accompanied by an indica- tion of the probable error involved. 7. DESCRIPTION OF RESULTS. Result 1. The reagents were divided into four groups representing different (1) British Jour. Psych. 1906, p. 106. 38 stages of mental development. Group III comprised 99 Grammar and High School students ; Group II, 38 older students whose earl} educa- tion had been cut short; Group IV included 16 college students; and Group I comprised 9 teachers, all below thirty-five years of age. All these persons were tested on the bird puzzle, the match puzzle and the geometrical puzzle, and the results for each of the four groups were calculated as to the average time, the median time and the mean variation from both the average and the median. This result was of course some- what preliminary, dealing in averages and not correlations. The intel- lectual homogeneity of each of the four groups was, however, to the personal knowledge of the writer, quite satisfactory, so that the results had some value after all. TABLE 1. Bird Puzzle. Group Reagents Av. Time M.V. Median Time M.V. Seconds Seconds III 94 95-58 42.16 75.00 35-90 II 38 95-42 32.15 86.00 30.73 IV 16 76.19 22.68 70.00 21.56 I 9 61.77 1500 60.00 14.77 These results are interesting in placing both in average and median time Groups III and II, both without advanced education, at the bottom of the list, while College students come next, with teachers safely in the lead. In both instances the academy students were most scattered, as shown by the mean variation, while the decidedly reduced mean varia- tion of the group of teachers increases the value of their record. TABLE 2. Match Puzzle Group Reagents Av. Time M.V. Median Time M.V. III 44 242.38 165.43 226 . 00 165. 11 II 19 214.00 126.68 201.00 119-58 IV 16 288.16 206 . 00 157-00 189.81 I 9 177.66 196.00 107.00 123.77 The general order of the bird puzzle is carried over into these results from the match puzzle. The lowest two are the untrained minds, while, 39 as before, the teachers are in the lead, in this instance even more so than before. TABLE 3. Geometrical Puzzle Group Reagents Av. Time M.V. Median Time M.V. III 94 120.49 91-38 68 80.78 II 38 55-8 31-55 48 30.47 IV 16 66.31 5I.3I 45 39-56 I 9 85.11 H4-33 222 72.00 In this experiment, the Academy students are again at the bottom and the college students next to the top. In the average time we find Group II in the first place and the teachers in the third, but the unusually large mean variation of the teachers' record tends to reduce the significance of this. In the median result, however, the teachers are far in advance of all, as before. So far as the general results of this experiment go, they tend to show that reagents with the least mental development are slowest at the tests, while those more advanced (college students) Come next, and those most highly developed (teachers) are in all but one instance most rapid at the puzzles. Result 2. Here the reagents were put into three groups on the basis of age, the youngest (Group 1) comprising the Grammar and High School students; the oldest (Group 3) the teachers, with the College and other young men and women in the intermediate class (Group 2). All three puzzles were worked with, and averages and medians calculated as in Result 1. TABLE 4. Bird Puzzle Group . Reagents Av. Time - M.V. Median Time M.V. I 94 96.58 42. 16 75 35.9 H 54 90.64 29.79 80 29.16 III 9 61.77 15. 60 14.77 Here the average shows skill to increase with the age of the groups; 40 the median puts the youngest ahead of the middle class, but the oldest ahead of all. TABLE 5- Match Puzzle Group Reagents Av. Time M.V. Median Time M.V. I 44 242.38 165-43 236 165. 11 II 3i I83-93 121.00 149 in. 84 III 9 177.66 196.00 107 123.77 These results worked out with complete regularity, in both median and average, to show an increase of skill with the increasing age of the group. TABLE 6. Geometrical Puzzle Group Reagents Av. Time M.V. Median Time M.V. I 94 120.49 9I-38 . 68 80.78 II 54 59-i 35-34 46 33-13 III 9 85.11 114.33 22 72.00 Here, in the average the tables are turned upon the middle and oldest groups, but in the median the results indicate a substantial gain in skill with advance in the age of the group. All of Result 2, dealing only in averages and median and being based chiefly on differences in age, contributes but indirectly to our particular problem. This group of results goes to show, however, that age does not appear as a serious disturbing factor. It is worth noting as a partial explanation of the close identity between Results 1 and 2, that while in one the grouping is on the basis of intellectual development and in the other on the basis of age, yet for the most part these two features coincide in the subjects experimented upon, so that there was not much change of personnel in the different groupings for these two series of computations. Result 3. We now pass on to the more satisfactory mathematical methods in which the results are given as correlation coefficients. Result 3 expresses the correlation between the general school rating of 51 academy students and their rating on the bird puzzle. It gives us R=.62±.o6. This is 41 an unusually high correlation with an extremely low probable error, and thus it constitutes a significant result. Result 4. Thirty-three reagents, High School students. Correlation between time on match puzzle and school rating. R=.548±.075. A high corre- lation with a low probable error. Result 5. Correlation between geometrical puzzle and school rating of 51 High School students. R = .0262±.o6. High coefficient, low probable error. Result 6. A group of students were tested on their retention of the method of working these puzzles. When they first saw the match and the geometrical puzzles, nothing was said to them about any further test on these. But exactly one month afterwards they were called in and the same two puzzles were again placed before them without warning. They were then rated on the basis of their improvement over the first working of the puzzles as indicated by the reduction of their sitting time. This list of the time-gains was correlated with their school ra- tings. In connection with the match puzzle, we have 22 reagents ; R = .4i6±.o93. Not bad. Result 7. Time gained on geometrical puzzle correlated with school rating: 45 reagents; R = .5i±.o64. Better still, with an insignificant probable error. Result 8. Here we have shown the correlation between the time listing of High School students on the maze puzzle and their school rating. Reagents 55; R = .5411 ±.058. A safe result from all points of view. Result 9. These next five results substitute for the general school rating the students' rating in mathematics only, obtained in the same way as the general school rating except for the absence of the teachers' opinions. Result 9 shows the correlation between the match puzzle and this mathe- matical ability. Reagents 32; R = .5i9±.o76. Result 10. Geometrical Puzzle and mathematical ability; reagents 43; R = .52± .065. 42 Result ii. Correlation between mathematical rating and time gained on the sec- ond working of the match puzzle. Reagents 18; R = .38o9±.io. Not a valuable result due to the small number of reagents, rather low corre- lation and a high probable error. Result 12. Correlation between mathematical rating and time gained on second working of geometrical puzzle. Reagents 47; R =.5163:^.063. This is much better than the preceding result. Result 13. Correlation between mathematical ability and the record on the maze puzzle. Reagents 52; Rrrr .5394^.059. A strong result. Result 14. The next four results substitute a rating in English (Literature and Composition) for mathematics. Result 14 expresses the correlation be- tween English rating and the record on the Bird Puzzle. Reagents 53 ; R =. 5384^-059- Result 15. Correlation between English Rating and Match Puzzle. Reagents 25 ; R = . 5769+. 086. Result 16. Correlation between English Rating and Geometrical Puzzle. Re- agents 50; R = .575±.o6. Result 17. Correlation between English Rating and Maze Puzzle. Reagents 52 ; R = .55±.059. If all correlation of .50 or over is high, these mathe- matics and English results, taking into account also the low probable error, are safely above the line of uncertainty. Result 18. The remaining results (twelve in all) represent a still furth'er stand- ardization of conditions in that they are based on groups of students all within two years of age. This does away with the factor of age vari- ation and largely eliminates the element of age as a possible source of error. In no case did the ages of those in the group extend over two full years, although the exact limits of these two years vary slightly for the different groups. Result 18 shows the correlation between the school rating of a group 43 of boys and girls, all within two years of age, and their work on the bird puzzle. Reagents 24; Age 15-17; R = . 51 — -087. Result 19. Correlation between school rating of the same aged group and match puzzle. The reagents 13; Age 15-17; R = .5o±.i2. Result 20. Boys' and girls' school rating correlated with time of the group on geometrical puzzle. Reagents 27; Age 15-17; R = 497 2± -o83. Result 21. Same as above except with the maze puzzle. Reagents 26; Age 15-17; R=r.4844±.o84. Result 22. The following eight results retain the two year age restriction and include the additional feature of sex limitation. Each group consists hereafter of all boys or all girls, and all within two years of the same age. In this way the remaining factor of sex has been eliminated as a possible source of error. Result 22 represents the correlation between the school rating of a two year group of boys and their work on the bird puzzle. Reagents 16; Age 15-17; R = . 36471b. 107. This is an unsatisfactory correlation coefficient with a dangerously large probable error. Result 23. Boys : Correlation between school rating and match puzzle. Reagents 10; Age 15-17; R = 48±.i36. The small size of this group weakens the result. Result 24. The school rating of boys correlated with time of group on geometri- cal puzzle. Reagents 18; Age 15-17; R==.5747±.ioi. A strong result. Result 25. Group of two year boys : Correlation between school rating and maze puzzle. Reagents 16; Age 15-17; R=r.4ii7±.io7. Result 26. A group of girls all within two years of the same age. Correlation between school rating and bird puzzle. Reagents 16; Age 14^-16^; R = .3882±.io7. This coefficient is too low to be significant. 44 Result 27. Two year group of girls : School rating correlated with match puzzle. Reagents 16; Age 14^-16^; R = .3882±.i6. Result 28. Group of girls : Correlation between school rating and time on geo- metrical puzzle. Reagents 14; Age 14^-16^; R = .3538±.n. Result 29. Correlation between school rating and maze puzzle of two year group of girls. Reagents 11 ; Age 14^2-16^; R = .52:±.i3. Of these twenty-nine results here reviewed the first two, dealing with averages and medians, are quite satisfactory as far as they go, but their mathematical accuracy and consequent value does not by any means come up to the results of the twenty-seven following instances expressed in the form of correlation coefficients. 45 TABLE 7- Exhibit o: All Correlation Results. - ****** * Re- Correlation No. agents Sex Age Between AND R + 3 5i Mixed 12-18 School Rtg Bird Puz. 62 06 4 33 Mixed 12-18 School Rtg Match Puz. 548 075 5 51 Mixed 12-18 School Rtg Geom. Puz. 6262 06 6 22 Mixed 12-18 School Rtg Gain-Match P. 416 093 7 45 Mixed 12-18 School Rtg Gain-Geom. P. 51064 064 8 55 Mixed 12-18 School Rtg Maze Puz. 54i 1 058 9 32 Mixed 12-18 Math. Rtg Match Puz. 5i7 076 10 42 Mixed 12-18 Math. Rtg Geom. Puz. 52 065 ii i8 Mixed 12-18 Math. Rtg Gain-Match P. 3869 10 12 47 Mixed 12-18 Math. Rtg Gain-Geom. P. 5163 063 13 52 Mixed 12-18 Math. Rtg Maze Puz. 5394 059 14 53 Mixed 12-18 Eng. Rtg Bird Puz. 5384 05 15 25 Mixed 12-18 Eng. Rtg Match Puz. 5769 086 16 50 Mixed 12-18 Eng. Rtg Geom. Puz. 575 06 17 52 Mixed 12-18 Eng. Rtg Maze Puz. 55 059 18 24 Mixed 15-17 School Rtg Bird Puz. 5i 087 19 13 Mixed 15-17 School Rtg Match Puz. 50 12 20 27 Mixed 15-17 School Rtg Geom. Puz. 4972 083 21 26 Mixed 15-17 School Rtg Maze Puz. 4844 084 22 16 Boys 15-17 School Rtg Bird Puz. 3647 107 23 10 Boys 15-17 School Rtg Match Puz. 48 136 24 18 Boys 15-17 School Rtg Geom. Puz. 5747 101 25 16 Boys 15-17 School Rtg Maze Puz. 4117 107 26 16 Girls 14^-16^2 School Rtg Bird Puz. 3882 10 27 16 Girls 14^-16^4 School Rtg Match Puz. 388 16 28 14 Girls 14^2-16^ School Rtg Geom. Puz. 3538 11 29 ii Girls 14^-161/2 School Rtg Maze Puz. 52 13 46 8. SUMMARY OF RESULTS. When one glances down the "R" column of Table 7 (which exhibits all the correlation results) it is at once apparent that by far the larger part of the correlation coefficients are safely within what Spearman calls high correlation (.5 or above). The showing as a whole therefore is significant and worthy of attention. Spearman declares that a dozen cases are sufficient to establish a cor- relation of .50, due attention being given to the probable error. We have in this list of twenty-seven results, seventeen which show "R" = .5 or above, and of these seventeen only one deals with less than twelve reagents — Result 29 being calculated on but eleven. Only two others have less than twenty-four cases (Result 19 with thirteen, and Result 24 with eighteen). There are seven results with over fifty cases each, and we have an average number of 37.8 cases for the entire seventeen results. It would appear then that there is no question about the value of the results in sixteen of these seventeen cases (dropping No. 29), for they all meet the necessary conditions as to number of cases and most of them are far above what is required. Investigation of the probable error in these sixteen results shows that in each case it is safely below one-third of the correlation coefficient — ■ in fact in only one instance does it approach even one-fourth (Result 19: R^.5±:.i2), while in the remaining fifteen cases it is less than one-fifth. From the point of view therefore of mathematical results we have at least sixteen cases of unquestionable significance, all based on a good number of reagents, all having a high correlation coefficient with a low probable error. Of those results which fall below R = .5 there are four which are too low to be considered, — viz.: No. 11, R = .3869; No. 22, R^.3647; No. 26, R = .3882; and No. 28, R = .3538. Of the remaining we have No. 20 (Reagents 27, R=:.4972±.o83), and No. 21 (Reagents 26, R = 4844 ± .084), which, on account of their close approach to .5, of the large number of cases in each and of the low probable error, may safely be in- cluded among the valuable results. It seems best, in order to be on the safe side, to throw out No. 6, No. 23, No. 25 and No. 27 because of the low coefficient (No. 6), the few reagents involved (No. 23), or for both these reasons (No. 25 and No. 27). What have we left then as a possible basis for declaring the existence 47 of a correlation between school intelligence and speed in working puz- zles? We have eighteen results, as shown in Table 8 which follows: TABLE 8. The Eighteen Accepted Correlation Results. Re- Correlation No. agents Sex Age Between and R ± 3 5i Mixed 12-18 School Rtg. Bird Puz. .62 06 4 33 Mixed 12-18 School Rtg. Match Puz. .548 075 5 51 Mixed 12-18 School Rtg. Geom. Puz. .6262 06 7 45 Mixed 12-18 School Rtg. Gain-Geom. P. •5i 064 8 55 Mixed 12-18 School Rtg. Maze Puz. ■541 1 058 9 32 Mixed 12-18 Math. Rtg. Match Puz. •517 076 10 42 Mixed 12-18 Math. Rtg. Geom. Puz. •52 065 12 47 Mixed 12-18 Math. Rtg. Gain-Geom. P. •5163 063 13 52 Mixed 12-18 Math. Rtg. Maze Puz. •5394 059 14 53 Mixed 12-18 Eng. Rtg. Bird Puz. .5384 059 15 25 Mixed 12-18 Eng. Rtg. Match Puz. •5709 086 16 50 Mixed 12-18 Eng. Rtg. Geom. Puz. •575 06 17 52 Mixed 12-18 Eng. Rtg. Maze Puz. •55 059 i.8 24 Mixed 15-17 School Rtg. Bird Puz. •5i 087 19 13 Mixed 15-17 School Rtg. Match Puz. •5 12 20 27 Mixed 15-17 School Rtg. Geom. Puz. •4972 083 21 26 Mixed 15-17 School Rtg. Maze Puz. .4844 084 24 18 Boys 15-17 School Rtg. Geom. Puz. •5747 101 All of these eighteen results are significant since all have a safely secured high correlation coefficient. How are these results distributed? We find that ten of them deal with general school rating (Nos. 3, 4, 5, 7, 8, 18, 19, 20, 21, 24), four each with mathematical rating (Nos. 9, 10, 12 and 13) and English rating (Nos. 14, 15 , 16, 17). We find that two (Nos. 7 and 12) deal with the gain in time on the second working of a puzzle, in both instances the geometrical puzzle. We find that, all told, the Bird Puzzle figures in three of these results (Nos. 3, 14, and 18), the Match Puzzle in four (Nos. 4, 9, 15 and 19), the Geometrical Puzzle in seven (Nos. 5, 7, 10, 12, 16, 20 and 24) and the Maze Puzzle in four (Nos. 8, 13, 17 and 24). We find that of these eighteen positive results 48 only five have a strict age limit (Nos. 18, io, 20, 21 and 24), and of these five but one (No. 24) adds the further restriction of sex limitation. One result therefore out of the entire twenty-seven fully meets all con- ditions, i. e. reagents sufficient in number, restricted as to age and sex, coefficient above .5 with low probable error. This does not indicate by any means that all the other seventeen results of Table 8 are to be thrown out. Yet it does emphasize the fact that as the groups of reagents became more and more homogeneous, the evidences of high correlation become fewer. This may be due in part to the smaller size of the more restricted groups, or it may be due to the elimination by means of these restrictions of sources of error. We must not forget, moreover, that the positive evidence of this one result is sufficient to counter-balance a number of cases giving purely negative evidence. Turning now to a brief summary of the differences between general school rating, mathematical rating, and English rating it will be seen that on the whole general school rating comes out more often with a pos- itive result. Rut this may very likely be due to the fact that general school rating is used as a correlation member much oftener among the twenty-seven results than either of the restricted ratings. Wherever the English rating is used (Nos. 14, 15, 16, 17) it comes out with a coeffi- cient above .5. The same is true of four out of five occurrences of the mathematical rating, the failure (No. 11) being on the gain in the second working of the match puzzle. The average correlation coefficient for the different kinds of rating is found to be as follows : General school rating, R .4852 ; Mathematics rating, R .4959; English rating, R .5600. (See Table 9.) When we compare the entire result of the four different puzzles, we find that the Bird Puzzle gave a high coefficient in three cases out of a possible five ; the Match Puzzle in four out of a possible eight ; the Geometrical Puzzle in seven out of a possible eight, and the Maze Puzzle in four out of a possible six. In the same general order are the averages of all the results involving each separate puzzle. The average coefficient of all Bird Puzzles is R .4842; of all Match Puzzles, R .4766; of all Geometrical Puzzles, R .5216; and of all Maze Puzzles, R .5077. (For averages of correlations see Table 10). It is worth bearing in mind that the Geometrical Puzzle, and the some- what similar Match Puzzle (one of which deals with solid surfaces and 49 the other with boundaries), naturally call for more concentrated and comprehensive thinking than the simple Bird Puzzle, which is so largely a matter of visual perception, or than the Maze Puzzle, where one cannot well see the solution from the beginning, but must proceed for the most part from step to step. There is surely a larger element of chance in the Maze Puzzle than in any of the others, and a larger dependence upon the simplest forms of perception in the Bird Puzzle than in any of the others. While the Match and Geometrical Puzzles must of course use perception also, yet the imaginative, comparing, judging, and reasoning activities of the mind are in these two puzzles called into use much more than in either of the other two. 50 TABLE 9. Distribution of Results Among Ratings Rating Average Correlation. % ;j; ^ ^ s|s sjj % No Re- Sex Age Gen. School Mathematical English agents Rating Rating Rating 3 33 Mixed 12-18 .62 4 33 Mixed 12-18 .548 5 5i Mixed 12-18 .6262 6 22 Mixed 12-18 .416 7 45 Mixed 12-18 •5i 8 55 Mixed 12-18 ■54i 1 9 32 Mixed 12-18 •517 10 42 Mixed 12-18 •52 11 18 Mixed 12-18 .3869 12 47 Mixed 12-18 •5163 13 52 Mixed 12-18 - -5394 14 53 Mixed 12-18 .5384 15 25 Mixed 12-18 •5769 16 50 Mixed 12-18 •575 17 52 Mixed 12-18 •55 18 24 Mixed 15-17 •51 19 13 Mixed 15-17 •5 20 27 Mixed 15-17 •4972 21 26 Mixed 15-17 .4844 22 16 Boys 15-17 •3647 23 10 Boys 15-17 .48 24 18 Boys 15-17 •5747 25 16 Boys 15-17 .4117 26 16 Girls 14^-16^ .3882 27 16 Girls 1454-16^ •338 28 14 Girls i4^-i6 T /4 •3538 29 11 Girls 14^-16^ •52 Averages, 4852 •4958 .5600 5i TABLE 10. Distribution of Results among Puzzles Puzzle Average Correlation. No. Re- Sex Age Bird Match Geom. Maze agents Puz. Puz. Puz. Puz. 3 33 Mixed 12- -18 .62 4 33 Mixed 12- -18 .548 5 5i Mixed 12- ■18 .6262 6 22 Mixed 12- ■18 .416 7 45 Mixed 12- 18 ■51 8 55 Mixed 12- -18 •54i 1 9 32 Mixed 12- ■18 •517 10 42 Mixed 12- -18 •52 ii 18 Mixed 12- -18 .3869 12 47 Mixed 12- ■18 •5163 13 52 Mixed - 12- -18 •5394 14 53 Mixed 12- 18 •5384 15 25 Mixed 12- ■18 •5769 16 50 Mixed 12- ■18 •575 17 52 Mixed 12- ■18 •55 18 24 Mixed 15- 17 •5i 19 13 Mixed 15- ■17 •5 20 27 Mixed 15- 17 ■4972 21 26 Mixed 15- •17 .4844 22 16 Boys 15- ■17 •3647 23 10 Boys 15- 17 .48 24 18 Boys 15- 17 •5747 25 16 Boys 15- ■17 .4117 26 16 Girls 14/2- ■i6/ 2 .3882 27 16 Girls 14^- •i6/ 2 .388 28 J 4 Girls 14^- ■16^ .3538 29 ii Girls 14/2- •i6/ 2 •52 Averages, .4842 .4766 .5216 .5077 52 9. CONCLUSIONS. When we endeavor to reduce the results of this series of experiments to definite conclusions we are soon ready to acknowledge that there are not a great many unqualified statements which can stand as being fully justified by the data gathered. The following, however, seem fairly to arise from the experiments reported herein : (i) The first results recorded, those dealing in averages and medians, point to the existence of a fairly close relation between school intelligence and the ability to work simple puzzles. The weakness here is not in the figures expressing these results but rather in the method pursued. Rough groupings and results in averages and medians, although widely used in this kind of investigation, "fall far short of reaching the exact- ness in results obtained by computing correlation coefficients. Taking these first two total results as they stand, however, there seems no good ground to question their testimony to the existence of such a close rela- tionship between school intelligence and the working of puzzles as we are investigating. (2) When we pass on to Results 3 to 29, which are calculated in terms of coefficient correlations we find only moderately satisfactory ground for supposing a substantial relationship to hold between school intelligence and the ability to work simple puzzles. When we take into account the fact that as the homogeneity of the groups increases the correlation co- efficient decreases, when we note that out of all these 27 sets of results there is only one where a high correlation is found in a group of the same sex and practically the same age, we are inclined to deny the exist- ence of any such correlation as we are seeking. This, however, would be going farther back than the data requires or warrants. There are at least 18 sets of results which must be reckoned with. We can only conclude that it is quite possible that school intelligence is represented on the average by rapidity in solving simple puzzles. We can not claim to have proved the presence of this relation in any constant high degree but we have established a probability in favor of its existence. (3) For the purpose of testing school intelligence the comparative value of the four different puzzles used seems to be established only to this extent : the geometrical and the quite similar match puzzles are the safest tests, the geometrical puzzle safest of all. Next comes the maze puzzle. Least valuable is the bird puzzle ; this is the easiest to work but has the least significance for our purpose. It seems, on the other 53 hand, that in the geometrical puzzle we are on the track of a test which, with more thorough and extensive investigation, may transpire to be of considerable value. This "lead" is worth following up. (4) As to the relative value of school rating, mathematical rating and English rating as one term of the correlation, representing school in- telligence, there do not appear to be sufficient grounds for any definite conclusion. Attention may be called to the higher average correlation of the English rating, but the significance of this for our purposes is largely offset by the fact that it can not represent school intelligence nearly as well as the school rating. This latter covers a good number of varied school subjects, instead of being confined to one, as is the Eng- lish rating, and it also finds approximately half its representative value in the estimate of students' mental acuteness by their teachers. (5) Another result worthy of mention is the obvious advantage of the correlation coefficient method over the cruder and more general meth- ods dealing in groups and averages. If we had only Results 1 and 2 to deal with our conclusion would have been strongly in favor of a gen- eral and high relation between school intelligence and the working of puzzles, for certainly the average-results and median-results there record- ed go to establish this conclusion. But when we subjected the work of a large percentage of the same reagents to careful computation accord- ing to Spearman's "foot-rule" no results appeared which justified such a conclusion. Surely no one can question the far greater preciseness and certainty of results obtained in this latter manner. Consequently they have for us much higher value. When, for instance, we find that in a group of 18 students, of the same age and sex, there appears a correla- tion coefficient of .5774 with a probable error of only .101 (Result 24) we have the satisfaction of knowing that this figure stands for an incontest- ible fact, and a fact of great suggestiveness and representative value. (6) These conclusions seem to be more closely allied to the many researches in which no correlation has been found than to the one or two, notably Spearman's, in which an exceedingly high correlation has been claimed. As a matter of fact, however, the present investigation comes out midway between these two extremes. Its results are negative only in the sense of failing to approximate Spearman's almost perfect cor- relation. Instead of the great majority of the coefficient results running between .0 and .025 in this report it will be noticed that none go so low as this and that all are practically grouped around .5. Now .5 Spear- 54 man declares to signify "high correlation." As a matter of fact, of course, it indicates a position just half way between no correlation at all and perfect correlation. It is worthy of note, therefore that the present re- sults hold closely to Rrz^.5. This shows correlation, but not truly high correlation. (7) It would appear, then, that the relative position, of the members of a fair-sized and reasonably homogeneous group of young persons, as established by the time it takes them to work some simple sort of geometrical puzzle, will correspond fairly closely to the relative positions of these same persons in school intelligence. By "fairly closely" is meant that the correspondence will be materially more than half way between no correspondence at all and perfect correspondence. 55 CHAPTER IV. Second Experimental Series. AN INTENSIVE STUDY OF PUZZLE LEARNING WITH SPECIAL REFERENCE TO INDIVIDUAL DIFFERENCES and METHODS OF LEARNING. i. APPARATUS. The puzzles used in this series of experiments were greater in num- ber and variety than those used in the first series. They were all motor, however ; verbal and mathematical puzzles being excluded. These puzzles were in five groups, with two or three puzzles in each group. In all groups one puzzle was relatively easy and the other more difficult. In the last group the three puzzles were of three distinct grades of difficulty. GROUP I. Match Puzzles. i. Puzzle I. Matches were laid in 16 squares (see Plate II. No. i ). The problem was to remove only four matches and leave twelve of the original squares. There are several ways of doing this, the simplest of which is to remove the four matches in the center of the figure. 2. Puzzle II. Matches were laid in six squares (see Plate II. No. 3). The problem was to remove five of the matches so as to leave three com- plete squares. The only way of doing this is indicated on the Plate. GROUP II. Geometrical Puzzles. 3. Puzzle III. Five pieces of cardboard were laid in a strip. The 56 problem was to rearrange them all so as to form a perfect square (see Plate II. No. 4). 4. Puzzle IV. Four pieces of cardboard were arranged in the form of a square (see Plate II. No. 2). The problem was to rearrange them in the form of a cross. In both these geometrical puzzles the cardboard was colored differently on the back side to prevent the reagent inadvertently turning a piece over, which would in most instances make it impossible to solve the puzzle. GROUP III. Tracing Puzzles. 5. Puzzle V. A figure (see Plate I. No. 3) was placed under a ground glass cover in a wooden frame, and the reagent was asked to trace the entire figure in an unbroken line without going over any part more than once. 6. Puzzle VI. The same problem as in Puzzle V, except with a different and considerably more difficult figure to trace (see Plate I. No. 4). GROUP IV. Maze Puzzles. 7. Puzzle VII. A rectangular maze was placed in the frame under the glass and the reagent was asked to trace an unbroken path through the open spaces from the outside of the maze to the center (see Plate I. No. 5). 8. Puzzle VIII. The same problem as in Puzzle VII, except with a more difficult maze (see Plate I. No. 6). GROUP V. Metal Puzzles. 9. Puzzle IX. Two heavy wire loops resembling horseshoes (see Plate I, No. 1) were placed in the hands of the reagent to be taken apart. 10. Puzzle X. Two twisted nails (see Plate I, No 8) were given the reagent with instructions to take them apart. 11. Puzzle XI. Two keys fastened together by their squares (see Plate I, No. 9) were laid before the reagent, who was asked to take them apart. 57 2. REAGENTS. There were in all eleven reagents. All of the puzzles in all their forms were given to each of these eleven reagents with one or two slight exceptions. One of the chief values in the results of this series of experiments lies in the unusually varied and representative features of this group of reagents. As to sex, six were male, five were female. As to age, the reagents ranged from the bottom to the top. One was 6 years old, one 13, one 14, one 17, one 25, one 28, one 33, one 34, one 35, one 45, and one was 70. Four were school children, seven were adults. A full appreciation of the results to be discussed later calls for a brief description of each one in this varied group of reagents. (1) Sb was a boy 6 years and 2 months old. Brighter than the average in school, as evidenced by the fact that at this age he was in the second grade in a small private but standardly graded school. Sb proved one of my most interesting cases, as will be shown below. (2) Bb, a boy of 13, a student in the first year high school, was ex- ceptionally good in his school gradings. (3) Bg was a girl of 14, selected because of her high standing in school. She also was in first year high school. (4) Db was another case of spec'al interest. A boy of 17 he had repeatedly proved himself a mischief maker in school, a leader of re- volt, and a general failure as a student. He had somehow managed to reach high school but had been dismissed from school on a number of occasions, sometimes for hopeless scholarship, sometimes for general incorrigibility. He had been reinstated on his earnest promise to do right, but had always soon brought suspension upon himself, and finally expulsion. These things need to be borne in mind when we come to examine his record. (5) Rd was another case of unusual value, being a marked ex- ample of retarded development. As a child he had endeavored to at- tend public school but was too slow and too much confused to fit into the machinery of the school room. He had, therefore, been kept at home and taught some things by his mother, whose intense sympathy tended to soften him rather than to spur him on to great endeavor. He had learned to read tolerably well and had read much in history, which interested him, and in the Bible- His reading ability at the age of 33 was equal to that of a fair 7th grade student. He could re- member but little of what he read. In figures he was unable to do 58 anything but the very simplest addition, no subtraction, etc., although several male relatives had labored long to teach him. Physically he was well and very strong, normal in all his functions, except with exagger- ated nocturnal emissions. Rd's general appearance was quite normal ; in the company of those not of his immediate family he was shy and awkward, with long stretches of inactivity and silence. Comparison of Rd's record with that of the others yields interesting results. (6) Mm, a young woman of 25 with a good business education and experience. (7) Mt, a young woman of 28 with general schooling. Mm and Mt are the only two reagents who are very much alike in general respects. Close comparison of their records on the tests thus approaches the "method of difference." (8) Ba, a man of 35, with a wide experience in life, recently earned the A.B. degree. (9) Mg, a married woman of 34, mother of several children, had had one or two years of schooling beyond high school. Mg was the mother of Sb, the 6 year old boy. (10) Pd, a man of 45, holder of four academic degrees including Ph. D. His case yielded some especially interesting results. He was the father of Bb, the bright boy of 13 years. (11) Gm, an elderly woman of 70; ordinary early education, was in full possession of all her powers, and was a great reader. Her record decidedly increases the range of the investigation. Gm was the mother of Mg, and thus the grandmother of Sb. We have then one instance of three generations in these records. These eleven reagents may be grouped for various purposes in differ- ent ways, viz. : 1. Males: Sb, Bb, Db, Rd, Ba, Pd. Females: Bg, Mm, Mt, Mg, Gm. 2. Retarded development Rd. Primary Sb. High school Bb, Db, Bg. Beyond high school, Mm, Mt, Mg. College degrees, Ba, Pd. 3. Within the high school group,— bright Bb, Bg ; dull Db. 4. Age, Sb 6 Bb 13 59 Bg 14 Db 17 Mm 25 Mt 28 Rd 33 Mg 34 Ba 35 Pd 4 5 Gm 70 3. PROCEDURE. A. In General. (1) Each reagent was tested privately. (r?) No sitting ran over 1^ hours. If more time was needed another sitting was arranged for. (3) Puzzles were presented in the order in which they are listed in the description of "apparatus" above. (4) Reagent was seated at a table. He received his instructions; the puzzle was laid on the table before him (or in the case of the matches, they were uncovered), and his time was opened on a stop-watch. When he finished his task he said "Done," according to instructions, and his record was closed on the stop-watch. (5) Each puzzle was presented in the same way to each reagent throughout its series, except that Puzzle II was always turned one-quarter way around after it was first successfully solved. (6) In addition to a time record, I listened for exclamations or re- marks from the reagent during the course of his work. (7) A record of false moves was also attempted. (8) Fatigue was watched for, and by occasional special inquiry was recognized about as soon as it appeared. It was thus possible to avoid irrelevancies due to this cause by discontinuing the immediate sitting as soon as fatigue appeared. (9) The reagent's instrospective report of how the puzzle was finally worked was also obtained. (10) Seven days after the reagents went through all the puzzles they were put through them once again, without in the meantime having been warned of this repeated test. Co B. In Particular. (i) The instructions were simple and brief. A few examples will suffice : (a) Puzzle I. "Here are matches arranged in 16 squares; remove any 4 matches so as to leave 12 complete squares. Do this as quickly as you can, and say 'Done' when you are through." (b) Puzzle III. "Here we have 5 pieces of cardboard forming a strip. Rearrange them so as to form a perfect square." (c) Puzzle VII. "Trace your way through the open spaces from the outside into the center of the figure." (d) Puzzle X. "Remove one nail from the other." (2) The reagent was first given the puzzle with such brief instruc- tions, but without any directions at all. (3) After he had either solved the puzzle or had failed and given up he was asked to listen to the reading of the directions, after which he was handed the puzzle to be worked again. The directions were about as plain as they could be without, being lengthy. It is important that these be known and they are therefore here given. (a) Puzzle I. "Remove the four matches in the center of the figure." There are several other ways to do this puzzle, and frequently a reagent had worked it without directions by one of these other methods. (b) Puzzle II. "Remove the middle match on one long side of the figure. Then remove the corner matches on both corners of the op- posite long side of the figure." (c) Puzzle III. "Place the small square piece somewhat diagonally for the center of the large square. Take one of the triangular pieces and place it up against one side of this small square so that its shortest side forms a direct continuation of a side of the "small square. Do like- wise with the remaining three triangular pieces." (d) Puzzle IV. "Notice that one of these pieces looks somewhat like an arrow-head. Take this and place it pointing upwards. Take the other large piece and fit it to the arrow-head by joining their longest edges one to the other. Take the next largest piece and put its longest edge to the remaining slanting surface of the arrow-head. Then add the small piece to the upper left-hand corner of the figure." (e) Puzzle V. "Begin at the top of the large triangle and run down the left side of the triangle, then across the bottom, then half way up the right side to where the inner triangle touches the outer triangle ; 61 at this point run on to the inner triangle and go completely around it, coming back to where it touches the right side of the larger triangle ; from here continue up this right side of the larger triangle to the top, then go around the circle." (f) Puzzle VI. ''Begin at the upper end oi the inside diagonal line, run down this diagonal, then run straight down to the circle, take the short diagonal line up to the right, cross to the left by the long straight line, take the short diagonal line down, run to the top by the long straight line, and keep this kind of route until you reach the upper end of the right-hand vertical line, then go around the circle, and come down this line to where the inner diagonal line runs into it." (g) Puzzle VII. "Throughout your course pass by the first open- ing from the outer into an inner square and always enter by the second opening you reach. As soon as an inner square is entered, always turn to the right of the direction you were going when you entered that square." (h) Puzzle VIII. "After entering the first square take the first opening into the next square ; to enter the next square take the second opening ; to enter the next square take the third opening ; to enter the next square take the third opening ; to enter the next square take the second opening ; to enter all the succeeding squares take the first opening. When you enter the outer square turn to the right; after that, upon entering a new square make every alternate turn to the right of the direction you enter, and the intervening turns make to the left." (i) Puzzle IX. "With the fingers of the left hand grasp one horse- shoe in the middle of the bend and hold in a horizontal plane with the opening toward the right. With the fingers of the right hand grasp the other horseshoe likewise and hold it in a vertical plane with the opening toward the left. Bring the longitudinal centers of the two horseshoes to the samejine and draw one from the other." (j) Puzzle X. "Hold a nail point in the fingers of each hand, and turn both heads straight up. Lift the right hand until the head of the right-hand nail passes over back of the other nail-head. Turn the right- hand nail so that its head will cut a semi-circle down toward the body, passing down to the left of the left-hand nail-head, and coming to a stop when pointing directly down. Throughout all this the position of the left-hand nail is not to be changed. Now push the two nails away from each other." 62 (k) Puzzle XI. "Notice that one key is larger than the other. Hold this large key in the left hand with its square on the side away from the body. With right hand hold shaft of other key straight up with its square towards the body. Now swing small key outwards and down until its shaft points straight down. Then twist it a half-circle to the left; which swings its square over the shaft of the larger key. Swing small key up towards the body until its shaft stands straight up. Then slide it to the left along shaft of large key. Swing head of small key in a semi-circle towards the body until it stands straight down. Twist it a quarter of a circle to the left and the points of its square pass out into the head of the large key. Work it around in the head until it escapes through the deepest of the four grooves." (4) After this the reagent was asked to read the directions once through to himself. Then he was given the puzzle to work the third time. (5) I then worked the puzzle before the eyes of the reagent, and im- mediately gave it to h'm to work again. (6) The last working of the puzzle was after I had helped the re- agent himself to do the puzzle with his own hands. We thus have the puzzle worked — (a) Without directions. (b) After hearing directions. (c) After reading directions. (d) After seeing the work done (demonstration). (e) After doing the puzzle himself and under guidance. (7) Between the different workings of the tracing and the maze puzzles all marks on the slate were washed off. (8) The three metal puzzles were always put back together out of the reagent's sight. (9) When the puzzles were again placed before the reagents after seven days the five different methods outlined above were once more used. TABLES Showing time records of each of the 11 reagents. Roman numerals on left margin designate the 11 puzzles as listed under "Apparatus" above. Numbers in parenthesis at head of the 5 double columns in- dicate the 5 methods of presentation as described under "Procedure 63 above. Column numbers in parenthesis are record of the control series. All time is, here given in seconds. "F" means failure. TABLE 11. Rd. (I) (2) (3) (4) (5) I F(7) F(6) F(5) 12(5) 6(6) II F(F) F(F) F(F) F(n) 16, F, 26, 9(F, 7) III F(6 3 ) FC113) F(i 7 ) F(i8) 60, 32, 15 (14) IVa ^3(90) 24(16) 20(11) 18(12) 19(10) IV F(95) F(95) F( 7 o) F(75) 28, 12 (14) V F(6 7 ) F( 4 2) F(32) F( 3 6) 35, 24 (30) VI F(F) F(F) F(F) F(F) 75 (70) VII 520(170) 240(140) 200(126) 190(135) i75(i44) IX 120(17) 10(6) 3(8) 2(9) 3(7) X F(43) F(i35) F(F) F(F) 11, 16 (7, 24, 18, 8) XI F(i27) F(F) F(F) F( 5 2) 195, 180 (42) TABLE 12. (1) (2) (3) (4) (5) I 150 ( 3) 4(2) 3(2) 3(2) 3(2) II F ( F) F "( 4) F ( 3) 4 ( 3) 45 ( 2) III 107 ( 31) 35 ( 11) 130 ( 0) 285 (10) 45 ( 9) IV 53 ( 16) 185 ( 7) 15 ( 9) 14 (7) 13 ( 6) V 280 ( 92) 25 ( 18) 23 (15) 22 (14) 20 (14) VI 255 (165) 90 (170) 67 (27) 58 (25) 58 (22) VII 594 ( 57) 90 ( 46) 80 (44) 72 (41) 70 (43) VIII 230 ( 63) 180 (122) 140 (53) 133 (49) 130 (46) IX 87 ( 4) 4(3) 3(3) 3(2) 3(2) X F ( 37) 45 ( 6) 12 ( 3) 9(4) 6(3) XI 310 ( 54) 27 ( 16) 16 (14) 14 (11) 13 (12) 64 TABLE 13. Ba. (1) (2) (3) (4) (5^_ I 60 ( 3) 3(3) 3(2) 3(2) 3(2) II F ( 2) F ( 2) 6(2) 3(2) 3(2) III 134 (20) 35 ( 7) 12 ( 6) 7(5) 6(5) IV 11 (14)' 7(8) 7(7) 6(7) 7(6) V 36 (10) 15 (8) 12 ( 8) 12 ( 7) 11 ( 8) VI 342 (26) 92 (14) 20 (12) 18 (11) 17 (10) VII 58 (28) 30 (20) 25 (19) 23 (21) 20 (19) VIII 72 (37) 45 (36) 30 (30) 25 (24) 24 (21) IX 6(3) 4(2) 3(2) 4(3) 3(2) X 13 ( 6) 18 (38) 6(4) 5(3) 4(4) XI 337 (16) 18 (16) 16 (14) 18 (11) 15 (13) TABLE 14. Pd. (1) (2) (3) (4) (5) I F ( 6) 4(4) 3(3) 3(3) 3 ( 3) II F ( 48) 58 (5) 3(6) 3(4) 3 ( 3) III 405 ( 22) 45 ( 14) 3S ( 12) 37 ( 11) 30 ( 12) IV 48 ( 24) 14 ( 20) 10 ( 16) 9 ( 17) 10 ( 14) V 95 ( 70) 24 ( 61) 15 ( 4.9) 17 ( 42) 14 ( 37) VI F ( 85) 94 (60) 40 ( 54) 35 ( 50) 30 ( 53) VII 130 (130) 78 (125) 72 (104) 67 ( 92) 63 ( 88) VIII 120 (170) 98 (140) 84 (129) 81 (132) 80 (123) IX n ( 12) 6(9) 5(8) 4(7) 5 ( 5) X F (180) 62 ( 90) 13 (12) 5 ( 10) 5 ( 6) XI 92 ( 45) 70 ( 47) 44 ( 19) 24 ( 17) 18 ( 19) 65 TABLE 15. Bb. (I) (2) (3) (4) 3 ( 3) (5) I 600 ( 3) 4 ( 3) 3 ( 3) 3 ( 3) II 510 ( 15) 22 ( 5) 6 ( 4) 3 ( 3) 3 ( 3) III 155 ( 19) 18 ( 20) 15 ( 18) 14 (16) 12 (15) IV 21 ( 22) 14 ( 7) 13 ( 7) 13 ( 6) 12 ( 7) V 155 ( 55) 30 ( 28) 22 ( 24) 20 (27) 20 (25) VI 254 ( 45) 400 ( 37) 470 ( 33) 49 (32) 40 (30) VII 165 ( 57) 178 ( 42) 80 ( 40) 65 (38) 54 (40) VIII 300 (195) 60 (163) 58 (124) 44 (60) 40 (49) IX 12 ( 4) 2 ( 3) 3 ( 2) 2 ( 4) 2 ( 3) X 135 ( 85) 54 ( 82) 34 (212) 11 (12) 10 ( 1) XI F ( 30) 40 ( 18) 10 ( 20) 8 (11) 8 ( 9) TABLE 16. Db. (I) (2) (3) (4) (5) I 75 ( 2) 4 ( 2) 4 ( 2) 4 ( 2) 3 ( 2) II 4 ( 3) 25 ( 2) 2 ( 2) 2 ( 2) 2 ( 2) III 246 (33) 16 ( 7) 16 ( 5) 12 ( 4) 10 ( 4) IV 47 (10) 8 ( 9) 7 ( 8) 6 ( 9) 7 (88) V 10 (15) 8 (11) 7 (12) 7 ( 9) 6 ( 9) VI 67 (65) 50 (30) 3? (11) 26 (12) 22 (11) VII 69 (19) 37 (20) 20 (18) 18 (19) 17 (17) VIII 45 (40) 34 (22) 26 (18) 24 (20) 24 (19) IX 6 ( 3) 5 ( 3) 5 ( 4) 4 ( 2) 3 ( 3) X 65 (30) 91 (45) 50 (11) 8 ( 6) 4 ( 7) XI 95 (12) 38 (20) 17 (13) 11 ( 6) 10 ( 9) 66 TABLE 17. Gm. (I) (2) (3) (4) (5) I 56 (130) 4 ( 3) 5 ( 2) 4 ( 2) 3 ( 2) II F (360) F ( 15) 80 ( 6) F ( 5) F,i8 ( 4) III F ( 34) F ( 15) 44 ( 11) 11 ( 8) 10 ( 9) IV 61 ( 56 22 ( 35) 18 ( 31) 16 (23) 17 (14) V 128 (106) 32 (35) 30 ( 30) 22 (24) 20 (28) VI 210 (170) 89 (100) 80 ( 90) 72 (48) 67 (35) VII 140 (158) 60 (118) 53 (101) 50 (go) 49 (84) VIII 210 (116) 90 ( 75) 92 ( 60) 84 (52) 80 (59) IX 5 ( 10) 4 ( 5) 4 ( 6) 3 ( 3) 4 ( 4) X F ( F) F ( F) F ( 35) 80 (18) 72 ( 7) XI F ( F) F (280) F (210) F (40) 90 (70) TABLE 18. Sb. (1) (2) (3) (4) (5; I - 25 ( 5) 23 ( 4) 6 ( 5) 5 ( 3) 4 ( 4) II F ( 3) 70 ( 4) 6 ( 4) 6 ( 3) 4 ( 3) III F (55) F (40) F (38) 3i (26) 26 (16) IV 28 (18) 24 (11) 12 (12) 8 (10) 7 ( 9) V F (27) F (28) F (25) 50 (36) 41 (24) VI F (41) F (42) F (36) 56,2 (40) 4 (38) VII 117 (44) 75 (42) 62 (40) 60 (38) 53 (33) VIII 126 (78) 100 (40) 67 (30) 47 (32) 50 (28) IX 4 (10) 14 ( 2) 7 ( 4) 5 ( 3) 3 ( 2) X 7 (10) 5 ( 5) 5 ( 7) 6 ( 4) 4 ( 5) XI F (20) 43 (14) 28 (20) 20 (15) 19 (16) 67 TABLE 19. Mg. (I) (2) (3) (4) (5) I 14 ( 2) 2 ( 3) 2 ( 2) 2 ( 2) 2 ( 2) II 62 ( 5) 8 ( 3) 3 ( 2) 4 ( 2) 3 ( 2) III F ( 9) 105 ( 7) 11 ( 8) 10 ( 7) 9 ( 8) IV 26 (27) 12 ( 9) 13 (10) 10 ( 9) 9 ( 8) V 60 (22) 11 (20) 5 (18) 5 (17) 5 (15) VI 75 (38) 26 (26) 19 (24) 13 (20) 10 (21) VII 80 (51) 45 (28) 65 (26) 50 (24) 48 (21) VIII 55 (35) 90 (30) 40 (30) to (25) 42 (24) IX 4 ( 2) 3 ( 2) 3 ( 3) 2 ( 2) 3 ( 2) X F ( 3) 85 ( 4) 7 ( 3) 5 ( 2> 6 ( 3) XI F (20) no (15) 2-1 (II) 13 (10) 14 (i3) TABLE 20. Mi. (1) (2) (3) (4) (5) I 54 ( 2) 4 ( 2) 2 ( 2) 3 ( 2) 2 ( 2) II 120 ( 2) 6 ( 30) 3 (27) 3 ( 3) 3 ( 2) III 152 ( 93) 22 ( 24) 18 (19) 20 (11) 17 (10) IV F ( 7) 365 ( 3) 3i ( 4) 25 ( 3) 18 ( 3) V 70 ( 72) 12 ( 7) 10 ( 7) 11 ( 6) 9 ( 6) VI 30 (172) 10 ( 17) 11 (11) 10 (11) 10 (12) VII 89 ( 44) 43 ( 36) 30. (3^ 28 (27) 24 (25) VIII 89 ( 50) 74 ( 45) 38 (42) 39 (40) 3i (36) IX 23 ( 50) 7 ( 6) 4 ( 4) 6 ( 3) 4 ( 2) X F ( 12) 90 (140) t6 (40) 8 (15) 6 (15) XI F (226) 240 ( 30) 210 (19) 145 (15) 90 (14) 68 TV ^BLE 21. Mm. (I) (2) (3) (4) (5) I 32 ( 6) 8 ( 2) 3 ( 2) 3 ( 2) 3 ( 2) II 72 (25) 3 ( 8) 3 ( 3) 3 ( 2) 3 ( 2) III 215 (24) 100 (12) 28 (11) 20 ( 9) 18 (10) IV F (13) 45 ( 7) 22 ( 6) 9 ( 6) 8 ( 6) V 30 (14) 10 (12) 10 (10) 9 (11) 10 ( 9) VI 375 (20) 60 (18) 12 (14) 8 (16) 8 (14) VII 135 (34) 80 (30) 62 (28) 30 (25) 29 (24) VIII 105 (40) 100 (38) 65 (29) 35 (31) 30 (28) IX 35 ( 2) 4 ( 3) 4 ( 3) 4 ( 2) 3 ( 3) X F (60) . 90 (11) 16 (12) 4 ( 9) 5 ( 7) XI F (55) 345 (30) 290 (27) 184 (28) 60 (21) 69 4 . DISCUSSION OF RESULTS. I have given first of all the tables showing the time record of each reagent. The figures (i), (2), (3), (4), (5), across the top refer respectively to the five methods of working the puzzle, viz. : 1. Without directions. 2. After hearing directions. 3. After reading directions. 4. After visual demonstration. 5. After solving it under guidance. Under these figures the first of each of the two columns shows the time in seconds on the first series of tests (the real experiments), the figures in parenthesis show the time on the control tests, 7 days later. "F" means failure. The roman numerals on the left margin indicate the eleven puzzles, as described above. A. PRELIMINARY. Before proceeding to discuss the results shown in these tables it is necessary to say a few words about the other attempted methods of recording results, dealing with false moves, exclamations, introspective reports, and fatigue. (1) First, as to the exclamations of the reagent during the course of a test (and under this word "exclamations" I include also all re- marks). Only in a very few instances did this record amount to any- thing. And this chiefly for two reasons. First of all, the exclamations were extremely few ; most of the reagents worked in perfect silence. To request exclamations now and then would have been to introduce an artificial and diverting element. The other reason why this method of seeking results amounted to so little was because when the exclamations were made they seldom were of such a nature as to throw any light on the mental processes functioning at that particular time. They were chiefly emotional, such as "Well!" "My!" "This is a tough one!" etc. Now and then a little information was revealed by such remarks as "Now I see it," "Here she comes," "At last !" etc., but in most instances such a course of events was indicated also by facial expression, or more generally by rapidity of movement to an immediate solving of the puzzle. What exclamations were of value will be noted in the discussion of the individual records below. 70 (2) The effort to keep an exact record of false moves was likewise exceedingly disappointing. And this for a number of reasons : for example, it was impossible to divide every series of movements into just so many moves; it was often difficult to tell whether a slight motion in the wrong direction, but immediately checked, was to be counted a move or not ; various moves would be right if they had been preceded by certain other moves, but not having been thus preceded, were they all to be counted false even though they were purposely aimed at the right re- sult? In short it was found quite impossible to reduce to any exact quan- titative expression the multitude of long, short, rapid, slow, accidental, purposeful, simple or complicated movements in the course of solving most of the puzzles. I had never before attempted any careful record of exclamations or false moves, but, encouraged by the report of Ruger, I had entered this undertaking with high hopes. My discovery of the seemingly insuperable difficulties involved was not, therefore, in ac- cordance with any mental prepossessions but rather contrary to such. (3) When the reagents were asked for a statement of their memory as to how they finally got through the puzzle, I occasionally got a gleam of real information, but seldom. In most instances they could not state any distinct memory. They had gone from step to step, often passing on by a mere chance move. In a few instances they had "seen through" the whole situation involved, but not often. Possibly the greatest regularity was in the case of the maze puzzles where a number of the reagents soon discovered that some of the openings from an outer to an inner square led to "blind alleys," and they therefore learned to run their eye on in advance to reconnoitre before tracing a line through an opening. None of them discovered for themselves the underlying prin- ciple of even the simpler maze ; the nearest to it was Db's observation that he went as far as he could before turning from one square into the next one. Of course the reagents had not been requested at the beginning to make special note of the way they solved their puzzles so as to report. Such would have proven a diverting element. As to the introspective reports then we may say : they seldom were definite, and wherever at all definite the reports of the different reagents were in quite general disagreement. This method contributed nothing positive, unless it be that feature on which there was the least disagreement, namely, that most of the puzzles had finally been solved by the "I don't- know-how-I-did-it" method. This does not mean, however, that chance 71 was the only factor in the solving, individual time records were too much in agreement to admit this. (4) As to fatigue, its influence was avoided as much as possible, as indicated above. The one exception to this rule was in the case of Mg, who became weary and nervous when about two-thirds through the sitting. She was continued, however, to the end of all the puzzles, and it is difficult to see any noticeable effect of this upon the time record of her last 3 or 4 puzzles. Her failure to get puzzles X and XI without directions is not far different from the experience of other reagents. See, for instance, Sb, Bb, Bg, Mm, Mt, Rd, Pd, and Gm. B. INDIVIDUAL RECORDS. Based on the Real Experiments. There remains only one basis of study which is exact, definite and continuous throughout, namely, the time record. On this as a basis let use note first of all some comparisons of the work of different reagents, making use of what exclamations or introspections we can as we pro- ceed. (1) Taking the high school group we have two boys and a girl. Of these one boy and the girl, Bb and Bg, were especially bright in school work, while the other boy, Db, was dull and disobedient, as de- scribed above. As to the two bright students, there is not a great deal of difference between them. The girl was somewhat the better student but the boy did better on the puzzles without direction. The girl failed in two puzzles, the boy in only one ; but that one the girl had done. Of those puzzles in which both succeeded the girl's total time was 1756 seconds, the boy's 1662. The surprise comes when we compare the work of these two bright students with that of the incorrigible and slow- minded (school mind) Db. He is in every respect ahead of both the others. He did not fail in the working without directions of a single puzzle, and, furthermore, in only one puzzle is he slower than both the others (III) and in only one other puzzle is he slower than either one of the others (IV). A glance at these three tables will show how very much quicker than the other two Db was in nearly all the puzzles. For instance, Puzzle V, Bb 155, Bg 280, Db 10. Again Puzzle VIII, Bb 300, Bg 230, Db 45. Db's total time in the 8 puzzles done by all these three reagents was only 565, approximately 3 times as fast as the others. Nor do we find Db's lead confined to any special class of puzzles. He 72 excells in them all, with the exception of the simpler tracing puzzle. In .one other respect Db excells his two bright fellow students. It will be noticed that it took Bb the second solving to give him a real grip of Puzzle II, the third solving for Puzzle VI, the third for Puzzle X, and the second for Puzzle XI. Likewise Bg failed absolutely on Puzzle II until the fourth attempt, and then at her next try she ran up from 4 seconds on the fourth to 45 on the fifth. Moreover she did not really grasp Puzzle III until the fifth solving, Puzzle IV until the third, Puzzle X until the third, and her fifth result on Puzzle VIII was still away up at 130. Now with all this slow and uncertain learning compare Db's record and we find only three such instances, and none of them ex- treme: Puzzle II needed a second try to fix its method (due undoubtedly to turning it quarter-way around), Puzzle X needed three solvings and Puzzle XI two, before Db was master of them. All this constitutes a remarkable record for such a scholastic and disciplinary outcast. In fact we may anticipate coming discussion and say that without any question the figures of Db make decidedly the best record of the entire group of eleven reagents, young and old. Here is ground for some valuable pedagogical research. (2) Let us next look at the record of the two college graduates, Ba and Pd, the latter a man in his prime, holder of four degrees. On the whole Ba's record is above the average. Most of his initial times are brief. He failed in only one puzzle. This becomes interesting when we note that it was the second match puzzle and was worked successfully by both the high school boys and by all three of the middle-aged women. All the weaker reagents, however, failed in this puzzle, that is, the 6 year old boy, the retarded development reagent and the aged woman. Why is this college graduate's generally excellent record weakened by such an inconsistent thing as agreement with the worst records in this comparatively simple puzzle? That his failure is not some sort of mistake is shown by the fact that even after hearing the directions read he failed again. (3) When we pass on to our university man, Pd, we are surprised to find his record the weakest of all outside our three abnormal cases (the small boy, the old lady and retarded development reagent). Pd has four initial failures — Puzzles I, II, VI and X. Puzzle X is admittedly difficult ; and yet it was done by Ba, Bb and Db, the latter two high school students, and, what is still more interesting, by the small boy 73 Sb in 7 seconds. Pd's failure in Puzzle VI, the second tracing puzzle, puts him in this item below Ba, below all three high school students, below all three of the middle-aged women, and even below the 70 year old woman, who solved this puzzle in 210 seconds. As to Pd's failure in both the match puzzles, it only goes to weaken his record the more. The retarded development reagent was the only other person failing in both these match puzzles. No one else at all failed in the first, and only Ba, Sb, Bg, in addition to Rd, agreed with Pd in failing in the second. Judged objectively Pd had by far the best mind of all the reagents, and yet in four out of the eleven puzzles he is completely outstripped by most of the others. Here we have another problem. (4) It will be interesting to examine the record of Gm, the 70 year old woman. Her initial failures are four, Puzzles II, III, X and XI. In the first two instances she failed also after hearing the direc- tions read ; in Puzzle X she failed the third time, after reading over the directions herself ; and in Puzzle XI she continued to fail until she herself had worked the puzzle under guidance. The significance of such, figures will be discussed below when we come to study the results of these five different methods of learning puzzles. It will be not'ced that, with one exception, as soon as Gm got the idea of a puzzle she worked it thereafter with no hesitation above that due to lack of practice. She approximated her physiological limit as soon as she had once solved the puzzle. The exception is in Puzzle II. There she worked it in the slow time of 80 seconds after hearing the directions read, and her fourth and fifth attempts were failures, she requiring to solve it under direction the second time before mastering it, as shown by her next record of 18 seconds. Taking Gm's record as a whole it is un- expectedly good in view of her advanced age. (5) We now swing to the other extreme and consider the work of Sb, the 6 year old boy. Here there are surprises. For instance there are only five initial failures. Rd has eight, Gm four, each of the middle-aged women three, and even the scholarly Pd has four. Moreover this lad solved several puzzles where others failed, even not counting Rd. He solved Puzzle I where Pd failed. He solved Puzzle IV, the second geometrical puzzle, where Mm and Mt failed. In Sb's case, however, this puzzle was reversed, he being shown the cross and asked to form the square. Moreover Sb solved Puzzle X, the twisted nails, when Mt, Mm, Mg, Gm, Bg and Pd failed. That Sb's working of this puzzle was 74 not by chance seems indicated by his low initial time, 7 seconds, which was more than maintained by his subsequent trials of 5, 5, 6 and 5 seconds respectively. There are only three puzzles in which Sb re- quired more help than the hearing or reading of the directions in order to be able to do the puzzle. In all these three (Puzzles III, V and VI) the technical nature of the directions was too much for him to grasp. Again, Sb's initial time in those puzzles which he did work without any directions is unusually low, for instance, 25, 28, 117, 126, 4 and 7 seconds. Of this list the first item only is longer than the general average of the other reagents, the other times are as good as the average or, in some instances, better. Bg for instance took 594 seconds on Puzzle VII, Bb 167, Gm 140, and even Pd 130, while Sb got through in 117 seconds. On the whole the record of this small boy is quite sur- prising. He was taken up at first with only a faint hope of any results beyond continuous failure, but he has proved to be one of the most il- luminating and valuable cases. (6) We now pass to the record of Rd, the 34 year old case of re- tarded development. Here we find almost unbroken failure until the fifth trial, and in one instance (Puzzle II) until the seventh trial. The additional figures under the fifth column of Rd's record represent his work on trials beyond the fifth. Before each of these additional trials the reagent was once more put through the working of the puzzle with his own fingers, under guidance. In Puzzle IVa, the figure was reversed for Rd as for the 6 year old boy — he was shown a cross and asked to rearrange in a square. Rd was however also tried on Puzzle IV in its regular form. Puzzle VIII, the second maze puzzle, was omitted with Rd. It will be noticed that this reagent worked by himself only Puzzles IVa, VII (first maze) and IX (horseshoe) ; on all the others he failed repeatedly.' This is in striking contrast with the records of the 70 year old woman, of the 6 year old boy, and most of all with the record of the dull and incorrigible high school student, whose work in the puz- zles leads the entire group. It is perfectly evident from these results that there is an intellectual gulf between the young man of retarded development and even the little boy. In fact Rd's mental isolation could hardly be more graphically or conclusively set forth than by these com- parative records of definite quantitative results. Outwardly his actions are reasonably normal for a quiet, reticent person, but the puzzles re- veal a totally unsuspected degree of psychical abnormality. The other 75 chief contribution of Rd's case is in connection with the method of learning puzzles, which will be discussed in its proper connection. (7) Before closing this review of personal differences, as revealed by the puzzles, it will be interesting to glance at some comparisons within families. I purposely secured as reagents two generations in one family and three in another. Bb was the 13 year old son of Pd. A comparison of the record of these two reagents shows the son to be more successful at puzzles than his father. Both as to the number of failures, as to the length of the initial time when the puzzle was worked without direction and as to the time required for the fifth or last working of the puzzle, the son shows up better than the father. The father leads, however, in the readiness with which a puzzle is grasped after directions are given. In five instances (Puzzles II, VI, VII, X and XI) the son required more than one giving of directions to bring him to a mastery of the puzzle. There are but four of such instances in the record of the father, and of these only two (Puzzles II and X) are serious. The other family group was comprised of Gm, the mother of Mg, who in turn was the mother of the 6 year old Sb. Here it is sufficient to note two things. First, the middle-aged woman surpasses her 70 year old mother, as might be expected. Second, the record of the young boy comes close to that of his grandmother in many respects, and in a few points surpasses it. For instance his initial time on Puzzle I is less than half his grandmother's time. The same is true of Puzzle IV. And in Puzzles VII, VIII and IX his time is also less, although not by so great a margin. A comparison of final times shows him to be decidedly below his grandmother in six instances, viz. : Puzzles II, IV, VI, VIII, X and XI. The foregoing discussion should be sufficient to outline the leading results having to do with individual differences. Let us now consider the records from another point of view. C. METHODS OF LEARNING. Based on the Real Experiments. This section of the discussion deals with the relative value and signifi- cance of the five different methods of learning to solve puzzles. These five, it will be remembered, are (1) without any directions, (2) after hearing directions, (3) after reading directions, (4) after seeing the 76 demonstration, and (5) after solving the puzzle oneself under guid- ance. (1) A statistical exhibit may serve as the first grouping of results under this head. The number of times each of these five methods was followed by the first actual solving of the puzzle, taking into count all reagents and all puzzles, is as follows : (1) Without direction, 87 times. (2) After hearing, 19. (3) After reading, 2. (4) After demonstration, 4. (5) After doing, 10. (2) These figures, however, are somewhat misleading in this form. The test of a really successful method of learning is, it would seem, not so much the ability to work the puzzle after a good length of time but rather the ability to work it intelligently, which must mean promptly. We must pass on then to ask, how often did each of these five methods prove to be the immediate antecedent of a prompt and ready working of the puzzle, with a time reasonably near the reagent's physiological limit? Only such a test can reveal the fact that the reagent has actually grasped the idea or principle of the puzzle as a whole. To illustrate — we find that on Puzzle III Mg failed at first, succeeded in 105 seconds on the second trial and then made the remaining three trials successfully in 11, 10 and 9 seconds respectively. Now it is obvious that the real mastery of the puzzle came at the third trial, when the time dropped suddenly from 105 seconds to 11 and stayed there. In this particular stage of our inquiry we can disregard method (1) (without direction), and compare the value of the four methods which were based on directions in some form. Of course it stands without discussion that most of the puzzles were grasped without directions; but we now raise the question. If one cannot learn how to master a puzzle for himself what is the best method of being taught how to master it? Here our results are differ- ent from those of the preceding table. Real puzzle mastery was at- tained by the different methods with direction as follows : (2) After hearing, 41 times. (3) After reading, 19 times. (4) After demonstration, 8 times. (5) After doing, 11 times. 77 (3) But even this exhibit does not finally represent the underlying facts. Many of the 41 instances of success under method (2) followed, not a complete failure, but a self-working of the puzzle, without di- rections, one, however, that took so long as to reveal a total absence of real mastery. So method (2) in these cases comprised in truth much more than the mere hearing of the directions read : it was the hearing of the directions plus the visual and motor memories of hav- ing actually solved the puzzle with one's own hands just previously. To be sure the time on these particular initial solvings was always very great. But this does not mean that all this time was occupied in actually solving the puzzle. Most of the t ; me was taken up in ex- perimenting with false moves, but when the correct way was struck the puzzle was then solved very promptly. Method (2), then, is far from being a pure method of auditory directions. No one can doubt that the experience of having just worked the puzzle added far more to the mastery of the process as shown under method (2) than did the hearing of the directions. This point is easily proved by a further comparison of figures. Mastery of a puzzle first appeared under method (2) in 41 instances. But in 40 of these instances the puzzle had been previously worked out by method (1), although with a long time record. There remains, then, only a single instance (Pd Puzzle I) where method (2) gave a mastery of the puzzle when only failure had resulted under the first method. There are 8 cases which some might wish to add to this solitary instance, viz. : Sb XI, Mm IV and XI, Mt XI, Bg X, Bb XI and Pd VI and X ; but the time record in all of these under method (2) is so high compared with the minimum reached under later methods that it seems impossible to claim that in any of these cases real mastery was obtained under method (2). Let us, then, make one more exhibit, and let us show in this how many times each method resulted in im- mediate mastery of a puzzle, when all preceding methods had resulted in failure. This ought to give us the unmixed value of each separate method. The result is as follows : (2) After hearing, 1 time (Pd I). (3) After reading, 1 time (Ba II). (4) After demonstration, 3 times, (Sb V, Rd II, Gm X). (5) After doing, 11 times (Sb III and VI; Rd II, III, IV, V, VI, X and XI; Gm II and XI). It might appear at first sight that Bg on Puzzle II should be in this list 78 under method (4) (time, 4 seconds) ; but the time of 45 seconds in the next trial shows that the puzzle had not yet been truly mastered by method (4). This last exhibit is exceedingly instructive. It demon- strates the unquestionable superiority of method (5) in leading to a prompt mastery of a puzzle when previous methods have proved un- availing. Nor does the fact that with Gm Puzzle II had to be repeated once by method (5) and with Rd the same Puzzle had to be repeated twice by the same method before success came, in any wise reduce the great lead of this particular method. The solitary instances under method (2) and (3) respectively are practically negligible. The three cases under method (4) reveal some real value in that method, but they are not to be compared with the value of method (5). (4) It should be noticed that the eleven cases just discussed under method (5) are all taken from the records of Sb, Gm and Rd — the 6 year old boy, the 70 year old woman, and the retarded development re- agent. The three cases under method (4) are also from these same persons. Inasmuch as these were the three reagents who might be called abnormal, these facts are worthy of note. How then, we may ask, did the normal reagents learn? This question is partly answered by the exhibits in paragraphs 1 and 2 above. And yet we must remem- ber that the exhibit in paragraph 3 shows all the instances where a prompt mastery of the puzzle followed previous failure to learn Out- side of these 16 cases the learning was gradual. This means that while two or more methods contribute toward the mastery, no single one led directly to it. Every repetition of the directions or of the labored working out of the puzzle helped bring the reagent to a mastery. To credit the mastery to the last one of several cumulative methods in cases like these would be an ungrounded conclusion. It is interesting to note that of the 121 instances of learning a puzzle (that is 11 puzzles, times 11 reagents) 11 times the mastery was gained in the initial working of a puzzle, JJ times the mastery came suddenly later in the series, while 2>2> instances do not show any sudden grasping of the situa- tion at all, but indicate a quite gradual learning. (5) These tabulated results reveal a peculiar feature of the learn- ing process. More than once a low time record seemed to indicate that the puzzle had been mastered. But we are immediately surprised to find the following time record jump to a high mark. This phenomenon appears, for instance, in the records of Bg, Puzzles II, III and IV; 79 Gm, Puzzle II; Db, Puzzle II; Sb, Puzzle IX; Bb, Puzzle VI, and in a number of other places. Bg explained this lapse, introspectively, by saying that she had learned the puzzle in question under one method but the presentation of a new method confused her. This cannot be accepted, however, without much question, since the procedure of solv- ing each puzzle was the same throughout, and the methods were not different ways of solving the puzzle but different ways of presenting to the reagent exactly the same form of procedure. It seems quite evident that the solution had not been truly mastered until all great rises in the time record ceased to appear. D. SUPPLEMENTARY TESTS. On Methods of Learning. This seems to be the best point at which to introduce the results of a brief series of supplementary experiments, arranged with the particular purpose of separating entirely the motor and the visual methods of learning. It will be noticed of course that in all the results discussed above every instance of the actual working of a puzzle (motor experi- ence) was done with eyes open and thus involved an additional element, i. e., visual experience. An effort was made to separate these two forms from all other kinds of learning. This necessitated arranging a new set of tests. (i) The puzzles used here were the three metal puzzles numbered IX, X and XI in our list above — the horseshoe puzzle, the twisted nail puzzle and the key puzzle. (2) The reagents consisted of 20 persons all near 25 years of age, 10 of these were men and 10 were women. (3) The procedure was two-fold. One part consisted in taking one of these reagents and working before him one of the puzzles, he watching the process, but not being permitted to handle the puzzle, and then he asked to work it himself as quickly as possible, his time being taken on the stop-watch. The other part of the procedure consisted in blind- folding the reagent and guiding his fingers through an actual working of one of the puzzles. After this learning experience the blind-fold was removed and the reagent was asked to work the puzzle as rapidly as possible, an exact record being made of his time. In every instance the learning process covered two workings of each puzzle, either by the visual or the motor process, as the case might be. 80 (4) Puzzles and procedure were alternated so that the following conditions were obtained: (a) each of the 20 reagents worked all three puzzles; (b) no reagent worked any puzzle both ways; (c) each re- agent worked some of the puzzles after visual learning and the rest after motor learning; (d) total records were obtained for an equal num- ber of visual and motor cases; (e) and also an equal division of the tests between the men and the women. Thus for each of the 3 puzzles we have 10 visual records and 10 motor records, 5 of each being men, 5 women. For all the puzzles we have 30 visual records and 30 motor records, equally divided among men and women. The record tables follow : TABLE 22. Women Totals Horseshoe- Visual 64666 Horseshoe-Motor 33366 28 21 Nails- Visual Nails-Motor 19 5 7 27 13 10 5 13 40 16 7i 84 Keys- Visual Keys-Motor 23 27 26 118 105 73 55 35 44 67 299 274 >jt >j< ;j< >j< % % TABLE 23. Men Totals Horseshoe- Visual 5 6 10 6 3 Horseshoe-Motor 3723s 30 20 Nails-Visual Nails-Motor 7 27 6 4 18 50 (6) 16 (6) 27 31 7 62 131 Keys- Visual Keys-Motor 24 37 21 23 37 29 43 12 22 26 142 132 (5) The time totals of these records may be summarized thus: (a) As to puzzles — Horseshoe ; visual 58 seconds, motor 41 : Nails ; Visual 133, 81 motor 215: Keys; visual 441, motor 406. (b) As to sex — Women, total on all puzzles, visual 398, motor 379, total time for women JJJ ; Men, visual 234, motor 283, total for men 517. (c) As to methods of learn- ing — total time on visual learning, 632 seconds ; total time on motor learning, 662 seconds. (6) Concerning these totals, we may remark, (a) the men worked, on the whole, more quickly than the women. (b) Aside from this there is no general sex difference' apparent — in those puzzles where the men's motor time was greater than their visual time the women's record agrees, and vice versa, (c) The most significant result is that having to do with the comparative times of the two methods of learn- ing. With both men and women in the two simpler puzzles (horseshoes and nails) the visual method leads by a safe margin, but, on the other hand, the more difficult puzzle (ke}'s) is solved quicker by both sexes after motor learning than after visual learning. (7) A slight variation was introduced in the cases of the first and third male reagents on the motor learning of the nail puzzle. The figures there found in parenthesis indicate the time required to work the puzzle a second time, following their successful working with motor plus visual activity. These secondary figures represent such a great gain in time as to suggest the conclusion that the value of the combined visual and motor methods is decidedly more than twice as great as the value of either of those methods separately. E. PUZZLE DIFFERENCES. Based on the Real Experiments. Brief note should be made of what might be called individual differ- ences among these 11 puzzles. (1) A comparison of the different puzzle records by the same reagent shows immediately that the puzzles differed considerably among them- selves as to ease or difficulty of solution. Some were worked in 3 or 4 seconds, others required several hundred seconds, and others still completely baffled the same reagent until instructions were given him. This wide range in the difficulty of the puzzles goes toward increasing the value of results in methods of learning. According to Mill's "method of agreement" all irrelevant circumstances should differ as much as pos- sible. 82 (2) It is interesting to note that there were only three puzzles which one or more of the eleven reagents failed to solve without di- rections. These are Nos. VII, VIII and IX. Puzzle No. IX, the horseshoe puzzle, is the simplest of the three metal puzzles and is ex- tremely easy to work. The other two puzzles, Nos. VII and VIII are the two maze puzzles. These evidently belong to quite a different class from the other 7 puzzles. All one needs with the maze is to keep at his task and to mark a record of his path so as gradually to discover where he went wrong and where right. The time element in this group of puzzles is therefore the only significant feature. (3) The puzzle of possibly greatest interest is Puzzle II, the second match puzzle. It seems impossible to reduce the results on this puzzle to any law. This puzzle was done without instructions by the three young women, Mm, Mt and Mg, by the bright boy Bb, and by the dull boy Db — not a very homogeneous group. All the other re- agents failed to do it without directions. In the case of the college graduate Ba, it was the only puzzle of the 11 in which he failed. More- over after the first instructions he failed again. Pd failed at first, then took 58 seconds to do it after the first instructions before suddenly dropping to his physiological limit on the third trial. Gm, the 70 year old reagent, failed the first two times, worked the puzzle in 80 seconds on the third attempt, then failed twice more, but succeeded in 18 seconds on the sixth try. The retarded development reagent failed repeatedly six times on this puzzle, then worked it twice, in 26 and 9 seconds re- spectively. The bright girl, Bg, failed three times in succession, worked the puzzle on the fourth try in only 4 seconds, but at the fifth attempt required 45 seconds to find her solution. There is no other puzzle com- ing anywhere near Puzzle II in this lawlessness. One feature of the difficulty in this puzzle arose from my practice of turning it bodily around 90 degrees after each successful working. This broke up simple visualizing and threw the reagent back largely on the principle involved. But this feature alone is not sufficient to explain the seeming irrationality of the puzzle. Further and more extensive experiments with this par- ticular puzzle would quite probably disclose some law underlying its variations. (4) On the whole a careful study of the tables of results leads me to prefer the two more difficult metal puzzles, Nos. X and XI, for producing the most satisfactory results in the testing of the learning 83 process. These puzzles possess at least the following desirable features : (a) A good degree of difficulty without instructions. A number of the reagents failed at first in one or both of these puzzles, (b) A solution consisting of several steps or movements, and this requiring a reasonable degree of application in order to master it. (c) The possibility of a very low physiological limit. This makes it possible to demonstrate promptly when the principle of the puzzle has been thoroughly grasped : the element of practice enters in but little. F. CONTROL EXPERIMENTS. (i) It remains to call attention to the control experiments. The time for this control series is indicated by figures in parenthesis on the foregoing reagent tables. On the whole there is a most satisfactory relation between the detail results of the control series and of the series of real experiments. This serves to give substantial and representative value to the figures in the real series, showing that they follow normal lines and are not controlled by any inexplicable caprice. (2) Attention may be called, in passing, to an interesting feature arising from the time results in the control series. A careful study of these records in comparison with the records of the real series will serve to substantiate practically every item of individual difference among the reagents, as discussed above. The dullness of the retarded development reagent, Rd, is again revealed ; the unexpectedly slow time of the Doctor of Philosophy, Pd ; the keenness of Db, the incorrigible boy and hopeless student ; the general normal records of the three middle- aged women, Mg, Mm and Mt; and the exceptional quickness of the 6 year old boy, Sb — all of these features are nearly as pronounced in the records of the control series as in those of the real series. (3) The control series, moreover, furnishes a standardized basis for a comparative study of memory or retention in these different reagents. A study of the records with this in view will yield several very sug- gestive results. Let it suffice for our present purposes to call attention to but one item, that having to do especially with methods of learning. If in the control series we take the total time required first to solve each puzzle by all reagents who mastered that particular puzzle in the real series by a gradual learning, we find the average time at which the puzzles were first solved in the control series is 63 seconds. Over against this a computation entirely similar except composed of the records of those 84 who in the real series mastered the puzzle suddenly, rather than gradually, gives an average of 36 seconds. So far as it goes, this seems to indicate that those who originally came to a mastery of their puzzle suddenly retain the ability of working that puzzle again after a seven day period about twice as well as those who originally learned their puzzle gradually. 85 CHAPTER V. CONCLUDING DISCUSSION. COMPARISONS AND RESULTS. The foregoing discussion of results has covered many points and ap- proached conclusions quite frequently. Let us now endeavor to sum up in a few brief sentences those leading conclusions arising from this investigation which seem to be abundantly borne out by the data thus obtained, leaving untouched many of the minor or not thoroughly sub- stantiated conclusions suggested by the preceding discussion. It may be said then — (i) That there are great differences among puzzles, and when puz- zles are used for the investigation of mental features they need to be carefully selected, and if possible several puzzles of different types should be used at the same time. (2) The use of puzzles reveals striking personal differences among individuals. The differences thus discovered are frequently quite un- suspected, not being apparent to the ordinary observer. (3) Puzzles guide the way to a grouping of individuals on a basis of what may be called one kind of intelligence — not book knowledge, nor school intelligence, but the readiness with which one adjusts him- self to and masters a strange situation all the factors of which are within his control. This mental power is fairly fundamental to the general activities of life. (4) The most efficient way of learning to do a strange thing is the combined motor-visual method consisting of the experience of actually doing the thing correctly, under guidance, thus coordinating motor with visual impressions. (5) Those motor experiences are best retained which come first to the mind in the form of a rather sudden and hence somewhat in- tense experience. 86 (6) There is little difference in the learning value of pure visual as compared with pure motor impressions, although the value of the latter tends to rise as the complexity of the mechanical problem increases. When these conclusions are compared with Dr. Ruger's work there is found some discrepancy but no real contradiction. The discrepancy arises largely from the fact that the two problems do not exactly coin- cide. While there is much in common between Dr. Ruger's monograph and this present paper, there are differences of point of view and of method. Ruger used only one method, with no control experiments : the present investigation makes use of five methods in the real series fully repeated in a control series. Again, Ruger endeavored to peer into the subjective workings of the human mind when dominated by the puz- zle consciousness, while the present study places much emphasis on objective methods of learning, in an effort to discover what are the most economical and therefore the most efficient means of bringing the mind to a mastery of a normal problem-situation. For these, as well as for other reasons, each of these two sets of conclusions has certain sec- tions peculiar to itself. As to those portions of the field possessed in common by these two researches there is fair agreement. Ruger found great individual varia- tions : so do I ; but I would not make the differences as arbitrary and lawless as he seemed inclined to do. Ruger touched the question of grading "intelligence" by the use of puzzles : I go much further into this problem, but at the same time I restrict the scope of the intelligence thus tested. Ruger concludes that the most efficient method consists of analysis and the adoption of new hypotheses. So far as my intro- spective reports extend and so far as they can be trusted they point in the same direction, although not with satisfactory certainty. Prac- tically none of my reagents furnished corroborated testimony of having seen clear through any but the very simplest of the puzzles. Here Ruger's reports are more definite, but, being purely introspective, we do not know to what extent we can trust them. In those portions of my work which do not parallel Dr. Ruger's investigation, chiefly those having to do with the relative values of different methods of learning — auditory, visual, motor, etc., and those touching the relative permanence of sudden as compared with gradual acquisitions — in these and other unique sections of the present study there is nothing that necessarily con- 87 tradicts any of the results obtained by Dr. Ruger. My conclusion as to the longer retention of those experiences which first come suddenly to the mind is in harmony with the generally accepted notions of the greater permanence of intense impressions and the greater usefulness of vigorous beginnings in the formation of habit. (i) This report ought not to close without embodying a few practical pedagogical suggestions rising out of the foregoing investigation. It may be said then, first that the teacher will do well to watch, preferably by means of puzzle tests, for those individual differences among his pupils which may very likely represent different capacities for learning. The pupil truly retarded will show it in these tests ; while more than one who is poor at books may be discovered to be very quick at other forms of learning. Such an one is therefore still thoroughly teachable, the problem is, to get at him in the right way. (2) And as to what way is the right way may also be suggested by puzzles. Set him to a concrete task in which the motor element figures prominently and see if he does not find a way out. This idea can surely be carried over in some form or another into the routine teaching process. (3) Another profitable line of application could be based upon the demonstrated superiority of the coordinated visual-motor process. If the instruction to be imparted in the school could be cast into this form the mastery of the situation would unquestionably be hastened and made more permanent. (4) It may also well repay the teacher to follow out the idea sug- gested by the high retention-value of sudden as compared with gradual masteries. (5) Again, the very form of puzzle-learning is suggestive. It in- volves the recognition of a definite problem. Now if the teacher can bring his pupils to see that the morrow's lesson, for instance, is their problem and that they are to work this out as much as possible for them- selves, great pedagogical gain will unquestionably be made. As far as possible let each pupil discover in connection with coming instruction his own problem. Give him some liberty of choice. Allow for individual differences in interest. Then when he has found his problem and feels that it is his let him work out its solution somewhat in his own way 88 and as far as he will on the strength of his own initiative. This is good teaching. This also is puzzle-learning in another form. (6) One thought remains, it grows out of the great difference be- tween what we may call the school-rating or book-learning rating of reagents, on the one hand, and their rating in the solving of puzzles, on the other. It is a tair question to ask: Which represents a better equip- ment for meeting the ordinary situations of real life? Now if all students were to become teachers or professors, our answer would be immediate, and in favor of book-learning. But when one looks out over the life if men and women in general, he can not help pausing thoughttully as he asks himself such a question as the above. Are our schools loading up boys and girls with an accumulation of learning which is largely conventional, and this to the exclusion of opportunities for development along lines of practical and motor response? If so, is this best? If it is the function of the school to prepare for citizenship; to prepare lor life ; to fit one to be the best possible member of the body politic, to contribute the most possible to the economic whole, to help '.reate and maintain the highest possible type of the family, to himself attain and to help others attain the largest possible form of self-realization — if this is the function of the school, is the school using the best means to accomplish this most practical and far-reaching end? All this may seem a long remove from the pyschology of puzzle- learning, but as a matter of fact it springs out of our present investigation of several points. To indicate but one, let us remind ourselves of Db, classified by the school system with which he had been in contact as a "reject." Incorrigible in conduct, hopeless in books, he was turned out and away. But in puzzle-learning he clearly outstripped all my other reagents and all but two of them (the small boy and the 70 year old woman) were unquestionably his superiors in schooling. Has the school nothing more for such a promising case? Is it taken for granted that he can never be a valuable citizen because he fails to meet certain academic requirements? Must he continue his training for life either on the street or under certain conditions of self-depressing social disapproval, tagged as hopeless if not harmful? There is far better stuff in this boy than the system can give recognition to. But one cheering sign of the times is the movement already under way to include such promis- ing but irregular cases within the scope of the school's preparation for 8q effective functioning as citizens in an enlightened state. A beginning has been made, but much yet remains to be done. The foregoing investigation while it has answered some questions has raised new ones : for every problem to which it offers a solution it calls attention to some other problem demanding further research. It may be well, in closing, to note some of these suggestions for further study arising out of the work here reported. (i) As to Pd's unexpectedly slow work with puzzles — is it due to a native weakness along this line, or did he once possess good puzzle ability which has been lost through years of abstract thinking? Is this true of all similar cases? (2) If this second alternative is not the true one with Pd, and for some reasons I am inclined to believe it is not, did Pd ever possess those qualities of mind which made it possible for him to master for himself new situations in any of the realms of learning? Was he ever an original thinker, a real discoverer? Or was he a man with but a good rote memory, easily able to accumulate and retain many facts, but lacking in fundamental strength of all inventive powers? Could he see and remember a thing in many relationships, when they were pointed out to him, while yet unable to seize upon new relations for himself? Did he always lack the critical and the creative mind? Does his record in puzzles indicate this? For a number of personal reasons I so believe. The wider problem is — can puzzles be trusted to reveal the native presence or absence of this particular form of mental power in any or all persons properly tested? (3) As to the small boy, Sb, should we find his unusual readiness to work puzzles indicating a type of mind which can readily grasp mathe- matical forms and processes — and would not this hold true of all such cases? (4) Should we not find that all instances of school dullness ac- companied by totally unsuspected puzzle brightness, such as we have in Db, would respond vigorously to various difficult forms of learning in connection with the manual arts? (5) Does it hold true universally that for simpler motor processes pure visual presentation is more effective than pure kinesthetic, while as the processes increase in complexity the kinesthetic presentation soon comes to lead all others as a method of learning? 90 (6) If so, can this principle be transferred to other than material subject matter, so that in abstract subjects and in the realm of pure ideas, the greatest economy of learning can be achieved by the use of the kinesthetic presentation, if such can be devised? 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