LB 1027 
 .B3 
 Copy 1 
 
WALTER P. BECKWITH 
 
DRILL 
 
 A CHAPTER OF PEDAGOGY 
 
 By WALTER P. BECKWITH 
 
 Principal of the State Normal 
 School at Saleiti, Mass. 
 
 » 
 
 SALEM, MASS. 
 Newcomb & Gauss, 1'rinters 
 
 1905 
 
LIBRARY oToONeHessJ 
 I wo Copies Meceivou I 
 
 MAR 2 1905 
 
 ^ Coi>yri£(iv triuy 
 
 CO 
 
 XXc. 
 
 
 c^^ 
 
 Copyright, 1905 
 By Walter P. Beckwith 
 
 Limited Edition 
 
 No. 
 
DRILL. 
 
 The ultimate result aimed at in mental training 
 is power. There are certain immediate or direct 
 results, such as the acquisition of knowledge and 
 the mastering of skill, and these are sometimes undu- 
 ly exalted in the minds of both teacher and pupil. 
 But it cannot be doubted that the best, the richest 
 and the highest result is the end to which the effort 
 made in acquiring knowledge and in mastering skill 
 contributes ; the knowledge and skill, so often esti- 
 mated to be the ends, are really, in a large view, 
 merely the means to the attainment of a higher end, 
 — the ultimate result of the process called education. 
 
 Not even the teacher is always conscious of this 
 ultimate end, — still less is the pupil. The activity by 
 which knowledge is acquired and skill mastered is 
 usually at the focus of the thought and consciousness 
 of all the parties concerned, so^that it is not strange 
 that many people,- — even intelligent people, — some- 
 times lose sight altogether of the most important 
 purpose. The oversight is promoted by the further 
 
fact that it is comparatively easy to test the imme- 
 diate results of the search for knowledge and the 
 effort for skill, while the growth of power is by its 
 nature a somewhat baffling and apparently intangi- 
 ble process. In every spiritual experience it is diiifi- 
 cult to observe with intelligence and to estimate 
 with justice and accuracy what one has attained, — 
 and the higher and finer the phenomena with which 
 we are dealing, the greater the diflficulty becomes. 
 
 This is not to say that the knowledge and skill 
 are in themselves unimportant, or that the processes 
 by which they are acquired are indifferent in effi- 
 ciency and value. On the other hand, the richer 
 the knowledge acquired, the more delicate the skill 
 mastered, the more rational the processes by which 
 both are sought, the finer and nobler will be the re- 
 sults in the form of power. It is our purpose, at this 
 time, to make a distinct application of this fact to 
 the teacher's work, and to show how some portions 
 of it may be done in a more reasonable manner than 
 is always the case, and according to such principles 
 as to yield a greater return. 
 
 Knowledge, — using the term in a very compre- 
 hensive sense, — is the first result of mental activity. 
 The teacher's part, in the acquisition of knowledge 
 by the pupil, is the work of instruction. The teacher 
 
himself is a mediator between the pupil and the sub- 
 ject or object to be known, and it is his function to 
 bring that subject or object into such relations with 
 the appropriate faculty that knowledge may be the 
 result. Many of the questions which arise at this 
 point as to ways and means are really answered by 
 natural inference ; other problems deal simply with 
 the conditions of effective effort. 
 
 The work of instruction, technically considered, 
 is complete when the right relations have for the 
 moment been established between the knowing 
 mind and that which is to be known. The pupil 
 then has a momentary grasp of what he is being 
 taught. But it is very evident that this grasp may, 
 and. in most cases probably does, fall far short of 
 what is necessary, if he is either to possess the knowl- 
 edge in any proper sense of the word, or to have 
 such facility in its employment as to make it really 
 valuable, or to gain any genuine and permanent 
 power from the exercise of his mental faculties. 
 
 The special purpose of instruction is a mastery 
 of general facts or principles. It employs a process 
 which is inductive, — speaking in a general sense ; it 
 is the method of the discoverer, of the explorer ; but 
 it may fail of complete conquest, and it certainly 
 does not enrich the conquered province by the apper- 
 
ceptive processes of the learner himself and give to it 
 that value which comes from assimilative interpre- 
 tation and from application. It is essential to 
 rational processes of learning, but it cannot be 
 regarded as the entire process of learning. 
 
 Much, therefore, remains for the learner to do, 
 and in the necessary further activity, there is much 
 work for the teacher, and the pupil still needs the 
 help of his teacher. The necessary further direction 
 has been given the name of drill, the purpose of which 
 is to bring all that has been learned within the ready 
 command of its possessor and to give him skill or 
 facility in its use. 
 
 The view frequently, — perhaps even commonly, — 
 held of the nature and functions of drill has unfortu- 
 nately been both imperfect and erroneous. In the 
 minds of many it has been supposed to signify 
 merely that mechanical and merciless repetition 
 which in reality ought to play a very small part, 
 relatively speaking, in school work, and which is 
 necessary with only a small portion of the subject- 
 matter with which schools deal. Repetition, in some 
 form or other, either open or concealed, is indeed 
 the essential and the distinguishing quality of drill, 
 and there are certain foims of knowledge as to 
 which it seems necessary to make it very effective, 
 
 6 
 
even if it proves to be somewhat irksome to the 
 pupils. The perfect command of certain arbitrary 
 symbols, — like figures, letters, signs and the like, — 
 and of certain elementary and frequently used items 
 of knowledge, — like the facts of the multiplication 
 table and the formation of plurals, — is so absolutely 
 essential that such command must be secured at 
 any cost of time or effort. The essential unattrac- 
 tiveness of even such work as this may be somewhat 
 mitigated by simple devices, but sight must not be 
 lost of the end to be attained. 
 
 It is, however a great mistake to suppose either 
 that this is the only department of school work 
 wherein drill is necessary, or that, being necessary 
 in other departments, it must be carried on in this 
 manner. From one or the other of these mis-con- 
 ceptions, arises the unflattering opinion, held by 
 both teachers and pupils, of drill. 
 
 The fact is, as we shall attempt to show, that 
 instruction and drill are supplementary to each 
 other in the work of the teacher, — the former being 
 inductive, the latter deductive ; the former giving 
 one the grasp of principles, the latter skill in their 
 application ; the former being theoretical, the latter 
 practical ; the former being the method of the explorer, 
 the latter of the settler ; the former making conquests 
 
of the unknown, the latter reducing it to the service 
 of truth and putting it into its proper place. 
 
 If, then, that part of the teacher's work which is 
 properly called drill is so extensive, varied, and im- 
 portant as the above contrasts would signify, it is 
 very plain that it must have other varieties and 
 other means of operation than mere repetition, 
 mechanical and unadorned. Bearing in mind its pur- 
 pose, — to give the pupil full mastery of the general 
 principles to which he has been introduced by 
 instruction, so that they may be present, not simply 
 for recall as verbal forms, but may be really a part 
 of the working equipment of the learner, — let us 
 inquire how this purpose may be attained. 
 
 It should be clear to every thoughtful student of 
 mental activities in himself and in others that merely 
 verbal mastery does not imply a sufificient degree of 
 possession. An elementary idea cannot be originally 
 received except through the senses ; a complex idea 
 cannot be communicated through its word, unless its 
 elements have been previously mastered and unless 
 the relations between them are clearly understood. 
 '' Ideas before words " is a fundamental requisite of 
 good learning, as well as of good teaching. In the case 
 of complex ideas an understanding of the relations 
 according to which the elements are combined is as 
 
 8 
 
essential as a mastery of the elements themselves. 
 This complete, working mastery is not assured by 
 the ability to recall and repeat the statement of a 
 given principle, even if it has been formulated as 
 the result of an excellent inductive process. No 
 induction likely to be employed in teaching is exten- 
 sive enough to assure a working command of a 
 general principle, — especially of one which is fairly 
 complex in its nature and far-reaching in its appli- 
 cation. One may seem to secure such a command ; 
 for the moment he may actually comprehend the 
 contents and bearings of the new truth, but the 
 experience of every teacher will plainly show that 
 such a command is extremely likely to be incomplete 
 in its nature and fleeting in its duration. 
 
 The inductive process needs to be supplemented 
 by deduction. The principle needs to be tested by 
 other applications, — differing in non-essential qual- 
 ities from the cases previously employed. Has the 
 child learned that the price multiplied by the quan- 
 tity equals the cost ? It is not enough that he knows 
 this for a single article at a given price and his 
 reflections regarding it must not be narrowed by 
 such conditions. He cannot be said to know the 
 principle, in the proper sense of the term, until his 
 applications of it, with any article at any price, are 
 
independent of any conscious re-statement, or even 
 of any conscious re-thinking of the verbal form of 
 the principle. 
 
 Has a pupil been taught, from the study of a few 
 examples, whose qualities and characteristics he has 
 well mastered, the nature of a river system ? This 
 inductive process will not insure his future command 
 or recall of the essential elements of that idea. His 
 future work must be adapted to do more than to 
 test his command of what he has already studied ; 
 it must make sure that he will be able to measure 
 other examples apparently similar by the standard 
 of his induction and to determine whether or not 
 they fall within its conditions. 
 
 A great variety and number of other illustrations 
 of the same sort, easily obtained, might not serve to 
 make the point more clear or emphatic. 
 
 It is not intended to disparage the inductive ele- 
 ment of the teacher's work. Much teaching is 
 doubtless faulty and ineffective by reason of imper- 
 fect inductions. It fails properly to lead the pupil 
 up to the mastery of general ideas and principles, 
 or, ignoring entirely the inductive process, it authori- 
 tatively declares the same. But, while all this is 
 true, it is at least a question whether teaching is not 
 quite as often weak and ineffective because the 
 
 lO 
 
teacher often regards his work as complete when 
 the generalization has been secured, by fair means^ 
 or by foul, and its statement extorted from the child. 
 
 The mistakes in this phase of teaching are not all 
 made in the elementary schools. In the high 
 schools, and even in the colleges, the work in the 
 sciences themselves, strange to say, is not infre- 
 quently open to the same criticism. The error 
 arises from the attempt to cover too much ground. 
 Many a course, in the higher institutions of learning, 
 would be far more profitable to those who pursue it, 
 if it presented fewer principles and insisted upon a 
 greater variety and thoroughness of applications. 
 
 The exceeding prominence of the lecture system, 
 supplemented, as it is, by written examinations for 
 testing the proficiency of pupils and students, coupled 
 with a meagre amount of laboratory and other indi- 
 vidual and independent work, contributes to the 
 partial failure of teaching on the deductive side. 
 Laboratory exercises and other forms of nominally 
 independent work that are offered are often so 
 weakened and emasculated by excessive minuteness 
 of direction and supervision as well-nigh to destroy 
 their value as agencies for the development of indi- 
 vidual power. Poor teaching is not made good by 
 giving it the laboratory label. No considerable 
 
observation of much of the work so designated is 
 necessary to convince an unprejudiced observer that 
 it is quite as easy to fritter away time and to secure 
 inadequate and unsatisfactory results in the so-called 
 laboratory courses as in those that bear the older 
 and more unpretentious designations. Facility of 
 manipulation, fullness of observation and accuracy 
 of inference undoubtedly require careful supervision 
 and direction, but these are elementary and prepar- 
 atory. A course which ceases at the point when 
 some slight power in these particulars has been 
 attained, which does not enable the worker to go 
 on with some individual and independent success 
 in testing and discovering other applications of the 
 principle he is studying has very slight value in the 
 development of power. 
 
 So-called laboratory work in scientific subjects is 
 also often very defective and unsatisfactory on the 
 expression side of training in the conventional forms 
 of language. If the study of science has the value 
 it is supposed to have, the student of such branches 
 is able to express his thoughts with clearness, vigor 
 and directness. Surely it is not going beyond the 
 bounds of truth to say that this result is rarely at- 
 tained ; the note-books of students in such subjects 
 are very often exceedingly faulty in these respects. 
 
 12 
 
One often feels in examining them that only sUght 
 attention has been given to this part of the work and 
 that the teachers themselves must either overlook 
 or ignore its great importance. 
 
 In excessive eagerness to make a given course 
 comprehensive and complete is to be found the 
 explanation of these failures. In other words, the 
 work ceases with a verbal mastery of the principle 
 involved, — ^a mastery as fleeting as it is imperfect. 
 
 Not many places, indeed, may be found where 
 all pretense of using the inductive method in 
 instruction is abandoned and where the learners are 
 simply directed to " learn the rule and then do just 
 what it says," — as was formerly very common. But 
 after the illustrative and explanatory examples have 
 led to the induction desired, it is still very common 
 for the teacher to delude himself and his class with 
 the belief that the work is complete. The mistake 
 consists in a failure to recognize the fact that in 
 true learning induction and deduction are not two 
 methods. They are, instead, two essential parts of 
 one method ; the deduction is as necessary as the 
 induction ; drill can no more be omitted than in- 
 struction. 
 
 An application of this direction to the teacher's 
 work does not contradict the general fact that drill 
 
 13 
 
always involves repetition. If one is endeavoring 
 to fix in his mind the form of an arbitrary character, 
 or the elementary and frequently used fact that 
 6 plus 7 equals 13, it is easy, of course, to recognize 
 the existence and use of repetition in the drill which 
 is given to secure the desired end. It is not, how- 
 ever, elementary and isolated facts alone that can 
 be repeated. Principles or general ideas are sus- 
 ceptible to the same treatment, and that is precisely 
 what they receive in the applications that should 
 be made of them when a temporary and verbal 
 mastery has been secured. It makes no difference 
 in the method of treatment from what department 
 of learning the principle is derived. All branches 
 of science and all other forms of knowledge which 
 are susceptible of being reduced to any kind of 
 generalizations call, according to their content and 
 their relations, for the same method of treatment 
 One easily sees an added dignity given by this 
 view to the work of drill, and it ceases to be in his 
 view a merely mechanical exercise. Because of 
 the necessary increase of variety, the interest of 
 the learner is vastly stimulated; because of his 
 added interest, a new pleasure, previously unknown, 
 will be experienced. Learning ceases to be drudg- 
 ery and becomes a process of the utmost attractive- 
 
 14 
 
ness. Genuine, thorough-going activity of the 
 mind is not irksome ; the parrot-like repetition of a 
 task, without variety or life, is always irksome. 
 The mature mind may make a secondary or derived 
 sort of interest serve the purpose; but the child 
 cannot do so, and even the adult is conscious of the 
 added effort and the consequent loss of fruitfulness 
 in his labor. 
 
 But there are other possibilities for fixing, clari- 
 fying and rendering practical the knowledge that 
 may be acquired, which should also be regarded as 
 coming within the range of drill. These consist in 
 a study of the various relations which exist between 
 different items of knowledge, whether these be 
 separate facts or generalizations. It is well to 
 remind ourselves that isolated facts, or even isolated 
 generalizations, are comparatively useless, and that, 
 therefore, our knowledge of such is also com- 
 paratively useless, unless it is brought into its 
 appropriate relations, in our thought, with other 
 facts or generalizations. This is only to say that 
 scientific knowledge is more valuable and effective 
 than ordinary knowledge. The acquisition of 
 knowledge, indeed, must begin with its elements; 
 this kind of work is characteristic of the young 
 child's activity. But even the knowledge of the 
 
 15 
 
young child must have its organization begun early. 
 There is no era in the development of a human 
 mind when it suddenly comes into the possession 
 of knowledge in its scientific form. The percep- 
 tion of scientific knowledge is, indeed, more charac- 
 teristic of and appropriate to the study of a later 
 period than at the beginning; but the beginning 
 should recognize so clearly the end to be sought 
 that the teacher may be able to apprehend without 
 error the part finally to be taken by each new 
 acquisition in the complete scheme. 
 
 It is only by understanding the vital and essential 
 relations between different ideas and thoughts that 
 an apprehension of the scientific conclusion can be 
 secured. It is our ideas, therefore, of the relations 
 of separate items of knowledge, that are of greatest 
 importance. We cannot, in fact, be said to know 
 a given truth, unless we understand its relations to 
 other truths. These relations are made evident 
 through comparison, and comparison is the very 
 essence of the act of thinking. Speaking of the 
 elements of knowledge, it is the absence of those 
 ideas which are the product of comparison that 
 makes the difference between the knowledge of a 
 child and that of an adult, or between the knowledge 
 of the desultory observer and that of a thorough 
 
 i6 
 
scientist. It is this power of apprehending relations 
 that is characteristic of a true scientist. 
 
 If this fact is accepted, there is no reason why 
 this form of study should not be recognized as a 
 valuable form of drill, which we have defined as the 
 means whereby knowledge is fixed in the human 
 mind and made available for skillful and facile use. 
 
 It is not a form to be used separately from and 
 independently of the forms already described and 
 advocated ; but it is an additional form to be used 
 sparingly or generously, according to the nature of 
 the subject-matter under consideration, the degree 
 of the learner's development, and the end sought 
 in mastering that particular portion of truth. 
 
 It may possibly serve us in attempting to realize 
 how vital a matter this is if we recall how generally 
 and extensively we employ forms of comparison in 
 our usual mental activity and in our daily language. 
 The comparison of adjectives and adverbs is a 
 much more important feature of our language than 
 the space it occupies in our grammars would lead 
 one to conclude. But nouns and verbs exist in 
 groups, — the members of each group capable of 
 being so arranged that they represent a scale of 
 meaning, proceeding from small to great, or from 
 weak to strong. Many conjunctions also serve the 
 
 17 
 
same purpose. The fact that these symbols exist 
 in every language proves that there are correspond- 
 ing processes in the human mind, the results of 
 whose operations men desire to express. 
 
 In fact, words themselves have little meaning 
 except as they are employed in relation to other 
 words. If the whole theory of number is not ex- 
 pressed by the hypothesis that it is based upon ratio, 
 this at least is a part of the truth, and the rest 
 must be sought in other hypotheses which still 
 involve some relation. If enumeration is the basis 
 of number, then the relation upon which number 
 is built is the equality of its units. In the study 
 of size, equality or inequality is the first idea that 
 is presented. The study of generalization itself 
 presents the same phenomena, in this respect, as 
 the studv of number. 
 
 Can these considerations be made more obvious 
 by the presentation of concrete illustrations of work 
 based upon them, that may fairly be called drill.'* 
 The purposes for which drill stands must be kept 
 in mind. Now suppose that the pupil is ready, in 
 his study of geography, to begin his consideration 
 of the continents. He is most likely to study 
 North America first, though, so far as our present 
 purpose is concerned, the especial one chosen makes 
 
 i8 
 
no great difference. He does his work according 
 to a definite topical outline, constructed so as to be 
 adapted to his mental ability and to the time at his 
 command. The shape, area, coast-line, land and 
 water conformations, river systems, primary and 
 secondary highlands, etc., etc., will be among the 
 points to which his attention is directed. This 
 study will put within his command for the time- 
 being, at least, the facts relating to the continent 
 in question. When this shall have been completed, 
 he takes up another continent according to the 
 same general plan. But at every point, he is re- 
 quired to make comparisons and to discover the 
 relations between the corresponding facts relating 
 to the two continents. Then a third one is studied 
 and the process of comparison — or the discovery of 
 relations, — is continued with the three continents 
 in mind. The work goes on, until all have received 
 consideration. At the end of this study, it is 
 safe to affirm that he will have the facts relating to 
 the one first studied firmly fixed in his mind, and 
 the knowledge so perfectly grasped that it will be 
 within his ready and easy command. 
 
 In such work, there is repetition, but it is secured 
 in such a manner that the process has not only 
 fixed the old knowledge, but has added to its 
 
stores. Such a method is susceptible of wide and 
 numerous applications. It is by no means peculiar 
 to geography, though other fine illustrations, — like 
 the study of trade centers, river systems, means of 
 communication and travel, animal and vegetable 
 life, and occupations, — could easily be drawn from 
 that field. 
 
 In history, this method might be employed, in 
 greater or less degree, in the study of different eras 
 of a nation'slife, of great men, of military campaigns, 
 of political parties, of important social movements. 
 In mastering the fundamental operations of arith- 
 metic, the process of long division, if the examples 
 are required to be proved, involves a review of the 
 three preceding processes. In grammar, everything 
 in a properly constructed course, leads up to the 
 analysis of the sentence, or, starting with the 
 sentence, descends to the words and comes back to 
 the sentence, making possible the same kind of 
 comparison and also involving application of princi- 
 ples, — the kind of drill previously discussed. 
 
 Other examples might be given almost with- 
 out limit of number. The net results are to fix in 
 the minds of the learners the fact originally acquired, 
 and to multiply to an enormous extent their knowl- 
 
 I 
 
 30 
 
edge of the relations existing among the different 
 items of truth. 
 
 Such work has other elements of utility. It is 
 not undertaken in the interest of a training of the 
 memory, but such is the community of interest 
 among the mental faculties, — as well as among the 
 separate portions of the great body of truth, — that 
 it promotes, — nay, it necessarily includes, — the 
 training of the memory. For it is a fundamental 
 element in the improvement of the memory that an 
 increase of the associations by which ideas are 
 held, — especially if those associations be of the 
 permanent and logical sort, — promotes both the 
 readiness and the accuracy of the memory. The 
 manner in which the original act of learning was 
 performed is the important factor in aiding recall. 
 If facts are originally mastered through their im- 
 portant relations to other facts, not only are asso- 
 ciations increased, but the right kinds of associations 
 are multiplied. The most difficult of all our mental 
 possessions to retain and recall are those that are 
 isolated and individual. So it is clear that the kinds 
 of drill which are rational and interesting serve us 
 better, — even for the lower acts of memory, — than 
 those which are purely arbitrary and mechanical. 
 
 Facts, indeed, may be fixed in the mind by simple 
 
 21 
 
MAR 2 19C3 ''K 
 
 repetition. But, in these days of rapidly widening 
 knowledge, when the call is for men who can use 
 what they know instantly and unerringly, it seems 
 a desirable achievement to make mental effort as 
 fruitful as possible. Industries are made profitable 
 by appliances that increase the product, that prevent 
 waste, that utilize every by-product. An analogous 
 result in mental training should be sought with at 
 least equal eagerness. To this end, every improve- 
 ment in methods of teaching will surely contribute. 
 
 LB,il'05 '-•"C. 
 
 
LIBRftRY OF CONGRESS 
 
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