Method in reading and number

Preface

These studies in method in reading and number are born of a desire to help the students in the writer's own classes in method in these subjects. There are many students who appreciate the necessity of the study of method in reading and number, and who are earnestly seeking help along the lines of a better method of teaching these subjects than that in use in many places. To give guidance to these students is the main idea which prompted to the preparation of these studies.

A second thought is, that many fellow teachers who have not had the time nor opportunity to make special studies in method in reading and number may receive help and guidance from these studies.

It is the aim of the present discussion (1) to investigate the theory aspect of method in reading and number in the light of the best educational thought of to-day; (2) to give an abundance of concrete illustrations of what these lessons should be in harmony with the theory; (3) to criticise existing practices in the teaching of reading and number which are thought to be bad. Thus the studies are theoretical, practical, and critical.

IV. PREFACE.

Simplicity and definiteness have been aimed at through the entire discussion to the end that direct help might be given to those who are beginning teachers in these subjects.

These studies are believed to be in harmony with the best educational thought of the present times.

So far as known no other definite and simple discussion of method in these subjects is in print.

G. W. N.

CHAPTER I. General Method, . . . . q_^i

The Teaching Act, - - - - 9

The Processes in It, - - - 9

Nature of Method as a Subject, - - - 10-11

Classes of Method, _ . _ _ yL

The Learner's Method, - - - - 11-13

The Teacher's Method, - - - 13-20

Method as a Physical Process, - - 20-25

Comparison of Teacher's and Pupil's Method, 29-30

Two Views of Method, - - . . 26-28

No Danger in Too Much Study of Method, - 29-30

Factors Determining Method, - - ' - 30-31

CHAPTER II. The Purpose of Reading, - - - 32-38

General Meaning, . - . _ _ 32

Importance of Definite Idea of Purpose, - 32-33

Classes of Purposes, or Aims, - - 33

The Main, or Primary, Aim, - - 33-35

' Evidence of Main Aim, - - - 35

Secondary, or Subordinate, Aim, - 36-37

Relation of These Aims, . _ _ 37

The Purpose of Reading and Literature, - 38

CHAPTER III. Nature of Reading as a Subject, - 39-43

The School Curriculum, - - - . 39

The Language Group, - - _ . _ 39-40

The Subject-matter of Reading, - - - 41-42

Definition of Reading, - . . - 42-43

CHAPTER IV. Procedure in Teaching Reading, - 44-74

Stages of Reading, - ... 44

VI.

CONTENTS.

The Preparatory Stage,

The Stage of Reading Proper,

The Starting Point, - - - -

Basis, - -

The First Unknown, - _ . . -

Methods of Beginning, . - . .

The Alphabet Method, - . . .

The Synthetic Method, . . _

The Sentence Method, . - _ The Analytic Word Method,

Definite Procedure, - - - - -

Adjectives, and Action Words, The, A, An, Is, Can, On, In, etc., Fixing the Vocabulary in Mind, Print and Script, _ - . . .

Reading of Simple Pieces of Discourse, Analysis Work, . _ . -

Working Out New Words as to Pronunciation, Diacritical Marks, . . - -

44-45 45-46

46 46-47

57-60

60-61

62-63

63-66

66-68

73-74

Second Stage, - -

Didactic and Symbolic Discourse, Steps in Symbolic Discourse, Steps in Didactic Discourse, -

Summary, ----- CHAPTER V.

Concrete Illustrations,

Advantage of, - - - -

Excelsior, . - - .

Erastus Wren's Virtue, - -

The Golden Touch,

Orchard Life, . - -

Abou Ben Adhem, - - -

CHAPTER VI. Common Errors in Teaching Reading, - 89-92

Opportunities for, ----- 89

The Use of the Alphabet Method, - - 89-90

Phonetic Work, or Sound Analysis, - - 90

Oral Reading to the Exclusion of Interpretation, 90-91

Lack of Thought Interpretation, - - 91

Indefinite, General Assignments, - - - 92

75-88

75-79

80-81

82-86

87-88

CONTENTS. VII.

CHAPTER VII. Supplementary Reading, - - - 93-98

Need and Value of, - - - _ _ 93

A Difficulty, ---... 93

Lists of Books, - - - . - 94-98

CHAPTER VIII. Nature and Origin of Number, - 99-106

Nature of Number, . . _ _ 99-IOI

Genesis of Number, - - - - - 101-102

Definition of Number, - - . . 102-103

Origin of Number, - - - - - 103

CHAPTER IX. Method op Procedure in Teaching Number

107-131

Points to Be Kept in Mind, - - - 107

Methods in Use, - - . . . 108

The Method of Symbols, - - - 108-109

The Fixed Unit Method, - - - 109-112

The Grube Method, - - - - 112-113

The Speer Method, - - - - 113-116

The Practical Method, - . - . 117

Two Stag-es of Number Work, - - - 117-118

Characteristics of Primary Stage, - - 118

Scope of Work in Primary Stage, - - 118-121

What Can Be Known of a Number, - - 121-124

What to Do with a Number in the Primary Stage, 124

The Number as a Whole, - - - 124

The One, the Measuring Unit, - - - 125-126

The Relations in the Number, - - 126-128

The Applications of a Numbef , - - - 128-130

Notation of the Number, - - - 130-131

CHAPTER X. Method of Procedure in Teaching Number

The Primary Stage, .... 132-135

The Number as a Whole, - - - - 135-136

The Relations in a Number, - - - 136-138 vnii

CONTENTS.

Thoroughness of Work, -

Fractional Relations,

Important and Unimportant Relations,

The General A])plications,

Picturing Problems,

Notation, _ . - -

Enumeration, _ . . .

The Multiplication Table,

Teachers' Helps,

CHAPTER XI. Procedure in Second Stage

General Scope,

The Formal Process of Addition,

The Formal Process of Subtraction, -

The Formal Process of Multiplication,

The Formal Process of Division,

Conclusion, . _ - _

154-164

CHAPTER XII. The Subject-matter and Purpose of Number

165-170

- 165-166 166

- 166-167

General Nature of Subject-matter, The Purpose of Number, - - -

The Knowledge-giving Purpose, The Guidance the Knowledge of Number

Gives, . - - -

The Disciplinary Purpose, Conclusions, - -

Chapter XIII. 167-169

169-170

Common Errors in Teaching Number, - 171-179

Prevalence of, - - -

Wrong Number Concepts, Figures instead of Number, Unsystematic Number Teaching, Teaching from the Form Side, Failure to Picture Problems, Exhausting a Number, Relations among Topics, Thoughts of Others,

Conclusion, - - - -

171-172 172 173

173-174 174

174-175 175

175-176

176-179 179

Chapter I. General Method

The Teaching Act. — The school exists as an organization in order that the most favorable conditions may be furnished for the act of teaching. It is in this act that the mind of the pupil comes into vital touch with the mind of the teacher. Here the miracle of the influence of one mind upon another is manifested. Here it is that an ^U-important duty of the teacher is involved. To this process all other processes of the school point. The school finds the idea that created it in the process of realization in the teaching act. The act of teaching is a process for it is a series of steps directed toward the accomplishment of an end. The teaching act is not a simple process for it is a large process made up of smaUer processes.

The Processes in It. — A brief analysis of the teaching act will show that there are three processes going on in it, — (1) the thinking the learner is doing; (2) the thinking the teacher is doing; (3)-a process of handling questions, directions, objects, assignments, and so on — the manipulation of means in teaching. The first two of these processes are spiritual, or mental, processes, and the third is external to the minds of both the teacher and the pupil and is a physical process.

Illustration. — In teaching the definition of a noun to a student, first, the student's mind goes through the process of thinking (1) that the noun is a substantive word; and (!?) that it expresses an object bynaming it. This is the process in the mind of the student in the teaching act. Secondly, the teacher thinks these same points through with the student, but he thinks several other things, too. This is the spiritual process of the teacher in the teaching act. Thirdly, there is a process of asking questions, answering questions, illustrating, possibly referring to text-books, etc., going on, and this is the physical process in the teaching act.

Nature of Method as a Subject of Study. — The question. What is the subject of method like? is often asked. It may be answered in a general way by saying it is a subject of study the pursuit of which has for its special object to make teachers more skillful in teaching than they would be without such study. But this much might be said of any pedagogical study — of psychology, for instance. To be more definite, method as a subject is that study which deals with the three processes in the act of teaching as indicated above. These three processes in their various phases constitute the material of all study in the subject of method.

The Subject-matter of Method. — By subject-matter is meant the '.material of study in any subject or lesson. It is the thought and feehng embodied in any subject or lesson which are to be got from such subject or lesson by study. It always consists of facts and relations among such facts. So the subject-matter of method, as a subject of study, is the three processes, one in the mind of the learner, one in the mind of the teacher, and one a physical process, in their relation to the growth in the life of the learner.

Definition o/ife^Aod— Method is thus seen to be a complex and comprehensive thing. Any definition, to be perfectly accurate, must include the various phases of these three processes. The following, it seems, does this: Method is the triple process in the act of teaching hy ichich the learner is induced to take the steps from his real condition to a higher condition held up as an ideal. This is the definition of method considered in its broadest and most comprehensive sense, and the sense in which its study will giv« the most help to the teacher.

Classes of Method. — Since there are three processes going on in the teaching act there are, in a sense, three methods,^ — the learner's method, the teacher's method, and physical method. These three will be studied somewhat in detail.

The Learner's Method. — The learner's method is the movement of his mind in gaining any point of knowledge. The pupil's method is thus a living, spiritual process internal to his life. Method from this point of view is mental growth. Tliat is to say, it is the change of potential mental activity into actual mental activity, and this is the essence of growth.

Illustration. — If the child learns in a number lesson that 8+7 = 15, the activity of his mind in thinking the following steps is his method: — (1) The mind rethinks the number 8; (2) the mind rethinks the number 7; (3) the mind thinks the number 8 and the number 7 together; (4) the mind thinks the name of the new number. These four steps are the mind's process in thinking the point of knowledge, and are, therefore, the mind's method. This phase of method calls attention to the fact that the thing to be watched and emphasized in teaching is the change in the learner's life by which he is constantly rising to a higher plane of living.

Definition of the Learner' s Method. — This phase of method may be characterized by the following definitions : —

1. Method is the process in the learner's mind in thinking a thing.

2. Method is the movement by which the mind of the learner identifies itself with the thought and feeling of the external world. The external world here means anything external to the mind of the learner.

3. Method is the mental activity in which the mind makes the objective the subjective. The objective means the external world, and the subjective means the self. And the self means one's original capacity to know, to feel, and to will, plus the effect of experiences on this power.

4, Method is the process by which the mind of the learner goes from its real condition to an ideal condition. One's real condition is his condition just as he is at any time. His ideal condition is one different from what he is in at any time, and which ^ actually has no existence except as an idea in the mind; hence the name ideal. The ideal condition is hot necessarily a better condition than the real, but may be either a better or worse condition.

The Teacher's Method. — The part the teacher performs in the process of teaching is a very important topic of study in the subject of method. This must be thoroughly understood by one who is to succeed best. To study this is to study the teacher's method. And to this we turn.

First, the teacher must think the thought in the point or points to be taught; that is, he must think the subject-matter. Secondly, he must see in terms of development of the learner's life the reasons for teaching the subject-matter; that is, he must see the purpose. Thirdly, the teacher must see the nearest related knowledge possessed by the learner which he can use as a foundation to build upon in teaching the new point; that is, he must see the basis. Fourthly, the teacher must see the activities the learner's mind pi^ts forth in mastering the points of truth in the subject-matter; that is, he must see the stex)s. Lastly, the teacher must see the means he may best employ in leading the mind of the learner to take the steps in mastering the subject-matter; that is, the teacher must think out the devices. Thus the teacher in teaching a lesson must think (1) the subject-matter; (2) the purpose; (3) the basis; (4) the steps; and (5) the devices. These five things every teacher does in some sort of way in teaching every lesson. Some think them out clearly and accurately, and some think them out scarcely at all, and do not know that they do even that much. A teacher can think the teaching of a single point, or of a whole lesson, or of a whole subject, under these five heads, and must do so with more or less accuracy in teaching. It is worth our while to study these five points further for the help the study will give.

Subject-matter. — In a general way the subject-matter is that which is to be mastered by study. It is the thought embodied in the thing studied by the mind of the learner. In a particular lesson the subject-matter is just that to be got from the lesson which the learner should have after the recitation. In a particular subject, as grammar or history, the subject-matter is just that to be got from the subject which the learner should be in possession of after the study of the subject. In this general sense the subject-matter of education is the whole world of thought. This study is too general to be very helpful. A closer study will reveal the fact that every subject-matter is composed of two things: 1. The facts to be taught or to be studied. 2. The relation in which these facts are to be taught or studied.

Illustration. — Suppose the words, inquiry, discourse, and aspirant are to be taught. Now, a spelling lesson might be made of it; and if it were a spelling lesson, the subject-matter would be, the words, inquiry, discourse, and aspirant, as to their correct written or printed forms. Thus the words inquiry, discourse, and aspirant are the facts to be taught or studied, and "as to their written or printed form" indicates the relation in which they are to be taught or studied. But these same facts might be used, and the lesson not be a spelling lesson at all. If the relation they are to be studied or taught in is as to their correct pronunciation the lesson would be one in orthoepy, and the subject-matter would be, the words, inquiry, discourse, and aspirant as to their correct pronunciation.

Further Illustration. — Suppose the facts of the revolution of the earth around the sun are taught, who can say whether the lesson is one in astronomy or one in geography? If, however, these are taught in their relation to the distribution of life, climate and relief forms on the earth's surface, the lesson at once reveals itself as a geography lesson. From these illustrations it is to be seen that a subject-matter consists of (1) the facts to be taught or studied; and (2) the relation in which these facts are to be considered. This relation is often called the organizing principle of the subject-matter.

General Statement of Subject-matter. — The statement of a subject-matter is not the subject-matter any more than a word is an idea, or a sentence a thought. The statement of the subject-matter bears the same relation to the subject-matter that the word bears to the idea and that the sentence bears to the thought; that is, the statement bears the same relation to the subject-matter that the symbol does to the thing symbolized.

The general statement of a subject-matter is very valuable to a teacher, whether it be of a single lesson, or of a whole subject. It is helpful to the teacher because it must do two things: (1) it must name the facts to be taught, and (2) it must tell the relation in which tnese facts are to be taught. Thus the general statement of the subject-matter of any subject is a perennial guide to the teacher in teaching that subject, in that it shows, in a general way, what to teach and in what relation (how) to teach it.

Purpose. — Purpose in reality is beginning and ond in every process. The purpose as idea — the beginning — moves forward in the process to its realization — the end. The purpose exists in the teacher's mind» but is to be realized in the life of the learner.

The purpose is the effe.ct the mastery of the suhjectmatter should have on the hfe of the child. In actual teaching the teacher is to go from the subject-matter by way of comparison with the effect the thinking the subject-matter has on his own mind to its effect on the child's life, which is the purpose. That is to say, there is no way to tell the purpose of any subject-matter except from the effect its mastery produces on the child's life. The course of study — the subject-matter — is usually provided for the teacher. So the teacher must start with the subject-matter and find out the purpose in teaching it. Much depends in the teaching act upon how well the teacher does this. If the teacher has definitely in mind just what he wants to do in the lesson he will be drawn steadily and constantly toward its accomplishment. A definite purpose saves time, economizes energy, emphasizes the important, organizes, and prevents aimless wandering.

It will be seen that I'd. teaching any lesson there are two phases of t*he "purpose: (1) To give knowledge valuable for guidance in living; (2) to give mental discipline; that is, to furnish a mental gymnastic to the end that the mind may grow strong by exercising it.

Basis. — This is the learner's nearest related knowledge to the new points to be taught, and upon which the teacher may build in teaching the new point. Basis is an important point in teaching. Many errors are made in teaching because the learner has not basis for learning the new point, or because the teacher does not see the basis. Teaching in harmony with the principle underlying basis, tlie mind naturally goes to the unknoionfrom the nearest related knoivn^ means a progressive development of a subject, each step becoming basis for the step succeeding it. There are many violations of basis in teaching, as often done.

Illustration. — If the lesson to be taught is that 5+4=9, the child must know the number 5 and the number 4 as basis before he could learn that 5+4 = 9. If the teacher should attempt to teach this lesson without having taught the numbers 5 and 4 he would meet with the difficulty of insufficient basis. Again, if a teacher attempts to teach the noun to a class without the class having a definite knowledge of an object, he will most surely meet a difficulty in the basis. The teacher to teach well must see and choose definitely his basis.

Ste2)s. — Steps are more or less complete movements of the mind. Tliey are mental things and in the teaching act are in the life of the learner. They are the advances of the mind in mastering the separate points of the lesson to be learned. Or in a more general sense they are the advances of the mind in mastering the various phases of a subject.

Illustration. — If the lesson to be taught were that 17 — 8=9, the steps would be: 1. The advance of the mind in rethinking the number 17. 2. The advance of the mind in rethinking the number 8. 3. The advance of the mind in thinking the number 8 away from 17. 4. The advance of the mind in thinking the number 9 as remainder. Again, if the lesson were to teach the definition of the triangle, after examining several triangles, the steps would be: 1. The advance of the mind in thinking that a triangle is 'a figure. 2. The advance of the mind in thinking a triangle has three sides. 3. The advance of the mind in thinking a triangle has three angles. 4. The advance of the mind in synthesizing these points into the definition, A triangle is a figure having three sides and three angles.

To know the steps the mind takes in working out any new lesson is a matter of much importance to the teacher. He must know something of the steps or he can not teach at all; and, other things equal, the more clearly the teacher has thought the steps, the better will he teach the lesson.

Devices. — The devices are the various things used by the teacher to lead the mind of the learner to think and feel in the manner desired. A synonym for devices is the term means. Devices, or means, constitute a very important factor in teaching. There is opportunity for the exercise of rare judgment, tact and skiU in the selection of devices. When it is understood that questions, text-books, and reference books; maps, globes, and school apparatus in general; blocks, sticks, etc., are devices in teaching, something of their importance in school work becomes evident. Devices are so important that among many, method means nothing more than the manipulation of devices. However important they are it must not be lost sight of that they are always determined in the light of the mental process they are to induce. They are means to an end, and in nature the end is always more important than the means.

Method as a Physical Process. — It is, perhaps, using the term method in its most popular significance to think of it as meaning some physical process external to the life of the learner. That is to say, it is using the term in the sense in which most persons commonly use it in speaking and writing. This idea of method is the one usually held by persons who have not made a careful study of what the term really ought to mean. There is a sort of indefiniteness in the minds of most of such persons as to just what they do mean by method. However, upon examination it will be found usually that the idea that method is the manner of doing some physical thing prevails, though even this is held in mind more or less vaguely. Prom thinking of method in this sense we have the following terms: — "Object Method," •'Concert Method," ''Consecutive Method," "Promiscuous Method," "Catechetic Method," "Lecture Method," " Socratic Method," and "Laboratory Method."

These all refer to the manipulation of objects, questions, and answers in the teaching act, and so are to be studied briefly under method as a physical process.

The Object Method . — By this is meant the handhng of objects by teacher and pupils in the process of learning. It is a good line of work, if used judiciously. It has its proper place in teaching number work, primary reading, nature work, primary geography, and primary language.

The Concert Method. — The concert method means having students to answer questions, read, and speak simultaneously in the recitation. There is much that may be said against concert work, but very httle to be said for it. It is objectionable because it (1) violates the law of self activity; (2) stifles individual effort and individual responsibility; (3) does not bring out clear, definite answers or thinking; and (4) leads to confusion, disorder, and chaotic class work. There may possibly be instances in which concert work may be used advantageously, but as a rule it should be avoided.

Tlie Consecutive Method. — The consecutive method of asking and answering in the recitation means beginning at some point, the head of the class, or at the name beginning with A, and proceeding in some regular order back to the point of starting. In proceeding in recitation this way the students know pretty well when the "turn" of each one wih. come. This method, like the preceding one, has many things against it, but little to recommend it. It is objectionable because it leads to (1) habits of inattention; (2) disorder and disorganization of the class; (3) habits of idleness; and (4) bad methods of study. However good a student may be, if, when he has answered a question, he knows to a certainty that he will not be called upon again for some time, the tendency is for him to relax his attention. If the student is not a good one, the tendency in this kind of work is for him to become worse, and since he is not called upon to attend closely he is prone to do something else, thereby causing disorder and disorganization. Idleness in the class is a direct result of inattention, and bad habits of study result from the student's being able to prepare just those points in the lesson which he has reckoned will come to him.

Promiscuous Work. — The promiscuous method of asking questions and receiving answers refers to distributing the questions and receiving answers from students promiscuously. No student knows to whom the answer to the question will fall. This method unlike the two preceding has much to be said for it and little or nothing against it. It is desirable because (1) it fosters habits of attention and concentration; (2) it is flexible ana gives the teacher the best opiX)rtunities for meeting the needs of individual students; (3) it fosters habits of order and organization in the class work; and (4) it tends to industrious habits, and right methods of study. By the use of the promiscuous method students are held constantly to attending to the question under consideration, to the careful preparation of the lesson as a whole, and to order and unity in the class. As a rule, the promiscuous method is certainly the best for class work.

Catechetic Method. — This is, in its original form, not much used any more, and so needs very little said about it. According to this method the question was written in the text-book and just after the question was the answer to it. The student's business was to read the question, and then commit to memory the answer. In the recitation the teacher with text-book in hand read the question and the student gave, in the words of the text, the answer. Such a manner of conducting a recitation has nothing to recommend it and so needs no further study.

Lecture Metliod. — The lecture method refers to teaching by means of talks or lectures. This method, perhaps, has its advantages and disadvantages. It is certainly not adapted to all kinds of school work, and probably not adapted to any kind of school work if used exclusively. There are, however, some phases of school work which may be profitably taught by talks, or lectures. To elementary school work the lecture method is not at all adapted, and but very poorly adapted to secondary school work. In the first eight years of the child's school life he must be taught differently than by this method. That stays with the child which he has an opportunity to see, hear, and think about. This, however, is not to be construed to mean that oral teaching should not be done in primary history, primary geography, nature work, etc. If the lecture method has any legitimate place in school work it is in the college and university. However it may seem theoretically, it remains as a fact that those things which are digged out by the student, recited upon in the class, and discussed by questions and answers are the things which in the end stay with him and do him good. Certainly the lecture method in the average teacher's school work is, to say the least, to be used sparingly, and with much caution when used at all.