r I I 'M H I I ( M 
 
BOUGHT WITH THE INCOME OF THE 
 
 SAGE ENDOWMENT FUND 
 
 THE GIFT OF 
 
 flenrg W. Sage 
 
 1891 
 
 ar2.>r5>oA lb) y|lb. 
 

 3 1924 032 705 554 
 
 olin 
 
The original of tliis book is in 
 tine Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924032705554 
 
RIVERSIDE TEXTBOOKS 
 IN EDUCATION 
 
 EDITED BY ELLWOOD P. CUBBERLEY 
 
 PROFESSOR OF EDUCATION 
 LELAHD STANFORD JUNIOR UNIVERSITY 
 
RIVERSIDE TEXTBOOKS 
 IN EDUCATION 
 
 RURAL LIFE AND EDUCATION. 
 By E. P. CuBBERLEY, Professor of Education, Leland Stanford 
 Junior University. $1.50 net. Postpaid. 
 
 THE HYGIENE OF THE SCHOOL CHILD. 
 
 By L. M. Terman, Associate Professor of Education, Leland 
 Stanford Junior University, ifi.65 net- Postpaid. 
 
 EVOLUTION OF THE EDUCATIONAL IDEAL. 
 By Mabel \. Emerson, First Assistant in Charge of the George 
 Bancroft School, Boston. $1.00 net. Postpaid. 
 
 HEALTH WORK IN THE SCHOOL. 
 By E. B. HoAG, M.D., Medical Director, Long Beach City 
 Schools, Cal., and L. M. Terman. $1.60 net. Postpaid. 
 
 DISCIPLINE AS A SCHOOL PROBLEM. 
 By A. C. Perry, Jr., District Superintendent of Schools, New 
 York City. S1.25 net. Postpaid. 
 
 HOW TO TEACH THE FUNDAMENTAL SUBJECTS. 
 By C. N. Kendall, Commissioner of Et'ucation for New Jersey, 
 and G. A. Mirick, formerly Deputy Commissioner of Education 
 for New Jersey. S1.25 net. Postpaid. 
 
 TEACHING LITERATURE IN THE GRAMMAR GRADES AND 
 HIGH SCHOOL. 
 
 By Emma M. Bolenius, formerly Instructor in English, Central 
 Commercial and Manual Training High School, Newark, N.J. 
 i!i.25 net. Postpaid. 
 
 PUBLIC SCHOOL ADMINISTRATION. 
 By E. P. Cubberley. gi.75 net. Postpaid. 
 
 THE PSYCHOLOGY OF THE COMMON BRANCHES. 
 
 By F. N. Freeman, Assistant Professor of Educational Psycbol- 
 ogy. University of Chicago. Si .25 net. Postpaid. 
 
 THE MEASUREMENT OF INTELLIGENCE. 
 By L. M. Terman. In Press. 
 
fioi|||i»iit|||ww|||iiiHi|||iii«iminin|nin|wiii|||ii<<ii|i|n>w|i»iH|i|H>W|m i|i|iniij|||iiHii|||iiiiii|||iiiiii|||jiiiii|||iiiiii{||iiHii|||ii>iii|||ii"ii|||ii"j 
 
 =-j.lriiiiilllliiiirlllliiiilllltiiiiilllliiiiilll I'll llllriiillllltiiillllliiiillllii.iiJlllliiiiilll llliiiiillllliiiillllliiiiillllniillllliiiillllr lIllii.illllliiiilllliiniilL-J 
 
 THE 
 
 PSYCHOLOGY OF THE 
 COMMON BRANCHES 
 
 BY 
 
 FRANK NUGENT FREEMAN PH.D. 
 
 ASSISTANT PROFESSOR OP EDUCATIONAL PSYCHOLOGY 
 THE UNIVERSITY OF CHICAGO 
 
 HOUGHTON MIFFLIN COMPANY 
 
 BOSTON NEW YORK CHICAGO 
 
 S-^|l»ni||tli>>il|||l»iil|no"il|||li"il|||li'iiH||li'<n|||li'«l|||U"il|||U"ir||| I|||l>'<ll|||l<''ll|||li"il|||liii||{||liiiii|j|ii>iii{||iiii|i|||ii<ui|||i |i| miimi^^ 
 
 lijiulllibiulllUiiiilllmiiinihiiiilllHioilfltiiiiillliuuillliiiiiillliiiiulltihiiillliiiiiilltiiimlltmiiilltii^ 
 
COPYRIOHT, I916, BT FRANK NUGENT FREEMAN 
 ALL RIGHTS RESERVED 
 
 tEie Sitnniat 9nM 
 
 CAHBRIDGB . MASSACHUSETTS 
 U . S . A 
 
 txe^c i rf J J 
 
 a^^ 
 
/ 
 
 EDITOR'S INTRODUCTION 
 
 The present volume is a very interesting as well as 
 a very successful attempt to apply the knowledge 
 which we have recently accumulated in the scientific 
 applications of psychology to the concrete problems of 
 instruction in the elementary school. It is neither a 
 scientific treatise on psychology nor a book of special 
 methods, though embracing something of the content 
 of each. Instead, the present volume occupies a field 
 lying between the two, being a presentation of the 
 psychological principles underlying the most eflfective 
 instruction in the commonly recognized subjects of 
 the elementary-school curriculum. 
 
 Textbooks on general and even applied psychology 
 almost of necessity deal with the fundamental prin- 
 ciples and generalizations of the science, and the ap- 
 plications are usually so remote from the practical 
 problems of the teacher that the application to class- 
 room procedure is seldom made. On the other hand, 
 our books on general and special methods, while often 
 very helpful and suggestive in their way, tend never- 
 theless to confine their attention to schoolroom de- 
 vices and certain general pedagogical principles, and 
 do not serve to develop in the teacher any tendency 
 to seek out or formulate the reasons for the special 
 methods which are being followed. 
 
vi EDITOR'S INTRODUCTION 
 
 In between these two extremes of psychology on 
 the one hand and special or general methods on the 
 other lie two new fields in applied psychology — 
 genetic psychology, which attempts to organize psy- 
 chological knowledge in terms of mental evolution, 
 and the psychology of the process of learning to write, 
 read, spell, calculate, etc. Genetic psychology lies 
 nearer to the pure psychology end, and the psychology 
 of learning lies nearer to the methods end. 
 
 The present volume is a treatise on the second of 
 these two intermediate fields, namely, the psychology 
 of the learning process, and as applied to the so-called 
 fundamental subjects of the elementary-school course. 
 For three of the subjects applications are made to the 
 high-school field as well. The attempt has been made 
 so to present the fundamental psychological facts as 
 to give a clearer understanding of the pupils' diffi- 
 culties, the best methods for overcoming these, and 
 the psychological reasons for the special methods to 
 be pursued. A leading purpose has been to show the 
 teacher how to follow or apply methods intelligently, 
 and especially how to adapt methods to the peculiar 
 needs of the individual pupil. 
 
 The order of treatment deserves mention, as it 
 follows the well-known pedagogical principle of pro- 
 ceeding from the simple to the complex. The volume 
 begins with the psychology involved in the teaching 
 of handwritings which requires a relatively simple 
 form of learning of the sensori-motor type. This is 
 
EDITOR'S INTRODUCTION vii 
 
 followed by the psychology involved in teaching 
 drawing, reading, and music, which are good examples 
 of what is known as "perceptual" learning. Next 
 follows the psychology of instruction in spelling, which 
 is an example of the fixing of associations. This in 
 turn is followed by history and geography, which are 
 examples of a more difficult teaching process, as they 
 involve the organization and extension of experience 
 through the use of the imagination. Next comes the 
 psychology of teaching mathematics, with applica- 
 tions to instruction in algebra and geometry as well 
 as arithmetic, studies which involve abstract thinking. 
 The volume closes witha consideration of the psycho- 
 logical principles involved in giving instruction in the 
 natural sciences, which involve the ability to general- 
 ize upon the basis of accumulated experience. Taken 
 in this order and together, the different elementary- 
 school subjects offer an excellent basis for the presen- 
 tation of the chief types of the learning process. 
 
 Such a volume as this would not have been possible 
 a decade ago, and the fact that it is possible to-day 
 serves to illustrate the rapid advances being made in 
 experimental education. It has required much tech- 
 nical knowledge and considerable skill in presentation 
 to organize, in a simple and non-technical form, the 
 practical results of the many scientific studies of the 
 learning process which have so far been made. As a 
 textbook in courses in elementary education in normal 
 schools and colleges this volume should find large 
 
viii EDITOR'S INTRODUCTION 
 
 usefulness, and it should also prove of much service 
 as a simple treatise on the psychology of elementary- 
 school methods for teachers organized into reading 
 circles or study clubs. 
 
 EliLWOOD P. CUBBEBLET. 
 
PREFACE 
 
 During recent years there has been a good deal of 
 investigation for the purpose of analyzing the learning 
 processes which are characteristic of the common 
 branches. The publication of E. B. Huey^s Psychology 
 and Pedagogy of Reading marked the first attempt to 
 bring together some of this material and present it in 
 such a form that it woiJd be serviceable to teachers. 
 Additional material on reading has become available, 
 and considerable work has also been done on writing 
 and spelling, and a little on number. The accumulation 
 of data has reached a point which seems to justify a 
 comprehensive account of the psychology of the com- 
 mon branches. The amount of experimental founda- 
 tion for the analysis of the different subjects varies 
 from a fau-ly satisfactory amount down to nothing. 
 In the case of the subjects which have not been directly 
 investigated, however, there has been experimentation 
 upon the mental processes which are very obviously 
 involved in them — as in the case of history — so that 
 most of the discussion has some experimental founda- 
 tion, direct or indirect. No apology is made for the 
 fact that a part of the analysis is in the nature of infer- 
 ence from general principles which have been thus 
 determined, beyond the acknowledgment that such 
 analysis is subject to later verification or revision by 
 
X PREFACE 
 
 direct experu^tation. One benefit to be derived 
 from making^^KmuIation, wlyn experimentation is 
 not yet completers that this serves to define some of 
 the problems and thus to stimulate investigation. 
 
 I take pleasure in using this opportunity to make 
 certain general and specific acknowledgments. For 
 the ea,rly direction and the continued encouragement 
 in the pursuit of psychology I am indebted to my col- 
 lege teachers. Professors A. C. Armstrong and Ray- 
 mond Dodge. Both in my work as a graduate student 
 and as an instructor I have been closely associated 
 with Professor Charles H. Judd, and owe the special 
 direction of my efforts, and much of the formation of 
 my views, to his influence. "He has also given helpful 
 criticism upon the manuscript of this book. Professor 
 S. C. Parker has given me valuable criticism and stim- 
 ulus, and I am indebted to Professor W. L. Miller for 
 carefully reading the whole manuscript. To many 
 others I am indebted, either for their general influence 
 and stimulus or for suggestions concerning the manu- 
 script. The help of all these, whether mentioned by 
 name or not, I gratefully acknowledge. 
 
 F. N. F. 
 
 Cbjcaqo, March 1, 1916. 
 
CONTENTS 
 
 I. Intbodttction I 
 
 n. Handwriting: Learning chiefly of a Sensori- 
 motor Chasacteb 6 
 
 The composition and development of the writing 
 
 habit. 
 Modifications due to age. 
 Individual differences and practice periods. 
 
 m. Drawing: Perceptual LEAiunNG .... 84 
 
 A demonstration experiment in drawing. 
 
 The nature of perception as illustrated in drawing. 
 
 Development of drawing with age. 
 
 General account of the nature of perception. 
 
 The value of sense training. 
 
 IV. Reading: Perceptual Learning .... 67 
 The relation of reading, writing, and spoken language. 
 The stages in learning to read. 
 Oral and silent reading. 
 E^dency in reading. 
 
 V. Music: Perceptual Learning 98 
 
 The recognition of intervals and melody. 
 
 Rhythm. 
 
 Harmony. 
 
 Tone-quality. 
 
 VI. Spelling: Fixing of Associations . . . .115 
 
 The assodations in spelling. 
 Methods of learning to spell. 
 The prindples of the drill method. 
 
xii CONTENTS 
 
 
 luAGINAsbN 132 
 
 General account of imagination. 
 
 The types d imagination employed in history. 
 
 The historical sense. 
 
 The grasp d historical development. 
 
 Critical examination of sources. 
 
 \U1. Gbogeaphy: Extension op Expeeiencb 
 
 THBOUGH Imagination 161 
 
 Growth of spatial imagination or orientation. 
 Maps and globes. 
 
 IX. Mathematics: Absteact Tbougbt . . . 179 
 
 Number an abstract mental process. 
 
 The early development of the number idea. 
 
 The development of the arithmetical operations. 
 
 The mental processes in algdwa. 
 
 The devdi^ment of geometry from measurement. 
 
 X. Natubal Scxence: Genkra t.tz a tion upon Ex- 
 PEBII37CE 839 
 
 Concept formation. 
 
 The devdopment of generalizatioii. 
 
 The practical aixd theoretical in scieDce teadiing. 
 
 Qdeshonb and Topics pob Dibcubsion . 285 
 Index 273 
 
THE PSYCHOLOGY OF THE 
 COMMON BRANCHES 
 
 CHAPTER I 
 
 INTRODUCTION 
 
 When the child takes pencil and paper and makes 
 his first attempt to write, he is beginning a long course 
 of training in the particular form of learning which we 
 call " sensori-motor," His first attempt is to make a 
 mark which shall look like the marks which are set be- 
 fore him as a copy, and the progress which he makes 
 as he practices consists in getting better and better 
 control over his movements so as to be able to pro- 
 duce letters and words which look more and more like 
 the copy. Writing does not require in any large degree 
 the exercise of memory, of imagination, or of reason- 
 ing. It requires, as the term " sensori-motor * implies, 
 the adaptation of movements to an object which is 
 perceived. In learning to read, on the other hand, 
 movements play a minor part compared with the ac- 
 quirement of the ability to recognize quickly and cor- 
 rectly the combinations of letters as they appear in 
 words, and to give them their true meaning. The un- 
 derstanding of number requires that one shall dis- 
 regard most of the qualities of objects and pay atten- 
 
2 PSYCHOLOGY OF COMMON BRANCHES 
 
 tion only to their number. Accordingly, we say that 
 learning number involves the process of abstraction. 
 Similarly, other subjects of the curriculum furnish il- 
 lustrations of other forms of learning. 
 
 There is a great deal of variation in the efficiency 
 with which these various kinds of learning are carried 
 on in the school. Some children learn rapidly, others 
 slowly. Some waste effort, others economize it. Some 
 reach a high degree of proficiency, others remain per- 
 manently at a low level. If we compare, not individual 
 children, but different classes or schools or school sys- 
 tems doing the same work, large differences in efficiency 
 still appear. 
 
 A certain proportion of the differences between 
 individual children, and even between different classes 
 or schools, may be attributed to differences in native 
 ability, but in large measure a child learns economically 
 and well, or the reverse, according as his learning is 
 supervised well or poorly. The child may stumble 
 along and by blind trial learn how to improve. In some 
 forms of learning, in fact, random trial forms a fairly 
 large part of the method. But when the child's efforts 
 are not intelligently guided, the amoimt of blind trial 
 is larger than necessary, and much time is wasted in 
 consequence. Experiments in supervised study have 
 shown that, even in the high school, the pupil needs 
 considerable help from the teacher to show him how to 
 go about his work in its more general aspects, and to 
 meet the special difficulties of each subject. How much 
 
INTRODUCTION 3 
 
 more is the elementary-school pupil in need of skilled 
 supervision! 
 
 In order to supervise the child's learning most 
 effectively, it is necessary to know what mental 
 changes take place in the different forms of learning 
 which he undertakes. Merely to know the result which 
 is aimed at is not sufficient — important as this is. 
 One can learn in a short time to distinguish between 
 good and poor writing, between an adequate and an 
 inadequate understanding of history or geography, or 
 between different degrees of proficiency in the pursuit 
 of a science. A clerk can correct examination papers 
 in arithmetic or spelling. These forms of discrimina- 
 tion make up the art of the examiner. When carried to 
 a high degree of perfection in the development of 
 standard tests of attainment, this art becomes more 
 difficult, and it becomes possible to use the results in 
 directing the pupil's efforts. But in the main the art of 
 the teacher is the far more dehcate one of following 
 the changes which take place in the mind of the pupil, 
 and of bringing to bear his influence upon them to 
 produce the highest degree of improvement with the 
 least expenditure of effort. In order to understand the 
 process which is going on in the child's mind when he 
 learns the various branches, it is necessary to have a 
 conception of the typical learning processes which are 
 involved in these branches. 
 
 It might be supposed that, having gone through the 
 learning processes himself as a child, the teacher would 
 
4 PSYCHOLOGY OF COMMON BRANCHES 
 
 have sufficient insight into their nature from his mem- 
 ory of his ovm efforts, without making any further 
 study of them. This memory of one's early struggles, 
 however, is not sufficient. In the first place, memory has 
 become very dim with time. From great familiarity 
 with the tasks which the child has to meet, one becomes 
 subject to the illusion that they are easy, and that the 
 only requisite for their performance is good-will. Let 
 the teacher try one or two of the tasks which are sug- 
 gested in the following pages as illustrations of learn- 
 ing of a sensori-motor or a perceptual sort, — such as 
 writing with the left hand or the toes, or gaining a 
 correct apprehension of the figure shown in chapter III, 
 — and he will get something of the baffled, helpless 
 feeUng which possesses the child which will set him to 
 searching for some way to help the child to find out 
 kow to meet the demands which are laid upon him. 
 
 A second reason why the teacher's early experience 
 is not enough to fit him for the task of guiding the 
 child in his learning is that the learning attitude and 
 the teaching attitude are different. The learner is 
 absorbed mainly in the result which he wishes to 
 accomplish, and he does not make much analysis of 
 the means by which he reaches his goal. In fact, he 
 sometimes will reach his goal more quickly if he does 
 not analyze the process very much. But the teacher 
 must have the analytical attitude. He must be con- 
 tinually thinking about how the act which he is teach- 
 ing can best be performed. For example, the child in 
 
INTRODUCTION B 
 
 writing does not pay attention to the movement so as 
 to know what simple movements compose it and how 
 they work together, but this information helps the 
 teacher to give the child exercises which will emphasize 
 the proper components. 
 
 While the analysis of the learning process in the 
 common branches, which occupies the following chap- 
 ters, does not go into the details of the methods of 
 teaching, the constant aim is to give practical assist- 
 ance to the teacher by giving the basis for an intelli- 
 gent use of methods. The different school subjects 
 taken together furnish a pretty comprehensive set of 
 examples of the various kinds of learning of which the 
 human mind is capable. The subjects are so arranged 
 that the simpler, more elementary, and less intellectual 
 forms of learning come first, and the higher types in 
 their order. The topics taken together furnish a fairly 
 complete account of psychology in its active or fun* 
 tional aspect, apart from the instincts and emotions. 
 
CHAPTER II 
 
 HANDWRITING: LEARNING CHIEFLY OF A 
 SENSORI-MOTOR CHARACTER 
 
 The sensori-motor form of learning of which hand- 
 writing is an example has for its purpose the develop- 
 ment of a motor habit.^ A motor habit exists when 
 such a connection has been formed between a set of 
 stimuli * and the movements which are made in re- 
 sponse to them, that the movements follow readily 
 upon the stimulus without the necessity of being guided 
 and directed in detail. Thus, when a person wishes to 
 write a word, it is not necessary to think about the 
 movements of the fingers or the arm which produce 
 the letters, nor is it necessary to think of the details of 
 the letters themselves. This is true of all sorts of 
 sensori-motor habits. 
 
 The composition and development of the writing hciblt 
 
 The problems of teaching writing are concerned very 
 largely with the development of an efficient movement. 
 We may, then, turn first to a consideration of the com- 
 
 ' A sensori-motor activity is one which consists in the adaptation 
 of a movement to a stimulus. 
 
 ' A stimulus is any object or event in the world outside the indi- 
 vidual which is capable of causing a sensation, an idea, or a move- 
 fnent — or, in other words, of producing a response. 
 
HANDWRITING 7 
 
 position of the writing movement and of the way in 
 which it is developed. 
 
 The writing movement is a very complex one. It is 
 composed of a great many elementary or simple move- 
 ments. In the first place, there is the movement of the 
 fingers and of the hand. Even if the letters are not 
 formed by finger movements, the fingers must be 
 employed in holding the pen. In doing this the first 
 and second fingers are separated in their action from 
 the third and fourth. The first two fingers with the 
 thumb hold the pen, while the third and fourth fin- 
 gers support the weight of the hand. This division 
 among the fingers is something which is more or less 
 artificial; that is, it is not the natural manner in which 
 the child grasps objects. The most primitive method 
 of grasping an object, which is seen not merely in the 
 child but also in the monkey, is to fold the four fingers 
 about it without using the thumb. The ability to 
 place the thumb against the tips of the fingers in 
 grasping an object is a distinctly human one and one 
 which develops later in the child than the other form. 
 The mere act of holding the pen in the conventional 
 manner, then, is a matter of considerable difficulty to 
 the child. 
 
 In addition to the adjustments or the movements of 
 the fingers there are movements of the various arm 
 joints. The wrist is frequently moved from side to side 
 during the writing of the letters of a word. This is not 
 a movement which is commonly appr'oved by writing- 
 
8 PSYCHOLOGY OF COMMON BRANCHES 
 
 masters, but it is very generally used. The hand also 
 is carried along the line by the movement of the elbow 
 and of the shoulder, together with the wrist. Whether 
 the greater part of the movement is made at the elbow 
 joint or at the shoulder will depend on the height to 
 which the arm is raised. If the arm hangs at the side, 
 none of the movement is made at the elbow. The 
 movement by which the letters are formed may also 
 be made partly at the shoulder joint. This movement 
 is sometimes called the forearm movement, but it is 
 not, as a matter of fact, made by the forearm. It may 
 be made with the arm resting on the muscle pad of the 
 forearm, but the muscles which produce the movement 
 are at the shoulder. The muscles in the forearm, on 
 the contrary, control the movements of the fingers, as 
 may be readily verified by placing the other hand on 
 the forearm and then closing the fingers. 
 
 These component movements cooperate in the total 
 movement. The writing movement to be most efficient 
 should be made lUp of a combination of these various 
 component movements, since each of them is particu- 
 larly suited to carry on some part of the whole task. 
 The side-to-side movement of the forearm, revolving 
 about the muscle pad as a center, should carry the 
 hand along from the left to the right side of the paper; 
 and this movement should go on while the letters are 
 being formed so that the writing does not have to be 
 interrupted. The movement of the whole arm from 
 the shoulder resting on the muscle pad of the forearm 
 
HANDWRITING 9 
 
 is well suited to carry the hand up and down so as to 
 play the chief part in making the upward and down- 
 ward strokes. It is probable that this large movement 
 produces a rhythm and regularity in the writing and a 
 smoothness of stroke which gives the written page a 
 good appearance. 
 
 Furthermore, it is probable that if a considerable 
 part of the movement is made with the arm, it is not 
 so fatiguing as when the fingers do the whole work. 
 The finer parts of the letters can most easily be made 
 with the fingers. Although the attempt is commonly 
 made entirely to exclude finger movement, it rarely 
 succeeds, and the most rational course is to recognize 
 that the fingers, as well as the arm, have their own 
 part to play. 
 
 Overslant at the end of the line may be corrected by 
 pronation. Besides these components of the writing 
 movement which produce the words, there is one which 
 is sometimes used to correct a fault resulting from the 
 mechanical conditions of writing. As the hand is 
 moved forward by the rotation of the forearm about 
 the muscle pad or the elbow as a center, the pen points 
 more and more to the right. This is illustrated in 
 Figure 1. This causes, unless it is corrected, an over- 
 slant of the writing at the right end of the line. In 
 order to correct this overslant, some writers turn the 
 hand and wrist over to the left, as it moves along the 
 line, so that the palm is more tumed-down or prone 
 and the penholder is more nearly vertical. This move- 
 
10 PSYCHOLOGY OF COMMON BRANCHES 
 
 ment is called " pronation." The reader may experi- 
 ment by comparing one series of strokes made while 
 the palm is prone and another in which the hand is 
 turned over toward the right, and he will see that those 
 
 Fio. 1. 
 
 CHANGE IN SLANT DUE TO THE MOVEMENT OF THE 
 HAND ALONG THE LINE 
 
 made with the hand turned down are more nearly ver- 
 tical than the others. Turning the hand down in pro- 
 nation, therefore, tends to correct the overslant of the 
 writing at the end of the line. 
 
 There are also adjustments of the eyes and of the 
 body. It will thus be seen that all the chief parts of 
 the hand and arm are used in writing, but this does not 
 exhaust the Ust of movements which are made or of 
 adjustments which must be maintained. The eye 
 moves in order to follow the writing of the letters and 
 to guide the movement. This must not be regarded as 
 
HANDWRITING 11 
 
 an unimportant part of the whole activity. It is so 
 important that it has been largely due to the recogni- 
 tion of the eye movements that important changes in 
 the teaching of writing have been made. In order that 
 the arm may be free to move and may have a solid 
 support, the body must be held in position. The posi- 
 tion which is taken will have an important effect upon 
 the ease and fluency of the movement. This also has 
 an important bearing upon the practical determination 
 of the type of writing which ought to be taught. 
 
 Health demands good posture. The correct posture 
 in writing is also determined by the demands of health. 
 In order that the eyes shall not be subjected to strain, 
 the writer must face the desk squarely and the paper 
 must be near the middle line of the body so as to bring 
 the two eyes the same distance from the writing. In 
 order that the spine shall not be twisted and bent to 
 the side, both arms should rest on the desk. In order 
 that the lungs, stomach, and other vital organs shall 
 have sufficient room, the body should be erect. 
 
 The application of correct posture to the position of 
 arm and paper. It was formerly thought that these 
 conditions necessitated vertical writing. Such is not 
 the case, but it is necessary that the body or the head 
 should not be turned or twisted. The paper may be 
 tilted about thirty degrees to the left so that the line 
 on the page is about at right angles to the line of the 
 forearm. This will enable the arm to carry the hand 
 along the line. The writing will then naturally have 
 
12 PSYCHOLOGY OF COMMON BRANCHES 
 
 a slant from the perpendicular by about the amount 
 to which the paper is tilted, as is shown in Figure 2. 
 This is based upon the fact that the upward and down- 
 ward strokes of the 
 writing naturally fall 
 approximately in the 
 direction perpendicu- 
 lar to the edge of the 
 desk. Writing which 
 has an angle of sixty 
 to seventy degrees to 
 the base-line is, then, 
 the best suited to 
 meet the require- 
 ments for an easy 
 movement and at the 
 same time to satisfy 
 the demands of hy- 
 giene. More particu- 
 lar specifications of method must be left to discussions 
 of the teaching of writing. 
 
 The first process in motor learning is the selection 
 of the appropriate movements. When the child first 
 attempts to write, he is deficient in that he is not able 
 to select just the movements which will be appropriate 
 to produce the desired result. The first point, then, 
 concerns the selection of the appropriate movements. 
 The child by the time he begins to learn to write has 
 sufficient general control over his bodily activities so 
 
 FIG. I. DIAGRAM OF THE RELATION 
 OF THE BODY AND ARMS TO THE 
 DESK AND THE PAPER 
 
HANDWRITING 13 
 
 that he can in a general way call into action the groups 
 of muscles which are to be used in such an act as 
 writing. H he sees somebody else write, he can imi- 
 tate very roughly the manner of holding the pen and of 
 making the movements. But his attempt does not re- 
 sult in the contraction of just the muscles which pro- 
 duced particular strokes. Many useless movements 
 are made. It may be seen from the observation of the 
 child in the earlier stages of his learning that this ex- 
 tension to tmnecessary movements is widespread. He 
 contracts the muscles of the face, twists the body into 
 unnatural positions, perhaps clenches the left hand, 
 and presents the spectacle of general muscular tension. 
 This preliminary stage in the development of move- 
 ment is called " diEFusion." The nervous energy has as 
 yet no well-connected channels of discharge, and there- 
 fore scatters over a large £irea of the nervous system. 
 Learning consists, then, in the first place, in confining 
 the nervous energy, so far as possible, to the particular 
 muscles which are needed to produce the effect. 
 
 Selection means also inhibition. This selection of 
 the appropriate movements or the reduction of diffu- 
 sion involves the inhibition ^ or the prevention of the 
 contrary movements. There are two possible methods 
 of attempting this selection. We may think particu- 
 
 * Inhibition means the checking or prevention of any activity, 
 whether movement or train of thought. Thus the thought of the 
 coldness of the water may inhibit the impulse to jump in, or the 
 contraction of the muscles which raise the foot in walldng inhibit 
 the contraction of the muscles which extend it. 
 
14 PSYCHOLOGY OF COMMON BRANCHES 
 
 laxly of the movement which is to be made or we may 
 fix our mind upon the movements which are to be 
 inhibited. In some cases, it is not weU to think of the 
 movements at all, but only of the result which is to be 
 obtained by them, in this case the formation of the 
 letters on the paper. Whichever object is in the atten- 
 tion, the same principle holds. This principle is that 
 it is better to fix the attention upon the movements 
 which are to be made or upon the result which is 
 desired, rather than upon the movements which are to 
 be eliminated or the r^ult which is not desired. A 
 stock illustration of this principle may be taken from 
 learning to ride a bicyde. When a person thinks of the 
 obstruction in the road or of the ditch at the side, he is 
 very likely to run into the obstruction or fall into the 
 ditch. His salvation consists in keeping his mind fixed 
 upon the path along which he wishes to travel. 
 
 Application. The application of this principle to 
 writing is that the child should not be made anxious 
 concerning the useless or superfluous movements 
 which he makes. In its application to the form of the 
 letters, he should be thinking chiefly of the form which 
 he wishes to produce rather than of those forms which 
 he wishes to avoid. It is, of course, necessary for him 
 to examine his own writing so that he may detect the 
 faults in it in contrast with the correctly formed letters. 
 He is apt, if this is not done, to fail entirely to see the 
 faults in his writing; but after the fault has been 
 detected, his attention is then to be fixed on the cor- 
 
HANDWRITING IS 
 
 rect form whidi is to be substituted f (ur the incorrect 
 one. 
 
 Along widi the selecti<Hi of the i^qin^riate move- 
 ments goes ttie organizatirai of ttiese separate move- 
 ments into flie total or combined movements. This 
 building together of movements is called " coSidina- 
 tion." ^ In a coordination the movements must be 
 adjusted to one another in such a way that each one 
 is made with the proper amount ci force. The failure 
 to have them pioperly adjusted may be seen from the 
 results of an esperim«at in Vrhidi the firessme eserted 
 by the thumb and the two fingors was measured. It 
 was found that in a strai^t downward stroke the 
 index fingv, as one should expect, eserts the chi^ 
 pressure, while the second finger and the thumb guide 
 the movement. If , now, the downward stroke curves 
 to the left, it is because the middle finger exerts an 
 undue amount of pressure. If each fing» does not 
 es«rt its due or pn^iortional amoimt (^f<ffce ia making 
 any particular hne, the stroke is thrown out of its 
 correct course. 
 
 The saccesave movements must also foOow one 
 another in the pn/per time. The smoothness and ease 
 of movement will dqiend very laigdy upon wfaetho' 
 or not the successive parts thus f (JIow one another as 
 they should. Hioe are certain gymmstk: feats, for 
 
 1 A motor coSidinatioo is a groop of siinide movements vlikji 
 comliine simahaaeoasly or socoesaTdy to produce some definite 
 resuh. 
 
16 PSYCHOLOGY OF COMMON BRANCHES 
 
 example, which are not difficult, provided one makes 
 the movement or exerts the effort at the proper time, 
 but which are impossible if this is not done. A simple 
 illustration of the failure to time the writing move- 
 ments correctly is taken from the relationship of the 
 movements of the arm in carrying the hand across the 
 page and the movements of the fingers in forming the 
 letters. Some writers alternate these two movements. 
 They use the fingers extensively in the formation of 
 several letters and then interrupt the finger movement 
 to lift the hand and carry it forward. A much better 
 relationship is maintained between these movements 
 by performing them simultaneously. 
 
 Rhythm is an important aid in timing the movements. 
 The best means of bringing about the correct timing 
 of the component movements of a coordination is to 
 make the whole movement rhythmical. When the 
 movement is carried on so that certain prominent 
 strokes are made at regular intervals of time, as in 
 marching to music, aU of the elements of the move- 
 ment are apt to fall into place at the proper time and 
 with the proper force. This principle is used in writing 
 when a class writes to count or to music It has been 
 found by experiment that the use of rhythm which 
 is suited to the age and training of the pupils increases 
 the speed and improves the quality of their writing. 
 K too rapid a rate is tised, the quality becomes poorer. 
 Not all the children of a class can profitably use the 
 rate which is suited to the majority and a few are 
 
HANDWRITING 17 
 
 deficient in the sense of rhythm, but if due provision is 
 made for the exceptional cases the use of rhythm is a 
 valuable means of teaching writing, or in fact any form 
 of motor coordination. 
 
 A movement is learned through repetition. The 
 method by which the coordination is formed through 
 the selection of movements and their organization is 
 the frequent repetition of trials. The coBrdination can- 
 not be formed by telling the pupil how the movement 
 is made. It is necessary that he find out for himself 
 through making an attempt, noting the results of 
 his attempt, and then endeavoring to • improve his 
 movement so as to retain these results which are the 
 ones aimed at and eliminate those which are not the 
 ones desired. This method of learning is sometimes 
 called the " trial-and-error " method and sometimes 
 the "trial-and-success" method,^ according as we are 
 thinking of the elimination of the wrong trials or the 
 retaining of the correct ones. The fact cannot be too 
 strongly emphasized that the only method by which 
 such a form of learning can succeed is through practice. 
 The child may be assisted in taking the correct posi- 
 tion by being instructed, or being shown how, and his 
 attention may be directed toward his mistakes. In a 
 variety of ways verbal instruction as to how the move- 
 
 ' The trial-and-error, or trial-and-success, method of learning is 
 one in which one learns to make an adjustment, not by studying the 
 problem which is presented, but by attacking it more or less blindly 
 and then gradually eliminating the unsuccessful, and retaining the 
 successful trials. 
 
18 PSYCHOLOGY OF COMMON BRANCHES 
 
 ment should be made is of great value to the learner, 
 but it only supplements the trials which he makes and 
 can never be a substitute for them. Moreover, it is 
 necessary that frequent trials be made. The mistake is 
 sometimes made, thou^ not so often as formerly, of 
 requiring the pupil to make a few copies only at each 
 practice period and to make each one slowly and labo- 
 riously. A much better method is to require him to 
 make a large munber of copies somewhat more fluently, 
 endeavoring to improve in each case over his preceding 
 trial. 
 
 As learning progresses, attention is freed from the 
 details of the movement. As the child learns better to 
 coordinate the movements, a change takes place in his 
 mental attitude toward his bodily response. At the 
 beginning it was necessary to think of each separate 
 movement and each stage in the malfing of a letter. 
 As he becomes more skilled, he is able to make a series 
 of movements or to form a letto* or a word, thinking 
 only of the whole group of movements or of strokes. 
 The recognition of the movement becomes simplified 
 and the details are ^ven over to the control of the 
 nervous centers which produce the movement. When 
 this simplification of the recognition is carried far 
 enough, we reach the automatic stage of the habit. 
 This means that the attention is turned to the thought 
 which is being expressed. 
 
 Increased skill makes possible the development of 
 riiythm. As the child's attention becomes freed from 
 
HANDWEITING 19 
 
 the details of the movements or of the letters, he is 
 able to recognize more fully some of the more general 
 features of the writing. One of these general features 
 which has already been mentioned is rhythm. The 
 child can write rhythmically only when he does not 
 have to stop to consider how to form the details of the 
 letters or to adjust his hand or fingers. Rhythm ap- 
 pears when the successive strokes are made in about 
 the same time. Measurements have shown that this 
 is true of the writing of the older child or the adult, 
 even thoTigh the successive strokes differ greatly in 
 length. The age at which the writing becomes thus 
 markedly rhythmical in the case of the majority of 
 children is nine or ten. We may conclude from this 
 fact that this is the age at which it is suitable to give 
 the child writing drills which require a high degree of 
 rhythm. 
 
 Changes in speed within the letter are more deter- 
 mined by the mechanical ease or difficulty in adult 
 than in children's writing. Another significant fact 
 which has been discovered by experiment and which 
 indicates that the child's attention is being withdrawn 
 from the details of the letters is that in the writing of 
 the older child and the adult the speed varies much 
 more in the different parts of the letter than in the 
 writing of the younger child. Where the mechanical 
 difficulties are considerable, as where there is an 
 abrupt change in direction, the movement continues 
 to be relatively slow, while where the mechanical diffi- 
 
20 PSYCHOLOGY OF COMMON BRANCHES 
 
 culties are slight, as on a long, sweeping stroke, the 
 speed increases. 
 
 Attention can be given to uniformity. Another gen- 
 eral feature of the writing besides rhythm to which 
 the child can give attention after the details cease to 
 trouble him is the uniformity of the words and letters. 
 This includes imiformity of slant, of alinement or of 
 spacing. Yoimg children commonly form their letters 
 carefully, but their writing presents an imeven appear- 
 ance. 
 
 The writing habit includes word and letter recogni- 
 tion as well as movement. We are accustomed to 
 think of such a habit as writing as being composed of 
 movements. This is true, but movements are not all 
 there is to the habit. The movements are made in 
 response to the sight of letters and words. At the very 
 beginning the writer looks at the letters and copies 
 them, thus holding the form of the letters in mind for 
 only a short time. Later on, the letters need not be 
 seen, but must be present in imagination. Later still, 
 the form of the letters may largely drop out of mind, 
 but even in this most advanced stage the thought of 
 the word exists in the mind and is the stimulus to the 
 movement. In the case of writing, then, we may sepa- 
 rate two phases of habit, that of the movement and 
 of the recognition of the stimulus. 
 
 Writing stimulates a study of letter forms. It is 
 appropriate to say in this connection that the writing 
 habit, considered as a form of movement, is of import- 
 
HANDWRITING 21 
 
 ance in the development of the recognition of the let- 
 ters. Before the child begins to write, it is necessary 
 that he shall be able to distinguish the forms of the 
 diflferent letters roughly. He may, however, distin- 
 guish them sufficiently for reading, but not for writing. 
 As he tries to reproduce the forms which he perceives, 
 he finds it necessary to pay more attention to the form 
 than he has previoufily done. Writing furnishes a 
 stimulus to a further study of the form of the letters. 
 Writing also furnishes an additional experience 
 which enriches the perception of form. After a person 
 has learned to write letters, his recognition of them is 
 not merely a matter of sight. There is a tendency, 
 when the letters are seen, to make the movement of 
 producing them. There are numerous illustrations 
 from our mental life which show that our recognition 
 of objects includes the experience which we have had 
 in handling them. K we lift two boxes which are the 
 same in weight, but of different size, we are subject to 
 an illusion. The smaller box appears to be mutfh heav- 
 ier than the large one. This is because in looking at 
 the boxes the sensation of sight produces an anticipa- 
 tory contraction of the muscles which would be used 
 in lifting the boxes. When, now, we do lift them, there 
 is a strong contrast between the amount of force 
 which is exerted in the case of the two hands, because 
 we had anticipated the necessity of lifting the larger 
 box more vigorously. This contrast causes the feeling 
 of greater strain in lifting the small box which makes 
 
22 PSYCHOLOGY OF COMMON BRANCHES 
 
 it appear heavier than the larger one. So also in our 
 rceognition of letter forms there is included something 
 of the motor experience of making them. 
 
 The writing movement becomes the means of ex- 
 pressing meanings. We have been discussing writing 
 as a form of movement which becomes organized so 
 that it becomes an effective means of producing the 
 forms of letters and words on paper. The true function 
 of writing is fulfilled when, in addition to this, it 
 becomes the expression of meanings. Meanings are 
 represented first in spoken words, and when we write 
 we commonly say over and hear inwardly the words. 
 Because meaning was originally associated with the 
 spoken and heard word, it is stUl embodied in internal 
 speaking and hearing. When writing advances to the 
 stage at which it is a ready means of expressing mean- 
 ings, it is carried on as a direct response to ideas em- 
 bodied in these forms. The consciousness of the move- 
 ments or of the details of the form of the letters recedes 
 to the background. When this stage is reached writing 
 has become automatic. 
 
 The habit may become automatic too soon. In the 
 
 development of writing toward this automatic ' stage, 
 
 there may be two opposite faidts. The habit may 
 
 become automatic at a stage when it is not sufficiently 
 
 well developed; that is, the person may learn to express 
 
 his thoughts through a form of movement which is 
 
 ' An activity is automatic when it is carried on with little or no 
 attention to the activity itself. Thus one may take a key from his 
 pocket and unlock a door automatically. 
 
HANDWRITING 23 
 
 irregular and which produces illegible letters. The 
 cure of this fault is to give attention to the habit imtil 
 it becomes developed to the point at which the results 
 of the writing are satisfactory. The results may be 
 unsatisfactory either because the movement is awk- 
 ward or because the writing is poor in quality. 
 
 Attention may be given to the details too long. The 
 opposite fault also sometimes occurs. In this case a 
 person never loses his consciousness of the writing 
 movement or of the form of the letters which he is 
 producing sufficiently to give his attention wholly or 
 chiefly to the thought. Persons sometimes possess two 
 styles of writing, one in which the habit is automatic 
 and the writing is very poor, and another in which the 
 writing is kept at a high grade through giving attention 
 to it. This development of two sorts of habit, one which 
 is used in the ready expression of thought and the 
 other in producing pleasing forms, is unfortunate. The 
 child should develop his writing habit to a sufficient 
 degree of perfection that he may produce good results, 
 but it should then become automatic. 
 
 Movement and form both require attention. Differ- 
 ent systems of teaching give different emphasis to the 
 development of a good motor coordination as com- 
 pared with the production of writing which presents 
 a good appearance. Some teachers believe that if care 
 is taken to develop good movement the form will take 
 care of itself, or at least will not need much atten- 
 tion. It is true that writing is to be thought of as a 
 
24 PSYCHOLOGY OF COMMON BRANCHES 
 
 movement habit, and that the principles which govern 
 its development as a movement are those which must 
 guide the teacher in the methods which he uses, as we 
 have already seen in detail. But a movement is made 
 in response to a stimulus, and it is to be judged by 
 the accuracy with which it is adjusted to the stimidus. 
 A movement is not judged merely according to its ease 
 or smoothness. The handwriting movement, accord- 
 ingly, may be smooth and easy, and yet the writing 
 may not be legible because the letters are pooriy 
 formed or not well spaced. 
 
 The child should study form. There are effective 
 and ineffective ways of calUng the child's attention to 
 the form of the letters which he is producing. One 
 method is merely to place a model before him and 
 require him to copy it. This method, if used alone, is 
 seriously deficient in two ways. In the first place, it 
 gives the child merely the finished product, and, if the 
 copy is engraved, a finished product that he could not 
 possibly imitate. In place of this copy he should have 
 an opportunity to see the form being produced. The 
 form does not in itself suggest the best method of 
 reproducing it. The form must be recognized by the 
 child in terms of the movement of producing it. In the 
 second place, merely to set before the child a perfect 
 model does not enable him to see just in what respect 
 his writing differs from it. To gain this end it is neces- 
 sary to show him how to make an analysis of the form 
 of his writing. 
 
HANDWRITING 25 
 
 Form should be analyzed. One means by wluch the 
 child may be helped to make such an analysis is to 
 show him series of charts in which progressive degrees 
 of excellence in each of the main elements of form are 
 illustrated.* For example, one series of charts may 
 show different degrees of uniformity in slant or aline- 
 ment, another different qualities of line or stroke, 
 another different degrees of excellence in letter forma- 
 tion, and another degrees of excellence in spacing. By 
 the study of such charts and an analysis of his own 
 writing the child may gain a clearer recognition of the 
 ways in which his writing deviates from the model. 
 
 The child can be guided in the development of the 
 best movement. If some teachers emphasize move- 
 ment to the neglect of form, others commit the oppo- 
 site error. It is clear from the whole trend of our dis- 
 cussion why this is a mistake. It is a far safer and more 
 economical method to guide the child in the formation 
 of those habits of movement which experience has 
 shown to be the most eflScient than to allow him to 
 blunder into a form of movement without any assist- 
 ance. Substantially the same form may be produced 
 in a variety of ways, and some of these are much bet- 
 ter than others. It is the business of the teacher to 
 help the child to find these better ways as rapidly as 
 possible. 
 
 ' Such a series is published in the appendix of The Teaching of 
 Handwriting, by the author, published by Houghton Mifflin Com- 
 pany (1914). 
 
26 PSYCHOLOGY OF COMMON BRANCHES 
 
 The elements which can be acquired through 
 instruction constitute good form. It has been said in 
 a former paragraph that the writing movement could 
 not be learned through instruction, but must be devel- 
 oped through the trial and success method. This 
 applies to what may be called the execution of the 
 movement. There are certain aspects of the movement, 
 on the other hand, which may be partly learned through 
 imitation or through instruction. The child may gain 
 help through these methods in learning how to hold 
 the pen, what position should be assiuned by the hand 
 and arm, and in a general way what parts to move in 
 making the strokes. These aspects of the activity may 
 be called " form." Form, in this sense, is, of course, 
 entirely different from the form of the letters or the 
 words. We use the term in the same sense as when we 
 speak of good form in playing tennis or performing a 
 gymnastic feat or riding a horse. There are elements 
 of good form in writing which there is not space to 
 enumerate here. A general idea of what they are may 
 be gained from the illustrations in Figures 3 and 4. 
 The acquirement of good form adds considerably to 
 the ease and accuracy of the writing movement, or of 
 any other activity. 
 
 Speed and quality should progress together. An- 
 other question of method is related to this issue be- 
 tween movement and form. Those who emphasize 
 movement to the exclusion of form often require the 
 child to write very rapidly from the start, while those 
 
Fig. 3. CORRECT POSITIO^'S OF BODY, AND ADMISSIBLE POSITIONS 
 OF THE HAND FOR YOUN(i CHILDREN 
 
 Body position from C. F. Zaner, Zaiier MetJiod, Manual no. 1. Hand positions 
 from W. A. Whitehouse, The Modern Writing Master, vol. i, no. 1. (With the 
 permission of the publishers.) 
 
Fig. 4. INCORRECT PUSITIOXS OF THE HAXD 
 
 From W. A. AVhitehouse, The Modern Wriihuy Masfpr, vol. i, no. 1. (With the 
 permission of the publisher.) 
 
HANDWRITING 27 
 
 who emphasize form chiefly pay little attention to 
 speed, particularly at the beginning. The practice of 
 allowing the child to write excessively slowly was criti- 
 cized above on the ground that it does not give the 
 pupil sufficient practice. It may also be criticized on 
 the ground that it does not give the pupil practice in 
 connecting the elements of the movement to make a 
 continuous process. When the child makes the letters 
 by a slow, drawing movement, he is not obtaining a 
 sensation of the whole movement in such a way that 
 he learns how it feels to write a letter or a word. On 
 the other hand, if the child is required at the beginning 
 to make the movement as rapidly as he will later, it is 
 impossible for him to form the letters correctly. As a 
 consequence he is not learning to make the movements 
 which he will later have to make. He is also forming 
 habits of carelessness and is failing to get a clear and 
 correct idea of the form of the letters. The solution of 
 this question, then, is that the child should progress 
 in accuracy and form together. 
 
 The child should be able to trace his own progress. 
 It follows, from this analysis of the quahties of good 
 writing, that the child should be able to trace his prog- 
 ress in both quality and speed. The more definite 
 his attainment can be made, the more stimulus he will 
 receive toward improvement. The common method 
 of grading the child's attainments by comparing him 
 with others in a rough, general way is very deficient, 
 because it does not give him a sufficiently definite idea 
 
28 PSYCHOLOGY OF COMMON BRANCHES 
 
 either of the degree of skill which he has attained or 
 the direction in which his improvement should proceed. 
 The child should, then, be compared with his own past 
 record rather than with that of dther pupils, and this 
 should be expressed in a form as definite as possible. 
 The speed may be measured by occasional tests and 
 the quality by analyzing it by the method which was 
 suggested above. 
 
 The correct habit should be practiced in all writing. 
 We have already seen that a person's writing habit 
 may be of one sort when he is writing for the sake of 
 good form and of another sort when he is writing to 
 express thought. The child should so develop his 
 writing habit that much the same result appears in the 
 ordinary work as in the writing lesson. In order that 
 this may be the case, it is necessary that some atten- 
 tion be paid to the writing which he produces in the 
 rest of his school work. It would be well to do this 
 throughout the latter part of the elementary school. 
 In the first three or four grades the child's attention 
 should not be distracted from the thought which he is 
 expressing by the necessity of thinking much about the 
 quality of the writing. He has great difliculty at the 
 best in expressing his thoughts in writing at this time, 
 since the unfamiliar habit distracts his mind; but in 
 the later grades it will not distract the child to exer- 
 cise a little care in order that the writing shall not 
 deteriorate. It is well, then, to give the handwriting 
 grade upon the quality of the work which is turned 
 
HANDWRITING 29 
 
 out in the other subjects as well as that which is pro- 
 duced in the writing lesson. In fact, this should prob- 
 ably be the main stimulus to progress in writing in 
 the upper grades. 
 
 Modifications due to age 
 
 Motor ability changes with age. What has been 
 said indicates that it is necessary to modify the method 
 of teaching writing to suit the age and stage of devel- 
 opment of the pupil. Some methods of teaching writ- 
 ing which are in wide use take no account of the differ- 
 ence in ability of the child at different ages. For 
 example, the same speed in writing is required of the 
 first-grade child as of the eighth-grade child. Studies 
 of the motor ability of children at different ages indi- 
 cate that there is a marked increase in the rapidity of 
 movement and in the steadiness and precision of move- 
 ment from the age of six to that of sixteen. A study of 
 the ability of children in different grades in making 
 a series of upward and downward strokes as rapidly 
 as possible demonstrates the same fact. A survey 
 of the rapidity of writing, in all the grades from the 
 second to the eighth among over thirty thousand 
 children, shows that on the average the first-grade 
 pupil writes less than half as fast as the eighth-grade 
 pupil. 
 
 The fundamental and accessory movement theory. 
 The difference in ability between the younger and the 
 older child has sometimes been ascribed to the devel- 
 
30 PSYCHOLOGY OF COMMON BRANCHES 
 
 opment from fundamental to accessory movements.* 
 The theory is that the younger child is able to make the 
 so-called fundamental movements more readily than 
 the accessory movements, and that improvement in 
 ability is chiefly in gaining control over these accessory 
 movements. The distinction between the fundamental 
 and accessory movements is not always clear. The 
 fundamental movements are sometimes described as 
 those which are old in the race, such as walking; while 
 the accessory movements are those which have been 
 acquired in human life, such as manipulation. Some- 
 times the distinction is made between the movements 
 of the large muscles, or large movements, which are 
 designated as " fundamental," and the opposite kind 
 of movements which are called " accessory." Finally 
 fundamental movements are sometimes described as 
 " central," that is, concerned with the trunk or with 
 the parts of the limbs next to the trunk, while accessory 
 movements are those toward the extremities. An 
 examination of the movements which are made by the 
 young child will indicate that this distinction is not a 
 very useful one. In the problem of learning we are 
 not concerned with instinctive movements, and other 
 movements do not develop in any consistent way from 
 central to peripheral or from large to small. 
 The suitability of movements for the child should be 
 
 ' A fundamental movement is one which is old in the history of 
 the race, is a large movement or is made with large muscles, and is 
 central (in or near the trunk). An accessory movement is the 
 opposite. 
 
HANDWRITING 31 
 
 judged on the score of their rapidity, precision, and 
 complexity. A much more valid distinction between 
 the movements which are suited to the younger child 
 and the older child rests on the facts which have 
 already been referred to. The young child is not capa- 
 ble of very rapid or precise movements. To this may 
 be added the further fact that movements are difiBcult 
 for him in proportion to their complexity. The com- 
 bination of a large number of movements in one com- 
 plicated coordination presents difficulties to the child 
 in proportion to his deficiency in motor control. 
 
 The difficulties should be lightened for the young 
 child. These characteristics of the child make the 
 acquirement of handwriting a difficult matter for him 
 and one which is attended with considerable nervous 
 strain. Care must be taken, therefore, to amehorate 
 for him the difficulty of the task. This may be done 
 by making the requirements for accuracy and rapidity 
 low and by placing the handwriting period at a time 
 when the child is not fatigued. The requirement for 
 speed has already been discussed. The avoidance of 
 undue accuracy of form may be reached by allowing 
 the child to write very large. At the beguming the 
 writing should be done on the blackboard. When the 
 child first uses paper, he should write with large letters 
 and with a pencil which offers Uttle difficulty in its 
 manipulation. The pencil should be fairly large and 
 the lead smooth. The paper should also have such a 
 surface that the mark is easily made upon it. As the 
 
32 PSYCHOLOGY OF COMMON BRANCHES 
 
 child grows older and gains in skill, the writing may 
 be gradually decreased in size and may become gradu- 
 ally more precise. 
 
 Individual differences and practice periods 
 
 Individual differences. Besides these differences due 
 to age, there are wide differences between individual 
 children in this as in other forms of ability. Some chil- 
 dren are superior in their writing ability to the average 
 of several grades above them, whereas others are equal 
 only to the average of several grades below. These 
 individual differences may be taken account of in sev- 
 eral ways. The ideal method would be to group chil- 
 dren according to their ability in each separate kind of 
 work, so that those of like abiUty are together and that 
 those who have reached a certain standard might be 
 relieved of further work in that subject. This, however, 
 is not possible so long as the rigid grade system main- 
 tains, and the best that can be done is to recognize the 
 differences among children of the same grade and to 
 adjust the demand made upon the different children 
 according to their various abihties. As was suggested 
 above, each child should be judged on the basis of his 
 past performances instead of by comparison with his 
 classmates. In the speed of writing it is very desirable 
 to have as many of the children as can comfortably do 
 so engage in rhythmic exercises to music or to time 
 marked in some other manner, but it is necessary that 
 the children who do not naturally fit in with this 
 rhythm should not be required to follow it. 
 
HANDWRITING 83 
 
 The length of practice periods. In arranging the 
 conditions so that the practice will be most effective 
 in producing improvement, it is necessary to take 
 account of the principles of economy in effort due to 
 the arrangement of the periods of practice. It has been 
 found by experimental investigation that the length 
 of period or the interval between the periods of prac- 
 tice affects the rapidity of learning. In the case of the 
 development of a motor habit, such as handwriting, 
 the same amount of time split up into rather short 
 periods is more effective than it it is all expended in 
 long periods. With the child in the earlier grades ten 
 minutes is probably the best length of period, and in 
 the upper grades not over half an hour can be spent to 
 the greatest advantage. 
 
 REFERENCES 
 
 1. L. P. Ayers: Scale for Measuring the Quality of Handumting of 
 School Children. Bulletin no. 113, Division of Education, 
 Russell Sage Foundation. 
 
 2. L. P. Ayers: Scale for Measuring the Quality of Handvmiing of 
 Adults. Bulletin no. E138, Division of Education, Russell Sage 
 Foundation. 
 
 3. Frank N. Freeman: The Teaching of HandwrUing. Houghton 
 Mifflin Company. 1914. 
 
 4. Frank N. Freeman: An Experimental Study of Handwriting. 
 Psychological Monographs. 1914. 
 
 6. Charles H. Judd: Genetic Psychology for Teachers. D. Appleton 
 & Co. (1903), pp. 84-97 and chap. vi. ■ 
 
 6. S. H. Rowe: Habit Formation and the Science of Teaching. 
 Longmans, Green & Co. 1909. 
 
 7. E. L. Thorndike: "Handwriting." Teachers College Record, 
 Columbia University. 1910. 
 
 8. W. A. Whitehouse: "Correct Penholding." The Modern Writ- 
 ing-Master. Boston, Mass. (1906), 1, 24-37. 
 
CHAPTER III 
 
 DRAWING: PERCEPTUAL LEARNING 
 
 In learning to write, the child develops habits of 
 movement and acquires the recognition of form, but 
 since the motor coSrdination is the more prominent 
 element, writing is taken as an illustration of sensori- 
 motor learning. Drawing also includes both the recog- 
 nition of form and its representation, but in this case 
 the element of recognition is more prominent, and 
 therefore drawing is taken as an illustration of per- 
 ceptual learning. Drawing is commonly regarded as 
 an illustration of the development of motor habits. 
 The production of the form upon the paper is thought 
 of as the chief element in the process. This, however, 
 is a secondary part of the whole process as will be made 
 clear by the following illustration. 
 
 A demonstration experiment in drawing . 
 In order that the reader may have in his experience 
 a concrete illustration of the development of the recog- 
 nition of form, the following simple experiment may 
 be performed. Upon page 36 will be foimd a figure 
 (Figure 5) which should not be looked at until the 
 directions given below have been read and clearly un- 
 derstood. The figure is to be observed for the brief 
 
DRAWING 35 
 
 interval of ten seconds, after which the attempt should 
 be made to reproduce it. During the time the drawing 
 is being reproduced, the book should be turned over so 
 that it cannot be seen. After the figure has been com- 
 pleted as well as possible, the paper should be folded 
 so as to conceal the drawing and another attempt made 
 in the same manner. This process shoidd be repeated 
 until the e^)erimenter is satisfied that the drawing is 
 reproduced substantially in its correct form. It is not 
 necessaiy that it shall be minutdy accurate, but only 
 that the chief dements shall be present in about their 
 true relations. 
 
 The act of drawing has produced conqileter recog- 
 nition. After the drawing has been made, the reader 
 should analyze his experience and test the correctness 
 of the following account. The first question for exam- 
 ination concerns the difference between the perception 
 of the figure after the figure has been drawn in the 
 final trial in comparison with the type of recognition 
 which existed before it had been mastered. It is dear 
 that, as a result of the study and the attempt to repro- 
 duce the figure, something has taken place which 
 materially modifies the reoc^nition of it. This has not 
 been in the nature of mental development in general, 
 but has rather consisted in the development of the 
 ability to recognize this particular figure. Before the 
 study, the figure was seen in a vague, indefinite man- 
 ner. It was noticed that there were a number of lines, 
 but the shape of the lines or their exact relationship 
 
36 PSYCHOLOGY OF COMMON BRANCHES 
 
 to each other was seen only very vaguely. In this first 
 preliminary recognition some persons emphasize more 
 the general outline of the figure and others recognize 
 one or two details clearly, but lose sight of the rest. 
 Whichever type one belongs to, after the study of the 
 figure, one is able to grasp the general outline and at 
 the same time the details of which it is composed. 
 
 no. 6 
 
 Completer recognition is gained through active 
 exploration. The next question to be considered is the 
 means by which the development has been attained 
 which results in this different manner of recognition. 
 In the great majority of cases, when the question is 
 raised, it will be found that one has begun the study 
 of the figure at a particular point, usually the left end 
 of the figure. It is instructive to ask ourselves why 
 most people begin at the left end rather than at the 
 right end. The explanation is undoubtedly to be foimd 
 in the fact that we have learned to recognize words on 
 
DRAWING 37 
 
 a printed page in this order and that we have learned 
 to write from left to right. This means, then, that we 
 bring to the study of this figure certain habits of explo- 
 ration which determine the kind of procedure we shall 
 take. 
 
 General ideas are employed. There are also other 
 features of the process of studying the figure which 
 indicate the existence of a definite series of mental 
 habits based upon our past experience. For example, 
 the number of lines was very likely determined by 
 counting. In this we use the general idea of number 
 or the habit of thinking of things by number as instru- 
 ments in developing the recognition of the figure. Very 
 likely also the kind of lines was noted and it was seen 
 that there were some straight lines and some curved 
 lines. The alternation of the straight and curved lines 
 was likely also to have been observed, and the fact 
 that the lines formed angles with one another and 
 that these angles were perhaps of about so many 
 degrees. Very often the figure is grasped by com- 
 paring it with familiar objects, such as a letter of 
 the alphabet, or stenographic signs. 
 
 The nature of perception as illustrated in drawing 
 
 Development of perception consists in organizing 
 
 impressions, not in gaining new ones.^ This description 
 
 of the way in which we set about such a task will show 
 
 ' Formal definitions of perception and sensation are given on 
 p. 51. 
 
38 PSYCHOLOGY OF COMMON BRANCHES 
 
 that we bring to it a vast number of ideas and habits 
 of procedure out of our past experience and that our 
 mode of gaining a mastery of the figure is not passively 
 to allow it to make an impression on the mind, but 
 rather actively to go about its study, using these ideas 
 and habits of procedure. We may sum up this experi- 
 ence by saying that the recognition of such an object 
 is not chiefly a matter of gaining impressions, but 
 rather a matter of actively analyzing the characteris- 
 tics of the object. Put in another way, this principle 
 means that the development of the ability to recognize 
 such an object is not primarily the development of 
 keenness of the senses, but rather the development 
 of a mode of arranging or organizing the sensations 
 which we receive from the object and giving to them a 
 meaning. 
 
 Such organization includes analysis and synthesis. 
 The analysis of such a figure into its parts makes pos- 
 sible the grasp of the figure as a whole. In the final 
 recognition we were not merely able to see each part 
 clearly, but we were able to grasp a larger number of 
 the parts because each one had previously been studied 
 for itself. The whole process consists of the clearer 
 recognition of the parts and better organization of the 
 parts in relation to one another. Put in technical 
 terms, such recognition is based on both analysis and 
 synthesis. 
 
 Example of the manner of directing the child in the 
 development of his perception. The fact that in order 
 
DRAWING 39 
 
 to gain a dear perception of an object it is necessary 
 to go about the study of it in an active manner finds 
 illustration in all the work of the school in which a 
 study is made of concrete objects. It gives the clue to 
 the manner in which the teacher can guide the child's 
 efforts to gain an accurate and comprehensive notion 
 of such an object as a plant or an animal. The child 
 should not be allowed merely to get a vague impression 
 by passively looking at the object, but he should be 
 led, through questions and discussion, to examine the 
 various parts in detail and to discover their likenesses 
 to the parts of other similar objects or their differences 
 from them. Thus, in studying a cow the child should 
 be induced to examine its teeth, to compare them with 
 the teeth of the sheep, the horse, the dog, cat, etc. 
 These facts are then to be related to the different kinds 
 of food which are eaten by the different classes of ani- 
 mals. In similar manner the child examines hoofs, 
 horns, etc. As he gains a clearer idea of these details 
 he is also at the same time putting them together so 
 that they combine to give him a complete notion of 
 the animal as a whole. 
 
 Past experience is involved in all perception. These 
 characteristics are true of our perception in general. 
 One of the most prominent characteristics of percep- 
 tion is that we depend for oxir recognition of things in 
 large measure upon the result of our past experience. 
 The bearing of our past experience upon our present 
 recognition and responses is easily recognized in cases 
 
40 PSYCHOLOGY OF COMMON BRANCHiS 
 
 in which the differences due to differences in past 
 experience are more obvious. In such cases the activity 
 of past experience in governing interpretation is called 
 " apperception." Many objects have a widely differ- 
 ent meaning to different persons because of their past 
 training or education. The artist sees in a rural scene 
 the beauty of the landscape; the farmer, on the other 
 hand, may see the possibility of raising crops; the 
 huntsman may think of it as containing game; and 
 so on. 
 
 All perception is apperception. The bearing of past 
 experience in such cases is obvious, but it is equally 
 present in every recognition. The setting-off of a few 
 of our experiences as being characterized by appercep- 
 tion^ as distinguished from others which we call "per- 
 ception " obscures this fact. Apperception is present 
 in every case of perception, and is therefore not any 
 unusual or j)eculiar characteristic of mental life, but 
 is rather present throughout its whole range. 
 
 Object teaching is not merely showing the child 
 objects. The practical application of this principle is 
 that different persons wiH give a different interpreta- 
 tion to their experiences because of the different back- 
 ground LQ which they are set. We recognize this in the 
 case of the more conscious interpretations we make, 
 
 • Apperception is a broad term which designates the part played 
 by the mind itself in determining the character of our experience. 
 What our experience is depends on our inherited cast of mind and on 
 our previous experience as weU as upon the stimuli which afiect us. 
 This activity of the mind in coloring experience is apperception. 
 
DRAWING 41 
 
 but it is also of great importance even in the perception 
 of physical objects. The mistake is sometimes made of 
 supposing that when we set up an object before a child 
 his recognition of it is the same as ours. Object teach- 
 ing does not merely consist in presenting things to the 
 child, but rather consists in giving him such modes of 
 interpretation that he can see in the object the thing 
 which the educated person sees. Likeness in the stim- 
 ulus does not guarantee likeness in the response. There 
 must be also a similarity in the form of development 
 of the two persons who are making the response. 
 
 niustration of the need of past experiences as a 
 background for the complete recognition of objects. 
 The task of the school with reference to the child's 
 recognition of the objects of the world about him is 
 systematically to furnish him with experiences or use 
 the e^[>eriences which he has so that he will have an 
 adequate background for their interpretation. One of 
 the common objects of the modem person's environ- 
 ment b the trolley car. To the majority of the adults 
 of the present, who did not leam about electricity in 
 their school days, the trolley car is a mystery. They 
 know there is something called electricity, which trav- 
 els along the trolley wire, and that when the trolley 
 is in contact with the wire and the motorman does 
 something with the handles before him the car starts. 
 In order to see more than this in a trolley car one has 
 to become familiar with the dynamo and electric 
 motor, to leam how a wire passing through a magnetic 
 
42 PSYCHOLOGY OF COMMON BRANCHES . 
 
 field generates an electric current, and that when a 
 current passes through a wire which is in a magnetic 
 field motion is generated. One thus comes to see that 
 the electric current is a means by which the motion 
 which is generated at the power-house through steam 
 or water power is reproduced at the wheel of the trolley 
 car. Thus we see that the complete recognition of a 
 trolley car depends on having a great many prelim- 
 inary experiences. 
 
 Drawing (with the other representative arts) selects 
 particular features for representation. The influence 
 of past experience upon the type of recognition has a 
 particular illustration in drawing. Drawing is not a 
 photographic representation of all that is seen. There 
 is always, either consciously or unconsciously, a 
 selection of features of the total appearance to be 
 represented. The history of the development of the 
 arts of drawing and painting indicates that those 
 aspects of objects which are selected to be represented 
 vary with the stage of progress which an art has 
 reached. The ultra-modern schools, as the Cubists 
 and Futurists, are attempting to develop new modes 
 of representation which will depict aspects hitherto 
 not represented, such as motion. 
 
 Representation by drawing depends on the mastery 
 of a drawing language. Learning to draw, in fact, may 
 be thought of as an acquirement of a language or a 
 mode of expression. This language has gone through 
 stages of development just as has spoken language. 
 
DRAWING 43 
 
 The early Egyptians were able to reproduce certain 
 characteristics of the form of objects, but lacked 
 entirely the ability to represent perspective, or the 
 differences in the distances of objects, by means of the 
 lines of their drawing. One object was represented as 
 being farther away than another merely by being 
 partly hidden by it. We may speak of the Egyptian 
 mode of representation, then, as one sort of dialect of 
 the drawing language. We may also compare the art 
 which has been developed in Oriental countries with 
 that of our own, and we find here also two different 
 dialects. Chinese and Japanese painting, for example, 
 consists chiefly in the use of lines instead of the masses 
 which are used in Western painting, and until recently 
 Occidentals failed to appreciate the significance of 
 these drawings. 
 
 One sees, in a measure, what one can represent. 
 These differences in mode of representation are not 
 merely differences in expression, but also represent 
 different modes of seeing the object. A person who has 
 had one type of training sees a particular aspect of the 
 thing and represents that aspect because he has ac- 
 quired the mode of representation which is suited to it. 
 He has developed a tool of expression, and as a con- 
 sequence he can see the things which are capable of 
 representation by this tool. 
 
 In his early experience the child learns to recognize 
 the real form from the appearance it presents. An 
 example of the way in which drawing serves as a mo- 
 
44 PSYCHOLOGY OF COMMON BRANCHES 
 
 tive to seeing things in a different manner or in a more 
 adequate manner may be taken from the development 
 of the child. When the child begins to draw, he is not 
 able to represent perspective by means of the lines and 
 their relationship to one another. The reason for this 
 is that he draws the objects which he sees as he knows 
 them to be rather than as they appear from a particu- 
 lar point of view. He has learned to see the object as 
 it really is and not to recognize the particular appear- 
 ance which it presents as he looks at it. The child's 
 form of recognition is one which he has bought at the 
 expense of a good deal of time and experience. When 
 the child first observes objects, he is imdoubtedly 
 impressed by their appearance, and he does not at 
 first realize that an object which presents one shape 
 from one point of observation and another from an- 
 other point is really an object which has its own con- 
 stant shape independently of the position from which 
 it is viewed. He learns this lesson thoroughly. For 
 example, he knows that the top of a table is rectangular 
 in spite of the fact that it appears from most positions 
 to have acute and obtuse angles. When now he draws 
 a table, he represents it in this rectangular shape. 
 
 Drawing is the representation of the appearance. 
 The difficulty in learning to represent perspective, — 
 that is, to draw the object as it appears from a particu- 
 lar point of view, — is that we are incapable at first 
 of clearly recognizing how the object does appear. One 
 must, then, learn to give attention to the appearance 
 
DRAWING 45 
 
 in order that he may reproduce this on paper, and thus 
 give the impression which the object makes upon him. 
 
 The recognitioii of the appearance comes from try- 
 ing to draw it. The child acquires this ability to pay 
 attention to the aspect of an object which is presented 
 from a particular point of view only through the 
 acquirement of technique of egression. Merely to 
 lecture to the child upon perspective or to discuss the 
 principle of vanishing points, horizon, and so on, as 
 was formerly done, does not give him the form of 
 recognition which he needs. The best method of doing 
 this is to lead the child to experiment in putting lines 
 in different relationships to one another so that they 
 shall correctly represent the object which is being por- 
 trayed. For this purpose the three lines which repre- 
 sent the three dimensions of an object may serve as 
 the basis of experimentation. After the child has 
 learned to place these lines in such a way that they 
 represent the appearance of a chair, say, or of a table, 
 he has acquired an added ability in seeing as well as a 
 new mode of expression.' 
 
 Illustration of the bearing of activity on perception. 
 As the recognition of form is made accurate and com- 
 plete by the active response of drawing, so also do the 
 active responses which we make influence very greatly 
 all our perceptions. We see and hear and touch in 
 
 ' This is the method pursued in the University Elementary School 
 of the University of Chicago under the direction of Professor Walter 
 Sargent. 
 
46 PSYCHOLOGY OF COMMON BRANCHES 
 
 order that we may effectively move and handle and 
 use. Sensations exist to guide actions. Therefore, the 
 natural and most effective stimulus to perception is a 
 demand for action toward the object in question. A 
 boy who has a chance to run an en^ne or an automo- 
 bile will soon find out enough about it for his practical 
 purposes, and the practical impetus which he thus 
 gains may carry him a good deal farther in his investi- 
 gations. Not only so, but the experience he has gained 
 in actually handling the machine ^ves him a far better 
 understanding and basis for further knowledge than 
 merely looking at it would have given. In a similar 
 way the girl is led to a far more intimate and exact 
 knowledge of food materials and cooking processes 
 by a little practical experience, accompanied by the 
 appropriate theoretical study, than by theoretical 
 study alone. 
 
 Development qf drawing with age 
 
 Children develop chiefily in tiie comprehenrion of 
 complex forms. The ability of the child to represent 
 objects varies to some extent with the stage of his 
 development. The stage of development is based to a 
 small d^ree upon the skill with which the pencil can 
 be handled, but also to a much greater degree upon 
 the extent to which the child can analyze an object and 
 can comprehend the different parts of it in relation to 
 one another. A test which has h»een made of school 
 children of different ages indicates that the younger 
 
DJIAWINO 47 
 
 itfid <)\i]i:r »;hil(lrwi 'lo no), (II(T«;r y/'-nUy i;i U«Jr ability 
 to r»?j>ro<luw miii\iU', foniHi.' I'lu; iri<Jivi(liJttl (i'lflirmn-Am 
 a/rionjf <;lill<lr«ni in Mh r«!«j)<'/rt ttr«? mtrra prouiirnrnt 
 limn »tr« f,li« <liff«!r<rnf!«w l«rf,w«r<rn cJiildnrn «rf (li(T<rnsnt 
 nt/,cM. 'Hw. »t(iil,(i,l>ilil,,y of n, fi^riini J,o lfi« aj^;*! or hUi(/i; of 
 <l<rv<rlo|>/(i<!(if, of tlifi rliild would mu^iit to Im; hme/l rrion; 
 on itM complexity than nj)f;n the lu-Amrtuy with which 
 a (mrUcular part nnif«l )«•, olwierved or nrprodtir^i^ij. 
 
 Tb« young child's AtAvrlng l» •ymboUc. BtmJicN of 
 tlm (Irawinj^x of <;liil(lnrti iiui'w.iiUi that th<rn» In u /narkfvl 
 (li(T(inin<'<i in l,li<r (U^nrcM Ut wliicli a «;lilhl ddincatcN tli<! 
 hiilividnal <\m.nu:U:rUl'u;n of an object, or tlin dttl.aiJH 
 of whkih il. in rt)iu\iiim<\. Tim uliild tii'uh-A^U tlio cliar- 
 iM!l,«ri»<l,i«'M wliicli rliwtin/^iilxli au ol»jw;t from oUurrx of 
 th« Narrio kind and ri',\m-Mi'.ulii o;ily xiich ti-aUircM a» 
 miaMo anollifir p«r«on U) know tli« gcn(!ral <!la«H U> 
 which the object liciongn. We i;x\m:HH thi» fiwit l)y 
 uvy\n^, that the drawing of a chihl m Mytribolic. At 
 about nine yuarM of ll^f,l^ tlm child Hocmn h> rwrognizc 
 more clearly the niM«l of more lutciirate and <lclailcd 
 r«pr<ii4cntation. An llhiMtralion of thlx traimition ai>- 
 peiiM ifi the f(M:t that before till* axe the majority 
 of children draw a fiix-e from the front view, whcrtiaH 
 ntU-ir IIiIn uko the majority draw it from the Hide view. 
 'I'lie Nlde view In ii. much «a«ier one Ixt ni|)r<!Hent, and 
 when the child en<l(MivorN to represent iu;cnral,4tly, ho 
 (ihooMeN the eaMier mode. 
 
 ' li'niiii nil iiti|iiilillnlii''>l Miii.iil,iM''n (liw«iirlitlJiiii liy H. 1'. C)iilnuu|ijin, 
 on lilt* III Mill llbmry of llin liiiivymily of ('Mfiiun. 
 
48 PSYCHOLOGY OF COMMON BRANCHES 
 
 Pictorial representation develops rapidly from the 
 transition stage to adolescence. The two elements of 
 pictorial representation which indicate its progress are 
 the increase in the fullness and accuracy with which 
 the particular characteristics of the individual objects 
 are presented, as distinguished from the presentation 
 of the characteristics merely which belong to the gen- 
 eral class of which the object is a member, and the 
 representation of perspective. The portrayal of per- 
 spective may be regarded as an artificial performance 
 in the sense that it requires a type of attention to the 
 appearance of objects which is not produced by the 
 ordinary demands of life, but is due to the special 
 demand of representing relations in three dimensions 
 on a two-dimension surface. That this is counter to 
 the usual type of perception is shown by the fact that 
 it took the race so long to develop it. Early Egyptian 
 art is almost completely lacking in perspective, the 
 Greeks attacked the problem but did not solve it, and 
 it was left for the painters of the Italian Renaissance 
 finally to develop the true representation of depth by 
 drawing. It is not surprising, therefore, that the child 
 does not represent perspective in his early drawing, 
 and its development is to be looked upon as depend- 
 ent upon the acquirement of the intellectual capacity 
 necessary to enable him to understand and adopt the 
 methods which have been handed down rather than 
 as a spontaneous growth. 
 
 Mechanical drawing and diagramming represent 
 
DRAWING 49 
 
 structure and relations of parts. Mechanical drawing 
 and diagramming more closely resemble in purpose 
 the drawing of the young child than they do pictorial 
 drawing. The distinction between diagramming and 
 pictorial drawing is brought out sharply in an investi- 
 gation, as yet unpublished, by Dr. Frederick C. Ayer. 
 The subject of Ayer's study was the relation of draw- 
 ing to the work in science. He first foimd that there 
 was little relation between the student's abihty in 
 pictorial drawing and his rank in science work. He 
 then studied the correlation between the abihty to 
 draw a diagram — for example, of the minuter struc- 
 ture of a feather, as seen imder a low-power microscope 
 — and ability in science. Diagramming calls for the 
 analysis of the object into its parts and the comprehen- 
 sion of the relation of these parts. The drawing does 
 not need to look like the object so long as it gives the 
 observer the idea of the relation. Similarly, mechanical 
 drawing does not give a realistic picture of the object. 
 A plan drawing or an elevation represent only one 
 face of an object, and often internal structure which 
 cannot be seen at all; and in representing the parts 
 which can be seen only shows enough to indicate the 
 structure. Even a mechanical drawing in persp)ective 
 is constructed according to rule, shows the object from 
 a set point of view, and indicates the structure only. 
 It can be made by any one who knows the rules and is 
 careful in making his measurements and drawing his 
 lines accurately. A comprehension of the structure of 
 
60 PSYCHOLOGY OF COMMON BRANCHES 
 
 the object and skill and accuracy in measurement and 
 drawing are required, but not ability in recognizing 
 relations in space as they appear to the eye, or the 
 abiUty to reproduce these appearances. 
 
 Diagramming begins early, mechanical drawing at 
 about adolescence. As has already been suggested, 
 the child's early drawing is a crude sort of diagram- 
 ming. His development in this type of drawing is 
 dependent mainly upon the development of his abihty 
 to analyze objects and to understand their relations. 
 Mechanical drawing, because it usually requires a 
 conception of internal structure, and always accuracy 
 in measurement and drawing, does not develop in any 
 large degree until about adolescence. 
 
 Individuals differ in their rate of development and 
 in the stage which is finally attained. While the devel- 
 opment in accuracy, as represented by correctness of 
 detail or by the degree to which perspective is shown, 
 develops rapidly up to adolescence, there are individual 
 differences in this respect, as in the others which have 
 been mentioned. Very many children do not at ado- 
 lescence equal the stage of development which others 
 have attained several years before. In suiting the 
 form of training to the child, then, the development 
 which is characteristic of the average child must be 
 taken into account, and also the different stages of 
 development which different children represent at the 
 same age. 
 
DRAWING 51 
 
 General account of the nature of perception 
 
 In perception impressions or sensations are given 
 an interpretation. The illustration of drawing has 
 shown that the recognition of objects which are strange 
 is not by any means a simple affair. When a child 
 recognizes the form of a figure, as we have seen, he 
 brings to bear upon the sensation which he receives 
 through his eye the ideas and the habits of attention 
 and of recognition which have been formed by his past 
 experience. This application of past experience to our 
 present impressions makes possible the interpretation 
 of the sensations through which they acquire a mean- 
 ing. When we receive a sense impression and add to it 
 the results of other experiences in order to give it an 
 interpretation, we call the mental process " percep- 
 tion." ^ In perception we usually bring to bear upon 
 the impression the results of past impressions which 
 have been received both through the same sense, and 
 also through different senses. This whole process of 
 recognition through the association of other experi- 
 ences which we have had in the past may be illustrated 
 by another example. 
 
 ' A sensation is a simple experience which is produced by the 
 stimulation of one of the sense organs; as, for example, the impres- 
 sion of a, color, or a soimd, or of a taste, or of a touch. Such a simple 
 experience does not of itself have any meaning. A perception is a 
 sensation which has acquired a meaning through its combination 
 with other sensations. In perception there is the recognition of 
 objects, while in sensation only a single quality is experienced. 
 Sensation is an incomplete stage in the development of perception. 
 
52 PSYCHOLOGY OF COMMON BRANCHES 
 
 Illustration of the complexity of perception. We 
 may take as an example the recognition of a cup of 
 milk by the child. The impression which the child 
 receives as he looks at the cup is one of sight, or of 
 vision. He sees the color of the cup; he recognizes its 
 outUne, or its form. In addition to this, however, he 
 thinks of the cup as having a certain degree of hard- 
 ness; that is, he recognizes that if he should touch the 
 cup it would offer resistance to his finger, and he does 
 not attempt to compress it as he would a rubber ball. 
 In this recognition he is applying the results of the 
 previous experience gained through handling the ob- 
 ject. Further, he recognizes that the cup has a cer- 
 tain weight. If he thinks of it as being full of milk, 
 whereas in fact it is nearly empty, and if he then 
 attempts to Uft the cup, he will exert too much force. 
 This may result in such application of force as to cause 
 the milk to be spilled. This gives an evidence that 
 there was in the recognition also a notion of the amount 
 of force necessary to lift the object. The child also has 
 some recognition of the sound which would be made if 
 he were to knock the cup against some other object, 
 and this expectation is illustrated when he strikes a 
 spoon against the cup. If it gave forth a different sound 
 from that which it usually gives he would exhibit 
 surprise. 
 
 There is also a variety of present impressions. In 
 addition to this obvious combination of the results of 
 past experiences of different senses, there is also a 
 
DRAWING 53 
 
 combination of different impressions received through 
 the two eyes. It is a well-known fact of psychology 
 that the recognition of the distance of objects depends 
 on the fact that we get a slightly different view of an 
 object through one eye from that which we get through 
 the other. These two views are combined in our per- 
 ception, and as a result of this fusion we recognize the 
 distance. Furthermore, the fact that our eyes have to 
 turn inward more to look at a near object than to look 
 at a far one gives us an experience of muscular strain 
 which we may use in distinguishing distances. When 
 the child turns his head to look at the cup, he also gets 
 sensations from the muscles and joints of the neck, 
 which gives him a recognition of the direction of the 
 object from his body. 
 
 Such a perception is a result of growth. This analy- 
 sis of the various elements which go to make up such a 
 simple perception as this is of no particular value 
 merely as showing that the experience is a complicated 
 one. Its value is rather in indicating that this percep- 
 tion must have had a growth or development; that it 
 is not something which the child has merely as a result 
 of the structure of his sense organs. Theories of per- 
 ception have sometimes been held which assume that 
 the object impressed itself upon the mind, or upon the 
 sense organs. On the contrary, the recognition of the 
 object is built up as a result of a variety of past experi- 
 ences and through a combination of a number of differ- 
 ent present elementary experiences. 
 
64 PSYCHOLOGY OF COMMON BRANCHES 
 
 Development is illustrated in overcoming illusions. 
 We must not expect, then, that the recognition of the 
 child is precisely the same as that of the older person. 
 As it is a result of growth, so the stage of growth which 
 has been reached in the child's mind is different from 
 that which has been reached by the adult. Ejqjeri- 
 ments have shown that recognition of objects by the 
 adult is not perfect. The person who has had experi- 
 ence in drawing, for example, has a more complete 
 
 Fig. 6. MTXLI.ERr-LYEE ILLUSION 
 
 recognition of form than has the ordinary individual. 
 Studies in optical illusions,' an example of which is 
 shown in the accompanying Figure 6, indicate that 
 while the ordinary person makes a large error in com- 
 paring the length of the lines in the recognition of such 
 a figure, he may overcome the error by sufficient prac- 
 tice. After about one thousand trials one can judge 
 correctly the relative length of the two lines. 
 
 * An illusion is a false or distorted perception. It is not com- 
 monly abnormal, but is a form of misinterpretation, common to 
 nearly all persons, which can be explained by ordinary psychological 
 principles. 
 
DRAWING 65 
 
 Sensations at first become combined into percep- 
 tions in the recognition of an object which has prac- 
 tical meaning. One might conclude, from the analysis 
 of perception which has been made, that the various 
 sensations are combined in perception in some mechan- 
 ical way or because the child has some inner tendency 
 or other to build together sensations into perceptions. 
 This would be an altogether false view of the matter. 
 The sensations are built together as they contribute 
 to the child's recognition of an object, and in the 
 majority of cases, as has been already said, the child 
 learns to recognize objects which have some practical 
 value or meaning to him. The cup of milk may be 
 taken again as an illustration. It is clear in this case 
 that the chief motive of the child in paying attention 
 to the cup and in learning to recognize its form, direc- 
 tion, distance, weight, etc., is the satisfaction of his 
 appetite for the milk. Those sensations which add 
 something to the recognition, so as to enable the child 
 more clearly to distinguish the cup and more quickly 
 and surely to grasp it and carry it to his mouth, are 
 built into the perception. Others are largely neglected. 
 While it is true that the child does exhibit some interest 
 in sensations, in discriminating between them and in 
 giving them names, he gives attention to them and 
 discriminates between them chiefly because they stand 
 for an object which has some practical meaning for 
 him. 
 
 Illustration: Double images are recognized as a 
 
66 PSYCHOLOGY OF COMMON BRANCHES 
 
 difference in distance. The fact that we pay attention 
 to those aspects of objects which have a meaning or 
 significance for us, and to other aspects only to this 
 end, is shown by the fact that many differences be- 
 tween our sensations are not recognized except in the 
 form of a meaning which is represented by these differ- 
 ences. For example, if we hold two fingers before our 
 eyes, one about twelve inches farther away than the 
 other, and look at the nearer finger, we can make out 
 a double image of the one farther away. This is due 
 to the fact that the image of the far finger is not 
 focused upon the corresponding parts of the retinae 
 of the two eyes. This, however, is not usually noticed 
 by us unless our attention is called to it; and as a 
 matter of fact many people find difficulty in distin- 
 guishing two images even when the fact of their exist- 
 ence is pointed out. We do not pay attention to the 
 double images for themselves; the doubleness is only 
 represented by a meaning — the meaning of nearer or 
 farther away. 
 
 Another illustration : A difference in the loudness of 
 a sound as heard in the two ears means direction. A 
 still more striking example may be taken from the 
 experiences which we have from the two ears. If a 
 sound is given midway between the two ears, we 
 receive substantially the same sensation in both, and 
 it is very difficult to give the exact location to the 
 sound. If, however, the source of the sound is at one 
 side, the loudness and the quahty of the sensation in 
 
DRAWING 57 
 
 the two ears is different, and we interpret this differ- 
 ence as meaning that the sound comes from a given 
 direction. We cannot tell from the examination of our 
 sensations themselves that we get any different sensa- 
 tions in the two ears. The fact that the perception of 
 direction is based on the difference in the sensation 
 from the two ears may be very strikingly confirmed 
 by giving two sounds simultaneously to the two ears 
 at different distances. This may be done by means of 
 two telephone receivers which are in the same circuit. 
 Under these circumstances we recognize a single soimd, 
 not in the real direction of either of the two soimds, 
 but rather in an intermediate direction, which corre- 
 sponds to the position of a sound which would give the 
 same relative loudness to the two ears as is given by 
 the two separate soimds. 
 
 One may distinguish finely in some fields and 
 coarsely in others. A good example of the place which 
 meaning has in directing our attention to a discrimina- 
 tion between sensations is given by Kirkpatrick. He 
 shows that the same person may discriminate finely in 
 certain fields, and much less finely in others. The prim- 
 itive man, for example, is able to discriminate very 
 finely between signs which represent to him the pas- 
 sage of an animal or of a human being through the 
 woods. The same signs pass entirely unnoticed by the 
 civilized person. On the other hand, the savage is 
 unable to discriminate between the small and intricate 
 marks on a page which to the civilized person who has 
 
58 PSYCHOLOGY OF COMMON BRANCHES 
 
 learned to read are entirely clear and easily distin- 
 guished. The difference is, of course, that the printing 
 has significance to the civilized person, and he has 
 therefore learned to discriminate in that field. This 
 whole matter will have a practical application in the 
 discussion of the question of sense tnuning. 
 
 Perception is influenced more by the development 
 of meanings than by increase of ability in discrimina- 
 tion. The foregoing discussion will pve a basis for 
 the distinction between the type of perception of the 
 child and of the older person. The development of 
 perception which takes place with the advancing age 
 of the child does not consist primarily in the ability 
 to make fine discriminations. The young child can be 
 trained to discriminate more accurately than does the 
 average adult. The ability which the child develops 
 with his education and with advancing age is the 
 ability to pick out of a whole situation certain aspects 
 of it which will have significance. If a child and an 
 adult walk down the street together and are ques- 
 tioned afterwards about what they have seen, it will 
 be found that the child has seen more miscellaneous 
 things than the adult. His mind is open to impressions, 
 but it is not directed to gathering impressions of any 
 particular sort. If his attention happens to be at- 
 tracted in a particular direction he will observe what 
 is going on very minutely. The adidt, on the other 
 hand, is likely to observe some particular sort of facts. 
 If he is a botanist and is walking throiigh the woods. 
 
DRAWING 69 
 
 he will observe the forms of plants, of flowers, etc., 
 with great accuracy and minuteness; not because he 
 has greater power of discrimination among sensations, 
 but because he knows what to look for, and knows the 
 significance of what he sees. 
 
 The child must develop habits of observation. We 
 may say, then, that the development of the child con- 
 sists in the formation of habits of recognition, or of 
 habits of observation in particular directions. This 
 may, it is true, close his mind to the observation of 
 other sorts of facts, so that the young child may ob- 
 serve a great many things which will be hidden from 
 the older person. The young child may be less easily 
 misled by the method of the sleight-of-hand performer, 
 which consists in attracting the attention of the audi- 
 ence toward one point while the trick is being done 
 somewhere else. One cannot rely on the child to keep 
 his attention on the spot where the performer intends 
 it to be directed, because he has not yet formed suflS- 
 ciently stable habits of observation. 
 
 The child is suggestible in reporting what he has 
 observed. The child is more easily deceived or more 
 suggestible than the adult in other ways. Having had 
 less experience as to what is likely to happen, he is 
 more ready to believe that anything which appears to 
 be true has actually happened. Furthermore, in recall- 
 ing what he has observed, he is more apt to confuse 
 what he has actually observed with what he has not, 
 but in spite of this unreliability he heis a most implicit 
 
60 PSYCHOLOGY OF COMMON BRANCHES 
 
 faith in his ability to report faithfully what he thinks 
 he has observed. Finally, he is more subject to per- 
 sonal influence than the adult in concluding that he 
 has or has not observed any facts which may be in 
 question. This makes it necessary to use a great deal 
 of caution in questioning the child. It is, of course, a 
 commonplace that the court does not give full recogni- 
 tion to testimony given by children, because of the 
 ease with which they are led to think they have experi- 
 enced that which they have not. The same caution 
 should be observed in questioning the child in school. 
 There is danger that the child wiU merely follow the 
 cue given by the teacher in the question, instead of 
 giving expression to his own knowledge or opinion. 
 Unless one is trying deliberately to develop a senti- 
 ment by means of suggestion, leading questions — or 
 questions that imply their own answer — should be 
 avoided. 
 
 The distinction between subjective and objective 
 observers. We sometimes hear it said that some per- 
 sons are good observers in general, while others are 
 bad observers. We mean by this that some ptersons 
 are able to report faithfully what they have actually 
 seen, whereas others are likely to read into what they 
 have seen the results of their imagination. Some 
 experiments have been made in order to determine 
 whether this difference actually exists, and as a result 
 the distinction has been made between subjective and 
 objective observers. Objective observers are those 
 
DRAWING 61 
 
 who see, perliaps, but a small number of objects, but 
 see them very clearly; while subjective observers may 
 take in a much larger range and give it an interpreta- 
 tion, but the meaning which is read into the facts is 
 apt to be erroneous and may cause the observer to 
 think he has seen what he actually has not. 
 
 Most persons belong to a mixed type. Something 
 corresponding to such differences undoubtedly exist, 
 although most persons do not belong to either extreme 
 type. When persons are tested with reference to their 
 observation in a number of different fields, it appears 
 that a person may be an objective observer in some 
 fields and a subjective observer in others. We may 
 say, then, that most persons belong to an intermediate 
 type. There are, undoubtedly, however, a few who 
 are extremely imreliable and who read into what they 
 see their own interpretations; while there are others 
 who are very reliable and who distinguish clearly be- 
 tween what they see and the meaning which they give 
 to it. 
 
 The value of sense training 
 
 Some educators advocate much sense training. As 
 distinguished from training in observation or in per- 
 ception in the true sense of the term, there are a num- 
 ber of educators who hold that it is desirable to train 
 the child in the ability to discriminate finely between 
 different sensations. This does not involve the recog- 
 nition of the meaning or the interpretation of the sen- 
 
62 PSYCHOLOGY OF COMMON BBANCHES 
 
 sation, but merdy sensoiy discriminatioii. Qlustia- 
 tions of the demand for this type of training may be 
 found in HsJleck's Education of the Central Nenous 
 System. In ch^tets 7 and 8 of this book the author 
 advocates the training, not only of the senses of sight 
 and hearing, but also of touch, taste, and smdl. He 
 gives a long and elaborate series of tests which may 
 be made in order to develop the child's ability to dis- 
 criminate and to recognize a great vaiKly of smdls 
 and tastes, and of objects which ^ve diSerrait sorts of 
 touch experience. Great prominence has heen given 
 to the demand for such sense trauiing also by the 
 Montessori meliiod. In this method, as applied to 
 kindergarten children, many exercises are given to 
 enable the child to discriminate between fine shades of 
 color, between different textures of doth, or of other 
 objects, and between sounds. The bdief underiying 
 the advocacy of this metliod is that when the child's 
 senses are trained, he will be enabled to observe better 
 and to use the results of his observations in his thinking. 
 Experience with a wide range of concrete objects is 
 of great value as con^>ared with soise training. In 
 considering the value of such suggestions we must 
 keep deariy in mind distinctions between sensory 
 discrimination and the familiarity with objects so that 
 they can be recognized and their meaning understood. 
 The child may have his senses very keenly developed 
 and yet know nothing of the common objects of the 
 worid about him. It is conceivable that the child 
 
DRAWING 63 
 
 might be put into a room with a few pieces of appara- 
 tus and have his senses very keenly developed, and yet 
 not know such objects as a tree, a bird, a cow, a calf, 
 a house, a trolley car, etc. There is sometimes failure 
 to distinguish between sense training, strictly speaking, 
 and this acquaintance with a large number of objects. 
 This knowledge of objects was studied by G. Stanley 
 Hall and reported in an article entitled " The Con- 
 tents of the Children's Minds on entering School." ^ It 
 was found that children were remarkably ignorant of 
 many of the objects which were talked about or read 
 about in the earlier grades. This lack is undoubtedly 
 a great handicap to the child, and anything that is 
 said in the following paragraphs in disparagement of 
 sense training must not be taken to mean a belittle- 
 ment of the value of a wide acquaintance with con- 
 crete objects on the part of the child. 
 
 Keen senses do not necessarily go with high intelli- 
 gence. Some light may be thrown upon the value of 
 mere keenness of the senses by facts which are either 
 common matters of observation, or have been estab- 
 lished through scientific experiments. It is well known 
 that certain of the lower animals have some of their 
 senses more keenly developed than the human being. 
 The dog has a much keener sense of smell than has 
 man. Some of the birds have a keener sense of vision, 
 and some insects can hear sounds which to us are 
 absolutely non-existent. The keenness of senses in 
 ' Reprinted in Some Aspects of Child Life aiid Ediuiation. 
 
64 PSYCHOLOGY OF COMMON BRANCHES 
 
 these animals does not produce in them a correspond- 
 ing degree of intellectual development. Furthermore, 
 if we compare the sensory keenness of backward chil- 
 dren, or even of feeble-minded children, with that of 
 normal children, we find that there is no great differ^ 
 ence. In order to find striking differences between chil- 
 dren of different degrees of intelligence, we most go 
 to such higher mental processes as reasoning, the rec- 
 ognition of logical relationships, and memory. 
 
 Discrimination should be keen enoa|^ to meet the 
 demands of perception. The discussion of perception 
 and its development has shown that, in the ordinary 
 course of life, we develop sensory discrimination as it is 
 found to be useful to us in meeting the denumds of our 
 practical life; that is, we distinguish between sensa- 
 tions with sufficient accuracy to enable us to get an 
 accurate perception. It would be possible for us to 
 develop our senses very much more highly than we 
 ordinarily do. The blind person has developed a sense 
 of touch in his fingers very much more than the person 
 who has sight. He also has developed the sense of 
 hearing more highly than has the average person. It 
 is undoubtedly true that all of us could develop our 
 senses more keenly than we have, but it is questionable 
 whether we should find that such development repaid 
 us for the effort which was exfjended. 
 
 Sensory defects should be discovered and, if possi- 
 ble, corrected. Whenever the child is deficient in 
 sensory capacity, there is, of course, danger that his 
 
DEAWING 65 
 
 mental development will suffer becatise of the lack of 
 the proper materials with which to think. We assume, 
 in the ordinary routine of school life, that the child 
 can hear the directions which are given him in the 
 schoolroom, and that he can see figures and words 
 which are written on the board. If the child is suffi- 
 ciently deficient so that he cannot hear or see these 
 things, he will unquestionably suffer. It is necessary 
 to find out whether a child has a degree of sensory 
 keenness which will enable him to profit in these 
 ordinary ways by the things which go on about him. 
 It is also necessary to correct defects wherever they 
 can be corrected. 
 
 The normal child does not need ^stematic sense 
 training as does the feeble-minded child. We must 
 clearly recognize that certain senses are very much 
 more important than others. Sight and hearing are of 
 importance out of all comparison to taste and smell, 
 and touch is intermediate between these in value. We 
 must also recognize that, although sense training is of 
 considerable value to the feeble-minded child, the 
 normal child gets out of his ordinary experience train- 
 ing which must be given to the abnormal child by 
 special exercises. The normal child learns to distin- 
 guish colors and shapes through the exercise of his 
 natural curiosity, which prompts him to play with 
 things and learn their names as he hears them spoken 
 by older persons. A little special attention by the 
 parent will serve to hasten this development and make 
 
66 PSYCHOLOGY OF COMMON BRANCHES 
 
 the child's knowledge more exact and comprehensive. 
 The feeble-minded child, on the other hand, does not 
 learn the common facts of his environment spontane- 
 ously, but needs special, systematic drill. It is a great 
 mistake to assume, as does the Montessori method, 
 that this training, which is necessary for the defective 
 child, is suited to be the main part of the education of 
 the normal child. 
 
 REFERENCES 
 
 1. E. Barnes: "Study of ChUdren's Drawings," Ped. 8m. (1892), 
 vol. 2, pp. 455-63. 
 
 2. A. B. Clark: Children's Attitude toward Perspective Problems. 
 Barnes's Studies in Education (1896-97), pp. 283-94. 
 
 3. G. Stanley Hall: Some Aspects of Child Life and Education. 
 
 4. R. P. Halleck: Education of the Central Nervous System. Mao- 
 millan (1896), chaps, vii and viii. 
 
 5. C.H.Sudd: Genetic Psychology for Teachers. D. AppIeton&Co. 
 (1903), chaps, i and ii. 
 
 6. C. H. Judd and D. J. Cowling: "Perceptual Learning." Psy- 
 chological Review, Monograph Supplements, vol. 8, Yale Studies 
 (n.b.), vol. 1, no. 2, pp. 349-69. 
 
 7. H. T. Lukens: "A Study of Children's Drawings in the Early 
 Years," Ped. Sem. (1896-97), vol. 4, pp. 79-110. 
 
 8. W. Sargent: Fine and Industrial Arts in the Elementary School. 
 Ginn & Co. (1912), chap. i. 
 
CHAPTER IV 
 
 READING: PERCEPTUAL LEARXIXG 
 Th<t rdation cf reading, ttriiing, and spokai language 
 
 Reading and miting are veiy dosdy related to one 
 anofter ftran the fact that boft are related to spoken 
 langnage. Writing is the eiqnession by graphic signs 
 of ideas which were previouslj- expressed in spoken 
 words. Reading is the ability to recognize words which 
 have been so written or printed. In both cases, then, 
 we are concerned not merely with the recognition or 
 production of certain forms, certain marks on paper, 
 but we are concerned with the recognition or the ex- 
 pression of ideas as they are repre^aated by printed or 
 written fonns. The written or the printed forms on the 
 paper stand for spoken words, or may be said to be the 
 symbols of the spok«i word. 
 
 Reading and writing should have meaning to tiie 
 child. The teaching of reading and of writing ought, 
 therefore, to be %-erj- dosdy related to the meanings 
 which are expressed in spokoi language. The chOd 
 ought, whai he writes, to be able to understand the 
 meaning of what he is writing. Cfe, more correctly, he 
 ought, in the main, in his writing, to be e^tressing 
 ideas. Sinulariy, we now insist that when the child 
 learns to read he shall be gaining the abihty not meidy 
 
68 PSYCHOLOGY OF COMMON BRANCHES 
 
 to pronounce words, but to read a meaning into the 
 words which he is pronouncing. 
 
 Drill is necessary for the perfection of skill. This 
 principle, that learning to write and learning to read 
 should be related to each other and that both should 
 be related to the spoken language of which they are 
 the expression, should not be taken to mean that no 
 drills should be given for the perfection of the ability 
 to write or to recognize words. We have seen, in the 
 case of writing, that it is often necessary to stop in the 
 process of expression of thought and to take time to 
 perfect the technique of form production or of the 
 development of the proper movement. What is here 
 meant is that writing and reading should always have 
 a meaning for the child, but it is not intended to imply 
 that this meaning should always be uppermost in his 
 mind. There should, in fact, be times when the tech- 
 nique of the production or of the understanding of 
 words is the thing which is uppermost. If we attempt 
 to develop skill merely as an incident to the recogni- 
 tion of meaning, we find that there are large gaps in 
 the child's ability. There are two extremes, then, 
 which have to be avoided. On the one hand, the 
 development of great technical ability which has no 
 meaning or significance for the child and which there- 
 fore cannot be used by him to serve its real purpose; 
 and, on the other hand, the failure to develop the 
 technique to such an extent that the acquisition may 
 be used as an efficient tool by the child. 
 
READING 69 
 
 Writing enhances the meaning of reading. A few 
 remarks may be made here as to the manner in which 
 reading and writing are related to each other. In the 
 development of writing in the race, reading and writ- 
 ing, of course, went together: that is, the race was able 
 to recognize those signs which it could produce; and it 
 could recognize only those which were produced be- 
 cause it was dependent on writing for the creation of 
 material to be read. The child, however, when he 
 comes to read, is confronted by a large amount of 
 material which has been developed in the past history 
 of the race, the origin of which he is entirely unac- 
 quainted with. A problem is then raised that may be 
 put thus: Shall we introduce the child to this accumu- 
 lated mass of printed matter as fast as he can learn to 
 read it, or shall we repeat the history of the race and 
 make writing keep pace with reading? It is not neces- 
 sary to make the faster process of learning to recognize 
 words keep pace with the slower process of learning to 
 write them. When the child does learn to write, how- 
 ever, it undoubtedly not only makes his perception of 
 the letters more distinct, as we saw in the chapter on 
 writing, but also gives him a better realization of the 
 fact that in reading one receives a message from an- 
 other person in the same way as in listening to another 
 person talk. This fact furnishes an argument against 
 deferring writing any longer than necessary. The con- 
 nection between reading and writing may be empha- 
 sized by relating both of them to oral expression. 
 
70 PSYCHOLOGY OF COMMON BRANCHES 
 
 Writing and reading should be related to oral ex- 
 pression. Both reading and writing may be related 
 to oral expression in the following manner. The child 
 or the class may be led to describe some experience 
 they have had; this description may then be written 
 out by the teacher and reproduced by the children, 
 or written out by the children with the help of the 
 teacher; and the children may then read what they 
 themselves have composed, first orally, and later in 
 writing. When the connection between oral composi- 
 tion, writing, and reading is thus made, the child comes 
 to think of writiag as having some use, as being a real 
 activity, and related to the expression of his ideas 
 instead of being merely a formal production of certain 
 meaningless signs upon the paper. Similarly, reading 
 comes to be the acquiring of ideas, or the gaining of 
 experiences from others rather than the ability to pro- 
 nounce meaningless words. When reading and writing 
 thus have acquired their normal meaning through 
 their association with each other, the time is ripe for 
 the development of a higher degree of technical skill 
 in order that the ability may be gained to express and 
 to recognize still more difficult ideas or ideas expressed 
 in a more difficult form. 
 
 The stages in learning to read 
 
 Learning what printed words are for. Following this 
 general account of the meaning and significance of 
 reading and writing, we may describe the stages 
 
READING 71 
 
 through which the child's recognition of words pro- 
 gresses until it becomes complete in reading. In the 
 first place, the child learns that printed words repre- 
 sent spoken words. This knowledge may be gained 
 before he is able to recognize any particular printed 
 word as meaning any particular spoken word. The 
 experience of seeing other persons read, the realization 
 of the meaning of street signs, of store signs, etc., will 
 give him this early type of recognition. The child 
 comes to understand this without any special form of 
 training, merely by casual observation of the actions 
 of people about him. 
 
 The word-learning stage. The child goes beyond 
 this general recognition when he learns to connect 
 certain words with the printed forms which repre- 
 sent them. He may do this before he is able to read 
 connectedly. He may, for example, recognize his own 
 name when it is printed, or the names of the members 
 of his family, or of familiar objects. This recognition 
 gives him a starting-point for more coherent and con- 
 nected reading. This association between the spoken 
 name and the written word is really not much more 
 complex or difficult than the connection of a spoken 
 name with the object. It, of course, soon becomes very 
 much more complex in virtue of the fact that different 
 printed words are made up of combinations of the same 
 letters, but at the start the child can associate a printed 
 form with a name in very much the same way in which 
 he associates the object with its name. The difficulty 
 
72 PSYCHOLOGY OF COMMON BRANCHES 
 
 arises when the child be^s to learn a large number of 
 words. The amount of difference between different 
 words is in many cases small, and it is necessary to pay 
 a good deal of attention to the details of a word in 
 order that it may be distinguished from one that is 
 similar to it. 
 
 The letters need not be learned first. This essential 
 similarity between the association of a printed word 
 with a spoken word, and the association of a name with 
 an object, is taken advantage of in present-day meth- 
 ods of teaching the child to learn to read. In the 
 older methods it was assumed that the child had to 
 be brought to this recognition by an indirect route; in 
 other words, it was believed that it was necessary for 
 the child first to learn the elements of which the word 
 is composed, and then to be able to put them together 
 into the word. The association was not between 
 spoken word and printed word, but first between 
 spoken names of letters and printed letters, then 
 between the printed letters as they were combined 
 into the word, and finally, by this indirect route, be- 
 tween spoken and printed words. 
 
 There are special difficulties in beginning with the 
 names of letters or the sounds of letters. The matter 
 was made still more complex by the fact that the let- 
 ters which composed the words did not represent the 
 sounds of the spoken language, but rather represented 
 certain names which did not in many cases correspond 
 with the sound. For example, in building up the word 
 
READING 73 
 
 cat, the names of the letters c-a-t do not stand for the 
 sounds of the spoken word, but are rather names 
 which are more or less unrelated to the soimd. This 
 diflBculty was somewhat remedied when the soimds of 
 letters were used instead of their names. The sounds 
 of the successive letters represent in some measure the 
 sound of the word as a whole, and the child can see 
 that the combination of the letters as represented by 
 their sounds represent the spoken word. Eypn here, 
 however, many diflSculties arise in such a language as 
 the English in which the spelling is not phonetic. In 
 such a word as though, the combination of the sounds 
 of the separate letters does not at all represent the 
 sound of the spoken word. At the best, even if the 
 language were entirely phonetic, there is no reason 
 why it would be necessary to begin with the elements 
 of which the words are composed. As has already been 
 said, the child may form the direct associations be- 
 tween the spoken and the printed word as the starting- 
 point of his reading. 
 
 The sentence is too complex to begin with. Some 
 have attempted to go still further than this, and make 
 the association first between a written sentence and 
 the spoken sentence. This method seeks justification 
 in the fact that an idea is commonly expressed by a 
 combination of several words in a sentence rather than 
 by a single word. In spite of this fact, however, the 
 word is a fairly distinct unit of speech, and if we trace 
 the development of speech in the child we find that 
 
74 PSYCHOLOGY OF COMMON BRANCHES 
 
 he first isolates single words from the trains of sen- 
 tences which he hears spoken by those about him. 
 We found in our description of the language develop- 
 ment of the child that he first uses sentence words. 
 Single words represent for him trains of thought; and 
 the supplementary parts of the idea are expressed 
 through facial expression, gesture, etc. In learning to 
 speak it is single words that first catch the child's 
 attention, and the same is true in reading. The child 
 may not be able to hold in his mind, at the beginning, 
 the minor parts of a sentence and put them together 
 into a sentence as a whole. We may, therefore, con- 
 clude that his reading, as his speaking, should begin 
 with words which form the core of a sentence or an 
 expression of thought. After he has gained the ability 
 to recognize a few important words, the others may 
 then be introduced, and he will come gradually to the 
 recognition of their meaning also. 
 
 After the early stage letters and their sounds must 
 be recognized. This gives the child the starting-point 
 for the recognition of words. He will not progress far, 
 however, until he understands that words which are 
 printed represent spoken words, not because they are 
 associated together in an arbitrary way, but because 
 the printed word represents a combination of sounds 
 in the same way that a spoken word represents a com- 
 bination of sounds. In other words, he must come 
 sooner or later, and in fact rather soon, to the under- 
 standing of the principle of the alphabet. Although it 
 
READING 
 
 75 
 
 a' 
 
 
 
 ■}) "^ 
 
 Sua 
 
 Moon 
 
 is not necessary for him to start with the recognition 
 of the alphabet, yet it is necessary that he gain this 
 recognition before he progresses far. 
 
 Written symbols were originally pictures of objects. 
 We may gain a clear idea of the meaning of the alpha- 
 bet by a survey of the course of its evolution. At the 
 beginning the writ- 
 ten signs which a ( • j 
 were used to ex- ^-^ 
 press ideas resem- 
 bled the objects 
 which they were b 
 supposed to repre- 
 sent. This is seen 
 in picture-writing. 
 Picture-writing, as 
 the name indicates, 
 conveys its mes- 
 sage through a se- 
 ries of pictures of ,.,, „„„ „ ^, .„. 
 
 '^ (After E. B. Hney, Psychology ana Pedagogy 
 
 objects which when of Reading, with tiie peimlssiou of the pub- 
 * Ushers.) 
 
 put together sug- 
 gest a connected story. Sometimes other signs, such 
 as a rough map, are used to indicate the relations 
 of the pictures to one another. The Chinese language 
 still retains this same principle of picture-writing in 
 that the signs which represent the words of the lan- 
 guage were originally pictures of the objects. For 
 example, the sun was represented by a circle with 
 
 "H^ 
 
 Light 
 
 Fio. 7. 
 
 ILLUSTRATION OP PICTURE- 
 WKITING 
 
76 PSYCHOLOGY OF COMMON BRANCHES 
 
 a dot in the middle. (See Figure 7.) As it became 
 easier to use straight lines rather than curved lines, 
 another sign was substituted for this, but the meaning 
 was still based on the original correspondence in 
 appearance of the sign and the object. The Chinese 
 language, then, instead of having twenty-six signs, as 
 has our language, has thousands of signs representing 
 individual objects or ideas, together with certain key- 
 signs which may be used in combination with them. 
 
 These pictures were then used to represent other 
 objects having names of the same sound. The written 
 language which we inherit, however, developed accord- 
 ing to an entirely different principle. The develop- 
 ment toward the 
 new forms of print- 
 ed signs probably 
 had its origin in 
 the necessity for 
 
 FlO. 8. ILLUSTRATION OP PICTDEE- Writing prOpCT 
 WRITING 
 
 (.AtU)T-E.B.nney, Psychology and Pedagogy l^mes. A proper 
 of Heading, with the permission of the pub- j^ajne CanUOt be 
 iisocrSi) 
 
 expressed by the 
 picture of the object which it represents, because the 
 distinguishing marks of an individual are difficult to 
 represent, and because it may be applied to a number 
 of different persons. This led to the device of break- 
 ing up the name into a number of parts each of which 
 could be represented by some object. The name then 
 was represented by a combination of the signs which 
 
BEADING 77 
 
 represented other objects. See, for example, the sign 
 which was used to represent the Aztec name, Itz-coatl. 
 The first part of this name is the word for knife, and 
 the second part, the word for snake. The name was 
 
 ^ 1 
 
 7 1 AA M 
 
 Fig. 9. EVOLUTION OF M 
 
 (From Judd's Oenetic Psychology for Teachers [Appleton, 1903], p. 208.) 
 " The figure shows the derivation of the letter M from the Egyptian 
 hieroglyphic owl. The four forms in the upper part of the figure are 
 Egyptian forms. The first form on the left of the lower series is an 
 ancient Semitic form. Then follow in order an ancient Greek form, and 
 two later Greek forms." (I. Taylor, in The Mphabet, pp. 9 and 10.) 
 
 then represented, as shown in Figure 8, by a combi- 
 nation of the picture of the knife and of a snake. 
 
 The simplified pictures were finally used to repre- 
 sent the first sound of a name. In early Egyptian and 
 Phoenician times this process was carried a step farther 
 by using the sign for a word, not to represent the word 
 as a whole, but the first sound in the word. In this way 
 there came to be developed a great many signs which 
 stood for single sounds. Thus the letter M was devel- 
 
78 PSYCHOLOGY OF COMMON BRANCHES 
 
 oped from the sign for the Egyptian word mulak (owl) 
 through a series of steps illustrated in Figure 9. In 
 many cases the same sound was represented by a 
 variety of signs, because different words starting with 
 the same sound might have signs to represent their 
 initial sound. The Egyptians apparently did not 
 develop a series of single signs to represent the various 
 sounds. This was carried forward by the Phoenicians 
 or the Greeks. 
 
 Our alphabet does not entirely suit our language. 
 As a result of this development we have a series of 
 signs which stand for the sounds of the language. In 
 the ancient Greek and Phoenician alphabets there was 
 probably a complete correspondence between a series 
 of sounds and of signs. In our own case, however, we 
 have inherited an alphabet and have applied it to a 
 language which is somewhat different from that for 
 which the alphabet was devised. Therefore, we have 
 some sounds which are represented by a number of 
 letters, and some letters which represent a number 
 of sounds. In other words, our language is not pho- 
 netic. 
 
 The child may make the association bettreen the 
 sound and the letter either by systematic drill or inci- 
 dentally. To return to our description of the develop- 
 ment of the child, we see that it becomes necessary for 
 him sooner or later to awaken to a recognition of the 
 sounds which are represented by the different letters. 
 This may be done in two ways. In the first place, the 
 
READING 79 
 
 child may be told what sound is represented by the 
 letter; or, in the second place, he may be led to make 
 an association between the sound of a letter by seeing 
 the same letter appearing in a large number of words. 
 We may call the first a definitely phonetic method of 
 teaching, and the second an incidental method. 
 
 A moderate amount of phonetic drill improves the 
 ability to recognize words. Some amount of phonetic 
 teaching is undoubtedly of value in helping the child 
 both to analyze the spoken words into their sounds 
 and to make the associations between the sound and 
 the letter which it represents. This prevents a waste 
 of time and leads to an earlier formation of the associa- 
 tion than would occur if the association were made 
 wholly by the incidental method. The need of making 
 the association between the sound and the letter be- 
 comes prominent when the child meets new words, 
 but it is possible to develop such associations incident- 
 ally, as is shown by the fact that the child who has 
 had no phonetic drill may be able to recognize new 
 words. But the phonetic drill may be carried to an 
 extreme, and when this is done the child becomes 
 expert in the recognition of the sound of words beyond 
 the development in ability to recognize their meaning. 
 There is some danger of overemphasizing the sounds of 
 letters in contrast to the meaning of the words which 
 they represent. 
 
 An added difficulty is due to the fact of a lack of 
 uniform correspondence between sounds and letters. 
 
80 PSYCHOLOGY OF COMMON BRANCHES 
 
 In the English language, which is highly unphonetic 
 in its spelling, the difficulty arises which has already 
 been mentioned. A letter may represent one sound in 
 one word and another sound in another word; and to 
 teach that a letter represents a particular sound does 
 not always enable the child to give it its appropriate 
 sound in all words. Attempts have been made to over- 
 come this difficulty by using additional signs to indi- 
 cate when a letter is to be given one sound or another 
 sound. These signs are called " diacritical marks." 
 Other devices which have been used consist in the for- 
 mation of a new alphabet, or in the invention of addi- 
 tional letters to those of our alphabet in order to sup- 
 ply this want. Whether or not diacritical marks or 
 additional signs in the alphabet are used, we must 
 recognize that they are for temporary rather than for 
 permanent use. The child must ultimately come to 
 recognize words which are printed in the ordinary let- 
 ters in common use without diacritical marks. The 
 question, then, is, whether he can better learn to 
 recognize the various sounds of ordinary printed let- 
 ters as they appear in different words by first using 
 diacritical marks, or whether he can better learn by 
 the incidental method. 
 
 Diacritical marks should be used sparingly. It is 
 undoubtedly true that we sometimes create difficulties 
 for the child by calling them to his attention, and by 
 the use of devices which have for their purpose the 
 overcoming of these difficulties. The child may recog- 
 
READING 81 
 
 nize the difference in the sound of a in say and in saw, 
 for example, without its presenting any particular 
 difficulty to him. But if a diacritical mark is used in 
 the one case, or in the other, or in both cases, he has 
 an additional thing to learn. Undoubtedly some con- 
 fusion in the mind of the child is inevitable, and the 
 use of a few diacritical marks is desirable to overcome 
 this confusion. A few years ago there was an extreme 
 use of such signs and of new or artificial alphabets, but 
 teachers are coming to discover that this extreme use 
 of supplementary signs is unnecessary and serves to 
 confuse rather than to help the child. Their chief use 
 is to enable the child to gain the pronunciation of a 
 word which is new to him in his reading and in his 
 speech, by consulting the dictionary. This need does 
 not arise in the early years. 
 
 Spelling necessitates a clear recognition of the let- 
 ters. The necessity for the recognition of the letters 
 as the elements of a word is due also to the require- 
 ments of writing. When a person writes words he 
 must know not merely the general form of the word 
 or the more prominent letters which compose it, but 
 he must be able also to give each individual letter in 
 its proper order. The requirement of spelling necessi- 
 tates more minute analysis of the word than the re- 
 quirement of its recognition. Furthermore, it has 
 been shown by the photographic method that the child 
 makes many more eye movements even in the recogni- 
 tion of words than does the adult. The child in the 
 
82 PSYCHOLOGY OF COMMON BRANCHES 
 
 first two or three grades moves the eye almost as many 
 times as there are letters in the word; whereas the 
 adult, as we shall see later, makes only four or five 
 pauses in an ordinary line of print. This is an indica- 
 tion that the child does not recognize words as wholes 
 to the same degree as does the adult, even though he 
 has been taught by the word method. On the score, 
 then, of the recognition of words and of the ability to 
 spell words in writing, it is necessary that the child 
 should finally get a clear recognition of the letters 
 themselves, and not merely of the words as wholes. 
 
 To read sentences fluently requires the develop- 
 ment of eye-movement habits. The ability to read is, 
 in addition to the ability to recognize words, the abil- 
 ity to recognize them rapidly and connectedly as they 
 appear in their order in the sentence. The sentence 
 consists in a combination of words which express a 
 coherent meaning. When the adult reads he takes in 
 during each of a series of eye pauses a group of letters 
 which make up a word, several words, or even phrases, 
 at the same time. The mechanism by which this 
 recognition of successive words and phrases take place 
 has been recently studied. The opinion was previously 
 held that the eye travels steadily along the line and 
 that the words are recognized while the eye is moving. 
 Experiments which have recorded accurately the 
 movements of the eye have shown that what really 
 takes place is a series of rapid movements separated 
 by eye pauses, and that the recognition of the word 
 
READING 83 
 
 takes place during the eye pauses. The number and 
 length of these pauses vary with different persons and 
 in the same person with different kinds of subject- 
 matter or with different sizes of type and length of 
 lines, etc., but it is fairly constant for the same person 
 under the same conditions. Each person has devel- 
 oped a certain habit of eye movement which accords 
 with his habits of reading, or which expresses the 
 habits of recognition which he has formed. It is a 
 question whether the eye movement is the factor which 
 determines the kind of a person's recognition, or 
 whether the eye movement is governed by the recog- 
 nition of meaning; but at any rate it is clear that one 
 of the necessities which confronts the child as he learns 
 to read is the necessity of building up these eye- 
 movement habits. 
 
 Progress consists in a decrease in the number of 
 movements and an increase in the scope of recognition 
 at each pause. As was mentioned previously, it has 
 been discovered that with the very young child these 
 habits of recognition of words, or large parts of words 
 at a time, has not yet been completely formed. The 
 child makes progress in the development of the habit 
 from the stage in which he makes a large number of 
 movements, corresponding to the individual letters or 
 small groups of letters, to the stage in which he makes 
 fewer movements corresponding to larger groups of 
 letters or words. Recent experiments indicate that 
 probably by the third grade, many if not most of the 
 
84 PSYCHOLOGY OF COMMON BRANCHES 
 
 children have developed these movement habits 
 sufficiently to read with a high degree of rapidity. 
 
 Words are connected into sentences by inner speech. 
 These facts in regard to eye movements throw light 
 upon what happens in order that we may recognize 
 words in reading. Evidently what we get of the printed 
 page is a series of glimpses. We are not aware of these 
 pauses in our reading, and in fact we are not aware 
 that we perceive the sentences of a page piecemeal, 
 but it seems rather as though we read continuously. 
 The reason for this is that as we perceive the words 
 we put them together and weave them into a whole as 
 though we were speaking the sentences. Words are 
 connected in oiu: minds in the first place through 
 speaking them in sentences and through listening to 
 others speak. When we read there is a tendency also 
 to repeat the sentence. With unpracticed readers this 
 is carried to such an extent that they move their lips 
 in the pronunciation of the words that are being read. 
 Even though a practiced reader does not give these 
 outward signs of pronimciation, yet it has been shown 
 by experiment that the vocal cords and the tongue 
 make very slight movements which correspond to the 
 words which are being read. The glimpses which are 
 got of the line in reading, then, serve to set up the 
 train of activities which correspond to the speaking of 
 the sentence. 
 
 Inflection, pitch, and tone quality correspond to the 
 meaning of the sentence as a whole. Not oidy are the 
 
READING 85 
 
 words reproduced in some form of imier pronuncia- 
 tion accompanied by the imagination of the sound of 
 the words or of the feeling which is produced in pro- 
 nouncing them, but we also have imagery which cor- 
 responds to the relationships of the words in the sen- 
 tence. When we speak a sentence the words are not 
 pronounced in a monotone, but they are given a cer- 
 tain emphasis and inflection which is due to their 
 relationship to the other words, independent of their 
 character as words taken separately. If we listen to 
 a person talking in another room, although we cannot 
 distinguish the words, we have some notion of the type 
 of sentence which he is uttering. We can distinguish 
 between a question, a declaration, and an exclamation, 
 etc. In a similar way the pitch and quality of the voice 
 represent the emotion which accompanies the words 
 as they are being articulated. Although one may, 
 when he has acquired the habit of rapid silent reading, 
 slur over the articulation of the individual words, yet 
 this modulation of the voice remains, and is repre- 
 sented in the imagination or in actual changes in the 
 vocal cords or in the other organs of speech which 
 correspond to such modulation. These tendencies to 
 inner speech are somewhat different from those which 
 complete themselves when one is actually speaking, 
 as is shown by the fact that they may take place dur- 
 ing inspiration of breath as well as during expiration; 
 but though they are thus modLQed in silent reading, 
 they have an important connection with the appre- 
 hension of meaning. 
 
86 PSYCHOLOGY OF COMMON BRANCHES 
 
 Inner articulation is more important in some kinds 
 of reading than in others. The importance of inner 
 articulation varies with the rapidity of the reading; 
 or with reference to the aim, according as it is merely 
 the rapid apprehension of meaning or some other form 
 of appreciation of what is being read. When one is 
 reading passages the value of which depends upon the 
 sound quality, it becomes necessary to read in such a 
 way that this sound quality will be recognized. In 
 poetry, for example, where the rhythm and the melody 
 and the alliteration, or other sound characteristics, are 
 important in the appreciation of the aesthetic qualities 
 of the poem, it is necessary to read in such a way that 
 one has time to get a clear experience of these char- 
 acteristics in the imagination. The same thing may 
 be true to some extent of literary prose. It is, however, 
 not correct to apply the principles which govern such 
 forms of reading to reading of all sorts. It is undesir- 
 able in much of our reading, which is so voluminous 
 that the meaning must be apprehended as rapidly as 
 possible, to dwell upon these elements of the sentence. 
 It is not necessary in a great many cases to pay partic- 
 ular attention to every detail which is being read, but 
 it is desirable to gather only the main ideas. 
 
 Oral and silent reading 
 
 Ability in silent reading is much more important 
 than in oral reading. This raises the whole question of 
 oral and silent reading, which must be considered 
 
READING 87 
 
 before we finally arrive at a conclusion with reference 
 to rapid reading. Traditionally the reading in the 
 schools has been chiefly oral reading, and little or no 
 attention has been paid to silent reading, or to reading 
 for the purpose primarily of getting the thought, and 
 not for the purpose of expressing it to others. The 
 relative value of these two sorts of reading must be 
 considered in reference to the use to which they will 
 be put in the child's after life. From this point of view 
 it is clear that silent reading is by far the more impor- 
 tant. Oral reading is the merest incident in the life of 
 the average adult; whereas silent reading plays a very 
 important part in his life. The only justification for a 
 comparatively large amount of emphasis upon oral 
 reading would be the assumption that it is a necessary 
 condition for the proper development of oral reading. 
 Proficiency in silent reading does not correspond 
 closely to proficiency in oral reading. One may hold 
 that while oral reading is not to be used, yet it is neces- 
 sary to the development of silent reading. If we com- 
 pare the oral and silent reading of the adult, however, 
 we are led to believe that there is quite a wide differ- 
 ence between the two processes. If the adult who has 
 become practiced in silent reading is required to read 
 orally, he will see that the apprehension of meaning is 
 less perfect than when he does not pronounce the words 
 aloud. The oral reading, then, is to some extent 
 an interference with the apprehension of meaning. 
 Furthermore, it is evident upon the briefest observa- 
 
88 PSYCHOLOGY OF COMMON BRANCHES 
 
 tion that a child may read orally and pronounce the 
 words with a fair degree of accuracy of inflection, etc., 
 and yet have very little comprehension of what he is 
 reading. 
 
 Oral reading is of little value for silent reading after 
 the early stages of learning. We must assume, there- 
 fore, that, although there is inner pronunciation in 
 silent reading, yet the development of silent reading is 
 mainly to be got by the suppression to a large extent 
 of the oral accompaniment, and the fixing of attention 
 on what is being read. Experiments in which the child 
 is encouraged to get the meaning from the printed 
 page rapidly and without pronunciation, or at least 
 without oral reading, indicate that he is capable of a 
 much higher degree of development in this direction 
 than we have been accustomed to think. Oral reading 
 is doubtless the natural and best kind of reading for 
 the beginner and perhaps during the first year. It 
 furnishes the most natural motive for the child to get 
 the meaning of the printed words, and his rate of 
 recognition is still so low that it cannot be retarded by 
 speaking. Aside from this early reading, however, 
 oral reading is chiefly of value, not because of its 
 bearing on the greater part of our silent reading, but 
 because it is of itself of importance in the development 
 of oral expression, and because it leads to an ap- 
 preciation of the aesthetic qualities of certain types of 
 material. 
 
BEADING 89 
 
 Efficiency in reading 
 
 Efficiency is meastured by speed and apprehension 
 of meaning. We have assumed that the chief purpose 
 of reading in the schools is to develop eflBciency in 
 silent reading. This assumption is entirely justified 
 by the use to which reading is put in after life. If this is 
 true the question next arises: In what does efficiency 
 consist? Undoubtedly one element in efficiency is 
 speed, and this has been incidentally referred to. 
 Rapid reading, however, is of little importance unless 
 the meaning is apprehended with clearness and ac- 
 curacy. We must include, then, the ability to repro- 
 duce or to use what has been read, as well as the 
 amoiuit which has been read, in our measure of effi- 
 ciency. The speed is easily measured by measuring 
 the amount that a person can read in a given time. 
 The degree to which the meaning is apprehended may 
 be measured in several ways. The pupil may be re- 
 quired to give an account of what he has read; or he 
 may be asked to answer questions on the material 
 which he has read. These are the tests which are com- 
 monly used, and when they have been applied, it has 
 been found that the rapid readers apprehend the 
 meaning about as well as slow readers. Furthermore, 
 when a person through a course of drill increases his 
 speed in reading, he is as likely to increase the ac- 
 curacy with which he apprehends the meaning as the 
 reverse. In fact, the increased speed of reading often 
 
90 PSYCHOLOGY OF COMMON BRANCHES 
 
 seems to heighten the attention or to increase the 
 amount of mental energy which is expended, and this 
 is expressed in the better apprehension of meaning as 
 well as in greater speed. The figures in Table I show 
 that the speed of reading in the lower grades may be 
 greatly increased, and that this may be accompanied 
 
 TABLE I 
 
 Improvement in reading from September to March^ 
 
 
 Rale in 
 words per 
 minute 
 
 Amount 
 reproduced 
 
 Percentage of 
 
 correct answers 
 
 to questions 
 
 Grade 3 
 September 
 
 76.4 
 
 149.1 
 
 72.7 
 
 92.7 
 
 163.3 
 
 70.2 
 
 lis. 
 
 129.2 
 16.2 
 
 128. 
 130.1 
 2.1 
 
 122.7 
 
 142.8 
 
 21.8 
 
 147.2 
 
 158.9 
 
 11.7 
 
 71.1 
 135. 
 63.9 
 
 133.8 
 
 212.9 
 
 79.1 
 
 62.2 
 70.5 
 18.3 
 
 62.1 
 85.3 
 S3.7 
 
 76.6 
 
 125.6 
 
 49.9 
 
 116.6 
 
 179.6 
 
 63.1 
 
 44.6 
 
 
 44. 
 
 Per cent gain 
 
 .6 
 
 Grade 4 
 
 66.7 
 
 March 
 
 60.9 
 
 
 6.6 
 
 Grade 5 
 September 
 
 16.3 
 
 
 25.6 
 
 Per cent gain 
 
 9.8 
 
 Grade 6 
 September 
 
 27.1 
 
 
 35. 
 
 
 8. 
 
 Grade? 
 
 September 
 
 42.7 
 
 
 48.3 
 
 
 5.6 
 
 Grade 8 
 September 
 
 55.3 
 
 March 
 
 62.5 
 
 Per cent gain 
 
 7.1 
 
 
 
 > From an unpublished master's thesis by K. D. Waldo, on file 
 in the library of the University of Chicago. 
 
READING 91 
 
 by an increase in the ability to apprehend the mean- 
 ing. 
 
 Rate of reading is not so important in the compre- 
 hension of difficult matter as in easy reading. There 
 is another element in efficiency which is not accurately 
 measured by the means which have been mentioned, 
 namely, the ability to relate what is read to one's past 
 thinking, or to examine it critically in order that one 
 may judge of the correctness or worth of what is read. 
 In some kinds of reading, also, it is necessary to spend 
 considerable time in order that the thought may be 
 apprehended. The tests which have been used have 
 referred chiefly to the types of reading-matter which 
 can be readily apprehended without stopping to think 
 through the ideas which have been expressed. It is 
 very likely that some modification will have to be 
 made in the conclusion with reference to rapid reading 
 when the other sort of test is made, and when different 
 kinds of reading-matter are studied. For example, in 
 solving problems in arithmetic or in other forms of 
 mathematics, much of the accuracy, or much of the 
 efficiency, depends upon the ability to grasp the mean- 
 ing of the problem as expressed in its statement. This 
 is one form of reading, and it must be included in 
 any comprehensive view of what efficiency in reading 
 means. 
 
 The rate of ordinary reading is usually too slow. 
 Even with this qualification, however, it must be said 
 that there is ample evidence that the majority of per- 
 
92 PSYCHOLOGY OF COMMON BRANCHES 
 
 sons read very much more slowly than is necessary. 
 The reading rate has probably been fixed largely by 
 the speed in oral reading, and this is one reason why 
 it is undesirable to overemphasize oral reading in the 
 schools. A little effort on the part of adults is sufficient 
 very materially to increase the rate of reading and the 
 experiments which have been made indicate that chil- 
 dren are also susceptible to this type of training. 
 
 Speed must be flexible. As was hinted in a previous 
 paragraph, the child must be taught to read each par- 
 ticular kind of subject-matter with its appropriate 
 speed. In other words, he must read only as rapidly 
 as he can grasp the thought. The test which was made 
 in one school showed that the sixth grade and the sev- 
 enth grade read the same passage with about the same 
 degree of speed, but the sixth grade was able to appre- 
 hend only a very small proportion of the ideas of the 
 passage. These sixth-grade pupils had not had the 
 proper training, or at least did not have the proper 
 attitude in this particular test. They should have 
 realized that they were not getting the meaning, and 
 they should have adjusted their speed of reading 
 accordingly. With some kinds of subject-matter it is 
 necessary that one learn to skim through and gain 
 merely a general notion of the thought which is 
 expressed. The newspapers, for example, furnish a 
 great deal of material which should be read in this 
 manner. When one has only learned to read carefully 
 word by word, he either has not the ability to go over 
 
READING 93 
 
 the amount of reading-matter which may advantage- 
 ously be read by the average educated adult at the pre- 
 sent time; or if he. does, he expends very much more 
 time than should be spent. 
 
 Rate of reading is increased by attending to the 
 meaning as distinguished from the mechanics. It is 
 not known with certainty what change takes place in 
 a person's reading habits when he increases his speed 
 of reading. Some change in eye movement must, of 
 course, take place. Either the movements are less fre- 
 quent, that is, fewer pauses are made to the line, or the 
 duration of each pause is less, or both of these factors 
 change together. If we compare rapid and slow read- 
 ers, we find that some rapid readers owe their ability 
 to the fact that they make their pauses of short dura- 
 tion, and others to the fact that they make few pauses 
 to the line. This, therefore, does not give an answer 
 to our question. Dearborn found that a reader tends 
 to fall into a set habit of eye movements in reading a 
 certain passage of a particular length of Une, size of 
 t3T)e, etc., and concluded that the habit was a more 
 or less accidental thing and that the speed was deter- 
 mined to a large extent by the eye-movement habit. 
 On the other band, the experience of those who in- 
 crease the rate of their reading indicates that they do it 
 chiefly by paying attention to the apprehension of 
 meaning. They attempt to fix their attention on the 
 things which are read about, and to pay little attention 
 to the mechanics of the reading itself. The suppression 
 
94 PSYCHOLOGY OF COMMON BRANCHES 
 
 of lip movement and of the images of the somid of the 
 word or of the pronunciation of the word assists in 
 rapid reading. When a person is thinking of each 
 word and hears it distinctly or feels how it is pro- 
 nounced, he can only read at a certain limited rate. 
 When the word, on the other hand, suggests certain 
 ideas, or images of things, and the reader frees himself 
 from the images connected with the word itself, he is 
 enabled to read more rapidly. 
 
 The variation in speed according to the subject- 
 matter shows the importance of apprehension of 
 meaning. The conclusion that rapidity of meaning 
 depends more upon the ability to apprehend the mean- 
 ing quickly than upon the habit of eye movement is 
 further confirmed by the fact that the rate of reading 
 varies considerably with the kind of subject-matter. 
 If the same person is tested in easy narrative and in 
 more difficult scientific exposition, it will be found that 
 he reads the former more rapidly than the latter. The 
 eye movements in the two passages woxJd not be af- 
 fected by the difference in the subject-matter, and 
 therefore we must conclude that they are not the pre- 
 dominant elements in determining speed. 
 
 The pupils should be trained in the rapid apprehen- 
 sion of meaning. If this conclusion is correct, the 
 training of the pupil in rapid reading can be brought 
 about best by some means which will call his attention 
 to the meaning rather than to the mechanics of the 
 reading. It is found that merely to urge the pupil to 
 
READING 95 
 
 read rapidly is an effective way of increasing his speed. 
 Any motive which will lead him to desire to get the 
 meaning quickly will be an effective one. This will at 
 the same time avoid the danger of the pupil increasing 
 the rate of his eye movements or of the pronunciation 
 of words without increasing his rate of apprehension, 
 so that the pupil tends to read in a mechanical fashion. 
 There are a number of devices which might be used to 
 assist the pupil in getting the meaning. Catch pas- 
 sages are sometimes used in which some absurdity is 
 hidden, and the pupil is directed to detect the absurd- 
 ity as rapidly as possible. Another means is to have 
 the pupil give a summary of what he has read, at the 
 same time trying to read rapidly; or to direct him to 
 read a passage for the sake of getting at some point or 
 the answer to some question which is given before- 
 hand. 
 
 Improvement with age above the fourth grade is in 
 ability to grasp more difl5cult subject-matter. The 
 conclusion that the rate of reading is connected more 
 closely with apprehension of meaning than with the 
 mechanics of reading is also indicated by the fact that 
 when pupils of different grades are given material 
 which is suited to their thought, those who are in any 
 grade above the fourth can read with about the same 
 degree of rapidity. That is, by the time the pupil 
 reaches the fourth grade the mechanics of reading are 
 suflSciently developed so that he can read rapidly any- 
 thing that he can understand. If, however, the lower- 
 
96 PSYCHOLOGY OF COMMON BRANCHES 
 
 grade pupil is given a passage which is suited in subject- 
 matter to a higher-grade pupil, the rate of his reading 
 as well as the accuracy of his understanding usually 
 drops. In the apprehension of meaning, as well as in 
 the speed of reading, there is a great deal of over- 
 lapping among children of successive grades One in- 
 vestigation, for instance, indicated that 42.6 per cent 
 of the children of the fifth grade surpassed the average 
 of the sixth grade in rate of reading. (See Table II.) 
 
 TABLE n 
 
 Percentage of children in lower grades exceeding the average 
 performance of children in higher grades in the same test ^ 
 
 
 Rate 
 
 Words reproduced 
 
 Percentage 
 
 
 6 
 
 7 
 
 8 
 
 6 
 
 7 
 
 8 
 
 6 
 
 7 
 
 8 
 
 Fifth .... 
 
 Sixth 
 
 Seventh . . 
 
 42.6 
 
 36.1 
 35.5 
 
 29.5 
 
 29.4 
 27.7 
 
 24.6 
 
 8.2 
 15.7 
 
 
 
 2 
 14.8 
 
 26.2 
 
 13.1 
 16.7 
 
 
 
 4 
 
 24.1 
 
 In reading as in writing the proper relation must be 
 kept between mechanics and meaning. The process 
 of learning to read illustrates very much the same 
 principles of learning as does learning to write. In the 
 first place, the child has to master certain mechanics 
 in order that he may be able to gather meaning from 
 the words on the printed page. In the case of writing, 
 the problem is to master the mechanics of expression 
 1 From K. D. Waldo. 
 
READING 97 
 
 so that a meaning which is represented in the mind of 
 the child will be expressed. In both cases the aim is 
 either the expression or the understanding of meaning. 
 When the final development is reached the mechanics 
 will fall out of attention, but for a time it is necessary 
 that the mechanics be perfected in order that they 
 may serve as an eflBcient medium for the recognition 
 or the expression of meaning. In both cases the me- 
 chanics may be too much neglected, or the attention 
 may be retained upon them too long. Efficient teach- 
 ing of reading, as of writing, consists in paying just 
 enough attention to the mechanics to make of them a 
 tool for the apprehension of meaning, but to give no 
 more time and energy to their development than is 
 necessary to serve this end. 
 
 REFERENCES 
 
 1. W. F. Dearborn: Psychology of Beading. Columbia Univeraify 
 ContributioTis to PhUosophy and Psychology, vol. 14, no. 1. 
 
 2. E. B. Huey: The Psychology and Pedagogy of Reading. Mao- 
 millan. 1908. 
 
 8. C. H. Judd: Genetic Psychology for Teachers. Appleton (1903), 
 chap. Tin. 
 
 4. K. D. Waldo: "Tests in Reading in the Sycamore Schools." 
 Elementary School Journal (1916), vol. 16, pp. 251-68. 
 
 5. F.Jenkins: Reading in the Primary Grades. Houghton MLfflin 
 Company. 1913. 
 
CHAPTER V 
 
 MUSIC: PERCEPTUAL LEARNING 
 
 The chapter deals with the process of learning to 
 read music. We shall consider in this chapter chiefly 
 the ability to read music as shown by the abiUty to 
 sing a melody from the printed score. We shall as- 
 sume that the child has learned to sing in a simple 
 fashion before he is to be taught to read. This neglects 
 the earlier phase of learning to recognize and sing 
 tunes from having heard them, but in the main we 
 shall assume that the child has learned to sing simple 
 tunes just as we assumed in our discussion of reading 
 that he had learned to speak. There are several con- 
 siderations which justify this apparent neglect of the 
 method by which the child learns to sing from ear, in 
 favor of a description of the method by which he learns 
 to read music. He learns to sing by ear by the simple 
 method of imitation, and there is not much of tech- 
 nique in the process. This is shown by the fact that 
 many children can follow a tune before they go to 
 school. Furthermore, the general principles of music 
 which are represented in singing by ear will be brought 
 out in the description of singing by note. Finally, the 
 importance of beginning the reading of music early in 
 the grades is being more and more recognized, so that 
 
MUSIC 99 
 
 now in many places the child learns to read music 
 almost as quickly as he learns to read printed matter. 
 Reading simple melodies is comparable in difficulty 
 to reading printed language, but reading music has 
 been deferred in traditional school practice because of 
 convention and tradition, and not because it was so 
 inherently difficult as to make this postponement 
 necessary. 
 
 The enjoyment of music is not treated in this chap- 
 ter, because, although this is one of the chief aims of 
 education in music, it is reached indirectly, and it is 
 the intellectual phase of learning music which is sub- 
 ject to analysis. 
 
 The child must first be able to carry a tune. Learn- 
 ing to read music, as has been said, presupposes that 
 a person is able to distinguish different tones, — or in 
 technical language that he can distinguish tones of dif- 
 ferent pitch, — and that he is able to carry a series of 
 tones in mind to form a melody. The ability to read 
 is, as in the case of reading words, the ability to make 
 the association between a series of printed notes and a 
 series of tones. One cannot connect the notes with the 
 tones unless the tones are already recognized. The 
 child, before he begins to read music, then, must have 
 had some training in the ability to carry a tune. This 
 training may take place in the kindergarten or in the 
 first grade or two, or even before this time. Many 
 children learn to carry simple tunes before they even 
 enter the kindergarten. 
 
100 PSYCHOLOGY OF COMMON BRANCHES 
 
 The recognition of intervals and melody 
 
 Reading is the recognition of tiie relationship of 
 tones and not of separate, individual tones. The recog- 
 nition that the printed score stands for music which is 
 heard or which is sung, as in the case of reading, is one 
 that the child gets merely by seeing music used. After 
 the pupil has learned that the notes on the score repre- 
 sent melodies, the next step is to be able to associate 
 certain particular notes, or rather certain connected 
 series of notes, with a particular melody. The recog- 
 nition of series or sequences of notes, and the corre- 
 spondence between these and the sequence of tones in 
 a melody takes place, not through the association of 
 the pitch of the individual notes on the scale with the 
 pitch of the individual notes which are sung, but 
 rather through the recognition of the relationships of 
 difPerent notes to one another. The recognition of the 
 relation of single notes to single tones makes possible 
 the ability to tell absolute pitch, which is a relatively 
 infrequent sort of ability. Very few persons can tell 
 when a note is struck on the piano what note on the 
 scale it is. The ability can be developed by training 
 and is the refinement of the ability which the moder- 
 ately trained person possesses of telling roughly the 
 pitch of a tone. The method of identifying a tone 
 which most persons pursue is first to have a basic pitch 
 given and then relate other tones to this one. 
 
 The recognition of intervals is distinct from the 
 
MUSIC 101 
 
 recognition of individual tones. The pupil learns 
 through practice to associate the interval between 
 two notes on the printed score with an interval in the 
 tones as he sounds them or hears them sounded by 
 somebody else. When the pupil reads the interval 
 
 g ) ~ \ ^ he can sing it, not because he 
 
 C-E 
 
 carries in mind the pitch of the two notes separately, 
 but because he carries in mind the difference in pitch 
 which is represented by the combination. The tone 
 which is sounded as C may be any tone whatever and 
 may not correspond to a tone which represents C on 
 any instrument. But whatever tone is chosen for C, 
 the interval between C and E is always recognized as 
 the same. 
 
 In learning to read, the child becomes familiar with 
 the various intervals of the scale. When the ability to 
 recognize the intervals between notes is completed, 
 the pupil can reproduce or name all the intervals on 
 the scale. This includes the intervals between adja- 
 cent notes as well as the notes which are separated by 
 one or more intervening notes. Let us pause a moment 
 to see what this means. If we consider merely adjacent 
 notes, it means that two of the intervals are recognized 
 as being but half as great as the other five. These two 
 intervals are designated 2 iu the accompanying figure 
 
 ^^^^^^^i 
 
102 PSYCHOLOGY OF COMMON BRANCHES 
 
 and the rest are designated 1. These smaller intervals 
 are sometimes called half steps and the larger ones 
 whole steps. The wider intervals than those between 
 adjacent notes are also affected by the existence of the 
 half steps. Thus the interval C-E is not the same as 
 the interval D-F. We may summarize these facts in 
 the statement that our music is written in a certain 
 conventional scale, ^ and that the pupil has to learn 
 to read melodies in terms of this scale. This makes 
 learning to read music a more complicated matter 
 than it would be if the intervals between adjacent 
 tones of the scale were all equal. The child, of course, 
 is prepared to recognize the intervals of the scale be- 
 cause of the fact that he has already become familiar 
 with it by ear, and he does not first learn them by cal- 
 culating that an interval is made up of so many whole 
 steps or half steps. Still, if the scale which the child 
 first learned by ear were made up of equal steps, the 
 recognition of various intervals on the printed scale 
 would undoubtedly be easier. 
 
 The child should learn to read simple music before 
 receiving formal instruction in the scale. The instruc- 
 tion of the child might be begun, as it has sometimes 
 been begun in the past, by the attempt to teach the 
 child in a formal manner the intervals of the scale. 
 This, however, is not necessary. The child acquires 
 sufficient familiarity with the intervals of the scale 
 
 • Only the major scale is considered here for the sake of simplicity. 
 The same principle applies to the minor scales. 
 
MUSIC lOS 
 
 to enable him to sing, without knowing the names of 
 the notes, without practice in striking intervals, or 
 even in running scales. The child may go further than 
 this and leam to read simple music and strike the inter- 
 vals which he meets in it by becoming familiar in an 
 incidental manner with all the possible intervals which 
 are to be found. 
 
 Formal instruction should later supplement reading. 
 While it is true that the child should not begin with a 
 formal study of the scale and its intervals and with 
 drill in reproducing intervals which are represented on 
 a printed score, it is equally true that some formal 
 study is desirable as soon as the child has gained sufiS- 
 cient mental maturity and has learned actually to use 
 the scale with some ease. The explanation of the whole 
 steps and half steps and the drill in striking intervals 
 quickly and accurately, which before the child has 
 learned to read at all is a dull and almost fruitless 
 grind, at its proper time clarifies his recognition of the 
 intervals of music. There is no scientific evidence at 
 hand to enable us to say just when this formal instruc- 
 tion should be given, but on the basis of the general 
 principles of the child's mental development it should 
 probably begin at nine or ten years of age. 
 
 A difficulty is caused by the use of different keys. 
 We have thus far assumed that musical compositions 
 are always written with the keynote at the same place 
 on the staff. This, of course, is not true. It is often 
 necessary for various reasons — for example, to adapt 
 
104 PSYCHOLOGY OF COMMON BRANCHES 
 
 a song to the pitch of a voice or to harmonize several 
 instruments — to shift the pitch of the keynote and 
 the whole piece up or down. Each position on the 
 printed staff represents (within slight variations) a 
 fixed and definite pitch. The only way in which a 
 piece can be written in a different key from the one 
 we have assumed as a standard — the key of C — is 
 to place the keynote at a different point on the staff. 
 This would not create so much diflSculty if the inter- 
 vals of the scale were all equal, but since they are not 
 equal, it is necessary, when the keynote of a piece is 
 shifted, to modify the pitch which is represented by 
 some of the lines or spaces. Otherwise the whole and 
 half steps would not come at the right place in the 
 scale. The modifications consist in shifting the pitch 
 of certain notes up or down a half step. A sharp (#) 
 means a shift upward and a flat (i»), a shift downward. 
 We may illustrate by indicating the shifts which must 
 be made when the keynote is D instead of C: — 
 
 i 
 
 ^^=^¥=^^^^ 
 
 =1*^ 
 
 ^^ ^ ^ 
 
 Formal instruction should follow the first practice in 
 reading. Here again the child might be taught the 
 differences between different keys in a formal manner, 
 and this method was formerly pursued, with the con- 
 sequence that it was made so diflScult that the young 
 child could not learn it. All that is necessary at the 
 beginning is that the child become accustomed to sing- 
 
MUSIC 105 
 
 ing in different keys and that he learn to recognize the 
 basic notes in a particular key as being situated on a 
 particular line or space. A device^ for helping to recog- 
 nize where the keynote is situated is used in a series of 
 books published by C. H. Congdon. In these books in 
 the earlier melodies of a new key, the space or line 
 upon which the keynote is situated is indicated by a 
 faint orange line. The use of this method, whether or 
 not accompanied by some such device, does not make 
 the learning a perfectly simple affair, it is true, but it 
 makes it very much easier for the child than it would 
 be to enter into an elaborate explanation of the theory 
 of the matter. In the case of different keys as in the 
 case of the scale itself, formal instruction is necessary 
 in order to complete the crude recognition which is 
 gained without it. The time at which this instruction 
 should be given is doubtless to be determined by the 
 time when the child grasps clearly the fundamental 
 characteristics of the scale. 
 
 Only formal instruction begins with the key of C. 
 The key of C has been taken as a starting-point for 
 convenience of description in this discussion, but it 
 should not be inferred that the child is to begin his 
 singing or reading in this key. The starting-point in 
 the practice of reading or singing should be at the key 
 or keys which suit the pitch of the child's voice. The 
 starting-point in the formal instruction, as in this dis- 
 cussion, may be the key of C. 
 
 1 This device is practicable only in the use of simple melodies in 
 which there is no change of key, or modulation. 
 
106 PSYCHOLOGY OF COMMON BRANCHES 
 
 Khyihm 
 
 The most fundamental element in music is rhythm. 
 We have taken melody — that is, the sequence of 
 tones — as the first element of music to be mentioned, 
 because it is the one which most readily attracts the 
 attention and the representation of which is most 
 prominent. As a matter of fact, however, melody is 
 not the fundamental element of music. There is an- 
 other element that precedes it in racial development 
 and also in the development of the child. This is the 
 element of rhythm. Music may in fact be regarded as 
 a specialization of the rhythmical activities. Rhythm 
 is used in a great variety of forms of action besides 
 music. The music which is characteristic of primitive 
 peoples consists chiefly of rhythm as illustrated in 
 their drum-beating. Rhythm also is characteristic of 
 many of our actions which we do not think of as at all 
 related to music. Many forms of work are carried on 
 in rhythm and can be done with the most economical 
 expenditure of energy in this way. Many of the physio- 
 logical processes, such as the heart-beat and breathing, 
 are rhythmical in their nature. Speech itself is rhyth- 
 mical, and this may be verified both in prose and 
 poetry. In the case of music, the rhythm is somewhat 
 more regular and is connected with the elements of 
 pitch and tone. 
 
 Rh3rthm consists in the regular recurrence of acts 
 divided into groups. In a rhythmical activity, such as 
 
MUSIC 107 
 
 music or dancing, the individual acts which compose 
 the entire chain of acts follow one another at regular 
 intervals and are also arranged in groups each contain- 
 ing, in the simpler cases, a uniform number of single 
 acts. Marching is a simple illustration. Each step 
 represents the single element, and each step takes the 
 same amount of time as every other step. These single 
 steps are usually put into groups of two each by accent- 
 ing by a drumbeat or the voice every other step, 
 commonly each step of the left foot. The rhythm be- 
 comes more complex in dancing, but it can always be 
 analyzed into these two elements, the regular succes- 
 sion of a series of steps or movements and the divi- 
 sion of the series into groups. 
 
 Music has developed out of dancing. This illustra- 
 tion suggests the relation which dancing holds to 
 music. Dancing was the more primitive form of expres- 
 sion and was developed as a part of the religious cere- 
 monies of primitive people. In order to unify the danc- 
 ing of a group of people and to intensify and emphasize 
 the feeling of rhythm, the dance was accompanied by 
 the beating on the drum and monotonous singing. In 
 order to furnish more varied accompaniment, musical 
 instruments were gradually developed and the songs 
 gradually acquired more definite and complex melody. 
 
 Training in rhythmical movements prepares for mu- 
 sic. It is necessary to recognize the fact that rhythm 
 has a deeper seat than the music which is sung or 
 played on an instrument. Rhythm which is only kept 
 
108 PSYCHOLOGY OF COMMON BRANCHES 
 
 by following the beat of some time-marker, such as 
 the metronome, must always be mechanical, formal, 
 and artificial. To be a significant form of expression 
 rhythm must be felt, and it is felt when the whole body 
 responds, and does in fact move in harmony with the 
 tempo of the music. This makes it clear that a com- 
 plete training in music must go back to the training 
 in rhythmical bodily movements. The training in 
 dancing, of the type which is being introduced into the 
 schools, is not only of value to secure bodily control 
 and poise, therefore, but is also a valuable introduc- 
 tion to the appreciation of music. 
 
 Rhythm is represented by notes and bars. While 
 the pitch of the tones is represented by the position of 
 the notes on the staff, the rhythm is represented by 
 appropriate signs, and the child has to leam to inter- 
 pret these. The duration of a tone is represented by 
 the kind of note which is used, and the length of each 
 unit group of notes is indicated by the division into 
 measures. The pupil has to leam to recognize the 
 type of rhythm which is represented in the different 
 kinds of time — two part, three part, four part, etc. ; 
 to hold the tones the length of time indicated by the 
 notes, at the same time fitting them into the rhythm; 
 and to indicate the divisions between measures, or 
 the lesser divisions between parts of measures, by 
 accent. 
 
 Formal instruction in tempo and its representation 
 should come after some reading ability is gained. A 
 
MUSIC 109 
 
 child may learn to give the proper duration to the 
 various notes, and to give the accent at the proper 
 place in the measure, and to associate these with the 
 aspects of the printed score which represents them, in 
 the same way in which he learns the meaning of the 
 different tones in a melody. He learns to associate the 
 elements of rhythm with the characteristics of the 
 score which represents them at first by the incidental 
 method. It becomes necessary in the course of time to 
 call his attention particularly to these facts and to 
 give him a clear idea of their meaning. Here again 
 the abihty fully to understand the complexities of the 
 elements of music and their representation need not 
 be developed before some ability in reading has been 
 gained. 
 
 Harmony 
 
 Harmony rests on the recognition of consonance and 
 dissonance. There is still a third characteristic in 
 highly developed music which the child can appreciate 
 to a greater or less extent, but which is not so funda- 
 mental as those of melody and rhythm. This char- 
 acteristic is harmony. Certain tones, when sounded 
 together, give persons who have a sense for mu- 
 sical harmony a pleasurable experience. Others when 
 sounded together produce displeasure. The psychol- 
 ogy of harmony and disharmony is not entirely clear. 
 All we know is that, for most persons, certain combina- 
 tions are pleasing and others are not. Some combina- 
 
110 PSYCHOLOGY OF COMMON BRANCHES 
 
 tions also are more pleasing than others. Among those 
 which are pleasing we recognize different degrees of 
 harmony. The octave, for example, is recognized as a 
 combination in which there is almost complete fusion 
 of the two tones. Certain other intervals — for ex- 
 ample, those which are separated by four steps or by 
 three steps, as the combination C and G, or C and F — 
 make what is called " perfect consonance," because 
 no disharmony appears when they are sounded to- 
 gether. Others separated by intervals of two steps, as 
 C and E, or E and G, make what is called " imperfect 
 consonance," because some disharmony is felt when 
 these chords are sounded. It is not necessary to go 
 into the various psychological theories which have 
 been offered to explain the difference between har- 
 mony and disharmony, particularly since the whole 
 matter is now put in question by certain newer types 
 of music, in which the previously accepted laws of 
 harmony are violated. 
 
 There are individual differences in the appreciation 
 of harmony. The ability to appreciate the difference 
 between harmony and disharmony requires higher 
 development than that required to recognize melody. 
 Children differ considerably in their ability in this 
 matter, and some are capable of a higher development 
 than others. Harmony is, of course, involved in part 
 singing, and it is necessary that when children engage 
 in this phase of music they should be able to appreciate 
 the simpler phases of harmony. It will probably, how- 
 
MUSIC 111 
 
 ever, never be necessary to go into the explanation of 
 the matter in any detail with them, and so we may 
 leave it without further discussion. 
 
 Tone quality 
 
 Another refinement which is involved when the 
 training in singing is carried beyond the mere ability 
 to strike the correct notes in singing melodies, or in 
 singing parts in simple pieces, is called " tone produc- 
 tion." This involves not merely the ability to sing a 
 certain note, but also the ability to produce it in such 
 a way that the quality of the voice is pleasing. A tone 
 possesses pleasing quality when it is rich and smooth 
 rather than thin or rough. The tone quality of a voice 
 or an instrument is called the " timbre " of the tone. 
 This is involved in the appreciation of the higher or 
 more developed phases of music, and it is necessary 
 that the child gain an appreciation of it and the ability 
 to produce good tone if he is given specialized training 
 which either looks toward professional equipment or 
 the higher degrees of amateur development. 
 
 While there is not time or opportunity to give much 
 individual attention to tone quality in the singing of 
 children in the school, considerable improvement can 
 be brought about by calling attention of the group as 
 a whole to the quality of their voices and by setting 
 up standards for imitation. Something may also be 
 done in this direction indirectly by requiring the chil- 
 dren to maintain good bodily posture. 
 
112 PSYCHOLOGY OF COMMON BRANCHES 
 
 Individual and age differences 
 
 Individual difierences in musical capacity should be 
 taken account of in selecting children for training. As 
 has been incidentally mentioned, there are large indi- 
 vidual differences in children's abiUty in music. An 
 attempt has been made to measure these individual 
 differences, and to determine their significance for the 
 child's ability to profit by training. C E. Seashore has 
 measured the ability of children to distinguish between 
 tones of different pitch and has laid down certain rules 
 as to the amount of training which children should 
 receive who have different degrees of discrimination. 
 Seashore has the following to say on this point :^ — 
 
 The capacity for the appreciation of music is partially 
 inborn and partially the result of training. Thus, in judging 
 the quality of an instrument or voice, the expert hears and 
 observes differences and peculiarities that entirely escape 
 the untrained ear; and ail differences in the so-called quality 
 and timbre of tone are reducible to pitch. But such hearing 
 represents a complex process of interpretation, which can be 
 mastered only after extensive training. The mere detection 
 of pitch difference is, on the other hand, a simple process 
 requiring only the slightest amount of training. 
 
 With reference to the bearing of the differences of 
 
 pitch discrimination upon the amount of training 
 
 which the child is capable of receiving, the author has 
 
 the following to say: — 
 
 Suppose we find four children of equal age, advancement, 
 and general ability sitting together, and one has a threshold, 
 
 • Psychological Monographs, vol. 13, no. 1 (December, 1910), p. 54. 
 
MUSIC 113 
 
 for pitch discrimination, of i vd., another 3 vd., another 12 
 vd., and 'another 25 vd. [The symbol vd. means the number 
 of vibrations which are produced in a second.] They are to 
 have singing lessons. How can we group them properly for 
 this period? Nine years ago the author proposed the follow- 
 ing classification as a tentative measure [Edticational Review, 
 June, 1901]: — 
 
 Below 3 vd. . . . May become a musician. 
 
 3-8 vd. . . . Should have a plain musical education. (Singing in 
 
 school may be obligatory.) 
 0-17 vd. • . . Should have a plain musical education only if special 
 
 inclination for some kind of music is shown. (Singing in school 
 
 should be optional.) 
 18 vd. and above. . . . Should have nothing to do with music. 
 
 The significance of these figures may be grasped by 
 the fact that 16 vd. represent one half of the difference 
 between middle C and D, the next note above it, or 
 about one half step in the scale. 
 
 Results of tests should be applied with discrimina- 
 tion. These should be taken as tentative standards, 
 and should be interpreted as indicating the degrees of 
 ability below which children should not be forced to 
 undergo training, rather than as rigid limits marking 
 off children who are not to be given training even if 
 they are willing or desirous of receiving it. In some 
 cases, as in that of a teacher, it is desirable to make an 
 especial effort to develop some ability in music even 
 though the native endowment in this direction is 
 limited. 
 
 Instruction may begin early. With reference to the 
 changes in age in discrimination. Seashore has the 
 following to say: " In a bright child with a good ear. 
 
114 PSYCHOLOGY OF COMMON BRANCHES 
 
 the physiological Umit can be established for all prac- 
 tical purposes as early as the age of five." This means 
 that the child can very early distinguish as clearly 
 between the different degrees of pitch as can the adult. 
 It does not mean, however, that the young child is as 
 capable of carrying tunes, or of appreciating the more 
 complex features, such as harmony and the composi- 
 tion of a piece. These abilities depend not merely on 
 the ability to distinguish between tones, but also on 
 the abihty to carry in mind the relationship of a large 
 number of tones to one another, and this abiUty is 
 only of gradual development. The significance of 
 Seashore's statement is that the child's musical devel- 
 opment may begin at an early age. The development 
 of the higher forms must be gradual. 
 
 REFERENCES 
 
 1. C. H. Congdon: The Congdon Music Readers. Chicago. 
 
 2. C. H. Farnsworth: Music in Education. Cyclopedia oj Edvea- 
 tion. Macmillan (1913), vol. 4. 
 
 3. C. E. Seashore: The Measurement of Pitch Discrimination. 
 Psychological Monographs (1910), vol. 13, no. 1, p. 64. 
 
CHAPTER VI 
 
 SPELLING: FIXING OP ASSOCIATIONS 
 
 Learning to spell is a form of memorizing. Memory 
 is the means by which those experiences which we have 
 had in the past are reproduced in our present experi- 
 ence. The particular kjnd of memory which we call 
 " memorizing " consists in reproducing certain defi- 
 nite associations which have been formed in the past. 
 Memorizing, then, consists in so making associations 
 between ideas, or between words which represent 
 ideas, that these words or ideas may be recalled in 
 the same order in which they were originally formed. 
 Spelling may be regarded as exactly the same sort of 
 learning. In the case of spelling, the associations which 
 are formed are between the successive letters of a 
 word, and between the word thus spelled and the 
 meaning. This might very properly be called memo- 
 rizing, and is one form of memorizing, though the 
 term is usually used to designate the formation of as- 
 sociations between words rather than between the let- 
 ters of a word. 
 
 Accurate spelling is demanded chiefly in writing. 
 The problem of learning to spell is one which arises in 
 connection both with reading and with writing, but it 
 would not be an acute problem if the child never had 
 
116 PSYCHOLOGY OF COMMON BRANCHES 
 
 to write. He would be able to recognize words with 
 sufficient precision if he did not know their exact 
 spelling. Only in certain cases of the close similarity 
 of words would any difficulty arise. When it becomes 
 necessary to write words, the problem of how to spell 
 them becomes important. The child might express his 
 meaning fairly intelligibly without learning to spell 
 accurately, and until recent times even educated peo- 
 ple expressed their meaning through writing in a satis- 
 factory way without spelling with any high degree of 
 uniformity. The extreme care which is now taken to 
 spell a word in a certain conventional way is a rela- 
 tively recent development. Formerly people did not 
 even spell their names consistently. The school is 
 compelled to take the situation as it is, and to recog- 
 nize that a person who does not spell words in the 
 conventional way is regarded as uneducated by other 
 persons, and that such a one is likely to meet with 
 difficulty in his business, professional, or social life. 
 
 The associations in spelling 
 
 The ability to spell may be based on associations 
 between movements or between elements of percep- 
 tion. While the problem of spelling first becomes acute 
 as a result of the need of writing, it nevertheless is 
 closely related to the problem of learning to read. The 
 reason for this is seen when we examine more closely 
 into some of the associations which lie at the bottom 
 of the ability to spell. Association must always be 
 
SPELLING 117 
 
 between certain ideas or experiences, and one type of 
 experiences which may be associated consist of motor 
 activities. In the case of spelling these activities may 
 be the writing of certain letters, and some persons can 
 spell the more difficult words only when they write, or 
 at least when they imagine themselves to be writing. 
 We call this type of association a motor association 
 because it consists of connections between movements. 
 Or the association may be between movements which 
 are made in the pronunciation of the letters of a word. 
 This was the common method of spelling in the earlier 
 days of spelling instruction. At the present time, when 
 the letters are not so much emphasized in learning to 
 read, this is not so common. There may be an associa- 
 tion, also, not between these forms of movements but 
 between ideas or percepts, based upon the perception 
 of the successive letters. Some persons can spell most 
 readily when they see a word or think of the way the 
 letters of the word look. It is with this type of asso- 
 ciation that reading has most to do. The impression 
 which is made through carefully scrutinizing the word 
 as it is read will then be of help in forming the asso- 
 ciation between the letters. A fourth type of associa- 
 tion, which is used by many in assisting them to spell 
 words, is between the letters as they are heard. One 
 may either pronounce the letters himself and hear them 
 as he pronounces them, or he may hear them pro- 
 nounced by another. This is of the same sort as the 
 association between the letters as seen, since it is an 
 
118 PSYCHOLOGY OF COMMON BRANCHES 
 
 association between the objects perceived rather than 
 between movements. This form of association does 
 not arise in connection with reading, but only in con- 
 nection with special training in spelling. 
 
 Spelling instruction should be closely related to 
 reading and writing. The fact that a necessity for 
 spelling arises in connection with reading and espe- 
 cially with Avriting, makes it necessary, if spelling is to 
 be taught in such a way as to have the most meaning 
 for the child, that it shall be closely connected with 
 reading and writing. This does not mean, as we shall 
 see in a later section, that there need not be special 
 drill given to spelling; but it means that the words 
 which are given in the spelling drill should be those 
 which the child uses also in his reading and writing. 
 It means that, although it is necessary that the child 
 give special attention to the spelling of words, the 
 words to which he gives special attention should not 
 be out of relation to his experience and meaningless 
 to him, but they should be related to the rest of his 
 thinking and of his school work. In choosing the 
 words which the child is to learn to spell, we must take 
 into account those words which he shall have use for 
 after he leaves school. Investigations have been con- 
 ducted to determine what these words are. When 
 these have been found, it is not sufficient merely to 
 introduce them into the spelling lesson, but they must 
 also appear in the other work of the child, in his com- 
 position, in his reading, and so on. 
 
SPELLING 119 
 
 Why may not the child spell entirely by sound? It 
 has been said that learning to spell consists in making 
 connections between the acts of writing the letters of 
 a word, or speaking the letters, or in making associa- 
 tions between the letters as they appear on the page, 
 or as they sound when spoken. The question may be 
 asked why it is necessary to make these associations. 
 Theoretically, as we saw in the chapter on reading, 
 the letters of a word represent the sound of the spoken 
 word. If this is the case, why, then, may not the child 
 merely form once for all the association between a 
 sound and its corresponding letter, and thus be able to 
 spell any word which he can pronounce? 
 
 Partly because pronunciation varies. There are 
 several reasons why this is not sufficient. One reason 
 is that the variation in the pronunciation of words 
 makes it impossible to be always sure, from its pro- 
 nunciation, how a word is spelled. An illustration of 
 this fact is given in a book by Owen Wister in which he 
 ridicules spelling reform. According to the story, a 
 number of enthusiasts for spelling reform met in a 
 convention, and attempted to agree how certain words 
 should be spelled so that the spelling should conform 
 to the pronunciation. One Southern delegate started 
 a riot by insisting that courthouse should be spelled 
 c-o-a-t-h-o-u-s-e, this being the way in which he pro- 
 nounced the word. 
 
 Partly because the same letter often represents a 
 variety of sounds. It was noticed in the chapter on 
 
120 PSYCHOLOGY OF CJOMMON BRANCHES 
 
 reading that the alphabet which is used in written Eng- 
 lish, in common with most of the European tongues, 
 has been inherited from the Greeks and Phoenicians 
 through the Romans, and that it does not completely 
 fit the English language. The same letter often repre- 
 sents a variety of sounds. Consider the sound of a La 
 bay, bat, ball, bar, ask, autumn, and ribald ; of the s in 
 sU and business, of the c in cat and receive. Such vari- 
 ations as these make it impossible to infer from the 
 spelling of a word how it shall be pronounced. 
 
 Chiefly because the same sounds are often repre- 
 sented by a variety of letters. The chief reason, how- 
 ever, why the spelling of English words cannot be 
 learned merely by the connection of sounds with let- 
 ters is that the language is not spelled as phonetically 
 as it might be. We do not spell the words so as to 
 correspond as closely to pronunciation as we might 
 even with our imperfect alphabet, and with the vari- 
 ety of dialects and modes of pronunciation which 
 exist. Various spelling-reform associations have made 
 us f amiUar with the great variety of cases in which the 
 same sound is represented in several ways or in which 
 the same spelling represents a variety of sounds. The 
 following examples may be taken at random. Con- 
 sider the different ways in which the sound of long o 
 is represented in the following words: so; sew; row; 
 though; bureau. So long as our spelling remains in its 
 present unphonetic condition, and we have no means 
 of knowing how long it may so remain, there is no 
 
SPELLING 121 
 
 possibility of a child's learning how to spell many of 
 the words of our language from their sound. It be- 
 comes necessary, then, for him to learn merely by 
 forming arbitrary associations between the letters. 
 
 Methods of learning to spell 
 
 So far as possible the child should learn to spell 
 from sound. Before going on to a consideration of the 
 way in which these arbitrary associations are formed, 
 we should keep clearly in mind the fact that in the 
 case of those words which can be spelled from their 
 sound, the child should learn to spell them through 
 connecting the sound with the spelling. The principle 
 here is the same one which is found to hold in the 
 case of memorizing. It is found that the material 
 which is to be memorized should be given a meaning, 
 as far as may be, and that rote memorizing should be 
 reduced to as small an amount as possible. Similarly, 
 we may say that so far as the child can get a clue to 
 the spelling of the word from its sound he should do so. 
 Furthermore, although there is a variety of ways in 
 which the same sound may be represented, yet the 
 number of ways is not so large but that the child can 
 learn what they are. The child's problem in spelling 
 a word which is not phonetically spelled is not to learn 
 a purely arbitrary spelling for it, but to learn which of 
 several ways of representing that sound is the one 
 which is used in this particular word. SpeUing is not 
 a purely arbitrary afiFair, and in the case of a great 
 
122 PSYCHOLOGY OF COMMON BRANCHES 
 
 many words the spelling can be deduced from the pro- 
 nunciation. Because the correspondence between the 
 sound and the spelUng is not complete is no reason for 
 faiUng to make the most of the degree of correspond- 
 ence which does exist. 
 
 All available helps from related words, rules, or 
 principles should be used to make spelling rational. 
 We may say, as a general principle, that wherever the 
 spelling of a word can be related to some inclusive rule 
 or fact, or may be connected with the spelling of 
 analogous words, this should be done. Such relation- 
 ships may be found not merely between the soimd and 
 spelling, but also between the spelling of different 
 words which have similar meanings. For example, 
 the word laboratory presents a difficulty particularly 
 in the syllable which is not accented — the second 
 syllable. The fact that o is used here may be connected 
 with the word labor. When the child once sees this 
 connection, he will easily remember how the longer 
 word is spelled. Even more or less arbitrary rules, if 
 they serve to bring the spelling of a word under a prin- 
 ciple and make of it not merely an arbitrary affair, 
 will be useful, such as the familiar rule regarding the 
 order of i and e in receive, believe, weigh, etc. 
 
 To fix the arbitrary association the incidental and 
 the drill method may be contrasted. After we have 
 done all we can to find a connection between the spell- 
 ing of a word and its pronunciation or to establish 
 other meaningful associations, there remain a certain 
 
SPELLING 123 
 
 number of purely arbitrary associations which have 
 to be made. There is no royal road to spelling. In 
 the formation of these associations, which are left over 
 after we have exhausted all the logical associations 
 possible, there are two general methods of procedure. 
 The educational opinion and practice have been di- 
 vided upon which of these two methods is the more 
 effective and economical. The first method consists in 
 allowing the child to learn to spell words merely as 
 they happen to come up in the course of his reading or 
 of his writing. Some special attention may be given 
 to the words as they appear, either in order to antici- 
 pate and prevent a child's spelling a word wrong, or 
 in order to correct a wrong spelling after he has made 
 it; but no attempt is made to give the child a drill in 
 the spelling of words in a separate period, or to select 
 series or lists of words upon which repeated drill is 
 to be given. This is the incidental method. The drill 
 method, which is opposed to the incidental method, 
 includes the characteristics which have been described 
 as being neglected by that method. It takes its name 
 from the fact that it applies the principles which have 
 been found through psychological investigation to 
 produce in the most economical and effective manner 
 the associations which are desired to be formed. 
 
 The investigations of Rice and Comman give sup- 
 port to the incidental method. Before attempting to 
 present more minutely the advantages and disadvan- 
 tages of these two methods, we may sketch very 
 
124 PSYCHOLOGY OF COMMON BRANCHES 
 
 briefly the experiments which have been performed 
 in order to compare the efficiency of the two methods 
 in actual practice. In the late nineties, J. M. Rice 
 startled the educational world by showing, through a 
 survey of the results of speUing from a large number of 
 cities, that a great deal of the time spent in spelling 
 exercises was wasted. This was inferred from the fact 
 that many cities in which a snmller amount of time 
 was spent secured as good results as did those in which 
 a much longer time was taken for spelling. This inves- 
 tigation was followed up by another by Comman, in 
 which the experiment was made of entirely eliminating 
 the spelling period from three Philadelphia schools, 
 and comparing the result of the incidental method 
 used in these schools with the results of the spelling 
 drill as used in the remainder. In the incidental 
 method, as used in these three schools, considerable 
 attention was given to spelling by calling the child's 
 attention particularly to the difficult words which he 
 was Ukely to misspell, and by collecting the mistakes 
 which he made in his written work. This experiment 
 showed that the three schools which used the inci- 
 dental method secured as good results as did the others 
 which employed the ordinary drill. 
 
 Wallin's investigation turned ttie scale in favor of 
 the drill method. These investigations seemed to 
 settle the question in favor of the incidental method. 
 There were, however, several weaknesses in the reason- 
 ing leading to such a conclusion, and these have been 
 
SPELLING 125 
 
 shown to be fatal to it in a more recent investigation 
 by J. E. W. WaUin, at Cleveland. The Cleveland 
 schools had for years used a carefully worked-out form 
 of spelling drill under the direction of Assistant Super- 
 intendent Warren E. Ificks. Wallin found that as a 
 result of this drill a degree of efficiency was reached 
 by the children of the Cleveland schools which far 
 exceeded that obtained by either the drill group or the 
 incidental group of the Philadelphia schools. 
 
 The incidental method is superior only to a poor drill 
 method. The results found by Wallin demonstrate 
 that the superiority in economy of the incidental 
 method, which was used in the three schools in Corn- 
 man's investigation, was due to the fact that the drill 
 method which was used in the other schools was not as 
 efficient as it might have been. On the other band, the 
 incidental method in the three experimental schools 
 was probably raised to its highest point of efficiency. 
 The average percentage of correctly spelled words in 
 the city was about seventy, with two or three per cent 
 advantage in favor of the schools which used drill. 
 Wallin, on the other hand, found a percentage of cor- 
 rectly spelled words, with words of the same character, 
 of about ninety-four. This clearly indicates that if the 
 drill method is correctly applied, it may give results 
 more than twenty per cent better than those obtained 
 by the incidental method. 
 
126 PSYCHOLOGY OF COMMON BRANCHES 
 
 The principles of the drill method 
 
 We turn now to a consideration of the principles of 
 drill which are necessary in order that the method may 
 be most effective. These principles may be derived from 
 the principles of habit formation in general, which is of 
 the same character as drill, and therefore are not to be 
 thought of as bearing solely upon the teaching of spelling. 
 
 The first principle of spelling drill is sufficient repe- 
 tition. As we saw in the chapter on handwriting, the 
 cardinal principle of the formation of arbitrary asso- 
 ciations is repetition. If we make an association once, 
 or several times, but not a sufficient number of times 
 so that it is fairly well fixed, we have wasted in a large 
 measure the time and effort required to make these 
 insufficient repetitions. A number of repetitions spent 
 upon a small number of words, sufficient in number to 
 make the ability to spell these words permanent, will 
 give a definite result. If the same number of repetitions 
 are spread over so many words that none of them are 
 learned thoroughly, they are largely wasted. This is 
 what happens in the case of the incidental method. 
 Words are only learned as they occur in the child's 
 reading and writing. It is then only a matter of chance 
 that the same word occurs with sufficient frequency 
 so that the child learns it in the most economical man- 
 ner. It is to supply this want that drill is introduced. 
 
 The second principle is adequate attention. The 
 next principle of drill has also been met in the consid- 
 
SPELLING 127 
 
 eration of writing, namely, that repetition made with- 
 out giving attention is of little value. This principle is 
 sometimes put first and is designated by the term "fo- 
 calization." When there is focalization of attention, 
 the child has his mind called sharply to the thing he is 
 doing. In the case of spelling, this means that when 
 he is learning to spell a word, he is thinking primarily 
 of its spelling, and not of its meaning, or of the form 
 of the letters as he writes them, or of some other fact 
 connected with it. When the child learns to spell 
 words incidentally in connection with reading or writ- 
 ing, his mind is divided between the spelling and the 
 thought which he is getting from the reading, or which 
 he is expressing in his writing, and perhaps the form 
 of the letters, as has already been suggested. Spelling 
 drill, in which the words are studied particularly for 
 the sake of knowing how to spell them, calls the child's 
 attention to this one fact or aspect of the word, and 
 therefore brings about the condition of focahzation. 
 
 The third principle is the avoidance of wrong asso- 
 ciations. A third principle which has also already been 
 met with, and which is particularly important in 
 spelling, is the avoidance of wrong associations. The 
 drill method attempts to do this in a systematic man- 
 ner by anticipating the words which the child is likely 
 to misspell and giving him special practice in their 
 spelling. An investigation by S. A. Zook^ has shown 
 
 • This investigation is reported in an unpublished master's thesis 
 which is on file in the library of the University of Chicago. 
 
128 PSYCHOLOGY OF COMMON BRANCHES 
 
 that it is desirable, in addition to calling the pupil's 
 attention to the word which he is likely to misspell, 
 to call his attention also to the particular parts of the 
 word where it has been found the children frequently 
 make errors. For example, it was found that there 
 was frequently confusion as to what part of the word 
 the c comes in, in the word scissors. If this is particu- 
 larly emphasized in teaching the child the word, many 
 errors will be avoided. This, of course, does not mean 
 that the wrong spelling is to be suggested, but that 
 the correct spelling of the difficult part is to be empha- 
 sized. 
 
 Drill may be made effective for spelling in connected 
 writing. One of the criticisms which has been made of 
 the drill method is that it does not enable the pupils to 
 spell the words which they have learned in their spell- 
 ing lessons when they write spontaneously, to express 
 thought. The results are said not to carry over from 
 the spelling lesson to the rest of the pupil's work. This 
 defect, however, can readily be avoided, as was proved 
 by Wallin's investigation, by giving the pupils prac- 
 tice not merely in spelling the words in a column test, 
 but also in using the words in sentences, and in con- 
 necting the Spelling with the meaning. This does not 
 violate the principle of focalization, since the spelling 
 is the chief subject of consideration. 
 
 Drill need not be uninteresting. Another criticism 
 which has been made is that the " spelling-grind " is 
 dull and uninteresting, and is deadening to the spon- 
 
SPELLING 129 
 
 taneity of the pupils. If the drill is properly conducted, 
 this criticism does not hold, and the belief that driU is 
 uninteresting to the child rests upon a false interpre- 
 tation of those things which give him pleasure. The 
 child is certainly interested in perfecting his abihty 
 in various forms of skill and spontaneously practices 
 doing many things which involve a large amount of 
 repetition and arduous practice. If the work is suited 
 to his capacity, and if he can be shown the results, and, 
 when necessary, if some external stimulus is given such 
 as is furnished by a contest between different rooms or 
 between different schools, as was done in Cleveland, 
 there is no difficulty in making such a drill of great 
 interest to the child. As has been suggested in previ- 
 ous chapters, it is desirable not merely to compare the 
 child's record with that of others, but also to give him 
 some record of his own progress from time to time. 
 Through this means it will be possible for him to see 
 the results of his efforts, even though he stands toward 
 the bottom of the class on account of deficient native 
 ability in this particular line of work. 
 
 The best method of presentation has been studied. 
 A good deal of experimentation has been carried on to 
 determine what is the best avenue of presentation of 
 words and of letters in order that they may be learned 
 most economically; and also to determine whether 
 persons differ in the avenue of approach which is best 
 suited to their individual needs. In attempting to 
 answer the first question, classes have been taught by 
 
130 PSYCHOLOGY OF COMMON BRANCHES 
 
 presenting the words to them through vision, that is, 
 by writing on the board, and the results have been 
 compared with the results from other classes to whom 
 the spelling of the words was given orally; and from 
 others who have seen the words written and have also 
 pronounced them; and others who have seen the words 
 and also have written them, etc. 
 
 Writing is the most effective single method, but a 
 variety should be used. In general it has been shown 
 that writing the words and seeing them written is the 
 most effective form of presentation for all pupils taken 
 together. Hearing the letters of the words pronounced 
 and pronouncing them, which is the old spelling-con- 
 test method, is not so effective. This is probably due 
 to the fact that the pronunciation of the letters is not 
 closely connected with the sound of the word, and is, 
 of course, not so closely connected with the way in 
 which the words are spelled in actual use, which is the 
 process of writing itself. In general, however, to use a 
 variety of methods of presentation is more effective 
 than to use one alone, and since there is no reason why 
 one needs to be chosen alone, the safe course is to 
 present the words to the child by writing, by having 
 him write them and pronounce them slowly, and pos- 
 sibly by having him say the letters as he writes them. 
 
 A variety of methods takes account of individual 
 differences. Another reason why a variety of modes of 
 presentation is desirable is that there is possibly suffi- 
 cient difference in the type of minds of different pupils 
 
SPELLING 131 
 
 to make it easier for some to learn through hearing and 
 pronunciation than through seeing and writing. The 
 differences among pupils in this respect have probably 
 been exaggerated, and we do not know with certainty 
 to what degree they exist. It is probable that there 
 are only a few who represent any extreme type. How- 
 ever this may be, there is no harm in presenting words 
 in a variety of ways, and if there are pupils who repre- 
 sent extreme types, this will be to their advantage. 
 
 Summaiy. We have attempted to bring out the 
 more general psychological principles which are in- 
 volved in speUing, and which may be illustrated in 
 spelling. In particular, spelling illustrates the drill 
 method, and the principles which have been found to 
 have a place in spelling are also appropriate wherever 
 we are concerned with the formation of more or less 
 arbitrary associations, and where we are dealing with 
 learning in which there is a gradual progress instead of a 
 solution of the problem by means of the understanding. 
 
 REFERENCES 
 
 1. O. P. Comman: Spelling in the Elementary School. Ginn & Co. 
 1902. 
 
 2. li.F. XyeTs: A Measuring Scale for Ability in Spelling. Riissell 
 Sage Foundation. 1915. 
 
 3. W. F. Jones: Concrete Inveatigaticm of the Material of English 
 SpeUing, etc. Uiuversity of South Dakota Bulletin. 1913. 
 
 4. J. M. Rice: "The Futility of the Spelling Grind." The Forum 
 (1897), pp. 163 and 409. 
 
 fi. J.'Ei.ViayLin: Spelling Efficiency, etc. Warwick and York. 1911. 
 6. H. Suzzallo: The Teaching of Spelling. Houghton MiflBin 
 Company. 1913. 
 
CHAPTER VII 
 
 HISTORY: EXTENSION OF EXPERIENCE THROUGH 
 IMAGINATION 
 
 General account of imagination 
 
 Learning in histoiy and geography depend upon the 
 imagination. Although the same mental processes are 
 used in various subjects, certain of them seem to be 
 more particularly involved in some of the school sub- 
 jects than in others. If we compare the study of the 
 two subjects which are about to be considered, history 
 and geography, with some of the more elementary 
 subjects, such as reading and writing, we find that they 
 are distinguished by the fact that the child is intro- 
 duced by them beyond his immediate experience. 
 Reading and writing as they are used carry the child's 
 mind beyond his immediate experience; but in learning 
 to read and write the child is dealing primarily with 
 material which is presented in perception. In history 
 and geography, on the other hand, he is required to 
 live through experiences which are remote in time 
 from his own life, or which are distant from him in 
 place. In history he learns about the lives of people 
 in the past, and in geography, he learns about places 
 and people who exist on other parts of the earth than 
 that in which his home is situated. The mental process 
 
HISTORY 133 
 
 by which he is able thus to carry in mind the thought 
 of distant or remote events, persons, and places, we 
 call imagination.* 
 
 Through imagination present institutions can be 
 explained by reference to their history. The school, 
 for example, has certain peculiar characteristics. The 
 division of the school period into eight years for the 
 elementary school, four years for the high school, and 
 four years for the college, has a definite historical 
 background. The methods of study which are pur- 
 sued, the subjects which are included in the curricu- 
 lum, and a variety of other matters, are to be explained 
 by reference to more or less remote past events. 
 
 Imagination connects our immediate life with events 
 taking place in distant parts of the earth. For the 
 explanation of many of the events which we observe 
 to be going on about us, we must be able to create in 
 our imagination persons and things which exist in the 
 present time, but in remote places on the earth. As 
 this is being written, much of the conduct of residents 
 in the United States is governed by the war which is 
 being waged in Europe. We are continually creating 
 in imagination the scenes of the European conflict and 
 considering its bearing on our lives. The world has 
 
 ' Imagination is the mental proceas by wliich experience is ex- 
 tended beyond the immediately present surroundings. This is done 
 in its simplest form in memory. But imagination also extends ex- 
 perience much more broadly so as to bring within the scope of 
 our thought objects or events which have never been experienced 
 by the individual in the form in which they exist in his thought. 
 
134 PSYCHOLOGY OF COMMON BRANCHES 
 
 come to be so much of a unit through means of trans- 
 portation and communication that the use of geogra- 
 phy is an everyday affair. 
 
 Imagination which may be present in memory pre- 
 pares for freer imagination. A form of imagination 
 exists in memory. When we picture to ourselves the 
 face of a person whom we know or recall the sound of 
 his voice or the pressure of his hand-clasp, we make 
 use of a memory image. The first step in the ability 
 to think over or to Kve over in our minds that which we 
 have never experienced consists in thus living over our 
 own past experience. In this way we first free our- 
 selves from the immediate present. In this the human 
 being is rather sharply distinguished from the animal. 
 So far as we know, the animal is pretty closely bound 
 to the sensations or perceptions which he receives 
 through stimulation by objects which affect his sense 
 organs. We have no evidence that the animal thinks 
 clearly of experiences it has had in the past, although 
 its past experiences affect its responses, through giving 
 objects various kinds of present meanings 
 
 Sensory experiences may be revived in imagination. 
 The human being, as has been said, may revive in his 
 experience various kinds of previous experiences. The 
 simplest of these are the sensations or simple percep- 
 tions. We can call to mind the appearance of the house 
 which we saw hours or days or years before. We can 
 call to mind, more or less clearly, the sound of the 
 voice of persons whom we have known, or the soimd of 
 
HISTORY 135 
 
 music which we have heard. The sensations of sight 
 and hearing are -the-ones which can be most clearly 
 reproduced in our imagination, but to some degree we 
 can recall the experience of touch and possibly of 
 movement, smell, taste, and temperature. 
 
 Images of words are prominent in thinking. There 
 is a particular form of imagination which deserves 
 special mention. We may recall to the mind not 
 merely the appearance of physical objects or of the 
 experiences which we get from contact with them, but 
 we may also call to mind the sound or the pronuncia- 
 tion of words. Words may be represented to us through 
 the sound of some particular person's voice or through 
 their appearance in writing or in print, or through the 
 movement sensations we get in speaking. The partic- 
 ular form of the image does not matter. The essential 
 fact is that ideas are represented by images of words. 
 Many ideas are of such a nature that we cannot think 
 of them most clearly by recalling any sort of object, 
 but rather by recalling statements in terms of language. 
 Take the law of gravitation. The word itself does not 
 refer to a thing which we have seen or heard or felt, 
 but to an idea, and the recall of the idea is through the 
 recall of the word. Or, if we go further and represent 
 to our mind the law of gravitation, — that* bodies are 
 attracted to one another according to the product of 
 their mass and inversely according to the square of 
 the distance, — it is clear that the words by which the 
 idea is expressed are the chief embodiment of the idea. 
 
136 PSYCHOLOGY OF COMMON BRANCHES 
 
 Take another case. We express the idea of relationship 
 of a person to his country by the word " patriotism "; 
 but although patriotism may have certain symbols, 
 such as the flag, or the ruler of the country, and so on, 
 these symbols do not stand for the idea with the same 
 degree of completeness as does the word. Very much 
 of our thinking, then, is done in words by saying over 
 words internally, or in the imagination. Even our 
 thinking in regard to concrete objects is accompanied 
 by the presence of images of words in our minds. We 
 may then distinguish between concrete imagination 
 which has to do with objects, and verbal imagination, 
 which has to do with words. 
 
 The importance of words in thinking must not be 
 overlooked. This fact that verbal imagination is an 
 essential means to all our higher and abstract thinking 
 should prevent us from misinterpreting the objections 
 to verbalism in teaching or learning. There is a danger 
 that the child shall learn to repeat words in parrot-Uke 
 fashion without an understanding of their meaning. 
 This is worse than useless. But to set words and their 
 use over against thinking, and to imply that we must 
 get rid of words in order that we may think, would be 
 like getting rid of our feet as a preliminary to walking. 
 We must be sure that the child has the experiences 
 which give a meaning to words so that he shall not 
 merely put words together into phrases and sentences; 
 but we must realize that one of the important results 
 of education is just this acquirement of meaning by 
 
HISTORY 137 
 
 words, so that they can be interpreted and used intelli- 
 gently. As the child grows older, we find that he leams 
 to use more and more verbal imagination, as distin- 
 guished from concrete imagination. While the older 
 person thinks somewhat in the images of things, yet 
 they tend to become less prominent, and he represents 
 his thoughts more largely in words. 
 
 There are wide differences in imagery among differ- 
 ent persons. Not only are there these differences be- 
 tween persons of different ages, but there are also 
 marked differences between persons of the same age in 
 the definiteness and clearness of their images in general 
 and in the preference which they give to images of 
 different kinds. Some persons are able to recall very 
 clearly such an object as the breakfast table, as was 
 found in an investigation by Galton. Others can 
 obtain only a very dim image of the articles on the 
 breakfast table. Some can recall more clearly things 
 which they have seen, others things which they have 
 heard, and others even the movements which they 
 have performed. 
 
 Methods of teaching should be adapted in some 
 measure to these differences. We must to some extent 
 take account of these differences, although not to so 
 great an extent as has sometimes been thought. The 
 way that these facts may be applied was mentioned in 
 the discussion of spelling. It is difficult, however, to be 
 always sure to what type a person belongs. He is not 
 able to tell us himself, unless he is a psychologist, and 
 
138 PSYCHOLOGY OF COMMON BRANCHES 
 
 there are no simple tests by which we may determine 
 the matter. We may apply these facts in two ways; 
 first, by so arranging the work that it will appeal to a 
 variety of forms of imagination in the children, and 
 second, by allowing a child to do a thing in the way in 
 which he seems to succeed the best. This does not 
 mean that he should be allowed to choose the kind of 
 work that he wishes, but rather that he should be 
 allowed to adopt the manner of doing the work which 
 seems to suit him best. 
 
 Free imagination begins by the modification of 
 memory. We turn now to a description of the different 
 grades of imagination and of the ways in which the 
 different kinds are used in the study of history. The 
 simpler type of imagination, as has been remarked, is 
 that in which we live over the experiences which we 
 ourselves have had in the past. By this means we 
 break away from the present. A person may Kve over 
 the events of the previous day, or a day in the past 
 month, or the past year. When he does this, he soon 
 begins to do more than merely to live over his past 
 life. He begins to dwell upon certain phases of his 
 experiences more than others, and it has been discov- 
 ered that the more pleasant experiences tend to be 
 retained longer than the unpleasant ones. Further- 
 more, he begins to change the character of his experi- 
 ences somewhat. Part of this is due to reading into 
 the past things which have happened since. Part of it 
 is due to putting together things which were not to- 
 
HISTORY 139 
 
 gether in our past experience. So in a variety of ways 
 we take liberties with our past life, and modify it, 
 either because of the frailty of our memory, or because 
 of a tendency in our nature to dwell upon certain 
 experiences rather than upon others. 
 
 The next step is to construct objects in imagination 
 different from those which have been met in actual 
 life. This modification paves the way for an entirely 
 different kind of imagination, or rather one which may 
 depart so widely from the first stage of the merely 
 reproductive imagination that it becomes radically 
 different from it. To take our illustration from the 
 life of a child, a child may first recall to mind experi- 
 ences he has had with an object, as, for example, a 
 dog. After he has become somewhat accustomed to 
 this procedure, he may follow a story which is told 
 him, relating to a dog, by supplying the picture of the 
 dog which he knows. He thus uses his past experiences 
 to fill out and make concrete events which are being 
 related to him. As he acquires wider experience with 
 dogs, he is likely to use, not the image of some particu- 
 lar dog, to make a story about a dog concrete, but an 
 image which differs from particular dogs of his ac- 
 quaintance and is constructed for the purpose of the 
 story. 
 
 Imagination uses old material, but combines it in 
 new ways. This illustrates a general principle regard- 
 ing imagination. Imagination does not create any- 
 thing absolutely new so far as the material of thought 
 
140 PSYCHOLOGY OF COMMON BRANCHES 
 
 is concerned, but enables us to rearrange into new 
 combinations or into new forms the materials which 
 have been furnished to us by our past experience. 
 We may create these forms in our imagination as a 
 means of following a story or description which is 
 made by another person, or we may spontaneously 
 create new combinations, as when we try to invent 
 a new machine or the plot of an original story. 
 When we merely follow the lead of another, the 
 process may be called " constructive imagination," 
 and when we spontaneously form in our mind events 
 or objects which have not been present in our past 
 experience, we term the process "creative imagina- 
 tion." The form of imagination in which we merely 
 live over our past experiences may be termed, in con- 
 trast with these, " reproductive imagination." The 
 distinction between these three is not always entirely 
 sharp, but they may serve to represent types which are 
 distinct in their main characteristics.' 
 
 The great stimulus to the development of imagina- 
 tion in the child is language. The use of words by 
 other persons is a continual challenge to the child to 
 form in his mind ideas which correspond to these 
 words. This he does by the recall of his previous 
 
 > Reproductive imagination is the type which is illustrated in 
 memory. Constructive imagination is involved in the study of 
 history and geography, in which we form in our minds ideas cor- 
 responding to definite requirements which are imposed upon our 
 minds from without. Creative imagination is involved in inven- 
 tion, or in literary productions. 
 
HISTORY 141 
 
 experiences, or by anticipating in imagination experi- 
 ences which he will have in the future. He hears older 
 persons talk about the happenings of the previous day, 
 and this causes him to recall them also to his own 
 mind. He hears discussed in the family circle the plans 
 for the next day or the next week, and this leads him 
 to look forward. The conversation of others creates 
 a stimulus to the formation in his mind of ideas which 
 have not been present at all in his past experience, 
 but which may be formed by putting together ele- 
 ments out of his previous experience. 
 
 The child's imagination is little hampered by re- 
 strictions set by natural law. A child's mind is par- 
 ticularly apt in creating with great freedom new com- 
 binations in his imagination. He has not had sufficient 
 knowledge of the ways in which different things 
 may be expected to combine, or of the laws which 
 govern their combination, so that he is particularly 
 hampered by such conditions. He can put things to- 
 gether in his imagination which are impossible for the 
 adult, from the fact that the adult is aware of their 
 improbability. To the child few things are improbable 
 and stiU fewer are impossible. The myths and fairy 
 tales with which he is regaled are appreciated by him 
 because the combination of events and of things which 
 are related in them does not strike him as absurd. That 
 Santa Claus can drive his reindeer through the air, and 
 can come down through the chimney, are, to be sure, 
 in contradiction of any events which he has ej^jcri- 
 
142 PSYCHOLOGY OF COMMON BRANCHES 
 
 enced; but tis sense of law and order is not yet suffi- 
 ciently developed to make it difficult for him to believe 
 that such things can happen. 
 
 The child cannot guide his imagination according to 
 definitely prescribed conditions. While the child's 
 imagination seems to be more active than that of the 
 adult because of his greater freedom from the restric- 
 tions which are imposed by natural law, he is inferior 
 to the adult in the kind of imagination which is de- 
 manded in history. As we shall see shortly, it is neces- 
 sary, in order to understand history, to construct an 
 idea of the physical surroundings, manner of Ufe, and 
 mental attitudes of persons who are remote from our- 
 selves in time and customs. This means that we must 
 break away in a measure from the restrictions of our 
 accustomed experiences, and also that in constructing 
 the new conception we must faithfully follow the pre- 
 scriptions which are laid down for us by the historian. 
 It is in the ability to follow definite prescriptions so 
 as to gain a faithful historical conception that the 
 child is deficient. 
 
 Imagination need not be fanciful, but may be based 
 on facts. The distinction which was made in the pre- 
 ceding paragraph suggests a characteristic of imagina- 
 tion which is in danger of being overlooked. We often 
 think of imagination as something which is purely 
 fanciful, something which is unreal or untrue to our 
 experience. The child is particularly adept at this 
 type of imagination. The other type which requires 
 
HISTORY 143 
 
 the construction in our mind, according to certain 
 definite principles, of conditions which are different 
 from those in which we Uve, is equally genuine, and is 
 one of the most important requirements of scientific 
 thinking. The geologists create a different world from 
 that which exists at the present time by taking a few 
 bones and fossils of plants and building an environ- 
 ment about them by the application of the laws and 
 principles which we find to be present in the world 
 about us. They determine what the conditions of Ufe 
 and the appearance of the earth must have been in 
 past ages, and are able to draw a picture or to con- 
 struct a model which represents in its general featiu-es 
 what these conditions were. The historian is able to 
 do the same thing for the life of people who have 
 existed centuries ago. This is the type of imagination 
 which is not at all fanciful, but which is determined by 
 fixed laws and principles. 
 
 The types of imagination employed in history 
 Imagination of concrete objects 
 
 Histoiy involves the creation of persons or places in 
 the mind's eye. Some kinds of historical appreciation 
 involve certain types of imagination, and others in- 
 volve others, and what these are we shall have to con- 
 sider more particularly. In the first place, we must 
 use in history the same type of imagination which we 
 use in the appreciation of fiction. When we tell the 
 
144 PSYCHOLOGY OF COMMON BRANCHES 
 
 child about historical persons, he has to create some 
 sort of image of these persons in his mind, in exactly 
 the same way as when we tell him about persons who 
 only exist in fiction. This type of imagination enables 
 the child to appreciate the earlier and simpler forms of 
 history, which we may designate the " Once-upon-a- 
 time " kind. It is not necessary that the child should 
 locate the persons in definite time, or in definite order 
 with reference to one another. By means of this kind 
 of historical narrative he becomes acquainted with 
 some of the important personages with whom he will 
 later deal in a more systematic way. The oiJy dififer- 
 ence between this kind of history and fiction is that in 
 the one case the characters have actually existed, 
 whereas in the other they have not. 
 
 Familiarity with the biography of historical persons 
 prepares for the appreciation of their historical rela- 
 tions. As has been said, it is worth while to use his- 
 torical personages in the stories which are told the 
 child, because it prepares him to weave these person- 
 alities into the web of historical account which will 
 later be related to him. It will then be easier for him to 
 follow the later accounts since the elements are familiar 
 to him. This type of history is suitable to the child 
 from the time when he can first appreciate it, that is, 
 from about the third year, until he is about nine or ten 
 years of age. 
 
HISTORY 145 
 
 Temporal imagination 
 
 Complete understanding of history includes placing 
 events in a time order. In order that the child may 
 progress beyond this stage, it is necessary that he be 
 able to place the historical personages in past time, 
 and in definite order in time with reference to one 
 another. This rests upon the development of another 
 type of imagination, which we shaU call "temporal 
 imagination." The stories relating to primitive life of 
 mankind, which are used in the primary grades, do 
 not give the child a true historical notion of the way 
 in which civilization has developed from primitive life 
 down to the hfe which we find about us at the present 
 time. They prepare him for a later appreciation of 
 such development, much as do biographies. That 
 they cannot give the child a notion based on the con- 
 ception of the succession of different stages of develop- 
 ment in time may be seen from the fact that, according 
 to the Binet Scale for testing intelligence, the average 
 child does not until his sixth year appreciate the differ- 
 ence between morning and afternoon. It is to be said 
 that this scale is too easy for the average American 
 child, but it is such a far call from the simple apprecia- 
 tion of the difference between morning and afternoon 
 to the understanding of development which has ex- 
 tended through thousands of years, that it is incon- 
 ceivable that the primary child gets much more than 
 a series of pictures from tales of primitive life. That 
 
146 PSYCHOLOGY OF COMMON BRANCHES 
 
 these tales are suitable for the child from other points 
 of view is, of course, not called into question. 
 
 The idea of long stretches of time is related to the 
 perceptions of short intervals. The child gets his idea 
 of the passage of time and of events, as being more or 
 less distant in the past or future, as an outgrowth from 
 his immediate experience with time. He first must 
 learn to distinguish between events which are near at 
 hand in the past or the future, and then, after time 
 has come to have a meaning for him, he can apply it 
 to the arrangement of more widely separated and 
 farther distant events. What we call " temporal im- 
 agination," or the idea of time, is undoubtedly based 
 to some extent on what may be called the " time 
 sense," or the immediate perception of the passage of 
 short intervals of time. Experiments with adults upon 
 the time sense indicate that it is subject to a good deal 
 of variability according to the circumstances. If a 
 person is anxiously expecting some event, such as the 
 arri val of a friea d. the time wiU seem very long. If, on 
 the other hand, he is not definitely expecting an event, 
 and is engaged in some occupation which absorbs his 
 attention, he may greatly underestimate the passage 
 of time. The overestimation of the passage of time is 
 expressed in the common proverb, " A watched pot 
 never boils." 
 
 The child is deficient in time sense. Both experi- 
 mentation and ordinary observation indicate that the 
 child's time sense is much less accurate than that of 
 
HISTORY 147 
 
 the adult, and that the variations due to the mannern 
 in which the mind is occupied are much greater in the 
 child than in adults. The child is deficient in the abil- 
 ity to imitate rhythm, and grossly misjudges the lapse 
 of time. A child becomes very impatient when wait- 
 ing for an expected event. On the other hand, if he is 
 absorbed, it sometimes appears that he has no sense 
 of time. If a child is sent on an errand, and if his atten- 
 tion is attracted by some occurrence on the way, he 
 does not realize the length of time which he spends 
 in stopping to watch the interesting occurrence, and 
 arrives home late. 
 
 The recognition of long periods of time depends 
 partly on the time sense and partly on the observation 
 of external events. The idea of time, or temporal 
 imagination, is undoubtedly based to some extent on 
 this fundamental time sense. The time which elapses 
 between breakfast and the midday meal and between 
 this and the evening meal is appreciated vaguely by 
 means of the direct experience we have of the passage 
 of time. In order that the time idea shall be more defi- 
 nite and extend to longer periods, it is necessary that 
 we observe other facts and use them to mark oflf defi- 
 nite divisions of time. The way in which the larger 
 divisions of time are marked off indicates that we are 
 thus dependent upon external events, and not merely 
 upon our own appreciation of the passage of time, in 
 order that we may get a unit of time and may apply it 
 in the estimation of the longer periods. The year, for 
 
148 PSYCHOLOGY OF COMMON BRANCHES 
 
 .example, represents changes in the seasons, the month 
 marks the phases of the moon, the day the rising and 
 setting of the sun, and so on. The smaller divisions of 
 the day, except those between midday and morning or 
 evening, are not distinguished sharply unless we have 
 watches or clocks which give us the means for marking 
 off the hours. The inferiority of the young child in the 
 recognition of periods of time, then, depends partly 
 upon an undeveloped time sense and partly upon the 
 fact that he has not been led to observe the signs which 
 mark the divisions of time, and to use them to set in 
 order his memories of what has happened in the past 
 or his anticipation of events in the future. 
 ; The child learns to distinguish periods of time 
 through his everyday experience. As indicated in the 
 preceding paragraph, the child first makes the distinc- 
 tions which are called to his attention by the practical 
 needs of his life. He will distinguish between morning 
 and afternoon, when during the forenoon he is prom- 
 ised something which is to occur in the afternoon. 
 Again, during the afternoon his recollection of the 
 forenoon and his discrimination of that period from 
 the rest of the day may be stimulated by conversation 
 about something which occurred then. The distinc- 
 tion between day and night is called sharply to his 
 attention both by the fact that the s.un goes down in 
 the evening and rises in the morning, and also by the 
 fact that morning and evening mark important turn- 
 ing-points in his experience, in that he goes to bed 
 
HISTORY 149 
 
 at night and gets up in the morning. Similarly, he is 
 led gradually to make the distinction between yester- 
 day and to-morrow through recalling the events of 
 yesterday or anticipating those of to-morrow. The 
 reward or punishment which he may have received for 
 acts done previously is one method by which this dis- 
 tinction is called to mind; and in a similar way, the 
 promise and fulfillment of results of his actions of 
 to-day call to his attention the coming of to-morrow. 
 
 Longer periods are recognized in the same way. 
 The recognition of larger divisions, such as that of the 
 week, is produced in a similar way by the events of his 
 life which occur at the end of the weekly period. When 
 the child goes to school, his attention is called to the 
 fact that Saturday is marked ofE by the holiday 
 which occxu-s on that day, and that Sunday brings a 
 still different manner of life, such as putting on his 
 best clothes and going to church or Sunday School. 
 The division into still longer periods of time is called 
 to his attention by the presence of other holidays or 
 vacations, or events which occur in a periodic way. 
 His birthday, for example, helps to bring to mind 
 vaguely, and later more clearly, the notion of the 
 year. 
 
 Number is necessary to the clear idea of long periods 
 of time. Any near approach to an exact notion of the 
 longer periods of time requires that the child shall not 
 only remember and anticipate in a general way, but 
 that he shall make definite the duration of time inter- 
 
ISO PSYCHOLOGY OF COMMON BRANCHES 
 
 vals through the use of number. We can, perhaps, get 
 an appreciation of an hour or a day merely by the 
 direct experience of the passage of time or by the time 
 sense; but the appreciation of a month in any definite 
 way means that we have a definite number idea of the 
 meaning of thirty as a multiple of one day. In the 
 case of the longer stretches, such as a year, it is obvi- 
 ously impossible to appreciate them merely by the 
 direct time sense. We may, therefore, assume that 
 the child gets only a very vague and indefinite notion 
 of longer time until he has a sufficiently clear idea of 
 number to put the time intervals into definite numer- 
 ical form. 
 
 The abstract notion of even the longer periods may 
 be made somewhat concrete by observing natural 
 events. The appreciation of time through the obser- 
 vation of such events, as well as by means of the num- 
 ber idea, rests upon forms of experience which the 
 child gets only gradually and does not attain at an 
 early age. All of these forms of analysis of the tem- 
 poral imagination indicate that it is a matter of grad- 
 ual growth on the part of this child, and make it clear 
 that the degree of clearness which is necessary for the 
 appreciation of definite historical sequences is not to 
 be looked for until the child has been in school for at 
 least three or four years. Even then the development 
 is not completed, but is only thoroughly started. 
 
 First historical narratives should be simple. These 
 conclusions, if well founded, can only lead to the posi- 
 
HISTORY 151 
 
 tion that the historical narratives which are designed 
 for the child must at first be simple and easy to follow. 
 In the first place, they must not cover very long periods 
 of time. Even the account of the life of a single indi- 
 vidual is beyond the grasp of a child at first. Further- 
 more, the various series of events must not be com- 
 plex. It is easier to follow the life of one individual 
 than it is to follow the lives of several individuals who 
 are contemporary with one another. It is easier to 
 follow the history of one section of a country than the 
 parallel histories of all sections. It is easier to follow 
 the history of one country than the history of several 
 countries which are interwoven in their relationships 
 with one another. The difficulty, however, does not 
 depend so much upon the breadth or ejctent of the 
 fields covered as upon the minuteness with which the 
 train of events within a certain field is followed out. 
 The life of one person may be very complicated if the 
 relationships of this person to others, and to the events 
 of the age in which he lived, are followed out in full 
 detail. On the other hand, the history of a country 
 may be made very simple by the selection of a few rep- 
 resentative events which portray certain phases of its 
 development. We may say, then, that the history 
 which is designed for a child must be simple, and 
 furthermore, that it is easier to simplify the history of 
 one country than it is of several related countries. 
 Therefore, it is best to begin with the history of a 
 single country, and after that has been followed and 
 
152 PSYCHOLOGY OF COMMON BRANCHES 
 
 the child has got some conception of its development, 
 it is time to relate the history of other countries to it. 
 
 Begin with recent histoiy and pass from that to 
 remote events. The problem then arises as to which 
 country should be treated at the beginning and as to 
 the way in which the history of the country which has 
 been chosen should be developed. The psychology of 
 the development of the idea of time, as it has been 
 outlined, throws some light on this problem. We have 
 found that the child first recognizes the differences of 
 time which are immediately in the past or the future; 
 that he begins with his own personal experience and 
 reaches out from it before and after. If we follow this 
 same process in the early history which the child is 
 taught, we should begin with his own country, with 
 which he has immediate experience, and should teach 
 the child comparatively recent history at first, rather 
 than begin with remote past time and work forward. 
 We cannot, of course, carry out the principle of begin- 
 ning from the present and working backwards, in the 
 full and strict sense, as one may reverse a moving- 
 picture film; but we may follow the psychological order 
 by relating the history of events which are near the 
 child and gradually extending them to those which 
 are more remote in the past. 
 
 This method connects history with present life. 
 When we do this, we make of history something which 
 is of immediate connection with the child's present 
 experience, and which lends significance to the prob- 
 
HISTORY 153 
 
 lems which arise in his own life and throws some light 
 upon their solution. History may be regarded as an 
 account of the origin of those facts and those beings 
 which are in existence at the present time. In tracing 
 the origin of those facts or beings, we begin with their 
 immediate past and then work gradually farther and 
 farther toward their more remote antecedents. If we 
 begin, in teaching the child, with the remote antece- 
 dents of present-day people, or with the remote causes 
 of existing physical objects, he loses the connection 
 between the present results and the remote past cause. 
 He then fails to get the conception of history as having 
 a direct and important relationship to his present-day 
 a£Pairs. 
 
 History involves spatial imagination. Historical 
 events are, of course, not only related in time, but are 
 also related to one another in space, since they take 
 place at particular localities upon the earth. The 
 child is required, therefore, in any complete apprecia- 
 tion of history, not only to be able to put the events 
 together in a certain time order, but also to create in 
 his imagination the geography of these events. This 
 form of imagination will be treated particularly in the 
 chapter on " Spatial Imagination," or " Geography." 
 
 The historical sense 
 
 The child at first fails to make allowance for the dif- 
 ferences between past and present life. When the 
 child is first told of persons or places which existed in 
 
154 PSYCHOLOGY OF COMMON BRANCHES 
 
 the past, he has a strong tendency to think of them as 
 like the persons with whom he has been f amiUar in his 
 own experience. He merely transfers in imagination 
 those things, those scenes, and those persons which he 
 has met in his own life to a previous period, and puts 
 them into the story which the history relates, modify- 
 ing them as may be necessary to suit the events. In 
 his early acquaintance with history, the child does not 
 recognize the difference in the physical surroundings, 
 or the difference in beliefs and mental attitudes, which 
 characterized people of past time in contrast to those 
 of our own time. 
 
 The difference in physical surroundings is appreci- 
 ated first. The ability to appredate the difference in 
 physical surroundings is the easier one to acquire, and 
 the one which the child can acquire in a more or less 
 superficial way by the use of pictures and other con- 
 crete means of representation. Still, it requires a 
 fairly good degree of ability in constructive imagina- 
 tion to picture to one's self clearly the houses, the land- 
 scapes, and the costumes of the people of past times. 
 
 The appreciation of differences in mental attitudes 
 is difllcult even for adults. The difficulty of realizing 
 to one's self the difference in physical surroundings is 
 very much less than that which attaches to the appre- 
 ciation of the differences between the mental attitudes 
 of persons of past time and those of our own contempo- 
 raries. Even our ancestors of one hundred years or 
 one hundred and fifty years ago differed from us so 
 
HISTORY 155 
 
 radically on certain questions that it is difficult for us 
 to understand how they could have held some of the 
 beliefs that were common. To take an example from 
 our own country, a justification of the attitude of the 
 colonial settlers toward witchcraft is inconceivable to 
 us. It is even becoming difficult for us to understand 
 how there could have been any real difference of opin- 
 ion on the question of slavery. If an adult finds it 
 difficult to project himself into the mental life of a 
 past people, even of those who are his immediate 
 ancestors, it is an impossibility for the child to do so 
 with any degree of completeness. 
 
 The historical sense extends the attitude of toler- 
 ance to persons who lived in the past. This type of 
 imagination, which has been called the " historical 
 sense," is in reality merely an extension of the process 
 which the educated adult carries on when he gains a 
 proper degree of insight into differing points of view 
 of other persons with whom he comes in contact. Vari- 
 ous groups of people in the same society differ in their 
 attitude on all sorts of questions. A hidebound adher- 
 ent to one political party can as little conceive how 
 any one can conscientiously uphold the fooUsh princi- 
 ples of the opposing party as can the average person of 
 this age conceive how a rational person could have 
 believed the things which our ancestors believed. What 
 we are considering here is merely the extension to wider 
 differences of this same tolerance and understanding. 
 This extension must be built upon somewhat more 
 
156 PSYCHOLOGY OF COMMON BRANCHES 
 
 abstract material. In understanding the attitudes of 
 historical persons we have to create for ourselves their 
 lives and attitudes on the basis of written records and 
 traditions, rather than on the basis of contact and 
 conversation with them. We believe that an increase 
 in tolerance is being attained by modem civilized 
 people, and similarly, the historians tell us that the 
 fuUy developed historical sense is distinctly a feature 
 of modem scholarship 
 
 The historical sense has little possibility of develop- 
 ment before adolescence. The child can begin at a 
 rather early age to gain in the appreciation of the 
 difference in physical surroundings of past people, but 
 the full development of even this type of historical 
 sense is not consummated early. The higher type of 
 historical sense, which deals with mental rather than 
 with physical facts, is probably very slightly developed 
 before adolescence; and then it has only a gradifal 
 growth. It appears from the recorded observations 
 and investigations of children that the abiUty to appre- 
 ciate the motives of others, to understand motives 
 which are different from one's own, and to judge of 
 one another's conduct by considering motive as well 
 as actions, is an attainment which is not reached be- 
 fore adolescence. If this is true, it is futile to attempt 
 to discuss with the child to any great extent the dif- 
 ferences in point of view between ourselves and people 
 of the past, and to explain them on the basis of the 
 growth of morals or of customs, as can be done with 
 the older pupil. 
 
mSTORY 157 
 
 The grasp of historical development 
 
 Two other forms of mental ability are prominent 
 in the appreciation or study of history in its full 
 meaning, although they are not, strictly speaking, 
 forms of imagination. In order to round out our ac- 
 count of the mental processes in the study of history, 
 however, we may include a brief discussion of them. 
 
 Histoiy attempts to explain events by previous con- 
 ditions and events. The first form of history in the 
 mind of the child is merely a narrative, that is, a series 
 of events occurring in time. These events are related 
 to one another, but not in such a way as to make 
 prominent the idea that the later events grow out of 
 the earlier ones as their cause. The degree to which 
 the study of cause and-fiffect can be carried on in his- 
 tory is a question on which there is a division of opin- 
 ion. Some students of history have attempted to give 
 a very minute account of the course of human events 
 as illustrating the law of cause and eflFect. The discov- 
 ery and formulation of general laws with reference to 
 historical development has been attempted. Although 
 one may not agree with the extreme form of this view, 
 yet historians do occupy themselves with such ques- 
 tions as are being considered at the time of this writing 
 with reference to the European war. Not only his- 
 torians, but all persons who have any interest in the 
 matter, are desirous of knowing what the causes of 
 such a tremendous confiict are. Was the war caused 
 
158 PSYCHOLOGY OF COMMON BRANCHES 
 
 by the machinations of a few individuals, or by the 
 ambitions and desire for territorial expansion on the 
 part of a war party; or was it caused by the expansion 
 of peoples, or their desire to gain for themselves the 
 good things of the earth; or was it caused by an inevit- 
 able conflict of races; and so on? In order to gain any 
 light at all on such questions, we must study events 
 which have led up to such a consummation as this, 
 and we must give these events an interpretation. As 
 in the case of the historical sense, it is probable that 
 children gain little appreciation of this phase of his- 
 tory until they reach the adolescent period. 
 
 Critical examination of sources 
 
 Another phase of the study of history has not to do 
 so much with the understanding of historical facts 
 after they have been gathered as with the method by 
 which they are gathered and determined upon in the 
 first place. Ancient historians discriminated very 
 little between tradition, which had no foundation in 
 fact, and reHable sources of evidence. We may say 
 that what is regarded as the scientific method of ob- 
 taining facts is the most prominent characteristic of 
 modern historical scholarship. 
 
 The examination of historical sources is an exam- 
 ination of witnesses under difficulties. In order to 
 ascertain the reliability of records which purport to be 
 historical, it is necessary that the same procedure be 
 carried out, in a modified and more difiScult form, that 
 
fflSTORY 159 
 
 is taken to find out the truth regarding contemporary 
 facts. Courts of law have developed an elaborate 
 procedure by which facts in a disputed case may be 
 discovered. We know that even in the case of current 
 events, it is difficult to be sure what is the truth and 
 what is fiction. The examination of witnesses and the 
 criticism of their testimony are now being studied in a 
 scientific way. We may regard historical records as 
 testimony of witnesses to be examined in the same way, 
 with the added difficulty that they cannot be cross- 
 questioned. The possibility of prejudice or of the dis- 
 tortion of evidence because of personal interests are 
 matters which have to be considered. When a his- 
 torian attempts to determine what are the facts in 
 regard to the conduct of a war, for example, he can 
 find conflicting evidence in newspaper reports which 
 are published in the different countries. It is his busi- 
 ness to decide what the truth is by comparison of the 
 different sources of evidence. 
 
 Critical examination of sources is too difficult for 
 high-school pupils. It is sometimes the fashion to use 
 a good deal of source material in the teaching of his- 
 tory to young people. It is questionable, however, 
 whether they are able to carry on the very difficult 
 and complicated sort of examination of sources which 
 is necessary to get anything of value from them. It is 
 perfectly possible and altogether desirable to make 
 historical accounts concrete and vivid by introducing 
 certain forms of source material whieh are agreed upon 
 
160 PSYCHOLOGY OF COMMON BRANCHES 
 
 as reliable and which do not need to be examined crit- 
 ically. But this is a different matter from the examina- 
 tion of source material for the purpose of determining 
 upon its reliability. It is probably safe to say that 
 practically none of this kind of examination of sources 
 is suitable for the pupil of high-school age, and that 
 little of it can be done to advantage before the later 
 years of college work. 
 
 Summary. In summary it may be said that the 
 study of history has its chief value and purpose in the 
 enrichment of the imagination of the child, by extend- 
 ing his experiences into the antecedents of the life in 
 which he finds himself. This extension of his experi- 
 ence backwards enables him the better to understand 
 the life in which he participates, and because he can 
 better understand it he can better take his part. As a 
 result of the study of historical development he may 
 grasp something of the trend of present events. He 
 may avoid repeating old errors and may help to carry 
 forward the community life in the direction of progress. 
 
 REFERENCES 
 
 1. J. R. Angell: Psychology, chap. 8. Holt, 1910. 
 
 2. H. E. Bourne: The Teaching of History and Civics. Longmans, 
 1903. 
 
CHAPTER VIII 
 
 GEOGRAPHY: EXTENSION OF EXPERIENCE THROUGH 
 IMAGINATION 
 
 In the introduction to the previous chapter, it was 
 shown that our experience may be extended beyond 
 the confines of our own immediate surroundings, in 
 the imagination of events in past or future time, or of 
 those events which are distant in space. It is with this 
 latter kind of imagination that we are concerned in 
 this chapter. The means by which the location of 
 places upon the earth becomes organized in our minds 
 is the systematic presentation of the facts which 
 constitute geography. It is not necessary to make a 
 sharp distinction between geography and the simpler 
 forms of astronomy, since we can understand the 
 occurrences upon the earth only by understanding its 
 relation to the sun, the moon, and the other heavenly 
 bodies. 
 
 This treatment does not disparage physical and 
 commercial geography, which are important. In con- 
 sidering the phase of geography which deals with the 
 location of places upon the earth, it is not necessary 
 to assume that other forms of geography, which have 
 become prominent in the schools in recent times, are 
 not to be included in the study of this subject. Physi- 
 
162 PSYCHOLOGY OF COMMON BRANCHES 
 
 cal geography, as an account of the way in which the 
 earth has developed, and of the varieties in physical 
 structure of the continents and the other features of 
 the earth's surface, is a desirable part of the study, 
 since it gives the child a conception of the origin of 
 the earth in its present form. Similarly, the study of 
 the natural products of various parts of the earth's 
 surface, and of the effect of altitude, or of latitude, or 
 of other physical conditions upon the life of men and 
 upon their occupations, — all of which we include 
 under the head of " Commercial Geography," — is 
 highly appropriate as a subject to be taught in the 
 school. 
 
 The other phases of geography belong to natural 
 science. While recognizing the importance of these 
 topics, we may still hold to the belief that the funda- 
 mental conception which underlies the understanding 
 of these other matters is the localization of the dif- 
 ferent parts of the earth. This means the abiUty to 
 picture in the mind different localities, their distance 
 from each other, and the direction which routes from 
 one place to another have with reference to each other. 
 Since the other two phases of geography are by nature 
 related more closely to natural science than they are 
 to location or place geography, we may include them 
 in a general way in the consideration of natural science 
 and confine ourselves here merely to what we may call 
 " spatial imagination," or localization of places upon 
 the earth. 
 
GEOGRAPHY 163 
 
 Growth of spatial imagination or orientation 
 
 The development of spatial imagination is gradual. 
 The ability to picture to one's self the location of a 
 variety of places on the earth with reference to one's 
 own location, and with reference to one another, or the 
 more compUcated form of imagination by which one 
 pictures the relationship of the planets to the sun or to 
 one another, and their movements, is subject to devel- 
 opment through certain stages, as is temporal imagina- 
 tion. The child comes only gradually to the fully 
 developed ability in this as in other forms of learning. 
 
 The idea of direction is based on the sense of bodily 
 position and movements. As in temporal imagination 
 the child first gains the ability to think of events in 
 the immediate past or future, so in the case of spatial 
 imagination he first becomes able to think of objects 
 or places which he does not see, but which are in his 
 immediate neighborhood. This ability is the out- 
 growth of the locahzation of sound which the child 
 gains when he hears a sound behind him and turns his 
 head in its direction. The child learns in the first year 
 to do this quite accurately. The later development 
 consists in imagining the source of a sound without 
 looking around, and then in imagining the location of 
 other objects which are behind him, or which are out 
 of the range of his vision, without turning around to 
 see them. In the earlier case one thinks of a sound 
 very much in the terms of the change in bodily position 
 
164 PSYCHOLOGY OF COMMON BRANCHES 
 
 which one would take in order to turn toward the 
 sound. This is one of the fundamental facts which is 
 characteristic through all forms of our ability to locate 
 direction. We think of the direction of a place with 
 reference to our bodily position, and the direction is 
 represented in our mind in a large measure in terms 
 of the change in bodily position, as in turning the head 
 or in pointing, which would bring us into a different 
 relation toward the place. 
 
 The localization of directions is gradually extended 
 to more distant objects. The development of this 
 ability to localize places which are not seen is gradu- 
 ally extended. The child leams not merely to place in 
 his imagination objects which are in the room or which 
 might be seen, but also those which are at a greater 
 distance and which cannot be seen from his present 
 position. After a few years, at perhaps four or five, 
 the child comes to have a fairly definite notion of 
 direction of buildings or of streets which are in the 
 immediate vicinity of his home, and he can point in 
 the general direction of familiar objects which he can- 
 not see. 
 
 Orientation with reference to one's self leads to 
 orientation of places with reference to one another. 
 The whole process of localization we call " orienta- 
 tion," ^ and it has become evident that orientation be- 
 
 ' Orientation is the localization of objects in imagination either 
 with reference to one's self, to one another, or to fixed, standard 
 directions. 
 
GEOGEAPHY 165 
 
 gins with the localization of places near one's self, and 
 that it has a close connection with one's sense of bodily 
 position. Orientation is in the first instance a sense 
 of the position of other objects with reference to one's 
 self, or the sense of one's own position with reference 
 to other objects. This primitive form of orientation, 
 which we may call, perhaps, "personal orientation," 
 or " variable orientation," is a step in the develop- 
 ment of a wider form of orientation jWhich is more 
 fixed in its nature. In this more highly developed form 
 the child learns to think of a number of places as hav- 
 ing a fixed relationship in space to one another. After 
 the child has learned the direction of different build- 
 ings and streets with reference to himself when he 
 occupies various positions among these places, he 
 builds up a notion of their directions and distances 
 with reference to one another, which does not depend 
 upon his position in the group. He learns to think of a 
 street, with the buildings which are located on it, with, 
 its relationship to other streets. This depends on the- 
 ability to take a detached view of a region as though 
 it were seen from a distance. 
 
 Objects are further oriented by being put into a 
 system of fixed directions. This development of a 
 more extensive and a fixed orientation usually takes 
 place through relating different positions or directions . 
 with reference to the position of some fixed object or of 
 some fixed direction. Whether or not this is always 
 the case in the young child, at least it is the means by 
 
166 PSYCHOLOGY OF COMMON BRANCHES 
 
 which the more complicated forms of orientation are 
 developed. The early mariners used the north star as 
 a point from which they reckoned their positions, and 
 the directions of places toward which they were sailing, 
 and we still use the north and other points of the com- 
 pass to enable us to organize the great variety of 
 directions and locations which we meet with in our 
 different experiences. The use of some such fixed point 
 of reference, then, is almost necessary for development 
 of any high degree of orientation. Here, again, we find 
 that bodily position and bodily movements play a 
 large share in the development of orientation.. After 
 one has determined upon the point of reference with 
 which the various places are to be located, he can form 
 the ideas of the location of these places by facing the 
 standard direction, and then, either actually or in 
 imagination, turning toward the different individual 
 places. 
 
 The coirectiGn of false orientation makes us con- 
 scious of the nature of the process. Such a system of 
 orientation as has been described is built up so gradu- 
 ally, and, in many cases, so early in hfe, that it is difli- 
 cult to recall the steps through which it has passed, or 
 even to realize that the system exists. It is brought 
 forcibly to mind, however, in those cases in which we 
 form a wrong orientation. If we go to a new town and 
 immediately get the directions correct and realize the 
 position of the town with reference to north, south, 
 east, and west, the whole system of orientation is built 
 
GEOGRAPHY 167 
 
 up without our being conscious of it. But when we 
 have made a mistake and have got these directions 
 wrong from the start, we find that the correction of 
 the mistake is very diflBcult. We become conscious of 
 the strength of the bonds between the various points 
 or directions of the place and the general points of the 
 compass when we attempt to change them, in order to 
 relate the buildings and streets in detail to a different 
 position of the cardinal points. 
 
 False orientation has to be readjusted piecemeal. 
 The great confusion which results in such a case of 
 mistaken orientation and the process by which it is 
 necessary to correct the mistake are instructive as to 
 the way in which orientation is built up in the first 
 place. We find in such cases that it is not possible to 
 correct the mistake we have made once for all, that is, 
 merely by recognizing that we have reversed the direc- 
 tions of north and south, or have thought of north as 
 east; but that it is also necessary to change the direc- 
 tion and locations in our mind of every part of the city 
 which we have formerly thought of with the wrong 
 orientation. It becomes necessary, so to speak, not to 
 turn about our idea of the city as a whole, but to re- 
 arrange it piecemeal, to readjust every small section, 
 with which we have become acquainted, by itself, 
 until finally the whole becomes readjusted. 
 
 Orientation is in part built up by relating parts indi- 
 vidually to cardinal points. This fact indicates that in 
 our first acquaintance with the different parts of a 
 
168 PSYCHOLOGY OF COMMON BRANCHES 
 
 place, we adjust each by itself with relation to the 
 cardinal points of the compass, and we think of each 
 part thereafter, without being fully aware of it, as 
 related to these cardinal points. Our idea of a house is 
 not merely the idea of its location in a certain part of 
 a city, but also of the house as facing east or west or 
 north or south. When we have thus become accus- 
 tomed to the direction of the facing of the house, we 
 have to readjust our ideas with reference to this house 
 itself and not merely with reference to the place as a 
 whole. At least, while it may not be necessary to 
 carry out the process in every detail, it is necessary to 
 go into a considerable amount of particular readjust- 
 ment in order to correct the original false orientation. 
 The child gradually gains a conception of the cardi- 
 nal points. Just as an adult, in coming to a new place, 
 gradually becomes accustomed to think of the parts 
 with which he becomes acquainted as having a certain 
 position in reference to the points of the compass, the 
 child gradually builds up, as well as his idea of the 
 directions of particular places, his notion of the cardi- 
 nal points of the compass themselves. This is prob- 
 ably done first with reference to some one place. The 
 child becomes familiar with the fact that the sun rises 
 in a certain direction and sets in the opposite direction 
 with reference to his own home and the neighboring 
 streets and buildings. He then, perhaps, acquires the 
 idea of north with reference to the rising and setting 
 of the sun and to the stars, etc.; and after these general 
 
GEOGRAPHY 169 
 
 notions have been acquired in connection with his 
 home town, he appHes them to other towns and then 
 makes the ideas more and more general. 
 
 Imagination extends sight experience, as sight' ex- 
 tends touch experience. The development of orienta- 
 tion, as it has been outUned, consists in the formation 
 of ideas of the direction of objects or places with refer- 
 ence to one's self, the development of the idea of dis- 
 tances between objects and of the direction which one 
 is from another, and of directions with reference to a 
 standard direction. We have now to consider the re- 
 finement of ideas of distances and directions between 
 places and of the way in which these ideas are built up 
 in some detail. When a person forms in his imagination 
 the idea of places with which he is familiar and the dis- 
 tances and directions between them, he is extending his 
 experience in much the same way that we extend the 
 experience which we get through handling objects and 
 through our direct contact with them, when we not 
 only touch them, but also see them. The blind man is 
 very limited in the extent to which he can organize 
 objects into a well-ordered whole. It is said that his 
 ideas of objects in relation to one another, so far as 
 they are clearly worked out, are limited by the amount 
 that he can span with his arms, that is, by the extent 
 of space from which he can get simultaneous sensa- 
 tions. We can organize objects in a better manner 
 when we experience them simultaneously than when 
 we experience them one after another. We may think 
 
170 PSYCHOLOGY OF COMMON BRANCHES 
 
 of the imagination as extending one's experience of 
 space beyond that which is apprehended through per- 
 ception, or through seeing objects, in much the same 
 way in which sight extends the experience which we 
 get through touch. To put it in another way, if a per- 
 son lacked the abihty to form an organized conception 
 of different places in his imagination, he would be lim- 
 ited, in comparison to the person who possesses the 
 ability to develop orientation through his imagination, 
 in much the same way that the blind man is limited in 
 comparison with one who sees. This does not mean 
 that the imagination supplies the place of seeing. The 
 blind man can fill out through his imagination what 
 he lacks through his vision. It serves merely as an 
 analogy to illustrate the fact that we have different 
 kinds of spatial recognition which are different in the 
 range of objects or places which they can include. In 
 the first place, we have the ability to recognize, 
 through touch and movement, the form of objects and 
 the position of objects which are within a very small 
 range. Broader than this is the sense of sight, which 
 enables us to recognize simultaneously wider ranges 
 of objects. Still broader is the imagination, which 
 gives us an orientation among places so widely sepa- 
 rated that they cannot be perceived at the same time, 
 even by sight. 
 
 Imagination may be stimulated by the sight of a 
 large district from a high place. The transition from 
 sight to imagination in the development of orientation 
 
GEOGRAPHY 171 
 
 may be bridged by taking the child to a high place, so 
 that he can get a sight of a larger number of places 
 than he ordinarily sees. This enables him, by means of 
 the broad range of vision, to obtain a unified view of 
 those places with which he has already become famil- 
 iar. A child may be taken to a tall building or the top 
 of a hill and given the opportunity to survey the 
 neighboring streets and buildings. He will then get an 
 idea of the whole, which he can hold in his imagination 
 while he walks about upon the ground and while his 
 vision is limited. He may be stimulated thus to keep 
 in mind the location of places in his imagination by 
 questions regarding the directions or distances of 
 places from the place on which he stands, or by ques- 
 tions regarding the direction of one place from another, 
 or their distance apart. 
 
 Maps and globes 
 
 Maps are symbols which are interpreted by the 
 imagination. This practice will prepare the way for 
 the child to form the idea of the relation of places to 
 one another, even though he has not seen them to- 
 gether. This transition from sight to imagination is 
 greatly facilitated by the use of maps. The child may 
 draw his own map of a region which he sees from a 
 high place, or the location of the places upon the map 
 may be pointed out to him as he sees them from the 
 eminence. The child is thus brought to the under- 
 standing of maps as signs or symbols of the relation of 
 
172 PSYCHOLOGY OF COMMON BRANCHES 
 
 places to one another. When he has learned through 
 this means what a map is for, and what it refers to, 
 he is able to use a map as a means of guiding his 
 imagination in understanding the relationship of 
 places which are so distant that they cannot be seen 
 at the same time. 
 
 Maps are necessaiy to insure accuracy in spatial 
 imagination of large areas. It is possible to get only 
 a very vague and rough idea of the location of widely 
 separated places unless a map is used. Suppose that 
 one should try to get an accurate idea of the relative 
 location of three places by traveling from one to an- 
 other. The three places might form the three apexes 
 of a triangle. In order to form an accurate idea of 
 their location, it would be necessary to keep in mind 
 not only the direction in which one is traveling in 
 going from one to another, but also the distances. If 
 an error was made in either the distance or the direc- 
 tion, it would introduce an error into the notion of the 
 positions of the places with reference to other places 
 and with reference to one another. On the map, due to 
 the fact that it is drawn to scale, the relative distances 
 as well as the directions are represented to the eye. In 
 attempting to get a clear notion of a region, one must 
 either consult a map which has been made of it or 
 make a map by means of compass and a measuring 
 device. It is difficult for one who has been brought up 
 to the early use of maps to imagine to himself the sort 
 of orientation which a person would have who had 
 
GEOGRAPHY ITS 
 
 never used maps; but it seems clear that a person 
 who does not have the assistance of maps will re- 
 quire a much longer time to become oriented in a 
 region than one who uses maps. 
 
 After being first used in close relation to the con- 
 crete, maps may be used abstractly. After the child 
 has learned the meaning of maps by associating them 
 with the regions with which he is familiar, he may 
 learn to use them without referring directly to the 
 actual world which is about him. It is not necessary 
 that a person in planning a railroad journey shall at 
 every moment think of the direction or the distances 
 which are represented on the map as related to the 
 place which he is occupying. He may be in one city 
 and be planning a railroad journey which is to start 
 from another city. In that case if he applies the map 
 to the concrete world, it must be by imagining himself 
 in the other place. It is very probable that we learn 
 to use maps in a highly abstract way for such pur- 
 poses, but, as in a great many other cases, the meaning 
 of maps will be greatly restricted if they have not in 
 the begiiming been closely related to the actual world. 
 It is, therefore, highly desirable that the child should 
 begin by a study of the region in which he lives, and 
 that he should learn the meaning of maps with refer- 
 ence to this region instead of beginning with a map 
 and attempting afterward to apply it to the real world. 
 
 Should the child begin to study his neighborhood or 
 the earth as a whole? This raises the question which 
 
174 PSYCHOLOGY OF COMMON BRANCHES 
 
 is similar to the one which confronts the teacher of 
 history, and that is whether the child studying geo- 
 graphy should begin with those facts which are open 
 to his observation and in his experience, and gradu- 
 ally work to those which are more remote; or whether 
 he ought to begin with the larger, more general facts 
 and then fill in the details by his later study. In the 
 case of geography there is, perhaps, more to be said for 
 the position that one should begin with the broader 
 facts. We may say that the child can best understand 
 the world when he reaHzes that it is a globe and that 
 it revolves about the sun, and rotates on its axis, and 
 so on. These facts are necessary for the comprehen- 
 sion of the seasons, for example. Furthermore, the 
 child cannot understand the setting of the region in 
 which he lives without knowing something of its rela- 
 tionship to the larger divisions of the earth. 
 
 Some home geography is necessaiy as a starting- 
 point and basis for broader study. On the other hand, 
 the general principle that the child's comprehension 
 of general facts should be based on his experience of 
 his immediate concrete surroundings holds in this case 
 as in the case of history, — at least, up to a certain 
 point. A map means nothing to a child unless he has 
 first learned the relation of a map to the region with 
 which he is acquainted. A globe means nothing to 
 him unless he realizes that it is a representation of the 
 earth upon which he finds himself. It is, therefore, 
 necessary that he have at least so much of an acquaint- 
 
GEOGRAPHY 175 
 
 anceship with his neighborhood that when he comes to 
 study the more comprehensive symbols he shall know 
 what they represent. This does not mean that he shall 
 necessarily progress continuously from the narrower 
 to the broader facts, but that he shall have a fairly 
 complete experience with the narrower facts, so that 
 when the broader ones are presented to him, they will 
 have a clear meaning. 
 
 The existence of the earth as a whole and of the 
 heavenly bodies is brought home to the child in his 
 everyday experience. The case of geography is a Uttle 
 different from the case of history. In the first place, 
 the rest of the earth and the other bodies which are 
 related to the earth are presented in some measure to 
 the child's present experience. He sees the sun and the 
 moon and he observes the sun rise and set. He can 
 see the outline of the shadow of the earth upon the 
 moon. Furthermore, the other parts of the earth than 
 that which is within his immediate experience exist 
 simultaneously with the parts with which he is ac- 
 quainted; and although he does not have direct experi- 
 ence with them, he meets references to them frequently. 
 He may hear about a war which is taking plaxie at some 
 distant place, or be told of events which are occurring 
 or have occurred in the past at other places. Perhaps 
 he was born in another town from that in which he 
 lives, or even in another country, and he hears these 
 places talked about. And so, in a variety of ways, he 
 learns indirectly about other parts of the world than 
 
176 PSYCHOLOGY OF COMMON BEANCHES 
 
 those which are in his immediate neighborhood. 
 Again, the different parts of the earth are related to 
 one another as a whole in a somewhat more intimate 
 way than are the different periods of history. For 
 these various reasons, then, it seems necessary to 
 introduce the knowledge of the earth as a whole, and 
 even of its relationship to the sun, the moon, and the 
 other planets, as soon as the child has had sufficient 
 concrete experience to give a meaning to the symbols 
 which are used, — that is, to the maps and to the 
 globe. 
 
 Care is needed properly to associate directions on 
 the map with the cardinal points. A difficulty with the 
 understanding of maps sometimes arises from regard- 
 ing a certain side of a map as representing the wrong 
 direction in the concrete world. By convention we use 
 the top of the map to represent north. This associa- 
 tion must, of course, be formed in the mind of the 
 child. It is probable that if his attention is not called 
 particularly to the matter he will naturally associate 
 the directions on the map with the directions on the 
 earth corresponding to it as it lies upon the desk. That 
 is, if the child faces the east or even if the map is on 
 the east wall, and nothing to the contrary is said to 
 him, he will think of the top of the map as represent- 
 ing the east. We have no experimental facts on the 
 matter, but observation by teachers seems to indicate 
 that it is desirable at first, in order to form the proper 
 association, that maps be placed so that the direction 
 
GEOGKAPHY 1T7 
 
 on the map corresponds to the direction on the earth. 
 As the child becomes more accustomed to the use of 
 maps, he can readjust his position in imagination, but 
 at first the connections between the symbols and the 
 facts is somewhat difficult for him to make at the best, 
 and it should be made as easy as can conveniently be 
 done. For this purpose maps which are drawn upon 
 the earth itself — for example, a map of the school- 
 yard made upon the playground or in the sand-box — 
 is the type of symbol which can be most easily associ- 
 ated in the mind of the child with the fact which it 
 represents, and this is the step which is the most nat- 
 ural to take first. 
 
 Excursions accompanied by map-drawing assist the 
 development of orientation. It goes without saying 
 that excursions properly conducted greatly assist the 
 child in the development of orientation. To be properly 
 conducted, from the point of view of geography, means 
 that the child shall during the excursion attempt to 
 keep the directions and distances in mind, and that he 
 shall draw a map of the region which is visited either 
 during the trip or after the return. The fact that a 
 person traverses a region does not mean that he has 
 comprehended anything of the location of its parts. 
 It is necessary that he himself actively observe the 
 directions and distances in order that he may get any 
 such notion. The leader is the one who knows where 
 he is going and who can find his way about because 
 he keeps directions in mind. A person who is not 
 
178 PSYCHOLOGY OF COMMON BRANCHES 
 
 attempting to lead becomes easily confused. There 
 should, therefore, be some motive, such as the neces- 
 sity of drawing a map, which shall lead the child to be 
 attentive to this feature of the experience. 
 
 Summaiy. As was said at the beginning of the chap- 
 ter, orientation is not by any means the whole of 
 geography nor perhaps the most important part of it. 
 It is the fundamental part, however, and without its 
 proper development the other parts are much more 
 difficult to learn properiy. Physical geography and 
 commercial geography are in the nature of natural 
 sciences, and since we are not attempting to distin- 
 guish between the different branches of natural science, 
 the general principles which are discussed in the later 
 chapter on this subject will apply to them, and may be 
 taken as sufficient discussion of them for the purposes 
 of this book. 
 
 REFERENCES 
 
 1. A. Binet: "Reverse Illusions of Orientation." Psychol. Rev. 
 (1894), vol. I, pp. 337-SO. 
 
 2. C. H. Judd: Introduction to Psychology, chap. 6. Scribners, 
 1907. 
 
CHAPTER IX 
 
 MATHEMATICS: ABSTRACT THOUGHT 
 Number an abstract mental process 
 
 In the mental processes and the forms of learning 
 which have been discussed so far the responses have 
 been governed in the main by the specific character 
 of the objects which served as stimuH to them. In 
 handwriting, the motor coordination is governed and 
 directed by the specific form of the individual letters. 
 In drawing, reading, and other forms of perceptual 
 learning, the aim is to develop the recognition of 
 objects in their particular character, and the facts 
 which are significant concern the special characteris- 
 tics of objects which distinguish them from others. 
 Even in imagination, in which experience is extended 
 beyond the concrete world which is present to the 
 senses, the reference is still ultimately, in large meas- 
 ure, to the nature of the world as it is presented in per- 
 ception. The characteristics of objects in which in- 
 terest and attention center are their " real " charac- 
 teristics, even though they are represented indirectly 
 in the imagination. In number we have to do with 
 a mental process which employs concrete experience 
 only as a starting-point. As soon as the number sym- 
 bols have acquired a meaning through concrete experi- 
 
180 PSYCHOLOGY OF COMMON BRANCHES 
 
 ence they become largely independent of it. How this 
 abstract number idea develops we shall see in the 
 following paragraphs. 
 
 . The child first distinguishes between one and two or 
 between more and less. The stages by which the child 
 comes to the fuU number idea are gradual. His earliest 
 idea of number is probably the distinction between one 
 thing and two things, or is little more than the distinc- 
 tion between more and less. If he has two balls or 
 playthings which are exactly alike, he knows when one 
 of them is missing, and this appears to be the earliest 
 manifestation of the recognition of the number of ob- 
 jects. 
 
 The number attitude is highly abstract. When the 
 child uses number to the extent of counting, his atti- 
 tude toward things undergoes a change. He regards 
 things now merely as counters which are to be put 
 together, and the interest is not in the things them- 
 selves, but in the fact that they can be put together 
 in thought to make larger or smaller sums. This atti- 
 tude toward things as being counters rather than hav- 
 ing an interest because of their individual characteris- 
 tics is a typical number attitude. We describe it in 
 technical terms by saying that in number the attitude 
 toward objects is an abstract one.^ We are thinking 
 only of one aspect of the objects, — that is, of their 
 
 ^ An abstract idea is one which does not merely reproduce the 
 experience with concrete objects, but deals with one phase or aspect 
 to the exclusion of the others. The use of language or other symbols 
 makes possible such a high degree of abstraction that the symbols 
 may have very little direct reference to the concrete world. 
 
MATHEMATICS 181 
 
 multiplicity, or of how many there are, — and we are 
 not concerned, so far as our interest is the number 
 interest, in their size, weight, shape, use, color, or any 
 other of their properties. 
 
 The use of objects as counters is illustrated by the 
 primitive herder. The use of objects as counters, 
 which makes clear the abstractness of the number idea, 
 is well illustrated by a practice which is occasionally 
 employed by primitive people to make a record of the 
 number of animals in their herd. Before counting has 
 been sufficiently developed, so that there are enough 
 number names to designate a good-sized herd, a prim- 
 itive herder sometimes records the number of animals 
 which he possesses by driving them through a stile 
 and putting down a pebble for each one as it goes 
 through. He then accumulates a pile of pebbles which 
 corresponds in number to the herd. Each pebble 
 represents one unit, and in the same way each sheep 
 represents one unit; therefore, in this case the owner of 
 the herd takes an abstract view of both the sheep and 
 the pebbles. The sheep and pebbles do not resemble 
 each other as concrete objects at all. They may not 
 even be ahke among themselves. The sheep may be 
 large or small, young or old, with a plentiful supply 
 of wool or a little supply; and the stones may be large 
 or small, of regular or irregular shape and of various 
 colors. In spite of the difference in all of these objects, 
 however, they are all thought of as alike because they 
 are regarded merely as counters. 
 
182 PSYCHOLOGY OF COMMON BRANCHES 
 
 Couiiting also illustrates the abstractness of num- 
 ber. The abstractness of number is also illustrated in 
 counting. When the child gets sufficient command of 
 the number names so that he can count readily, he is 
 very much interested in counting all sorts of objects. 
 He may count the buttons on his shoe, the chairs in 
 the room, the houses in the block, or the trees in the 
 yards, and so on. In thus applying the number names 
 to a great variety of objects it becomes clear that he 
 regards these objects, not from the point of view of 
 their concrete character, — that is, of their use or their 
 appearance or any other quality which leads one or- 
 dinarily to classify objects together, — but that he 
 regards them in the highly abstract character of units 
 or counters. In the application of any other names 
 there is a more intimate similarity between the objects 
 which are grouped together. Tables have in common 
 the flat tops which we use for setting things upon; 
 chairs have in common the fact that they are used to 
 sit upon; and so on; but the objects which are counted 
 have nothing in common but the fact that they are for 
 the moment regarded as units and that they are put 
 into a series of groups to which are applied the num- 
 ber names. The same number names may be used in 
 counting any objects whatever. 
 
 Number names or counters are sjrmbols. The illus- 
 trations which have been given of the simple use of 
 numbers bring out one of the fundamental character- 
 istics of numbers. In both cases a series of objects is 
 
MATHEMATICS 183 
 
 represented by a series of other objects which stand 
 for them as signs or symbols. When the stones are 
 used as representatives of the sheep, they are thought 
 of only as symbols of the sheep and of merely the 
 number of sheep. When the number names, "one," 
 "two," "three," etc., are used to designate objects 
 they stand as a sign or symbol of the number of the 
 objects, each being regarded as one unit. 
 
 The early development of the number idea 
 
 There is a one-to-one correspondence between sym- 
 bols and objects. In both these cases there is one sign 
 or symbol for each object which is counted and there 
 is one object for each of the symbols which is used. 
 This correspondence is called a "one-to-one corre- 
 spondence." It has been illustrated by Royce in the 
 example of horses and their riders. If there are a group 
 of horses and a group of riders, we pair them oflf by 
 giving one horse to each rider and one rider to each 
 horse. If there are any of one or the other left over, it 
 indicates that there are more of one than of the other. 
 
 The child does not at first apply this principle in 
 counting. This one-to-one correspondence is such a 
 simple and fundamental matter that it may seem un- 
 necessary to mention it. The child, however, does not 
 grasp it when he first tries to count. If one watches 
 the early beginnings of counting, one will see that the 
 child frequently points to a number of objects to corre- 
 spond to a single number name or uses several names 
 
184 PSYCHOLOGY OF COMMON BRANCHES 
 
 for one object. He has not grasped the notion that 
 one name must be given to each object and that each 
 object must have its name in order that the final num- 
 ber name shall represent the number of the objects 
 which have been counted. 
 
 What is taken as a unit depends on the purpose in 
 counting. It is worth while emphasizing that for the 
 application of this one-to-one correspondence which 
 is represented by counting, as well as the other forms 
 of number into which it develops, it is not necessary 
 that the objects used as units ^ be all of the same kind. 
 We may count together any things which we choose 
 to think of as units. In this case we do class them 
 together sufficiently to put them into the same group. 
 For instance, for the purpose of counting one may 
 class together chairs, tables, beds, couches, etc., when 
 the purpose is to count all the articles of furniture in 
 the house. The influence which the purpose that the 
 individual has in mind has upon the objects which he 
 regards as units may be illustrated further in the case 
 of counting all of the trees in a certain area, say an 
 acre. In this case one will count every growing thing 
 which is called a tree. One might, however, wish to 
 count, not all of the trees, but all of a certain kind, as 
 beech trees or pine trees. In this case the unit which is 
 selected is of a more restricted nature. This is what is 
 
 ^ A unit is anything which for the time being is taken as single 
 tor the purpose of pairing, counting, grouping, or any of the number 
 operations. 
 
MATHEMATICS 185 
 
 meant by saying that we may choose to call anything 
 a unit which for the time being we choose to put into 
 a certain group or class. 
 
 The idea of quantity implies similar units. The dis- 
 tinction should be made between number, in which the 
 multiplicity of units is the chief idea and the concrete 
 nature of the units is not important, and quantity, in 
 which there is included also a different idea. We apply 
 the idea of quantity to such matters as the amount of 
 water in a tank, or the number of acres in a field, and 
 so on. In other words, we use the term "quantity" 
 to designate the number of identical units which exist 
 in a certain total amount of material. To illustrate 
 the difference from the example which was cited above, 
 we find the number of trees by counting, and in this 
 case a small tree counts for as much as a large tree. If 
 we wish to find out the quantity of lumber in an acre 
 of forest, however, we take as the unit a foot or a 
 thousand feet of lumber, and calculate how many of 
 these similar units there are in the grove. In this case 
 every unit is the same as every other unit and the same 
 number of units will always express the same quantity 
 wherever it is found. 
 
 Early number is related to the fingers. The con- 
 sideration of the act of counting, which is the applica- 
 tion of the one-to-one correspondence by applying a 
 series of number names to a series of objects, leads us 
 to the question of the origin of the number names, and 
 of the development of the understanding of number 
 
ise psychcojOgy op ctmatos eraxches 
 
 DABi^si in ibecbaid. We hare ckar eridmce tliat mtm- 
 betaamaweiecttea Bat devdoped thrott^ vnaimg 
 oalheSngea. Id fact, the vord iriudiire me to desi^' 
 nate a lin^ onmbCT sjrmbol, **iaeX^ indicatCT tiist 
 tbe fiupas bad a dote nlatknsdiq) to Uie cariT* derd- 
 opment of mmib«. Fmflier erideoce fliat eountio^ 
 wax developed dnot^ the ok oC die ^gen qypean 
 in die dechnal sjctem, in wfaidi tfae mtnikex' of tibe 
 fii^eef fonns tiie basis o( gfoa{niis. We ihall leam 
 more partifwlari|y about tins in a lat« paragrafA. 
 
 Tbe ntmiber names Bij^ of^iaallf bare x«9ce«eitfe4 
 pociiioa M a seiies. b the diacacter of tbe eaify 
 naines of fpedfie nnmbets tbete it dear evideaee of tbe 
 origin o^ QxunJ-jen {trim coontioig on tbe fingecs. In 
 tbe ca^ of fome primiti re tabet, buthtaaote, tbe 
 minib»n&ixKs are tbe iiacses of partieolar &^H3 and 
 not modjr <->F anj of tbe Sagea indiffaentfy. Tlw 
 i»&ates tbat tbe ^pixs vete eoonted at a eertatn 
 fixed order and wiggnrfs tbat foaiSkij the eai&ct 
 nmnba' idea was ooe of a pr^sition in a series ndber 
 tihan of a i^jap of objects taken all tfj^eihet. 
 
 Two iSbaitraiioia of *.r.« tne of naixies of particolar 
 fin^^n as namber lizxsfs. kBom. 
 
 Tbe ^'.Aifja'BajYi^iamfjs tse tbe toBowinjZ nm u lj er 
 
 H. hiUuldeemiml <- middle fin^aer (of weoad :jaiA). 
 10. eerkOkoka > Httle finder. 
 
MATHEMATICS 187 
 
 The Jiviros of South America had the foUowmg 
 names: — 
 
 5. alacotegladu = one hand. 
 
 6. intimutu = thumb (of second hand). 
 
 7. tannituna = index finger. 
 
 8. tannituna caMasu = finger next to the index 
 finger. 
 
 9. bitin otegla cahiasu = hand next to complete. 
 10. catogladu = two hands. 
 
 Number names mean to the child, at first, position 
 in a series rather than a group of objects. However 
 this may be in racial development, it appears to be the 
 natural order of development in the child. As the 
 child is taught number by the common method of 
 counting on the fingers, he at first thinks of each num- 
 ber name as being the name of one of his fingers. The 
 name does not at first include all the fingers in the 
 series up to the one in question, but merely the one 
 which has been reached at the time when the name is 
 spoken. In other words, the first idea that the child 
 gets from counting is the ordinal rather than the car- 
 dinal idea. The numbers mean to him first, second, 
 third, fourth, and so on. After he has learned to count 
 the same series of objects in different orders, or to 
 count other things than fingers, he gradually comes to 
 realize that numbers represent a whole group of ob- 
 jects rather than one object which has a certain posi- 
 tion in a series. 
 
 Our number system is based on a grouping by tens. 
 
188 PSYCHOLOGY OF COMMON BRANCHES 
 
 Before the child has proceeded very far in learning to 
 count, he comes upon a very significant fact in our 
 number system. This fact is that we have enough dif- 
 ferent number names to extend only a small way in 
 the number series. We employ only ten different 
 digits. As has been mentioned already, this is related 
 to the fact that we have only ten digits on our hands. 
 When we get to the end of this number of digits, we 
 do not add other names, but begin over again, using a 
 sufficient modification of the names to indicate that we 
 are repeating the series a second time. When we have 
 finished with the series a second time, we begin and go 
 over it the third time, with a modification which is 
 derived from the second digit, which indicates that 
 this is the second time the series has been duplicated. 
 The name and the symbol for twenty are directly 
 related to two, and thirty to three, and so on. 
 
 This system of grouping reflects our inability to com- 
 prehend more than a small number of ungrouped ob- 
 jects. The limitation of the number of entirely distinct 
 number names is due to another fact besides the 
 origin of number in connection with the fingers. This 
 fact is that the number of objects which we can hold 
 in mind at the same time is limited. It is impossible 
 for us to achieve an immediate and distinct recogni- 
 tion of a large number of objects unless we divide 
 them into groups. This is precisely what we do by our 
 system of number names. When we get beyond a 
 number which constitutes the limit of a manageable 
 
MATHEMATICS 189 
 
 group, we begin a new group, and then designate it 
 as being a second one. It is as though the primitive 
 herder, in laying aside pebbles for his sheep, should 
 put them into one group until he had got as many as 
 he could grasp mentally at once, and then begin a 
 second group. 
 
 The choice of ten as the unit of grouping is not the 
 best possible. The name " decimal system " indicates 
 the number of digits which are included in each group. 
 It can be shown that it would be better, from the 
 standpoint of the use of numbers, to take a different 
 number for the unit group. Instead of using ten, 
 twelve would be a more manageable number, because 
 it has a larger number of factors. Ten can be factored 
 only by two and five, whereas twelve can be factored 
 by two, six, three, and fotir. It was an accident due to 
 the fact that counting grew out of the use of the fingers 
 that ten forms the basis of our system. 
 
 The grouping system facilitates the number opera- 
 tions. This division of numbers into manageable 
 groups is of value not only because it enables us the 
 better to grasp the meaning of larger numbers, and 
 facilitates the systematic development of number 
 names without extending the number of different 
 names indefinitely, but also because it facilitates the 
 processes of addition, subtraction, multiplication, and 
 division. In adding the numbers twenty-three and 
 forty-four we do not attempt to comprehend the com- 
 bination of the two numbers as composed of single 
 
190 PSYCHOLOGY OF COMMON BRANCHES 
 
 units, but first add the single units which compose the 
 fractional parts of the groupings, namely the three 
 and four, and then combine the two larger groups; 
 and finally obtain the result by combining the units 
 and the larger unit groups. If the number is such that 
 the sum of the single units come to more than ten, the 
 excess above ten is put into the result as units and the 
 group of ten is added to the other larger groups. 
 
 Grouping creates the distinction between higher 
 and lower units. What the decimal system amounts 
 to, as this illustration shows, is a method of using num- 
 bers to indicate the different kinds of units. By this 
 means we may regard a digit as representing either a 
 single unit or a group of these units. In our decimal 
 system the group which can be represented as a higher 
 unit is composed of ten of the lower units. 
 
 The distinction between higher and lower units is 
 expressed clearly in our notation system. This dis- 
 tinction between a higher and lower order of units is 
 most easily grasped by the use of the written numbers 
 for illustration. The group system may be used for 
 calculation even though it is not expressed in the nota- 
 tion by written numbers. The decimal system was 
 used in Roman times in manipulating calculating 
 machines similar to the abacus, while the written num- 
 bers were expressed in the clumsy Roman notation. 
 A written number notation, which shall express the 
 decimal system adequately, must represent in some 
 manner the fact that a digit may stand for a single 
 
MATHEMATICS 191 
 
 unit or for a group unit, that is, for a lower or a higher 
 unit. It is a commonplace with us that this is done by 
 having only ten signs and using the same sign to ex- 
 press by its position either a single imit or a group of 
 units. When we think of the application of the deci- 
 mal system in calculating, then, we inevitably picture 
 it in mind as expressed by numbers, and think of bor- 
 rowing and carrying, for example, as they are worked 
 out by our so-called Arabic notation. 
 
 Other experiences besides counting assist the child's 
 deTelopment in number. These illustrations of the 
 appKcation of the decimal system have taken us some- 
 what ahead of the development of the child. We have 
 seen that counting gives the child first the idea of 
 position in a series and that he can by counting pro- 
 ceed to the recognition or the manipulation of fairly 
 large numbers. He may by this means, it is true, 
 recognize cardinal numbers, but the elaboration and 
 perfection of this recognition can be carried out more 
 easily by the addition of certain other forms of expe- 
 rience. 
 
 The idea of number develops out of experience with 
 concrete objects. There has been considerable differ- 
 ence of opinion as to the kind of concrete experience 
 which is best suited to the development of the idea of 
 number in the child. It is well recognized that some 
 experience with things is necessary at the beginning, 
 to develop the early stages of the number idea, before 
 it has become highly abstract. While the number idea 
 
192 PSYCHOLOGY OF COMMON BRANCHES 
 
 is not complete until it has become independent of the 
 thought of any concrete things, yet it is developed 
 first through the experience of the child with concrete 
 objects. 
 
 Measurement of quantity, or grouped objects, may 
 be used to give concrete basis for number. The two 
 forms of experience which are commonly used to carry 
 the child beyond the counting stage are measurements 
 of length or of area or of cubic contents; and grouped 
 objects, as marbles or balls or sticks. The measure- 
 ment of objects means the dividing of an object into 
 equal units and then the determination of the quantity 
 of the object by calculating the number of the units 
 into which it is divided. When the length of an object 
 is to be measured, the calculation of the quantity is a 
 simple matter of the appUcation of a measure unit to 
 the object. When an area is measured, the child may 
 conceive it as composed of the small squares which 
 may be used as units. The measurement of volume is 
 still more complex. When sticks, or marbles, or balls 
 on a frame are used, each unit is represented by a 
 different object, and the combinations of numbers, 
 their manipulation, and various operations may be 
 illustrated by grouping these objects. The fundamen- 
 tal laws of number may be represented by the different 
 ways in which a group of objects may be broken up 
 into smaller groups, and then may be arrived at again 
 through combining these smaller groups into the larger 
 group. 
 
MATHEMATICS 193 
 
 Both methods may be used in combination to advan- 
 tage. While divergent views may be held as to the 
 value of the two forms of concrete experience which 
 may be used in teaching the early numbers, it is not 
 necessary that we choose either to the exclusion of the 
 other. Each has its own advantages, and one may 
 very well be made to supplement the other. The situa- 
 tion is not the same as it is in the case of some other 
 dififerences of procedure in education which are mutu- 
 ally contradictory. It is probably desirable that more 
 than one method be used in order that the child may 
 the more readily handle the number processes inde- 
 pendently of concrete material. If he learns with ref- 
 erence only to one kind of objects, he may find it 
 necessary to refer to this one object in making his reck- 
 oning, but if he uses now one and then another he is 
 more hkely to become independent of both. 
 
 Grouped objects illustrate the decimal system par- 
 ticularly well. There are many number processes or 
 ideas wiiich may be illustrated conveniently by the 
 method of grouped objects. One of these is the deci- 
 mal system. The decimal system is primarily one of 
 grouping. In it we set aside a certain number of units 
 and regard them as units of a higher order. In using 
 grouped objects this may be represented by counting 
 ten and then setting these aside as a group, and then 
 counting ten more and setting them aside, and then 
 regarding as units the groups which are themselves 
 made up of smaller units. 
 
194 PSYCHOLOGY OF COMMON BRANCHES 
 
 Number operations may be expressed as forms of 
 grouping and regroupiiLg. This grouping method may 
 also be well used to illustrate the aspect of number 
 which Judd has dwelt upon in his chapter on "Num- 
 ber" in Genetic Psychology for Teachers. It is there 
 pointed out that the number operations may be de- 
 rived from the fact that if a group be divided up into 
 a variety of groups, these groups when recombined 
 always give the original number. For instance, if 
 we take a group of twelve objects we may divide it 
 into two groups of six each, into three groups of four 
 each, etc. After the division has been made, we may 
 recombine the smaller groups again and always 
 get the original twelve. In other words, the total 
 number always remains the same whatever the group- 
 ing. 
 
 Grouping is a convenient means of teaching the fun- 
 damental operations. This is the basis of the under- 
 standing of the processes of division, multiplication, 
 subtraction, and addition. The child by manipulating 
 a group of objects may readily learn the various ways 
 in which it may be broken up into smaller groups. For 
 example, he may readily find that twelve may be 
 broken up into three groups of four each, or four 
 groups of three each, or two groups of six each, or six 
 groups of two each. This is probably a more direct 
 way of learning these facts than is measurement, 
 though the same facts may be learned through the 
 other method. Grouped objects are more easily ma- 
 
MATHEMATICS 195 
 
 nipulated than are units of length or of area, on ac- 
 count of the ease with which one may break up a 
 group in a variety of ways and see the way in which 
 the units may be recombined. The objects are more 
 flexible and can be modified more readily than quan- 
 tities which are suitable for measurement. 
 
 Measurement makes less prominent the units, but 
 more prominent the size of the whole number. The 
 use of measurement to make concrete these same proc- 
 esses may be illustrated. If a stick is measured into 
 inch lengths, the child may coimt the inches two at a 
 time and see that he has six, or may coimt the sixes 
 and see that he has two. In the same way, he may 
 divide the total length into three groups of four, or 
 four of three each. Measurement- makes more promi- 
 nent the quantity as a whole than it does the individ- 
 ual unit, and it would seem to require a greater ability 
 in abstraction on the part of the child to get a clear 
 notion of the unit in this case, as compared with the 
 use of distinct objects as units. From another point 
 of view measurement is particularly suitable, since it 
 calls the child's attention particularly to the size of 
 the number as a whole, and is therefore useful in 
 enabling him to see clearly the relative size of two 
 numbers. If he has a stick twelve inches long and 
 another six inches long, he may measure them and 
 then, comparing the length of the two sticks with his 
 eye, get a notion of the relation between the number 
 six and the number twelve. We shall return to this 
 
196 PSYCHOLOGY OF COMMON BRANCHES 
 
 matter of the learning of the fundamental processes 
 in later paragraphs. 
 
 Grouping is conveniently illustrated by the means of 
 the abacus. The use of grouped objects to illustrate 
 the simple number processes has been developed in 
 the apparatus which is called the "abacus." This is a 
 frame containing a series of parallel wires upon which 
 are strung wooden balls capable of being moved back 
 and forth. This instrument was formerly used widely 
 in the United States, and there is a revival of this or 
 some similar device at the present time. It has been 
 developed in more complicated forms in Europe and 
 is there used extensively. 
 
 In general we teach the meaning of numbers and 
 their operations before teaching their symbols. The 
 procedure which has been described assumes that the 
 child learns to understand about numbers before he is 
 taught to go through the formal processes of reckoning 
 with figures. In the very beginning the child has some 
 comprehension of the meaning of " one " and " two." 
 He does, it is true, usually learn to coimt by a mechan- 
 ical repetition of the number names before he has 
 developed the understanding of the meaning of the 
 different numbers very far, but, after this has been 
 done, we commonly teach him the meaning of numbers 
 through concrete objects before he learns to write 
 them. Further, he learns the processes of addition, 
 subtraction, multiplication, and division before he 
 learns to use the plus, minus, multiphcation, and divi- 
 
MATHEMATICS 197 
 
 sion signs; and he learns what it means to combine 
 numbers and express their equivalence to a larger 
 number before he uses the sign for equality. In general, 
 the understanding of the process in concrete terms 
 comes before the ability to express it in written figures 
 and signs. 
 
 Teaching the s3/inbols formerly preceded the teach- 
 ing of the number fact. This order of procedure, in 
 which the child learns the meaning of the number 
 operations before he is taught how to express them, 
 has not always obtained in teaching practice. In the 
 early part of the nineteenth century a revolution took 
 place in the method of teaching arithmetic in the 
 United States. Up to this time the child had been 
 first taught to write the figures and to go through the 
 various operations with figures in a mechanical way. 
 He learned as a matter of rote memory that four and 
 five make nine, and learned by the same method to 
 put the figures down in the proper way. It was not 
 beUeved that it was possible for him to understand 
 why he put down nine rather than eight or ten, or at 
 any rate, it was not realized that it was a desirable 
 thing that he should understand the process before he 
 learned to carry it out. 
 
 Except in the beginning, mathematical operations 
 are still frequently learned without an understanding 
 of the reasons for them. The same difference in the 
 method of teaching still runs through the higher 
 branches of mathematics as well as arithmetic. It is a 
 
198 PSYCHOLOGY OF COMMON BRANCHES 
 
 possible mode of procedure, and one which is often 
 actually practiced, to cause the pupU to learn the 
 various algebraic formulae, and to apply them, with- 
 out any clear conception of what they mean. When 
 the student comes to geometry, the demonstrations of 
 the theorems are sometimes learned without any 
 understanding of their meaning in terms of the figures 
 which illustrate them. In arithmetic an illustration of 
 the more complicated form of problems may be taken 
 from the extraction of the square root. This may be 
 taught in such a way that the pupils learn merely 
 what to do next and how to proceed with the figures, in 
 which case it becomes merely a sort of juggling feat. 
 On the other hand, by the use of an appropriate figure, 
 pupils may be taught, to some extent at least, to reahze 
 why they go through the various steps. 
 
 The question as to which of these methods should 
 be pursued is one which arises early. When we come 
 to the borrowing and carrying operations, as in sub- 
 traction and addition, and particularly when we come 
 to long division, we have cases in which the form of 
 procedure is rather complicated, and in which it may 
 be plausibly argued that it is unnecessary and a waste 
 of time to attempt to give the pupil an understanding 
 of the reason for the performance of each step in the 
 process. 
 
 In general, the more clearly the pupil understands 
 what he does the better. The detailed answer to this 
 question may be left to the discussion of methodology. 
 
MATHEMATICS 199 
 
 but at least we may say as a matter of general princi- 
 ple that it is highly desirable to develop in the pupil 
 ability to understand what he does in contrast with 
 the habit of carrying on a process in a mechanical way. 
 The history of the development of number teaching 
 has indicated that a pupil can be led to understand 
 very much more than used to be required of him. 
 While there may be details of some of the processes 
 which it is not practicable to enable him to understand, 
 he should at least know what he is aiming at, and have 
 a general understanding of the reasons for the proce- 
 dure which he takes. The question may be left open as 
 to whether this understanding can be or should be 
 made complete. It probably will be found that the 
 procedure must be somewhat varied to suit the vari- 
 ous capacities of the different children. Some, who are 
 rather dull, may not be able to understand the pro- 
 cedure without too much time being spent or possibly 
 even when an indefinite time is spent; and yet it is 
 desirable that pupils should have a sufficient command 
 of the simpler number operations to use them in 
 practical life. On the other hand, for the pupil who 
 is above average ability it is highly desirable that 
 he shall acquire the habit of understanding clearly 
 everything that he does. This is one of the most valu- 
 able attitudes of mind for a person who is to advance 
 beyond the most elementary stages of intellectual 
 achievement. 
 
 The understanding of the number processes must 
 
200 PSYCHOLOGY OF COMMON BRANCHES 
 
 be supplemented by drill in peifonning fhem. While 
 there is danger of erring on the side of making the 
 learning of the pupil too mechanical and of neglecting 
 to cause him to understand the process which he car- 
 ries on, there is also a possibiUty, and even danger, of 
 erring on the opposite side. There is danger of assum- 
 ing that after the pupil has understood the procedure, 
 he has gained all that he needs to gain from that topic. 
 This is altogether a mistake. We have, up to the most 
 recent years, reacted against the use of drill as a means 
 of developing in the pupil the abiUty to perform in an 
 efficient way certain simple activities. We have al- 
 ready referred to this matter in connection with spell- 
 ing. The same fault has been seen also in work with 
 numbers. There has recently been a reaction against 
 this neglect of drill and an emphasis upon the neces- 
 sity of the pupil's being able to perform quickly and 
 easily certain simple operations. We may merely 
 repeat here the statement that to understand a process 
 is not sufficient to enable the pupil to carry it out as he 
 should. The effort to recollect how a process is to be 
 carried on, or what the meaning of a problem is, makes 
 the process slow and difficult. On the other hand, if 
 sufficient practice has been undertaken so that as soon 
 as the problem is presented the result comes to mind, 
 or, if it is a longer problem, the mode of procedure 
 comes to mind quickly, much time and energy are 
 saved. There should be sufficient drill in all the proc- 
 esses that the child is likely to have need for in his 
 
MATHEMATICS 201 
 
 practical living to enable him to carry them on with- 
 out hesitation and without making an undue number 
 of mistakes. 
 
 The development of the arithmetical operations 
 
 The best order of teaching addition, subtraction, 
 etc., is a matter of debate. Another question of pro- 
 cedure, the solution of which rests upon the analysis 
 we make of the number operations, concerns the order 
 of teaching the fundamental operations, — addition, 
 subtraction, multiplication, and division. The tradi- 
 tional method is to teach addition, subtraction, multi- 
 pUcation, and division in the order named. There is 
 some ground, however, for thinking the order should 
 be reversed, and that we should begin with division 
 and multiplication and then proceed to subtraction 
 and addition. We may examine the grounds for these 
 two forms of procedure and attempt to determine 
 which one of them is the better adapted to introduce 
 the child to the complexity of the number processes. 
 
 Multiplication and division involve the equality of 
 the smaller groups. We may first contrast addition 
 and subtraction taken together, with multiplication 
 and division. Addition and subtraction differ from the 
 other two processes in that in them we deal with un- 
 equal groups. When we separate a group into a num- 
 ber of smaller groups, in division, we obtain groups 
 which are of equal size. In the same way, when we 
 multiply, we take the same group a number of times 
 
202 PSYCHOLOGY OF COMMON BRANCHES 
 
 until we arrive at the larger group which results from 
 this multiplication. This fact of the equality of the 
 groups in multiplication and division would seem to 
 make these processes simpler than those of addition 
 and subtraction. 
 
 Addition and subtraction are probably simpler to 
 the child. On the other hand, addition and subtrac- 
 tion may be carried on one step at a time, as when we 
 have four and add one to it, or when we add two to 
 four. In this case it is necessary to keep in mind the 
 first number and the number which is added and the 
 resulting number. When we multiply, we have to keep 
 in mind the number of the smaller groups, the number 
 of groups which are taken, and the final result. To 
 the adult who is familiar with the result of such a com- 
 bination it seems to be fully as simple an operation as 
 is that of addition. But it is doubtful whether the 
 child who is learning the meaning of multiplication 
 and division in the first place can readily jump from 
 the idea of a certain number of equal groups to their 
 combined number. He, in all probabiUty, has to pro- 
 ceed by taking one group at a time and calculating the 
 result by the addition of each succeeding group to the 
 preceding ones by a process of counting. The idea of 
 the equality of the groups, then, is in reality a compli- 
 cating element which makes the whole process more 
 difficult. The same line of reasoning appUes to divi- 
 sion. The child probably has to approach the process 
 by taking away one group at a time and counting the 
 
MATHEMATICS 203 
 
 remainder instead of by making a division into several 
 groups all at once. It appears from observation that 
 he begins multiplication or division by counting and 
 that he arrives at the result first without using the 
 idea of the equahty of the groups. This procedure will 
 be sufficient in addition and subtraction, but in order 
 to understand multipUcation or division he must have 
 grasped the fact also that the groups are equal. 
 
 To take addition before subtraction seems to be in 
 harmony with the child's habits. The further question 
 may be asked whether we should take subtraction 
 before or after addition, and division before or after 
 multipUcation. Here again the traditional method has 
 been to begin with addition and multipUcation and 
 then go to subtraction and division, but there has been 
 some disagreement with reference to this practice. In 
 the case of addition and subtraction, the child clearly 
 has the habit more firmly fixed of proceeding from a 
 smaller to a larger number than a habit of proceeding 
 from a larger to a smaller number. This is true in the 
 case of counting, and it is illustrated by the fact that it 
 is very much easier for the child to count forwards 
 than backwards. So far as the manipulation of grouped 
 objects is concerned, it is of course easy to take several 
 objects from a larger number and determine how many 
 there are left, but, on the other hand, it is just as easy 
 to add a number of objects to a smaller group and 
 count the number which results. 
 
 Division presents more possibility of difficulty than 
 
204 PSYCHOLOGY OF COMMON BEANCHES 
 
 multiplication. There is a more radical difficulty which 
 attaches to the process of division as contrasted with 
 multiplication. This difficulty is due to the fact that 
 not all numbers can be factored and that numbers 
 which can be factored have only a few factors. The 
 child can be taught to divide first by using only the 
 numbers which have factors and using only those fac- 
 tors which result in no remainder. Here again, how- 
 ever, there seems to be no greater difficulty for the 
 child in putting together the series of equal groups and 
 determining what the result is than in dividing a 
 larger group into a number of smaller groups and 
 determining the size and number of each smaller group. 
 Since there are greater possibilities of difficulty in 
 division, it seems to be the better plan to defer this 
 process and begin with multiplication. 
 
 Multiplication and division introduce the principle 
 of ratio. This description of multiplication and divi- 
 sion shows that they involve the idea of ratio, or at 
 least the idea of ratio may be developed from them. 
 When the child recognizes the fact that a number — 
 as, for example, six — may be divided into three 
 groups of two units each, it is but another way of 
 looking at the same fact to say that two is one third 
 of six. That three twos are six, and two is one third of 
 six, may be presented as different ways of stating the 
 same fact. There is no need of making the matter 
 mysterious or difficult by any discussion of the ratio 
 idea in the simpler number processes, as is sometimes 
 
MATHEMATICS «05 
 
 done. It may be said that the idea of number involves 
 the idea of ratio from the start. The idea of four is 
 implicitly four times one, and the idea of the unit is 
 implied in the idea of the number, but to discuss this 
 matter with children is to attempt to call attention 
 to a matter that is entirely taken for granted, and 
 this raises a serious difficulty. The idea of ratio, then, 
 comes in most naturally when the child deals first with 
 multipUcation and division. 
 
 Ratio may be represented by grouped objects or by 
 measurement. This ratio idea may be very readily 
 represented by the use of grouped objects. If objects 
 are arranged in a regular fashion, — for example, if six 
 objects are arranged in three groups of two each, — 
 we have a very simple and easy mode of representa- 
 tion of the idea that two is one of three groups which 
 make up six, or is one third of the group. The ratio 
 idea may also be represented by measurement, and 
 for the simpler ratios this is, perhaps, somewhat more 
 direct and easily grasped. The traditional illustration 
 of a pie which may be divided into three or four or 
 more parts is apropos in this connection. 
 
 Fractions are merely symbols to express ratio. In 
 explaining the method of representing fractions in 
 number rotation, it is possible to make unnecessary 
 difficulties for the child by going into too much minute 
 detail. The first association may be merely between 
 the term " one third " and the symbols of the one and 
 the three expressed as a fraction. When we go further 
 
206 PSYCHOLOGY OF COMMON BRANCHES 
 
 to explain what the one and the three mean, it may be 
 explained that the numerator refers to the number of 
 groups which are represented in the fraction and that 
 the denominator refers to the number of groups in the 
 total number which is represented. 
 
 Operations with fractions are easily illustrated with 
 grouped objects. In the operation with fractions, such 
 as in addition of fractions, grouped objects are prob- 
 ably more readily 
 applied than 
 measurement. All 
 that is necessary 
 in this case is to 
 represent both ra- 
 tios as a part of 
 total groups of the 
 same number of 
 
 no. 10. ILLUSTRATION OF THE USE ObjCCtS. ThlS IS 
 OF GROUPED OBJECTS IN NUMBER tbp Ponprptp mnHp 
 OPERATIONS ^ concreie moae 
 
 of representing the 
 reduction of the fractions to a common denominator. 
 An illustrative case is shown in the accompanying figure. 
 In order to add three fourths and one sixth we may let 
 both fractions be represented by the appropriate part 
 of the larger group of twelve. In the one case this 
 group of twelve is divided into four groups and in the 
 other case into six. If we then take three of the first 
 division and one of the second, we can determine what 
 our result will be by merely counting the number of 
 
 o 
 
 o 
 
 o 
 
 o 
 
 
 o 
 
 o 
 
 o 
 
 o 
 
 
 o 
 
 o 
 
 o 
 
 o 
 
 
 o 
 
 o 
 o 
 
 o 
 o 
 
 o o 
 
 o 
 
 o 
 
 o o 
 
 o 
 
MATHEMATICS 207 
 
 units in the various groups. Some such concrete 
 method is undoubtedly desirable to give the child an 
 understanding of the meaning of fractions and of the 
 operation with them. 
 
 Percentage is a special case of fractions. Percent- 
 age is merely the extension of the principle of fractions 
 to a special case and the use of a special means of 
 representing these fractions. After the child has 
 grasped the decimal form of grouping, as it exists in 
 our number system, he is prepared to understand that 
 percentage represents a case of fractions in which the 
 denominator is ten or a multiple of ten. Expressed in 
 concrete terms, this means that the whole group, of 
 which the fractional part is represented in a percent- 
 age, is always made up of ten, one hundred, or another 
 multiple of ten. 
 
 Decimal notation applies to fractional parts of a unit 
 the principle we have already considered. In a similar 
 fashion our mode of representation of percentage may 
 be grasped as an extension of the mode of representing 
 whole numbers. The child has already got a notion of 
 the meaning of the places in writing a number, and 
 understands that the digits in the first place represent 
 single imits, those in the next place to the left represent 
 higher units each of which is a group of ten, and those 
 of the next place a higher unit each of which is a group 
 of one himdred, and so on. If we now extend the num- 
 ber system to the right of the units place, we have a 
 series of representations of fractional parts of a unit. 
 
808 PSYCHOLOGY OF COMMON BRANCHES 
 
 In particular, if we suppose that the unit as represented 
 in the units place be divided into ten parts, then the 
 number in the next column to the right represents the 
 number of these parts which are designated. The 
 number in the next place represents a division in a like 
 manner of each unit of the first decimal place into ten 
 smaller units, and so on. Or if we start with the right 
 end of any number, whether it include decimal places 
 or not, each place to the left represents a unit which is 
 ten times the unit represented by the next number to 
 the right. 
 
 Decimal notation is easily illustrated by grouped 
 objects. These various units of higher and lower 
 orders, and their significance in the different places of 
 the number notation, may be represented by using 
 grouped objects, as has been suggested. If we use 
 grouped objects to represent decimal fractions, we 
 start out by making the units which are represented 
 in the first or imits place, not single objects, but a com- 
 posite unit, or a group. The child has become famihar 
 with a composite unit from the earlier familiarity 
 which he has with the meaning of the tens, hundreds 
 place, etc. If the first place, then, represents a unit 
 made up of ten parts, it may be clearly seen that the 
 next place to the right — that is, the first decimal 
 place — will represent a number of these smaller units 
 which are of the lower order. 
 
 The difficulty of grasping the niunber idea and its 
 mode of representation should be separated in order 
 
MATHEMATICS £09 
 
 that the child may understand as much as is practi- 
 cable. We have here brought home to us a fact which 
 was referred to earlier, namely, that the child is con- 
 fronted with two sources of difficulty in his study of 
 number. He is required not only to understand the 
 number relations themselves, but also the means by 
 which they are represented by the number symbols. 
 Very frequently the difficulty which he has is mainly 
 with the symbols. This emphasizes the conclusion 
 that the two difficulties should be separated to the 
 extent that the child should grasp the idea first in its 
 concrete form, and then the mode by which it is repre- 
 sented through the number ^mibols, making the con- 
 nection between the two. When he starts with the 
 number symbols they are meaningless to him, and he 
 has no clue to the understanding of their complexities. 
 The only course which is open to him, in this case, is 
 to memorize the processes by rote memory and trust 
 solely to his memory to guide him. Thus mathematics, 
 instead of being a means of the development of think- 
 ing, becomes merely a blind, mechanical exercise of 
 memory. This is unfortunate and is to be avoided as 
 far as may be. 
 
 The mental processes in algebra 
 
 Algebra is a further development of arithmetic Up 
 to this point we have traced the development of num- 
 ber into more and more complex forms so far as it is 
 included in the phase of number which we call " arith- 
 
210 PSYCHOLOGY OF COMMON BRANCHES 
 
 metic." In the common-school practice this has been 
 marked off sharply from another form, which we call 
 " algebra." In reahty the two are not radically differ- 
 ent, but algebra is merely an advance over arithmetic 
 in the same direction. Algebra is fundamentally Hke 
 arithmetic in that it represents relations of numbers to 
 one another. It differs, it is true, as we shall see, but 
 the difference is not such a complete one that it is 
 necessary to separate the two into entirely different 
 subjects of study. As a matter of fact, it is desirable 
 to introduce some of the algebraic forms of procedure 
 into the later stages of arithmetic. 
 
 Illustration of the arithmetical and algebraic meth- 
 ods of solving the same problem. We may first make 
 clear the relation of algebra to arithmetic, as well as 
 the difference between them, by an illustration; and 
 then discuss the meaning of this difference more par- 
 ticularly on the basis of this concrete example. The 
 following example may be worked either by an arith- 
 metical form of procedure or by using an algebraic 
 method. It is an example given by D. E. Smith in 
 The Teaching of Arithmetic, page 74. The problem is: 
 " If some goods are sold for $1,012.50 at a profit of 
 121 per cent, what did they cost? " 
 
 The common method of solving this problem accord- 
 ing to arithmetic is to let 100 per cent represent the 
 cost and 100 per cent plus 12^ per cent, or 112| per 
 cent, represent the selling price. Then, dividing 
 $1,012.50 by 1.12|, we have as a result $900, which 
 
MATHEMATICS gll 
 
 represents the cost. This form of procedure will give 
 the answer, but it is difficult to make the child under- 
 stand why it is taken. Why do we let 100 per cent 
 represent the cost, and why do we divide $1,012.50 
 by 1.12J? It is difficult to make the child recognize 
 that this is more than an arbitrary procedure. 
 
 The other procedure is to let some letter, such as 
 c, represent the cost. This is a natural letter to take, 
 since it is the first letter of the word. Then the seUing 
 price is o plus 12^ per cent of c, since the proJEit was 
 12^ per cent reckoned upon the cost. The selling price 
 then is 1.12^ c. This in terms of the equation becomes 
 1.12i = $1,012.50. 
 
 The equation may then be solved by dividing both 
 terms by 1.12 J, when we get as a result — 
 - $900.00. 
 
 By using illustrations from concrete numbers the 
 procedure of dividing both terms of the equation by 
 the same number may be justified without going into 
 a full explanation of it at this time. 
 
 The symbols of algebra are more abstract than those 
 of arithmetic, since they do not represent definite 
 numbers except as they are defined by other elements 
 in a problem. This method of solving a problem illus- 
 trates the essential advance of algebra beyond arith- 
 metic. In arithmetic, each symbol, such as the sym- 
 bol S, represents a definite number. Each number 
 may be illustrated by reference to various kinds of 
 concrete objects. It is abstract in so far as it may be 
 
212 PSYCHOLOGY OF COMMON BRANCHES 
 
 applied to any sort of objects which vre choose to 
 regard as units. In the algebraic symbol, however, we 
 have a means of designating any number whatever. 
 The symbol c which was used io this problem repre- 
 sents a number which is not known imtil the problem 
 is solved. The advantage of this is that we may use 
 this symbol as a term in our number manipulation 
 without knowing what actual number it represents. 
 The symbol represents a definite number so long as the 
 other terms used in the problem are defined, but if we 
 take an algebraic formula in which all of the symbols 
 are of the indefinite algebraic sort, then the formula 
 will hold true whatever definite numbers are substi- 
 tuted for the algebraic symbols. If certain of them 
 have numbers substituted for them, this restricts the 
 possibilities for the others. The only requirement then 
 is that the same symbol be represented by the same 
 number throughout the solution of the problem. 
 
 Arithmetical symbols may represent indefinite 
 quantities, but in a roundabout way. It will be well to 
 clear up a question which may occur with reference to 
 the statement which has just been made. One may ask 
 how it is that, if the arithmetical symbols — that is, 
 the digits or numbers made up of them — can repre- 
 sent only specific numbers, and the algebraic symbols 
 alone can enable one to solve problems in a different 
 way because they represent unknown numbers, or 
 may represent a variety of definite numbers, the above 
 problem can be solved by arithmetical means. In 
 
MATHEMATICS 21S 
 
 order to answer this question, we must qualify the 
 statement that the arithmetical symbols represent 
 only definite numbers. We have already seen in the 
 p^e^^ous discussion of arithmetic that a combination 
 of numbers in the fraction, representing a ratio, may 
 represent a more abstract relationship than is repre- 
 sented by a single number. Three quarters represents 
 nine when the total group which is thought of is 
 twelve, but it represents twenty-four when the total 
 group is thirty-two, and seventy-fi^^ when the total 
 group is one hundred. The use of percentage as a form 
 of ^plication of ratio enables one to use the symbol 
 xdiich may have a variety of definite numerical quan- 
 tities. In the case before us the cost was represented 
 by 100 per ceat, that is, by the ratio {H aad the 
 profit by 18J per cent, or i^. Thrae ratios, then, are 
 of the same nature as the algdiuraic symbol c. The 
 difference is that the unknown quanti^ may be more 
 conveniently represented by a sj^mbol which does not 
 imply any definite number than by a ratio which is 
 itself made up of two definite numbers. It is more 
 eaaly grasped as a symbol which represents an un- 
 known quantity than is the numerical ratio. It is 
 true that both methods may be pursued in such a case 
 as this, but in the more complicated forms of opera- 
 tion, the use of symbols which evidently represent an 
 unknown quantity is easier and better understood. 
 
 Manq)ulation of tiie equation is a central element in 
 algebndc {trocedore. The shove problem illustrates 
 
214 PSYCHOLOGY OF COMMON BRANCHES 
 
 also another fundamental fact in regard to algebraic 
 processes. After the algebraic symbol had been intro- 
 duced, the problem was stated in the form of an equal- 
 ity between two quantities, one of which contained 
 the symbol for the imknown quantity. This statement 
 of an equality is the equation, and the equation, with 
 the rules and the principles for manipulating it, is one 
 of the most fundamental elements in the algebraic 
 form of procedure. 
 
 The equation merely states the result in arithmetic, 
 but is used to obtain the result in algebra. The equa- 
 tion is implied from the very beginning of the study 
 of arithmetic. When the child realizes that three 
 groups of four each are equivalent to a group of twelve, 
 he is recognizing an equality between two forms of 
 grouping, and may state the equality in the form of an 
 equation. In arithmetic, however, the operations are 
 all performed on one side of the equation and the 
 equation is used merely to state the result of these 
 operations. Take a more complicated form of multi- 
 plication, such as 24 times SO. In this case the multi- 
 plication of the two numbers is carried on as a series 
 of processes and then the result is stated in the form, 
 24 X SO = 720. The equation only expresses the re- 
 sult of the multiplication which has been carried on 
 with the terms on one side of the equation. In algebra, 
 on the other hand, the problem is stated first in tlje 
 form of an equation, and the solution is reached by 
 manipulating the terms or the symbols not merely on 
 
MATHEMATICS 216 
 
 one side, but on both sides, or by adding, subtracting, 
 or performing other operations alike with both sides. 
 
 An illustration of the use of the equation in algebra. 
 Here again we may make the matter dearer by illus- 
 tration. Take as a problem one of Sam Lloyd's puz- 
 zles. The following problem serves the purpose: " At 
 a certain time between seven and eight o'clock, the 
 two hands of a clock are at equal distance from the 
 mid-point of the dial at the bottom, that is, from the 
 point that represents the half-hour. At what time are 
 the hands in such a position? " 
 
 The conditions of the problem must first be put into 
 algebraic symbols. It is obvious that we have here a 
 complicated set of conditions which are difficult to 
 express or to work out by using only the definite quan- 
 titative symbols of arithmetic. Suppose, then, that 
 we use a symbol to represent one of the unknown 
 quantities, which, if it were known, would enable us 
 to answer the problem. Let x, tliis unknown symbol, 
 represent the number of minutes past the hour which 
 the minute-hand has progressed, or in more general 
 terms the number of minutes past the hour which is 
 represented by each of the two hands. We may now 
 make up an equation from these assumptions. The 
 position of the minute-hand to the right of the bottom 
 or the mid-point of the dial will be represented by the 
 difference between thirty minutes and the minutes 
 past the hour which the hand indicates; that is, the 
 position will be represented by 80 — x. This distance 
 
216 PSYCHOLOGY OF COMMON BRANCHES 
 
 is equal, according to the conditions of the problem, 
 to the distance from the bottom mid-point to the 
 hour-hand. This distance we can also represent by 
 means of our symbols. Since the hour-hand progresses 
 through a distance representing five minutes on the 
 dial, in the same time that the minute-hand progresses 
 throughout a distance representing sixty minutes, and 
 since they progress at a proportional rate of speed, 
 the distance which the hour-hand has traveled from 
 the seven o'clock point toward the eight o'clock point 
 will have the same ratio to five minutes that the dis- 
 tance the minute-hand has to travel has to sixty min- 
 utes. Since the distance the minute-hand has traveled 
 is represented by x, the distance which the hour-hand 
 has traveled is represented by 
 
 1 . X 
 
 —r of X, or — -. 
 12 12 
 
 The position of the hour-hand beyond the bottom 
 mid-point, then, is 5 -I- — , since it started at the begin- 
 
 ning of the hour at a point five minutes beyond the 
 thirty-minute point. According to the conditions of 
 our problem, these distances are equal, and we may 
 state the problem in mathematical terms as follows: — 
 
 S0-a;=5 + :^. 
 12 
 
 The equation must then be solved. So far the prob- 
 lem has been merely to put into algebraic terms the 
 statement of the question. The rest of the solution of 
 the problem consists in so manipulating the equation 
 
MATHEMATICS 217 
 
 which we have stated that the value of x will be found. 
 The operations are represented according to the 
 familiar manner, as follows: Transposing the 5 and 
 the X so that the numerical quantities are on the same 
 side and the values of x are together, we get as a result 
 
 —r-X=25. 
 
 12 
 
 Then a;=i=X 25, or 23A. 
 
 If we apply this value of x to our problem, we find 
 that the distance which the minute-hand is from the 
 thirty-minute point is 30— 23A, or 6if, and that the 
 
 hour-hand is distant from this same point — -r- + 5, or 
 
 12 
 
 the same number, 6}|. The process which is involved 
 here, besides setting the problem into algebraic terms, 
 is the solution of the problem by manipulating the 
 equation. This latter part of the solution necessitates 
 learning the principles which govern what can be done 
 with an equation. In general, these may be summed 
 up by saying that what is done to one side of the equa- 
 tion must also be done to the other. This principle, 
 of course, works out into many detailed forms of pro- 
 cedure, but it is one of the fundamental principles of 
 algebraic work. 
 
 Algebraic expressions may be made concrete by 
 substituting numerical quantities for the symbols. 
 When an algebraic operation, which is represented 
 by the algebraic symbols and their manipulations, be- 
 comes obscure, the matter may be cleared up and the 
 
218 PSYCHOLOGY OF COMMON BRANCHES 
 
 terms made more concrete by the substitution of 
 numerical quantities for the symbols. This is, in prin- 
 ciple, the same sort of process that is carried on when 
 we substitute concrete objects for numbers in early 
 number work, — as when the child uses splints or 
 marbles, or measures areas or lengths, in order to illus- 
 trate or make concrete the meaning of numbers and 
 of their combinations. In the same way we approach 
 the concrete in algebra when we substitute definite 
 numbers for the algebraic symbols. 
 
 Negative numbers require an intricate mode of 
 representation. Some of the notions which are em- 
 ployed in algebra may be represented concretely, 
 though by somewhat intricate devices. One of these 
 is the idea of negative numbers. If we substitute 
 numerical quantities for negative algebraic symbols, 
 we cannot manipulate them in the same way in which 
 we do positive numerical quantities, and we cannot 
 illustrate their meanings in the same simple way by 
 substituting concrete objects. In order to grasp the 
 meaning of negative numbers and of the operations 
 which are made with them, it is necessary to use some- 
 what more complex spatial relations and to illustrate 
 by a combination of these relations and of movements 
 through space. 
 
 Addition and subtraction may be illustrated by dis- 
 tances on a line from a middle point. To represent 
 positive and negative quantities for the purpose of 
 addition and subtraction is fairly simple. All we have 
 
MATHEMATICS 219 
 
 to do is to use a straight line with a dividing point in 
 the middle, and represent positive quantities by dis- 
 tances toward the right and negative numbers by dis- 
 tances toward the left. If we have to add a positive 
 and a positive number, we merely add the correspond- 
 ing distances in the same direction and we arrive at a 
 result which is equal to the sum of the two numbers. 
 The addition of a positive and a negative number is 
 represented by a distance toward the right and then a 
 
 
 
 HH — 1 — I — I — I — i—i — I — I — I — ►— H — I — K-l — I — I— < — t-H 
 
 +* ■» , 
 
 .-2 
 
 ^}+«-(-3) 
 
 Fig. u. concbete kepresentation of opeeations 
 with negative numbers 
 
 distance from this point to the left, each corresponding 
 to the size of the number. (See Figure 11.) The opera- 
 tion then is performed by subtracting the negative 
 number from the positive, or the positive from the 
 negative, and affixing the sign of the larger number. 
 The subtraction of one number from another can be 
 represented by movements in the direction opposite 
 from that indicated by the sign of each number. 
 Thus, if we subtract a negative from a positive num- 
 ber, it is the equivalent of adding two positive num- 
 bers. 
 In the case of multiplication we must resort to a still 
 
220 PSYCHOLOGY OF COMMON BRANCHES 
 
 more complex form of concrete representation. Mul- 
 tiplication of negative numbers may be illustrated by 
 the accompanying Figure 12, adapted from Myers's 
 First Year Mathematics. The line AB may be taken 
 to represent a bar which turns about a fulcrum in the 
 center. The distances along this bar toward the right 
 
 Fig. 13. CONCRETE KEPEESENTATION OF OPEE- 
 ATIONS WITH NEGATIVE NUMBERS 
 
 are represented by positive, and along the left by 
 negative, numbers, as in the case of addition and sub- 
 traction of negative numbers. A force acting upward 
 upon this bar represents a positive number and a force 
 acting downward, a negative number. The two num- 
 bers which are to be multiplied are represented, one 
 by a position upon this bar to the right or the left of 
 
MATHEMATICS 221 
 
 this fulcrum, and the second by a force acting upon it. 
 The result is represented by the turning of the bar, 
 and when this is in a direction opposite to the move- 
 ments of the hands of the clock, it is designated as 
 positive, and when it is in the direction the same as the 
 movement of the hands of the clock, it is designated as 
 negative number. The sign of the product may then 
 always be found by representing one of the numbers 
 which is to be multiplied by a position on the bar 
 corresponding to its sign, the other number acting in 
 the direction corresponding to its sign, the sign of the 
 result corresponding to the movement produced on 
 the bar. Thus a positive number multiplied by a 
 positive, represented by an upward force acting upon 
 the right side, always results in a positive result or 
 multiplicand. Similarly, a negative number multi- 
 plied by a negative results in the same way. On the 
 other hand, a negative number multiplied by a posi- 
 tive always results in a movement in the negative 
 direction. 
 
 These illustrations make clear the abstractness and 
 complexity of algebra. It is evident that we are here 
 getting into an abstract matter, since we represent 
 the mathematical relationship by such a combination 
 of directions, distances, movements, and resultant 
 movements. These may serve as examples of some of 
 the more important of the ideas which are developed 
 in algebra. They go beyond the arithmetical proc- 
 esses; and in virtue of this fact, they make it possible 
 
22a PSYCHOLOGY OF COMMON BRANCHES 
 
 to handle number relations in a way that is not possi- 
 ble in using the more definite and less manageable 
 number symbols. Algebra is both a more complex and 
 a more valuable tool than is arithmetic and requires 
 for its mastery a higher degree of abstractness and » 
 higher type of intellectual process. 
 
 The development of geometry from measurement 
 
 In the discussion of number and its development in 
 arithmetic and algebra we saw that the various rela- 
 tions of numbers may be illustrated by means of 
 measurements of lengths, areas, or volumes; and that 
 these may be used as illustrations of the relationships 
 between numbers and the various number operations, 
 such as addition, multiplication, etc. From that point 
 we have traced the lines along which the development 
 of number has been speciaUzed. We have met more 
 and more complicated ways in which numbers may 
 be dealt with in the various operations of arithmetic, 
 and have seen how, by the use of more abstract sym- 
 bols, the more general operations of algebra are possi- 
 ble. The early form of measurement which is used to 
 illustrate number is developed in another direction by 
 giving particular attention to the relations of forms 
 and spaces and distances, and to the general principles 
 which govern them. The development of the princi- 
 ples governing the spatial relations is called "geom- 
 etry." The relations of geometry to measurement 
 may be seen from the word itself. In its origin, the 
 
MATHEMATICS 223 
 
 word meant the measurement of the earth, and, in 
 conformity to this meaning, geometry was developed 
 out of measurement of land for practical purposes. 
 
 In the school and in the histoiy of the branch there 
 is a distinction between meastxrement and foimal 
 geometry. In the school curriculum there has been a 
 sharp division between the early measurement which 
 the child carries on and which may be used to represent 
 the number processes and the later refinement of these 
 same studies of spatial relations as it appears in the 
 form of EucUdian geometry. The distance or gap 
 which separates the early or crude measurements from 
 the formal study of the principles of the relations of 
 space is one which has resulted from the fact that our 
 geometry is inherited from the Greek philosopher 
 Euchd. Geoemtry in the English schools has always 
 been called by the name of Euclid, who first system- 
 atized the principles of the subject. Many of these 
 principles were known in a concrete way before 
 Euclid. Many of the general propositions of Euclid 
 were discovered by practical experimentation, and 
 were practically applied, before Euclid worked out 
 their proof and formulated his principles. The Egyp- 
 tians understood the relations between the diameter 
 and the circumference of a circle and between the 
 hypothenuse and the legs of a right-angled triangle, 
 but they had not worked out the formal demonstra- 
 tion of these relationships. 
 
 Accurate measurement may give the child an early 
 
224 PSYCHOLOGY OF CX)MMON BRANCHES 
 
 knowledge of many geometrical principles. These 
 historical facts suggest that many of the facts regard- 
 ing space may readily be learned by the child before 
 he undertakes the study of their rigid proof. The gap 
 between the early crude measurements, which are 
 connected with the first appreciation of numbers, and 
 the formal study of geometry might then very well be 
 filled in by a somewhat more exact use of measurement 
 through which the general principles of the spatial 
 relation could be experimentally discovered. This 
 would prepare the child who is to go on to the formal 
 study of geometry by giving him a better concrete 
 basis for his more abstract study of principles, and it 
 would furnish to the child who is not to go on the direct 
 knowledge of spatial relations which would be of 
 value to him. 
 
 Many geometrical generalizations may be worked 
 out concretely before the child can understand their 
 demonstration. That geometry has been placed later 
 than algebra in the high-school curriculum is due to 
 the fact that the extremely abstract form of geom- 
 etry, or the study of space, has been used to the exclu- 
 sion of the more concrete study of the same facts. If 
 geometry is studied through measurement, it may be 
 considerably more concrete than algebra or even some 
 of the topics of arithmetic. Thus, a pupil may gain a 
 practical appreciation of the fact that the area of 
 a rectangle is measured by the product of the length 
 of the two adjacent sides, or even of the fact that the 
 
MATHEMATICS 226 
 
 square on the hypothenuse of a right-angled triangle 
 is equal to the sum of the squares on the two legs, 
 without going through any rigid demonstration of 
 these facts. Thus the child will come to recognize cer- 
 tain geometrical facts in the same way that he learns 
 to make other generahzations. This procedure consists 
 in recognizing that a fact holds true in a number of 
 cases, and in the conclusion that it is true in general. 
 Take the first illustration which was used. If the 
 child has measured a large number of rectangles, and 
 finds that the squares which are made by drawing 
 lines at unit distances to connect the opposite sides 
 are equal in number to the product of the unit dis- 
 tances on the adjacent sides, he will arrive at a general- 
 ization that this is always true of rectangles. There is 
 no reason why he might not properly make this gen- 
 eralization before he has learned its rigid proof. We 
 do not wait to teach the child generalizations in nat- 
 ural science, until he is able to appreciate their sci- 
 entific demonstration. 
 
 The Pythagorean Theorem may be illustrated con- 
 cretely. Take two illustrations of the appreciation of 
 spatial relations of a fairly complex sort through the 
 method of measurement, or of direct apprehension, 
 rather than through demonstration. The Pythagorean 
 Theorem serves as a good example. In Figure 13 we 
 have a special case of the theorem. It may be illus- 
 trated for the child by having him construct a right- 
 angled triangle with one leg four units long and the 
 
226 PSYCHOLOGY OF COMMON BRANCHES 
 
 other three units long, and then having him construct 
 the squares upon the three sides. He will find that the 
 hypothenuse measures five units long, and then, if he 
 divides each of the squares into smaller squares of 
 
 FlO. 13. nJLUSTEATION OF THE SOLUTION OF 
 THE PYTHAGOBEAN THEOREM BY MEA6DBE- 
 MENT 
 
 unit length on each side, he will find that the two legs 
 are measured by squares of sixteen and nine units, 
 and the hypothenuse by a square of twenty-five imits. 
 Thus he can see that in this particular case the square 
 upon the hypothenuse is equal to the squares upon 
 the two legs. 
 
 A more general mode of representation may also be 
 used. A similar relation for right-angled triangles in 
 
MATHEMATICS 
 
 227 
 
 K 
 
 general may be well illustrated by Figure 14, which is 
 a little more complex and suited to a more advanced 
 stage. ABC is a right-angled triangle and ABKD is a 
 square constructed ^ 
 
 on the hypothe- 
 nuse. ACEF and 
 BCHG are squares 
 constructed on the 
 two legs. Let the 
 child connect D 
 and F, extend CE 
 and drop the per- 
 pendiculars KJand 
 KI. He may then 
 determine by meas- 
 urement or by su- 
 perposition that 
 KJEI and BCHG 
 are equal. There- 
 fore, the irregular 
 figure KJFACI 
 represents the squares on the two legs. If this figure 
 can be shown to be equivalent to ABKD, the gen- 
 eral truth of the theorem is evident. This can be 
 done by superimposing ABC on AFD and BIK on 
 KDJ. 
 
 This generalization is to be distinguished from 
 rigid proof. In the stage that we are supposing, the 
 child is not expected to prove the equivalence of the 
 
 / F 
 
 N 
 
 \ 
 
 4 
 
 
 
 \ 
 
 
 
 n 
 
 £ 
 
 
 B 
 
 FlO. 14. ILLUSTRATION OP THE SOLU- 
 TION OF THE PTTHAGOKEAN THEOREM 
 BY MEASUREMENT 
 
228 PSYCHOLOGY OF COMMON BRANCHES 
 
 two figures. He may, however, see that they are 
 equivalent by measuring the various parts as indi- 
 cated, provided that the figure has been constructed 
 with sufficient care so that it is accurate. The proof 
 of such a conclusion as this requires much more than 
 the demonstration that it is true in one particular 
 figure. The child may recognize its truth and may 
 generalize upon this so as to conclude that it is true 
 for all figures of certain specifications; but to prove 
 that it must be true for every figure which meets these 
 specifications is a different matter. 
 
 Rigid proof bases conclusions on assumed axioms 
 or on previously proved conclusions. An advance to 
 the geometry of proof depends on the appreciation of 
 logical requirements. The final stage of development 
 in geometry, then, is not merely the recognition that a 
 certain relation holds true, but rather the appreciation 
 of the answer to the question why this relation must 
 be true. The very obviousness of the fact that a fact 
 is true is frequently the greatest source of difficulty to 
 the pupil in determining why it must be true. To raise 
 a question that the shortest distance from a point to 
 a straight line is a perpendicular seems a foolish thing 
 to do, and this is true also of many other geometrical 
 theorems. The pupil is not ready for this demonstra- 
 tional type of geometry until he can appreciate the 
 requirements of a logical series of steps, each of which 
 depends upon some assumption which is either an 
 axiom or a previously demonstrated theorem. 
 
MATHEMATICS 229 
 
 ^ Geometiy proceeds from concrete to abstract as do 
 arithmetic and algebra. When the form of proof has 
 been gone through in this manner, it becomes a general 
 or abstract affair which does not rest merely upon the 
 appreciation of a relation in a certain concrete figure. 
 In geometry, as in arithmetic and algebra, we begin 
 with the understanding of certain concrete relations, 
 or relations among concrete objects, and then gradu- 
 ally progress until the relations can be understood 
 abstractly. When this stage is reached, the pupil uses 
 a concrete figure only as an illustration or a mode of 
 representing the conditions of the problem to his mind. 
 The proof of this problem rests upon the appreciation 
 of the dependence of the theorem upon a series of 
 previously demonstrated theorems. 
 
 An illustration of the discovery of a geometrical 
 proof. The following illustration may serve to show 
 how one proceeds in geometrical proof. Suppose that 
 we set out to prove that a straight line which is per- 
 pendicular to each of two intersecting straight lines 
 at their point of intersection is perpendicular to the 
 plane P of these lines. This means that the line must 
 be proved to be perpendicular to any other straight 
 line whatever of the plane P which intersects at the 
 same point. In Figure 15, assume the line AO perpen- 
 dicular to OB and OC in the plane P. To prove that 
 the line AO is perpendicular to any other straight line 
 in the plane drawn through the point 0, as OD. 
 
 The conditions of the problem are first clearly real- 
 
230 PSYCHOLOGY OF COMMON BRANCHES 
 
 ized. The pupil first attempts to get dearly into mind 
 what the conditions of the problem are, and then to 
 cast about for methods of proving, on the basis of the 
 
 conditions which 
 are known, that 
 which is to be 
 proved. We know 
 thai. AOC and AOB 
 are right angles, and 
 we wish to prove 
 that AOD is a right 
 angle. One method 
 with which the stu- 
 dent has already 
 become familiar is 
 the use of triangles. 
 One may construct 
 a number of trian- 
 gles by drawing the 
 lines AB, AC, and 
 CB, then another 
 triangle may be 
 constructed, or a series of triangles, by connecting A 
 with the point of intersection of OD and BC at D by 
 the line AD. 
 
 The student follows up promising clues. This, how- 
 ever, does not seem to lead directly to the proof. An- 
 other form of procedure which is commonly used is 
 to extend a line, such as AO, through the plane to an 
 
MATHEMATICS 231 
 
 equal distance on the other side, represented at E, 
 By connecting B, C and D with E, we have another 
 series of triangles. It is obvious that if the triangle 
 AOD can be proved to be equal to EOD, the angles 
 AOD and EOD will be proved to be right angles. A 
 number of triangles are easily proved to be equal, as 
 AOC and EOC, and AOB and EOB. This suggests 
 that the triangles ABC and EBC may be shown to be 
 equal, because the three sides are equal, and that by 
 this means the triangles ADC and EDC can be proved 
 to be equal. As a consequence AD and ED are equal. 
 This makes it possible to prove the equality of AOD 
 and EOD, and therefore of the angles AOD and EOD, 
 and proves that they are right angles. 
 
 The process of problem-solving is ustudly more ran- 
 dom. The student in solving this problem would com- 
 monly not have arrived at the steps in such a direct 
 manner. A great many more useless ideas would have 
 been considered and rejected before the series of steps 
 which led to the final solution was finally hit upon. 
 The degree of directness with which the student pro- 
 ceeds to the conclusion depends somewhat on the 
 amount of his previous experience in solving such 
 problems, and upon his familiarity with the various 
 possible methods of approach. 
 
232 PSYCHOLOGY OF COMMON BRANCHES 
 
 Problem-solving 
 
 Problems are solved by analyzing conditions pre- 
 sented and following up clues. The procedure which 
 is taken in solving such problems illustrates the gen- 
 eral method of attacking such problems, and fur- 
 ther illustrates the method of problem-solving or of 
 reasoning in general. We may very briefly summa- 
 rize the characteristics of such procedure. In the first 
 place, one starts out with a problem, which may be 
 in the form of a certain conclusion which is to be 
 tested. With this problem in mind, the conditions are 
 analyzed, or broken up, in order that one may get a 
 clear realization of the various elements of the prob- 
 lem. One then casts about in his mind for various 
 clues to the way in which the solution may be ap- 
 proached. In this he is aided by methods which have 
 been found to be suitable in similar cases in the past. 
 The methods which are suggested are then tried out 
 until one is found which leads to the appropriate series 
 of steps and finally to the conclusion. These steps 
 must be so connected that each following one de- 
 pends upon the one preceding. 
 
 Solving a problem is radically different from fol- 
 lowing the statement of a completed proof. The means 
 by which the steps in a solution are stated after the 
 solution has been reached must not be confused with 
 the steps through which one goes in reaching the con- 
 clusion. The identification of these two is responsible 
 
MATHEMATICS 233 
 
 for the fact that many students of geometry never 
 learn to attack the problems themselves. The demon- 
 strations are stated by building up the proof in a logi- 
 cal manner, step by step, by beginning with known 
 facts and proceeding in an orderly way to the conclu- 
 sion. The proof is reached by tlie student, however, 
 by beginning with the conclusion which is to be proved 
 and working back to the facts which may serve as the 
 basis for such a proof. In a measure the two processes 
 begin at opposite ends, and one should distinguish 
 them in mind as well as in practice. 
 
 Problem-solving appears most prominently in geom- 
 etry. This consideration of problem-solving in geom- 
 etry leads us to the question of problem-solving in 
 number work in general. Problem-solving is a some- 
 what more intimate part of the work in geometry than 
 of arithmetic and algebra, because of the fact that 
 each new theorem is a new problem in itself and is a 
 step in a whole series of problems which are closely 
 knit together. In the case of arithmetic and algebra, 
 the particular problems which the child is set to solve 
 are grouped about certain general types of solutions. 
 The pupil is led to apply a certain method of solution 
 to a large number of concrete situations. In this proc- 
 ess he is not developing a new proof or the proof of a 
 new fact, but is applying to a variety of situations a 
 method which he has learned to use. 
 
 The grasp of the statement of the problem is im- 
 portant in arithmetic and algebra. Although there is 
 
234 PSYCHOLOGY OF COMMON BRANCHES 
 
 this difference in problem-solving in geometry and in 
 the other branches of mathematics, yet the general 
 features of the mental process are the same in the dif- 
 ferent fields. In the case of arithmetic and algebra, 
 however, we meet with a phase of the matter which is 
 prominent in them and which is one of the important 
 conditions which govern the ability to solve prob- 
 lems. It has been found by experiment that the diffi- 
 culty in solving an arithmetic or an algebra problem 
 depends in a large measure upon the ability of the 
 pupil to understand what the statement of the problem 
 means. Courtis found as reported in Bulletin num- 
 ber 2 of the Courtis Standard Teds, August, 1913, that 
 the same problem could be stated in a variety of ways, 
 and that the success of the pupil in solving a problem 
 varied remarkably with the variation in the manner of 
 stating it. There is a distinction between the appreci- 
 ation of a mathematical relationship, or a method of 
 manipulating mathematical symbols to obtain certain 
 mathematical results, and the ability to apply these 
 mathematical processes to a practical concrete prob- 
 lem. One may understand the mathematics itself very 
 well and yet not know what process to choose to solve 
 a special concrete problem. 
 
 Understanding a problem usually Involves a clear 
 grasp of concrete objects and relationships. The first 
 step in solving a mathematical problem is the under- 
 standing of what it means in its concrete terms. The 
 failure to reach this understanding is seen sometimes 
 
MATHEMATICS 235 
 
 not merely in problems in arithmetic and in algebra, 
 but also in geometry. The student of geometry, par- 
 ticularly of solid geometry, sometimes fails to realize 
 that the lines which are used to represent the figures 
 represent spatial relations. Until a student can get a 
 clear grasp of the sort of figures which are intended, he 
 is not in a position to understand in any measure the 
 problem or its demonstration. In the case of problems 
 in arithmetic or in algebra, the first requirement is that 
 the pupil shall be able to picture to himself just what 
 the meaning of the problem is. This very frequently 
 means the ability to form an image of certain concrete 
 objects. Whether such an image is absolutely essential 
 or not, it is very likely that it is in all cases beneficial, 
 and that the clearness of grasp which is attained by 
 the pupil will depend upon the clearness with which he 
 can picture to himself the concrete setting of the prob- 
 lem. Take the familiar problem concerning the rate 
 with which a tank would be filled if water flowed in 
 through a pipe of a certain size and out through a pipe 
 of another size. The ability to picture the conditions 
 of this problem will make it easy for the pupil to know 
 what sort of formula to use in its solution, or at least 
 will prepare the ground for the knowledge of the math- 
 ematical form of procedure which should be used. 
 
 The significance of the mathematical procedure 
 must be clearly understood. The next step is obviously 
 to turn the problem into mathematical terms or to 
 know what form of mathematical solution ought to be 
 
236 PSYCHOLOGY OF COMMON BRANCHES 
 
 used in a particular case. This means that the pupil 
 should grasp not merely the meaning of the problem 
 as it is stated, but also the meaning of the various 
 forms of solution which he has learned. It frequently 
 happens that pupils are able to solve problems which 
 are classified under the form of procedure which is 
 appropriate for them, but are not able to solve similar 
 problems when they are arranged in miscellaneous 
 order so that there is nothing to indicate which mathe- 
 matical formula is to be used. When a pupil shows a 
 great difference between his ability to solve the classi- 
 fied and unclassified problems, the probability is that 
 the problems have not been real to him, either be- 
 cause he did not appredate their meaning, or because 
 he did not imderstand the meaning of the mathemati- 
 cal formulae used. In either case his solution of the 
 problems is merely a matter of mechanical juggling of 
 terms without an understanding of their use and is 
 of no value to him from the standpoint of intellectual 
 development. 
 
 Much practice in discoveriog tiie general mode of 
 solution of problems is desirable. It is well for the 
 pupil to have a large amount of practice in the under- 
 standing of problems in their concrete statements uid 
 in determining what form of solution should be used 
 for them. This can be done by arranging series of 
 statements of problems and requiring the pupil not to 
 work them out in detail, but to put their meaning in 
 other words and to state bow one should proceed in 
 
MATHEMATICS 837 
 
 general to solve them. By this method the pupil will 
 learn to distinguish and understand the general fea- 
 tures of the various methods of procedure because he is 
 not confused with a mass of details. 
 
 Number illustrates the higher thought processes. It 
 has become evident, from this whole discussion of 
 number and mathematics in general, how mathematics 
 constitutes a form of thought which is not a direct 
 reaction to the concrete things of the physical world, 
 but rather consists in the development of complex 
 systems of thought processes which enable one to deal 
 with the concrete processes in an indirect manner. 
 One first selects from the multifarious attributes of 
 things the number aspect; and then develops forms of 
 procedure with numbers wholly or largely abstracted 
 from the concrete objects themselves; and finally 
 applies the results of these operations to the concrete 
 things. Instead of constituting an immediate reaction 
 to the physical object, such a response is made up of 
 a series of thought processes which are carried on for 
 a time with little reference to the objective world. 
 The next chapter will be a further illustration of this 
 higher form of response. 
 
 REFERENCES 
 
 1. S. A. Courtis: "Standard Scores in Arithmetic." Elementary 
 Sohool Teaoher (1911). vol. 12, pp. 127-37. 
 
 2. Frank N. Freeman: "Grouped Objects as a Concrete Basis for 
 the Number Idea." Elementary Sohool Teaoher (1912), vol. 12, 
 pp. 806-14. 
 
 3. C. H. Judd: Qmetio Psyohologyfor Teaohera, chap. 9. Appleton, 
 1903. 
 
238 PSYCHOLOGY OF COMMON BRANCHES 
 
 4. J. A. McCIellan and J. Dewey: Psychology 0} Number. Apple- 
 ton, 1895. 
 
 5. W. S. Monroe: "Warren Colbum on the Teaching of Arith- 
 metic." Elemeniary School Teacher (Wli), vol. 12, pp. 463-80. 
 
 6. D. E. Smith: The Teaching of ArMmetic. Teachers College, 
 Columbia University, 1909. 
 
 7. H. Spencer: Education, chap. 2. Appleton, 1861. 
 
 8. 3. W. A. Yoimg: The Teaching of Mathematics. Longmans, 
 1907. 
 
CHAPTER X 
 
 NATURAL SCIENCE: GENERALIZATION UPON 
 EXPERIENCE 
 
 Summary. We have seen how the child makes vari- 
 ous kinds of responses to the experiences which are 
 furnished him by the stimuU from the external world. 
 He has to begin with a variety of native responses 
 called "instincts." He adds to these or builds upon 
 them a great variety of responses which are not in- 
 stinctive. One type of response is the response of 
 movement to stimulus, and we call the mode of learn- 
 ing by which these responses are formed "sensori- 
 motor learning." In other cases it becomes necessary 
 to organize the stimulus itself so that one comes to 
 recognize it as having a meaning and becomes able to 
 distinguish the meaning among the different objects 
 which he finds it necessary to respond to. Not only 
 does the child learn to respond by giving interpretation 
 to objects, but he is able to retain impressions made 
 upon him so that he may recall them at some future 
 time and take them into account in making his re- 
 sponses. He is also able to present to himself, in his 
 imagination, events or objects which are distant in 
 time or space. The child is also capable of responding 
 to certain abstract features of the surrounding world 
 
240 PSYCHOLOGY OF COMMON BRANCHES 
 
 and can bufld up systems of thoo^t by considering 
 these dements. Tliis abstraction is illiistrated by 
 number. 
 
 Natural science deals with generalizations. In the 
 study of natutal science we find still another mode of 
 dealing with experience. This consists of developing 
 ideas or modes of response wbidli are equaDy applicable 
 to a variety of objects or experiences. Ta^ an illustia- 
 tion from the very eariy experience of the child. In his 
 eaAy dealings with the phyacal objects about him the 
 child has not yet learned the common laws which 
 govern them. He has to learn by experience sndi a 
 fundamental fact as that an object ^en released falls 
 to the ground. After he has seen this happoi -mth one 
 object after another, he teams how to prevent objects 
 from f alling and acquires the habit of expecting to see 
 objects fall wben they are released. He appears to 
 pass throu^ a period when he becomes conscious of 
 this general mode of action of things, and ddi^ts in 
 dropping objects partly for the pleasure in esp^ienc- 
 ing the fulfillment of his eapectatians. Such an idea, 
 which applies equaify to a \diole dass of objects, we 
 cjJl a "generalization."* 
 
 A child's fear of a balloon is explained by tiie fact 
 that it violates his e^iectation. A good illustration of 
 this expectation in the mind of the diild, that objects 
 
 ' A gemeraliiatian is an idea which is the ootgnnrth of a mode of 
 Teqmnse whid is found applicable to a wfa<de dass of objects. It is 
 usnaDy onbodied in the statement of a genora] princqtle. 
 
NATTBAL SCIENCE 241 
 
 win fall wben rdeased, m^ be seen in the fear ^diidi a 
 diikl exhibited when he saw a toy balloon, wfakh did 
 not act in the e^iected way. Hs« is an object, wiiich 
 according to all prerioos espeiiences (m^t to fall when 
 it is rdeased, bat instead of that it rises in the air. 
 The (jiild who was the subject of this observation was 
 vay mnch&i^tened by this e^)eriaice, and it required 
 some time for him to become accustamed to llie on- 
 famihar acticHi cl the balhxm and to eiqoy pJaying with 
 iL The diild acquires an espectatian that things will 
 act aoorading to certain r^olar modes of action or 
 laws. He finds that in liie world about htm certain 
 regular kinds of action can be eqiected. In the eariy 
 stages he devdtqjs these expectaticms nnccHiscions^, 
 bat Jhis f cams the basis fox the devdcqanent ol more 
 oansdons geneiaSzaticHis later (hi. 
 
 Concept formabon 
 
 The child fonns coaicepts, or ideas ol dasses ci 
 objects; and general principles, or ideas d the diarac- 
 teristics or modes ol action ol fliese dasses. Hie 
 child's generalizaticm npon his esperioice proceeds in 
 two ways. In the first place, he leams to distinguish 
 those dasses or groups (tf things wiiich have a certain 
 common mode of actitai or ^diich have something sim- 
 ilar, as a result of which one is led to put them into a 
 dass. The second jxtxsedure is to examine in more 
 detail the diaracteristics or modes of action of objects 
 ¥diidi have been dassed togethK. To illustrate liiese 
 
242 PSYCHOLOGY OF COMMON BRANCHES 
 
 two processes, the child may exhibit an interest in 
 distinguishing between cats and dogs, horses and 
 cows, etc., and in learning to recognize the members of 
 the different groups; or he may become more interested 
 in learning about the habits or characteristics of the 
 cat or the dog or the horse. For example, he learns to 
 distinguish between cats and dogs by certain marks of 
 difference, and by further experience to learn more 
 about the particular habits of cats — that they meow 
 and scratch, and of dogs — that they bark and bite. 
 We may distinguish these two by naming the first 
 "concept formation," or the formation of general 
 ideas; and the second, the formation of general princi- 
 ples or laws. It is evident from the illustration that 
 there is not a sharp distinction between the two 
 processes. 
 
 The child early classifies objects according to their 
 use. The earliest form of a child's scientific develop- 
 ment consists in learning to class objects together 
 which have common characteristics. The basis on 
 which a child first learns to group objects, and to re- 
 gard them as belonging to a common class, is their use. 
 If a child below nine years of age is asked to tell the 
 meaning of common objects with which he is familiar, 
 he gives the definition in terms of their use. He will 
 say that a fork is to eat with, a chair to sit upon, a 
 table is to set things on, a horse to pull a carriage, and 
 so on. What a thing can be used for and what it does 
 is the characteristic which attracts the child and which 
 
NATURAL SCIENCE 243 
 
 leads him to put an object into one class rather than 
 into another. 
 
 The development of concepts is hastened by the 
 use of names. A child begins to classify things roughly 
 before he can talk. The infant early distinguishes be- 
 tween things as good to eat or good to play with, and 
 distinguishes between his own family and others, and 
 between those within his own family. The use of names 
 greatly facilitates this form of development and leads 
 to a finer distinction between things. When a child 
 finds a name given to an object, this immediately 
 directs his attention to that feature of the object which 
 it has in common with other things which are given the 
 same name. He would probably be much slower in 
 making distinctions and comparisons if he were left 
 merely to his own oljservation in the matter. 
 
 The mistaken application of names illustrates how 
 they operate. The kind of mental process to which the 
 child is led by the use of names is illustrated in cases 
 where he makes a mistake in the apphcation of a name. 
 It is related by Preyer that a little boy had been accus- 
 tomed to hear his grandmother given the familiar 
 name. There was no means of knowing what he 
 thought it was which led this name to be applied to 
 his grandmother, until one day he saw another old 
 lady who also wore a cap. He thereupon called her 
 "grandmother" also, thinking apparently that a 
 grandmother was a person who wore a cap. This illus- 
 trates the fact that he had, without thinking particu- 
 
«44 PSYCHOLOGY OF COMMON BRANCHES 
 
 larly about it, selected a certain feature to which he 
 thought the name apphed, and when he saw another 
 who possessed the same characteristic, he extended 
 the name to her also. 
 
 Mistakes emphasize the importance of selecting the 
 essential feature as a basis for classifying objects 
 together. Another illustration shows how a child may 
 group a great many diverse things together by select- 
 ing in each case some feature which is common to two 
 things and thus finally reaching in his cliain of thinking 
 an object which is widely different from the one with 
 which he started. A little boy saw a duck upon a pond 
 and heard the word "quack" applied to the duck. 
 He did not clearly separate in his mind the duck and 
 the water and so applied the name to both. Later he 
 used " quack " to refer to water or even to any liquid. 
 Further, he applied the name to other birds than the 
 duck, then to an image of an eagle upon a coin, and 
 finally to coins themselves. We see how far this 
 process of association may carry the child from the 
 original object to which the name was given. These 
 cases of accidental or erroneous association emphasize 
 the opportimity and need for the direction of the child's 
 thinking in the formation of his concepts or general 
 ideas. They bring out also the fact that a concept is 
 built upon the analysis of an object so as to determine 
 what the essential feature is. It is necessary, in order 
 that the child may have the correct notion, that he 
 should select the essential feature and not some acci- 
 
NATURAL SCIENCE 245 
 
 dental feature upon which to base his classification of 
 the object. This thought process in selecting the cor- 
 rect feature is of considerable value, and names, there- 
 fore, may form a stimulus to valuable thinking on the 
 part of the child. 
 
 The development of generalizaiion 
 The child's early explanations are superficial. It 
 may thus be seen that the process of grouping things 
 together goes parallel with the process of familiarity 
 with the characteristics of the things themselves. The 
 more one knows about individual objects, the better 
 he is able to tell to what class they belong, and to 
 divide them up into finer and finer groups. In the 
 begiiming the child shows a disposition to follow the 
 practice of primitive man and to depend upon a super- 
 ficial similarity in putting things into the same class. 
 When he meets with new objects, he shows a disposi- 
 tion to think of them after the analogy of things which 
 he already knows. In this he is not unlike mankind in 
 general, but as he gains in intellectual growth he is 
 able to distinguish the characteristics of new things 
 which make them fundamentally different from objects 
 which he has met before. This tendency to interpret 
 new things after the analogy of familiar things is 
 shown in the story of the Indians, who, when they 
 first saw a steam engine, were greatly puzzled until 
 they explained the running of the machine by saying 
 that there were horses inside. They were oblivious to 
 
246 PSYCHOLOGY OF COMMON BRANCHES 
 
 the fact that the running of a horse is as mysterious a 
 thing as the working of the steam engine, for since 
 they were familiar with the horse's activity, it did not 
 present this difficulty to them. The difficulty to them 
 lay in the unfamiliarity of the new thing rather than 
 in an appreciation of the problem which really existed 
 in explaining it. 
 
 The child is ready first to learn the more obvious 
 and external facts about things. The child's early 
 scientific procedure is after the same manner. It con- 
 sists in gaining familiarity with the mode of action or 
 with the characteristics of a great variety of things, 
 without going very deeply into their explanation. 
 Animals and plants are particularly suitable for the 
 child's early study, both because of his native interest 
 in them and in their habits, and because the familiar- 
 ity which he gains with them will serve as a basis for 
 the later, more penetrating study which he will have 
 to make. He is very much interested in learning about 
 such facts as the habits of animals. He may be told of 
 the nest-building of birds, the differences in the kinds 
 of nests built by different birds, the way in which the 
 beavers build their homes, the different modes of 
 gathering food and caring for the young, and so on. 
 These facts should not merely be taught to the child 
 through verbal instruction, but he should also be led 
 in the early period to be^n the habit of observation. 
 It is surprising what a fund of information a child may 
 gather if he once becomes interested in such a j^ursuit. 
 
NATDBAL SCIENCE , 247 
 
 In a similar maimer the child may leam about the 
 habits of plants; the different kinds of seeds which are 
 piodaced by different jJants; the ways in which seeds 
 are carried from one place to another, or are given 
 such form that they wifl leadity spread; the other 
 means of growth of plants, as bom bulbs, seeds, cut- 
 tings, etc He may leam also of the care which is 
 necessary for the growth of plants as well as of animals. 
 
 Care for plants and animals stimulates the child's 
 interest and gives him moral training. Subjects of 
 study of this sort are particulaily appropriate for 
 another reason. Ttey give the child an opportunity, 
 if conducted in the proper manner, of doing something 
 with things, as well as learning about them. The child 
 may find out about animals and plants by actually 
 caring for them. The care of a pet and the cultivation 
 of a gardod plot greatly stimulate his interest and lead 
 him to leam a variety of things in a way in which he 
 win not forget. Incidentally the child learns many 
 lessons whidi are not directly related to scientific 
 training, such as the lesson of thoughtfulness and sym- 
 pathy in caring for animals, and the lessons of indus- 
 try and order. 
 
 This simple type of sdence suits the child until the 
 intermediate period. By such e^i^ences as these, 
 the child gains a familiarity with the more obvious 
 characteristics and habits of natural objects. This 
 f omis the foundation for his later scientific work, but it 
 needs to be carried much farther in order to be fully 
 
248 PSYCHOLOGY OF COMMON BRANCHES 
 
 developed. The type of observation and learning of 
 facts which have been described is suitable to the 
 younger child. The child can begin at least in the 
 kindergarten period, and carry forward this type of 
 work until some time in the intermediate period in 
 school life. At this time he is ready to begin a some- 
 what more systematic and thorough form of study. 
 
 More systematic study is necessary to get at many 
 of the facts of the world about us. Many of the facts 
 of the world about us may be gained by such observa- 
 tions as the child can make in this early scientific work, 
 but the facts must be on the surface and not require 
 too much thought or too sustained observation in 
 order that they may be discovered. For the discovery 
 of many scientific principles, which are commonplace 
 with us, the casual observation of mankind has not 
 been su£5cient. Adults miss many of the generaliza- 
 tions which would be very valuable to them and very 
 closely related to their welfare if they were discovered, 
 and the child is less capable of systematic observation 
 and generalization than is the adult. Many illustra- 
 tions of the weakness of unscientific observation are 
 at hand. The farmer may go on for generations raising 
 com without discovering the best method of improving 
 his product, although all the facts which are necessary 
 to the discovery of such a method are at hand for his 
 observation, and although it is greatly to his interest 
 to discover them. A little scientific observation and 
 experimentation enables one to discover these princi- 
 
NATUEAL SCIENCE 249 
 
 pies. For a long time man suffered disease and death 
 from yellow fever without discovering that it is related 
 to the mosquito, although this fact was at hand all the 
 time for ol^servation. In many cases also mankind has 
 clung to the £brst generalization, although systematic 
 observation would prove their falsehood. This is the 
 case with such common superstitions as that a rabbit's 
 foot gives good luck, or .that Friday and 13 are likely 
 to bring bad luck. 
 
 Science is based on systematic observation and 
 experimentation. The means to a more scientific and 
 reUable form of procedure, leading to better estab- 
 lished principles, have been incidentally indicated. 
 They consist in a systematic observation of facts 
 together with making a record of the results of the 
 observations in order that they may be compared; and 
 in experimenting in order that various possibiUties 
 may be tried out and their results compared with one 
 another. Both of these methods imply that one starts 
 out with a definite problem in mind, and conducts his 
 observation or his experimentation in such a way as 
 to gain an answer to the problem. One must be able 
 to control his investigations and guide them continu- 
 ously and systematically toward the solution of a par- 
 ticular question. The ability to carry on such scientific 
 work is one which develops gradually, and does not 
 appear until the child has at least reached the period 
 of his intermediate school life. 
 
 Systematic observation leads to generalization con- 
 
250 PSYCHOLOGY OF CX)MMON BRANCHES 
 
 ceming the sun's movements. The way in which 
 observation and experimentation make generahza- 
 tions more exact, and lead to the discovery of relation- 
 ships which would otherwise be mmoticed, may be 
 illustrated by two concrete cases. The first is an illus- 
 tration of more exact generalization through system- 
 atic and directed observation. In certain realms we 
 cannot carry on experiments because the forces which 
 are to be observed or the events which are to be re- 
 corded are beyond our control. In astronomy, for 
 example, we have to confine ourselves to the observa- 
 tions of events as they take place. Thus, a child may 
 notice certain general and superficial facts, but may 
 require controlled observation to carry his generaliza- 
 tions beyond the more rough-and-ready ones. One 
 notices without giving especial attention that the sun 
 rises in the east and sets in the west, and that it is 
 higher in the summer than it is in the winter. To find 
 out more exactly the movements of the earth in rela- 
 tion to the sun, one may make a systematic study of 
 the shadows which are cast by some object. Suppose 
 the child marks on the floor the position of the shadow 
 of the comer of the window, or of some object upon 
 the window, from day to day. If he keeps a record of 
 this position, he will notice that it has the same east 
 and west position at a particular hour every day, but 
 that it shifts north and south with the change of the 
 season. This will lead then to a more definite and 
 exact statement of the movement of the sim. 
 
NATURAL SCIENCE 251 
 
 Exact science often reqtdres fiie use of ntnnber. 
 Take anotl]^ pioUem, — the relationship of the length 
 of the shadow to the hd^t of the object which casts it. 
 One may readUy recognise, without using any exact 
 means of measurement, that the taDer object casts the 
 longer shadow, but the comparison oi differait objects 
 and the shadows which they east enables one to make 
 the generalisation that the shadow is esactly propor- 
 tional to the hdght of the object which casts it. This 
 illustration shows how the more exact generalizations 
 in science require the use of numbers, just as we found 
 that the retx^nitian of the long» stretches of time 
 necessitates putting time into terms of numb^s. This 
 is one reason wl^ the more exact and comprehensive 
 forms of generalisation cannot be made until the 
 child has attained a certain degree of mental devdop- 
 ment. 
 
 In ezperimentatioii causes are stadied by introduc- 
 ing or vaiyiiig one at a time. (Mten the facts which are 
 needed for the solution of a sdaitific problem can be 
 obtained more quM^kJy by an e^p^iment than by wait- 
 ing until they present themselves for observation. An 
 expmment sdso has another advantage, whidi is that 
 the particular fact which we wish to obsrave can be 
 made to appear an^^; or at least we can observe the 
 effect of certain conditions by vaiying tiiose condi- 
 tions while others remain constant. Suppose that we 
 wish to determine what conditions are necessaiy for 
 the best growth of jdants. We may, through esperi- 
 
252 PSYCHOLOGY OF COMMON BRANCHES 
 
 ment, try out one condition after another, taking one 
 at a time. We may vary the amount of water supply, 
 or the amount of air, or the amount of sunlight, or the 
 kind and amount of fertilizer with which the plant is 
 furnished; and by keeping an exact record of the 
 changes which we introduce and of the results which 
 follow in the condition and growth of the plant, we 
 may gain an exact generalization as to the bearing of 
 these different factors. 
 
 Science is based on the attempt to solve problems. 
 These illustrations indicate, as has already been re- 
 marked, that scientific investigation consists in carry- 
 ing on systematic observations and experiments to 
 answer certain problems. The importance of this 
 problem-solving process for the education of the child, 
 particularly in natural science, has been very greatly 
 emphasized, and with good reason. K the child merely 
 learns by rote those conclusions which have been 
 reached by others, he may gather a very large amount 
 of information, but he will not be forming those habits 
 of thought and action which will enable him the better 
 to meet those problems which may confront him in the 
 vocational or other situations of his lite. The presenta- 
 tion of the work in such a way that it will arouse ques- 
 tions in the mind of the child and lead him to an inves- 
 tigation of these questions is of great importance. 
 
 The discovety of problems is also important. The 
 illustrations which have been used and the principles 
 which have been indicated bring out also another form 
 
NATUEAL SCIENCE 253 
 
 of scientific work. The ability to do work of a scientific 
 character depends not merely upon the capacity for 
 working out problems, but also, and perhaps in a still 
 more important degree, on the ability to see problems 
 where they have not before existed to the mind of 
 other observers. The successful scientist, or the suc- 
 cessful investigator in any field, b the person who sees 
 questions in what the ordinary individual takes as a 
 matter of course. This principle is to be applied both 
 in the natural sciences or in the sciences in a technical 
 sense, and in any field of human endeavor which ad- 
 mits of study by scientific methods. It applies to the 
 problems of everyday life. The conditions which are 
 favorable or unfavorable to health should be studied 
 by each person for himself, so as to learn what condi- 
 tions are necessary in order that he shall be kept in 
 the best working condition. This, to a large extent, is a 
 matter for individual investigation. Many problems 
 arise also in each person's vocation which should be 
 attacked by applying the scientific method. There- 
 fore, we should encourage the child to look for prob- 
 lems, to give attention to them when he sees them, and 
 to be alive to the questions which may arise in connec- 
 tion with his own life and with the world about him, 
 in addition to training him in the ability to attack 
 problems when they are pointed out. 
 
 Exact generalization is induction. When generaliza- 
 tion is carried to the point which has just been de- 
 scribed, — that is, when it has been made definite and 
 
e»4 PSTCHOLOGT OF COMMON BRANCHES 
 
 exact and has resulted from a scientific fonn of inqoiiy, 
 — TTe can it ■■ indmSJon." Indoetioii, tiiai. is the 
 eTaminatkai of facts in a systematic fa^hkHi in order 
 to deti^mine &om this invcstigatkta what genoal 
 pnnciides goTem these &cts. 
 
 Hie foonatian of genoaHzatiais makes concepts 
 m(H% exact. In the foregoing descnption, scientific 
 procedme ha^ been described as the fbrmaticai of 
 geaooalixatirais. We may eqaaQy w^ describe it as 
 the derelc^aDent of oor ideas or oar cements. TThen 
 the chikl kanas aboat the halats ot hfe ot an animal, 
 beades devdt^ang ge&end prim^es as to the activi- 
 ties ol this animal, he is making faDer and mooe exact 
 his c(HicQ)t Of notioa c^ ^rhat the animal i5. In sim- 
 Oir fashicm, Adien the child is tao^t abtnt the hea- 
 Teoly bodies and leams tiie general psincq:^ 'which 
 goT»n the movemaits d the mocm and of the planets, 
 and dbtinguishes the movemoits of these bo«fies from 
 the ccanpaiatrre fixity of the stars, he i> making more 
 exact his coDoqition of the meaning of star ai^ planet 
 and moon. 
 
 Sdoice also creates conQepts. Sdenti&c work, in 
 imA, goes still beytmd the process of rendering con- 
 cepts more joecise and exact. In its hi^i» form it 
 means the acdoal oeatioo of new omcqits to esplain 
 the facts as they are oheerred. Moch of the science 
 with tihich we are &miliar uses ideas xthich could 
 never arise from the sensatious c» pacq>ticHis we get 
 frcHU objects. We may think of our idea of a talile, or 
 
NATURAL SCIENCE 255 
 
 of a chair, or of a horse, as developing from the per- 
 ception of a large number of these objects, and from 
 our experience in using them, or in responding toward 
 them. Such an idea as the atom, however, or of gravi- 
 tation, or of ether vibrations, we would never get by 
 such sensory experiences. These are creations of the 
 imagination, which are brought into being to explain 
 the events which we do observe in the physical world 
 about us. 
 
 This abstract fonn of science is beyond the compre- 
 hension of the child below adolescence. Scientific 
 investigation, and the thinking which results in the 
 development of these more abstract forms of concept, 
 represent a higher stage of development, both in the 
 history of science and in the life of the child, than the 
 simpler classifications and generalizations of those 
 events which can readily be observed. They require a 
 type of imagination which goes beneath the physical 
 facts which impress the senses, and which is dependent 
 on a larger amount of mental development than the 
 young child is capable of. We may say in a general 
 way that the science which has as its aim the explana- 
 tion of physical facts by the creation of such concepts 
 as these is beyond the child below the age of adoles- 
 cence, and that only the simpler forms are usually 
 grasp>ed even at this age. 
 
 Generalizations need to be tested. We have spoken 
 of the development of scientific principles as though it 
 consisted merely in generaUzation upon facts, and the 
 
256 PSYCHOLOGY OF COMMON BRANCHES 
 
 form of intellectual procedure which has its culmioa- 
 tion in induction. There is another procedure which is 
 continually used by scientific students, and which is 
 important for all kinds of scientific procedure. One 
 develops general principles, as has been said, by sys- 
 tematically examining the facts and attempting to 
 find a principle which will explain them. After this 
 has been done, however, the generalization is not 
 sufficiently certain until the principle which has thus 
 been found is tested. 
 
 Testing a proposed explanation is illustrated in the 
 diagnosis of a pupil's poor work. This double proce- 
 dure of seeking an explanation for observed facts and 
 then testing the explanation may be illustrated from 
 the experience of a teacher. The teacher discovers 
 that a pupil is doing very poor work. He first casts 
 about in his mind to find the explanation for this fact. 
 He may examine the home life of the pupil to see if he 
 has the proper surroundings and the proper encour- 
 agement. He may consider the physical conditions of 
 his life, the amount of his food, sleep, rest, and recrea- 
 tion. He may consider his mental capacity and the 
 question whether the work which is given to him is 
 suited to his general ability, or to the special type 
 of abihty which he may possess. He may examine 
 the pupil's interests and see whether he is distracted 
 from his work by other and more powerful inter- 
 ests. He may conclude, as a result of this examina- 
 tion, that the pupil is doing poor work because the 
 
NATTJEAL SCIENCE 257 
 
 work is not suited to his capacity. This, then, is a 
 generalization. He may now test this generalization 
 by changing the work in such a way that it will seem 
 better suited to the pupil. If this results in improve- 
 ment he may assume that the hypothesis which was 
 laid down was at least in a measure correct. 
 
 Another illustration may be found in the discovery 
 of the planet Neptune. We may take as another illus- 
 tration an example from the larger scientific world. 
 We are all famihar with the law of gravitation. This 
 is a generalization made upon a large number of occur- 
 rences, such as the falling of bodies to the earth, the 
 revolution of the moon about the earth and of the 
 planets about the sun. The law of gravitation received 
 a very remarkable confirmation through its appUcation 
 in one particular case. For a long time the movements 
 of the planet Uranus were found not to be in accord- 
 ance with the mathematical calculations of its course 
 on the basis of the law of gravitation. Various theories 
 were held to account for this, one of them being that 
 the irregularities in movements were caused by the 
 existence of another planet which had not yet been 
 discovered. Two mathematicians worked out theo- 
 retically the position and character of a planet which 
 would account for these irregularities in movement. 
 Astronomers then searched in the region of the sky 
 at which such a planet should be located and discov- 
 ered the existence of the planet Neptune. By this 
 means the correctness of the theory was confirmed by 
 
258 PSYCHOLOGY OF COMMON BRANCHES 
 
 the fact that the discovery of an object which previ- 
 ously had not been known was predicted and then 
 actually made. 
 
 Deduction supplements induction. This mental 
 process, by which we apply a general principle and 
 work out its implication in the facts of the world about 
 us, is called "deduction." These two forms of thinking 
 are both important in scientific generalization. The 
 one leads to the formations of generalizations; and the 
 other to their testing, and to either their confirmation 
 or rejection. 
 
 Summary of the child's development in scientific 
 thinking. Scientific thinking in its highest form may 
 be seen, from the previous description, to be the refine- 
 ment of forms of thinking which the child uses from 
 the beginning. We must not think of the scientific 
 method as something which is an entirely new devel- 
 opment at a certain period in a child's life, and which 
 amounts to a radical change or to the adoption of a 
 new form of intellectual activity. From the earliest 
 years the child begins to make generaUzations, to 
 form ideas, and to try out his generalizations by com- 
 parison with the facts of his observation. As he grows 
 older, he learns to observe in a more systematic 
 fashion, and to experiment, in order that his generali- 
 zations may be broader and more firmly founded. He 
 learns to look for problems in the events which he has 
 before taken for granted. As he grows still older, he 
 sees still deeper problems and can appreciate the 
 
NATURAL SCIENCE 259 
 
 search for concepts or ideas which will serve to illu- 
 minate or explain them. He is still making generaU- 
 zations, he is still forming ideas, but they are of a more 
 abstract character. He learns to see the connection of 
 events which previously have had no connection with 
 one another in his mind. He substitutes for the erro- 
 neous conclusions, which have been created by popu- 
 lar opinion to explain facts of experience, a more scien- 
 tific and exact method. His development proceeds 
 through the application of the general forms of think- 
 ing which he has used right along, but the application 
 of them becomes more regularly arranged, follows 
 better principles of procedure, and leads to more reli- 
 able results. 
 
 The practical and the theoretical in science teaching 
 
 The child's interest develops from the practical to 
 the theoretical. We have seen that the child's scien- 
 tific interest grows out of the desire to generahze and 
 to ex{>lain the facts of his experience. He is interested 
 first in the more immediate problems, and his atten- 
 tion is attracted to those situations which have a prac- 
 tical meaning and which call for activity on his part. 
 The interest in the generalizations of science is accom- 
 panied by still stronger interest in the apphcations of 
 these generalizations. The boy's interest in the theo- 
 retical principles of physics is subordinate to his inter- 
 est in wireless telegraphy or in X-rays; and the girl's 
 interest in the principles of chemistry is less keen than 
 
260 PSYCHOLOGY OF COMMON BBANCHES 
 
 her interest in the apphcation of these principles in 
 cooking. 
 
 The interest in practical applications is generally 
 recognized. This interest which pupils manifest in the 
 working of general scientific principles in the world 
 about them is generally recognized by teachers of 
 science in the elementary or the high school and by 
 writers of textbooks for elementary or high-school 
 pupils. A comparison of recent texts with those writ- 
 ten less than a generation ago makes this clear. A 
 glance at the illustrations of modem texts will show, 
 besides the diagrams which give a graphic representa- 
 tion of the abstract laws, and the cuts of laboratory 
 apparatus, illustrations of engiaes and telephones; 
 pictures of forests and lakes; of animals or articles of 
 food. 
 
 Science teaching may develop goieral piindples 
 from concrete problems or begin wi& general princi- 
 ples and then proceed to apply them. While the use of 
 a large amoimt of concrete material is a common 
 feature of the prevailing methods of teaching, there is 
 coming to be a shsup distinction in the way in which 
 this concrete material is used. The customary method 
 in the past has been to develop first the theoretical 
 and abstract scientific principles and aftraward make 
 application of them to the practical concerns of every- 
 day life. For example, the general principles of the 
 mechanical effects of heat are first developed and 
 they are then applied to explain the action of the 
 
NATURAL SCIENCE 261 
 
 steam engine through the expansion of water under 
 the influence of heat. 
 
 Beginning with general principles means teaching 
 the sciences separately. A consequence of this method 
 is that the pupil is at first introduced to the highly 
 differentiated branches of science. In the history of 
 scientific development the tendency is toward a 
 greater and greater spUtting-up of the whole field, due 
 largely to the interests of those who carry on advanced 
 scientific investigation. When we teach pupils by 
 beginning with the abstract, general principles, it is 
 natural to treat the sciences according to the scheme 
 of classification which has been gradually built up in 
 the course of the development of science. The conse- 
 quence of this mode of treatment is that the pupil is 
 introduced immediately to highly abstract aspects of 
 the physical world. 
 
 Illustration of the opposite procedure. The effort is 
 being made in many quarters to begin at the other 
 end, by introducing the pupil first to typical problems 
 as they arise in everyday life, and gradually develop- 
 ing the abstract generalizations from these. To use 
 the example which has already been cited, one would 
 first, in following out this procedure, introduce the 
 pupil directly to the study of engines, and out of this, 
 and other similar cases, arrive at the general mechani- 
 cal principles which serve to explain their action. 
 
 Concrete situations usually involve several sciences. 
 But there are other principles involved in the expla- 
 
262 PSYCHOLOGY OF COMMON BRANCHES 
 
 nation of the engine than the mechanical principles of 
 physics. Engines derive their energy from some form 
 of combustion. In steam engines the combustion 
 takes place outside the engine proper, while in gas 
 engines it takes place within the engine; but in both 
 cases the energy is released by changes in the composi- 
 tion of the fuel. The explanation of this phase of the 
 action of the engine requires the grasp of chemical 
 principles. Again, if we investigate the sources of fuel 
 energy, we are led to a study of the way in which com- 
 plex chemical substances are built up in the growth of 
 plants and stored in the wood of trees, or in the earth 
 in coal or oil. In this study we get into the province of 
 botany and even geology. 
 
 Two methods of procedure in this case are open. If 
 we begin with such concrete situations as this, two 
 forms of procedure are open. On the one hand, a full 
 explanation may be sought for all the problems which 
 arise, and the search may be pushed into whatever 
 field may need to be explored to reach the object; or, 
 on the other hand, each practical situation may be 
 used to illustrate only the general principle which is 
 most prominently revealed in it, and the situations 
 may be so selected as to illustrate a progressive and 
 coherent group of principles. Even the second method 
 would not involve the rigid separation of the principles 
 of the various sciences, but would necessitate a con- 
 tinuous intermingling and correlation. For example, 
 to understand the flow of sap in a tree it is necessary 
 
NATURAL SCIENCE 263 
 
 to have some grasp of the physical principle of capil- 
 larity. 
 
 The general principle is clear; the details remain 
 to be worked out. Just how the relation between 
 concrete situations and general scientific principles 
 will be worked out in detail remains to be seen. This 
 is a problem for the special workers in the field. A 
 widely used text in general science, that by Caldwell 
 and Eikenberry, makes the following division into 
 large topics: (1) the Air; (2) Water and its Uses; 
 (3) Work and Energy; (4) the Earth's Crust; (5) Life 
 upon the Earth. Without committing ourselves to 
 this or any particular choice of subjects, as a final list, 
 it is clear that the general procedure which is here 
 represented, of beginning with the objects of the pupil's 
 environment and the problems which they present, 
 and working from these concrete situations to the 
 general principles which serve to explain them, is the 
 procedure which is in accord with the development of 
 the child's scientific thinking as it has been described 
 in this chapter. It is also fairly clear that this involves 
 some breaking-down of the rigid limits between the 
 highly developed special sciences in the early stages 
 of the student's scientific work. After he has attained 
 some conception of the most important modes of the 
 working of the physical world, he is ready to pursue 
 the special laws of some particular class of facts in 
 greater detail and with greater precision, and to follow 
 some of the more abstract theories and speculations. 
 
QUESTIONS AND TOPICS FOR 
 DISCUSSION 
 
 CHAPTER I 
 
 1. Show that the different school subjects require of the child dif- 
 ferent kinds of learning. Think out illustrations of your own. 
 
 2. Can you give any evidence that learning, if it is properly super- 
 vised and directed, may be made more economical than it would 
 otherwise be? 
 
 S. Support by any argument you can the view that a knowledge 
 of the learning process is of value to the teacher. 
 
 4. Why is the teacher's childhood experience in the school not 
 suffident to give this knowledge? 
 
 CHAPTER n 
 
 1. Give all the illustrations you can of motor habits which are 
 trained in the schooL 
 
 5. Compare the complexity of the writing movement with the 
 walking movement. Why does the diild take longer to learn to 
 write than to walk? 
 
 3. What conditions determine the slant of writing? 
 
 4. If the same conditions operated, what would be the slant in left- 
 hand writing? 
 
 6. What important diange in the method of writing has been made 
 in order to conform to the demands of hygiene? How have 
 these demands been met subsequently in a different way? 
 
 6. Does "selection" of ^propriate movements mean conscious, 
 deliberate selection? If not, what is the method? 
 
 7. Give illustrations of inhibition in other kinds of behavior, sudi 
 as thinking. 
 
 8. Illustrate the value of rhythm. 
 
 9. Discuss the s^ing, "Practice makes perfect." 
 
 10. What changes in writing accompany the automatization of the 
 movement? 
 
 11. Discuss the statement, "If the child is trained in the correct 
 movement, the form of the letters will take care of itself." 
 
266 QUESTIONS AND TOPICS FOR DISCUSSION 
 
 12. Compare two methods of stimulating the child to a study of the 
 form of his writing. 
 
 13. IllustTate good form in other movements than writing. 
 
 14. Compare the two methods of grading the child's work. 
 
 15. Why should the correct habit be practiced in all writing? Put 
 this rule in the form of a general principle and illustrate from 
 other subjects of study. 
 
 16. Compare the movements made by a child of three years and of a 
 child of eight or nine and inquire whether the fundamental and 
 accessory theory explains the difference. 
 
 17. Considering the motor development of the child and the need of 
 making writing automatic, when do you think writing driU 
 should be emphasized mo-st? 
 
 18. Discuss the aim of bringing all the children of a grade op to a 
 grade standard and giving none drill who are above this stand- 
 ard. 
 
 CHAPTER m 
 
 1. Is perceptual learning well described as the acquisition of knowl- 
 edge? Compare it with learning the facts of history or geo- 
 graphy. 
 
 2. Give other illustrations to show that perception is not a matter 
 of passively gaining impressions. 
 
 3. Look up other definitions of apperception. Is there any reason 
 for retaining the term? 
 
 4. What is necessary, besides the presentation of an object to the 
 senses, for the success of object teaching? 
 
 5. How are recognition and appreciation related to expression, as 
 illustrated by drawing? 
 
 6. On what fact does the difficulty in representing perspective rest? 
 
 7. Is the nature of the child's early drawing due solely to his in- 
 ability to master technical difficulties? 
 
 8. Gather or observe some drawings of young children and show 
 what is meant by describing them as symbolic. 
 
 9. Compare diagramming with the child's early drawing. 
 
 10. Does interpretation as a feature of perception mean the same as 
 the interpretation of a poem? 
 
 11. If you have opportunity, practice with some illusion until it is 
 overcome or reduced in amount. The Poggendorf illusion, or the 
 illusion of the circles, mentioned in chapter i of Judd's Genetic 
 Psychology for Teachers, are good ones to use. 
 
 12. What is the chief motive for improvement in perception? ^"hat 
 b the place of formal training in sensory discrimination? 
 
QUESTIONS AND TOPICS FOR DISCUSSION 267 
 
 13. If it is available, consult Winch's Children's Pereeptions (War- 
 wick and York, Baltimore) and find illustrations of any princi- 
 ples of this chapter. 
 
 14. Why is sense training to be distinguished from perceptual train- 
 ing? 
 
 15. Get some facts, if you can, to show the need of diagnosing and 
 correcting sensory defects. 
 
 CHAPTER IV 
 
 1. Compare formal drill and the expression or the recognition of 
 meaning in both reading and writing. 
 
 2. Should formal drill precede, accompany, or follow the recogni- 
 tion of meaning? 
 
 3. Is the statement, "The letters need not be learned first," equiv- 
 alent to saying, "The letters need not be learned"? Why? 
 
 4. Is learning to say over the alphabet what is meant by learning 
 the letters, in question 3? 
 
 B. Compare the child's progress in learning to recognize a word with 
 the process in learning the figure in chapter m. 
 
 6. Mention three stages in the development of the alphabet. 
 
 7. Find an illustration of phonetic drill in a first-grade reader and 
 . describe it. 
 
 8. Why is the incddental metiiod uneconomical when used alone? 
 
 9. Compare the type of eye movement in reading with other types 
 of movement you may be able to observe. Is the reading habit 
 fouid anywhere else? 
 
 10. What other activities correspond to the reading of the sentence 
 as a whole? 
 
 11. Why do you think oral reading has been so prominent in the 
 school? 
 
 12. Is oral reading of equal value in different stages of the child's 
 development? Why? 
 
 13. Measure your rate of reading and your ability to reproduce 
 what is read when reading carefully, at ordinary speed, and 
 rapidly. Try the experiment with different kinds of subject- 
 matter. Do your results agree with the conclusions of the 
 chapter? 
 
 14. In what chiefly do the upper grades excel the lower ones in 
 reading? 
 
 16. How are the mechanics of reading developed? 
 
268 QUESTIONS AND TOPICS FOR DISCUSSION 
 
 CHAPTER V 
 
 1. Supplement the discussion in the book by suggesting a method 
 of teaching the child to sing from ear. 
 
 2. Test the ability of several people, first, in the recognition of 
 absolute pitch, and, second, in the recognition of intervals. 
 Compare the amount of erroi in the two cases. 
 
 3. Similarly, test the ability of several persons to strike a single 
 note or an interval from the printed score, and compare the 
 errors. 
 
 4. Is the discrimination between the whole and the half steps on 
 the musical scale a clearly recognized matter in the mind of the 
 person who has not had special musical training? 
 
 5. Can you show that, while the recognition of diffsrences in inter- 
 vals may not be explicit, the untrained person nevertheless uses 
 the conventional scale as the basis of his recognition of musical 
 melody? 
 
 6. What analogy is there in another form of learning already stud- 
 ied to the practice of deferring formal instruction in the scale 
 until the child has gained some reading ability? 
 
 7. What is the chief difficulty incident to the use of different keys? 
 
 8. Is formal instruction in scales and keys desirable? Why? 
 
 9. Name all the cases of rhythmical involuntary activities you can. 
 What inference is suggested? 
 
 10. What is there in the appreciation of rhythm in music besides 
 the mere understanding of the meaning of musical notation? 
 
 11. Is there a sharp distinction between harmony and disharmony? 
 
 12. Why is tone quality not one of the chief objects of musical train- 
 ing in the school? 
 
 13. If a child cannot distinguish the pitch of middle C and C sharp, 
 what would you advise regarding his musical training? How 
 would you determine his ability in pitch discrimination? 
 
 CHAPTER VI 
 
 1. May inaccurate spelling be adequate for reading and not for 
 writing? Illustrate. 
 
 2. What are the movements which may be associated in spelling? 
 
 3. Why must learning to spell English words be in a measure 
 arbitrary? 
 
 4. Examine the words in some spelling book, — or better, two 
 spelling books, an older one and a recent one, — and estimate 
 the proportion of the words that are in common use in the writ- 
 ing of the average person. 
 
QUESTIONS AND TOPICS FOR DISCUSSION 269 
 
 B. Why should the child, so far as possible, learn to spell by sound, 
 analogy or rules? 
 
 6. Why were the inferences from the Philadelphia investigation 
 not conclusive? 
 
 7. Compare the essential principles of drill in spelling and in writing. 
 
 8. Cite any illustrations you can of children's enjoyment of drill. 
 
 9. Why is a variety of modes of presentation best? 
 
 CHAPTER Vn 
 
 1. Show some of the ways in which the child's imagination is 
 stimulated before he enters school. When does imagination 
 develop? 
 
 2. Compare memory and imagination. 
 
 3. Illustrate further verbal imagination. 
 
 i. Investigate differences in imagery among persons of your ac- 
 quaintance, and report. 
 
 5. Is it correct to say that the child is more imaginative than the 
 adult? Amplify your answer. 
 
 6. Is biography history? 
 
 7. How do you think of events at different past and future dates? 
 How is the time represented in your mind? 
 
 8. Make an experiment upon the time sense of another person by 
 asking him to estimate an interval when he does not know, and 
 another when he does know, that you are observing him. 
 
 9. Describe your notion of the following time periods: second, 
 minute, hour, day, week, month, year, century. 
 
 10. What does simplicity in early history mean? 
 
 11. Make a brief outline of beginning history that would conform 
 to the principles laid down in the chapter. 
 
 12. Illustrate methods of developing the simpler form of the his- 
 torical sense. 
 
 13. How is tolerance, historical or otherwise, developed? 
 
 14. Is the higher form of the historical sense connected with the 
 grasp of historical develc^ment? 
 
 Id. Illustrate helpful and futile use of sources with high-school 
 pupils. 
 
 CHAPTER Vm 
 
 1. Can you show that the understanding of physical and commer- 
 cial geography is dependent upon a knowledge of place geo- 
 graphy? 
 
 2. What is the practical application of the fact that localization oi 
 places is the outgrowth of the sense of bodily position? 
 
270 QUESTIONS AND TOPICS FOR DISCUSSION 
 
 3. Relate any case of false orientation you have experienced and 
 interpret your experience. Did false orientation have to be 
 readjusted piecemeal? 
 
 4. Compare cases in which your sense of direction was good with 
 cases in which it was poor, and explain the difference. 
 
 B. How may the gap between experience with a narrow range of 
 objects and the notion of a broad region be bridged? 
 
 6. If maps are used abstractly by adults, why need we try to give 
 them concrete meaning to the child? 
 
 7. Outline briefly some lessons in home geography to show their 
 general nature. 
 
 CHAPTER IX 
 
 1. Make a list of other abstract ideas besides nmnber, — if iieces- 
 sary, after the consultation of a textbook on psychology, — and 
 point out their common feature. 
 
 2. Mention other illustrations of objects used as counters. 
 
 3. If symbols imply the abstractness of fin idea, have we met any 
 abstract ideas in connection with the subjects previously dis- 
 cussed? In what way is number more abstract than these? 
 
 4. Show the importance of counting in the child's early number 
 development. 
 
 5. Use X and y as number symbols for 10 and 11 in order to carry 
 the unit group to 12 instead of 10; turn the numbers 47 and 58 
 into terms of this notation. Turn the numbers 12 and 23 into 
 the new notation; multiply and turn the answer into ordinary 
 symbols to prove. 
 
 6. Illustrate the multiplication of 4 by 5 by using the two types of 
 concrete experience, measurement, and grouping. 
 
 7. Illustrate the number 23 by groups of dots. 
 
 8. How far do you think it is possible to go in leading the child to 
 an understanding of the niuuber symbols and processes? 
 
 9. Mention several forms of number drill. 
 
 10. What are the reasons for treating addition and multiplication 
 before subtraction and division? Is the implication that the 
 study of the first two should be completed before the second 
 two are studied? 
 
 11. What is a fraction? 
 
 12. Why are percentages more easily manipulated than other frac- 
 tions? 
 
 13. What is the essential difference between algebra and arithmetic? 
 
 14. State and illustrate some of the processes which can be em- 
 ployed to modify the form of an equation. 
 
QUESTIONS AND TOPICS FOR DISCUSSION 271 
 
 15. Make the following equation concrete by substituting for the 
 algebraic symbols numerical terms and show that the equation 
 (x-\-y) {x—y) = x^—y^ holds true. 
 
 16. Illustrate a method by which the child may be led to recognize 
 through concrete experience what is the sum of the angles of a 
 triangle and of a quadrilateral. 
 
 17. How might the relation of the length of the diameter to the 
 circumference of a circle be approximately determined by a 
 concrete method? 
 
 18. Compare the stages in the solution of an original problem in 
 geometry with the stages in the reasoning problems given by 
 Dewey in How We Think, chapter VI. 
 
 19. Apply to some other field the distinction between problem 
 solving and following another's demonstration. 
 
 20. Look up some problem in arithmetic, and distinguish between 
 the understanding of the conditions of the problem and of the 
 mathematical process used in solving it. 
 
 CHAPTER X 
 
 1. Give three scientific generalizations and three generalizations in 
 other fields. 
 
 2. Mention other expectations which the child forms and which 
 imply some generalization upon his experience without an 
 explicit formulation. 
 
 3. Collect and compare definitions from children of different ages, 
 or find instances in child-study literature. 
 
 4. Can you show the effect of names in stimulating concept forma- 
 tion from your experience in this course.' 
 
 fi. Compare your explanation of some fact in a field in which you 
 have studied with the explanation you can give of a fact in an 
 unfamiliar field. 
 
 6. State some popular beliefs which rest on superficial observation. 
 
 7. Give one other illustration than those given in the book of the 
 light thrown by scientific study upon the affairs of everyday life. 
 
 8. How much original investigation of a scientific sort do you 
 think the child can do independently? Is there any intermediate 
 type of investigation between independent research and learning 
 from others? 
 
 9. Give an illustration of your own of experimentation. 
 
 10. Show that induction and deduction may be used in the investi- 
 gation of some practical problem. 
 
 11. Is it correct to say that the child has no theoretical interest? 
 
 12. Do you think the natural order is from the theoretical interest 
 to the practical application or the reverse? 
 
INDEX 
 
 Abacus, 196. 
 
 Absolute pitch, 100. 
 
 Abstract ideas, 150, 173, 179 
 
 S-. 221. 
 Accessory movement, defined, 
 
 30. 
 Activity in learning, 36, 45. 
 Addition, 201 Jf., 218. 
 Age, changes with, 29 g., 43, 46, 
 
 69, 95, 112 /., 141 /., 146 ff., 
 
 156, 159, 242/.. 256. 
 Algebra, 209/. 
 Alphabet, 74/. 
 Angell. J. R.. 160. 
 Apperception, 40; defined, 42. 
 Application in science teaching, 
 
 260/. 
 Arithmetic, 1S8/. 
 Arm position in writing, 11. 
 Association, 116/., 127. 
 Attention in learning, 126. 
 Automatic activity, defined, 22. 
 Automatization, 18, 22. 
 Ayer, F. C, 49. 
 Ayers, L. P., 33, 131. 
 
 Barnes, E., 66. 
 Binet, A., 146, 178. 
 Biography, 144. 
 Bourne. H. E., 160. 
 
 CaldweD, O. W., 263. 
 Cardinal number, 187. 
 Cardinal points, 166, 167/., 176. 
 Causes in science, 251 /. 
 Chinnappa, S. P., 47. 
 CUrk, A. B., 66. 
 aeveland, spelling in, 126, 128/. 
 Conant, L. L., 186. 
 Concept. 241 if., 254. ^ 
 
 Concrete experience, 160, 173, 
 
 191, 217, 224, 234, 260. 
 Congdon, C. H., 105, 114. 
 Copy in handwriting, 24. 
 Cormnan. O. P., 124, 131. 
 Counting, 182. 
 Courtis, S. A., 234, 237. ' 
 Cowling, D. J., 66. 
 
 Dancing, 107. 
 
 Dearborn, W. P., 93, 97. 
 
 Decimal system, 189, 193, 207. 
 
 Deduction, 258. 
 
 Definitions, child's early, 242. 
 
 Dewey, J., 238. 
 
 Diacritical marks, 80. 
 
 Diagramming, 48. 
 
 Diffusion in learning, 13. 
 
 Digits, 186. 
 
 Discrimination, 67, 64, 112. 
 
 Division, 201 /. 
 
 Double images, 65. 
 
 Drawing, analysis of, S4/., 42/. 
 
 Drill, 68, 78, 96, 122/., 200. 
 
 Eikenberry, W. L., 263. 
 
 Equation, 213/. 
 
 Euclid, 223. 
 
 Excursions, 177. 
 
 Experimentation, 249/ 
 
 Eye adjustments in writing, 10. 
 
 Eye movements in reading, 82. 
 
 Famsworth, C. H., 114. 
 Feebleminded child, 66. 
 Form of letters in writing, 20, 24/. 
 Fractions, 206 /. 
 Freeman, 26, 33, 237. 
 Fundamental and accessory 
 movements, 29. 
 
274 
 
 INDEX 
 
 Fundamental movement, de- 
 fined, 30. 
 
 Fundamental operations in arith- 
 metic. 194,201/. 
 
 General ideas, 87. 
 Generalization. 227 /., 245, 255; 
 
 defined. 240. 
 Geography, physical and com- 
 
 meroal. 161 /. 
 Geometry. 222/. 
 Globes, 171 #. 
 Good form in learning, 26. 
 Grouping in number, 187, 189 /., 
 
 193/.. 205/.. 208. 
 
 Habit. 6, 28. 
 Hall, G. Stanley, 63, 66. 
 HaUeck. R. P.. 62, 66. 
 Handwriting, speed. 19, 26. 
 Handwriting and spelling, 115, 
 
 lis. 
 
 Handwriting movement, 7, 25. 
 Harmony, musical, 109 jf. 
 Hicks, Warren E., 125. 
 Historical development, grasp 
 
 of, 157. 
 Historical sense, ISSff. 
 Home geography, 173/. 
 Huey, E. B., 75/., 97. 
 
 Illusion, defined, 54. 
 Imagination. 132 Jf.. 140, 161/.; 
 
 defined, 133, 140. 
 Incidental method, 78, 122. 
 Individual differences, 32, 50, 
 
 110, 112/., 137. 
 Induction, 253. 
 Inhibition, 13. 
 
 Inner speech in reading, 85 /. 
 Intervals in pitch, recognition 
 
 of, 100. 
 
 Jenkins. F., 97. 
 Jones. W. F.. 131. 
 Judd. Charles H., 33, 66, 77, 97, 
 178, 194, 237. 
 
 Keys, musical, 103/. 
 Kir^trick, E. A., 57. 
 
 Language, I3S, 140, 243. 
 Lloyd, Sam, 215. 
 Lukens, H. T., 66. 
 
 McCldlan, J. A., 238. 
 Maps, 171/. 
 Meanings, 22, 58, 67/.' 
 Measurement, 195, 222/. 
 Mechanical drawing, 48. 
 Melody, 100/. 
 Memorizing, 115, 134, 138. 
 Monroe. W. S.. 238. 
 Motor coSrdination. 15. 
 Multiplication, 201/., 220/. 
 Myers, G. W., 220. 
 
 Names, 243. 
 
 Natural science, 162, 239/. 
 Negative numbers, 218. 
 Neighborhood history, 152/. 
 Neptune, discovery of, 257. 
 Notation, musical, 101, 104, 108. 
 Notation, number, 190, 207. 
 Number, 149/., 179/., 251. 
 Number names, 182/., 186. 
 
 Object in perc^tion, 55. 
 Object teaching, 40. 
 Observation, 59, 249 /. 
 One-to-one correspondence, 183. 
 Oral expression, 70. 
 Oral reading. 86/. 
 Ordinal number. 187. 
 Orientation. 163/.; defined. 164. 
 
 Percentage, 207. 
 Perception. 51 /., 116. 
 Perceptual learning. 36/. 
 Perspective, 43. 
 
 Philadelphia, spelling in, 124/. 
 Phonetics, 73/., 79. 119/. 
 Picture writing, 75. 
 Posture in writing, 11. 
 Practice periods, 33. 
 Presentation, method of, 129/. 
 Preyer, S. 243. 
 
 Principles, general, 241 /., 260. 
 Problem solving. 229/., 252. 
 Pronation, 9. 
 
INDEX 
 
 875 
 
 Proof, 228 f. 
 
 Pythagorean theorem, iiiff. 
 
 Quality in handwriting, 26. 
 Quantity, 185. 
 
 Ratio, 204 Jf., 213. 
 Reading efficiency, 89 ff. 
 Reading and spelling, 118. 
 Repetition in learning, 17, 126. 
 Rhythm, 16, 18, 106/. 
 Rice, J. M., 123/., 131. 
 Rowe, S. H.. 33. 
 
 Sargent, Walter, 46, 66. 
 Scale, musical, 101 /. 
 Scope of attention, 188 /. 
 Seashore, C. E., 112/., 114. 
 Selection in learning, 12. 
 Sensation, 51, 134. 
 Sense training, 61 ff. 
 Sensori-motor activity, 6. 
 Sensori-motor coordination, 8, 
 
 15. 
 Sensory defects, 64. 
 Sentence reading, 73, 84. 
 Silent reading, 86/. 
 Singing by ear, 98 /. 
 Slant in writing, 9. 
 Smith, D. E., 210, 238. 
 Sound localization, 56. 
 Sources in history, study of, 
 
 158/. 
 
 Spatial imagination, 153, 169 /. 
 
 Spelling in reading, 81. 
 
 Spencer, H., 238. 
 
 Stimulus, 6. 
 
 Subtraction, 201/., 218/. 
 
 Suggestibility, 69. 
 
 Suzzalo, H., 131. 
 
 Symbolism in early drawing, 47. 
 
 Symbols, 75, 182/, 196, 211/. 
 
 Taylor, I., 77. 
 
 Temporal imagination, 146 /. 
 
 Thorndike, E. L., 33. 
 
 Time sense, 146. 
 
 Tolerance, attitude of, 155/. 
 
 Tone quality. 111. 
 
 Transfer of training, 128. 
 
 Trial and success (trial and error) 
 
 method, defined, 17. 
 Types, mental, 60. 
 
 Uniformity in writing, 20. 
 Unit, 184/., 190. 
 Uranus, planet of, 257. 
 
 Waldo, K. D., 90, 96, 97. 
 Wallin, J. E. W., 124/., 131. 
 Whitehouse, W. A., 26, 33. 
 Word learning, 71. 
 
 Young, J. W. A., 238. 
 
 Zook, S. A., 127.