Question and Answer.—On account of the large use of questioning as a means of directing and testing the pupils' selecting of old knowledge, or interpreting ideas, the developing method is often identified with the question and answer method. But the real mark of the developing method of teaching is the effort of an instructor to assure himself that, step by step, throughout the learning process, the pupil himself is actively apprehending the significance of the new problem by a use of his own previous experience. It is true, however, that the method of interrogation is the most universal, and perhaps the most effective, mode by which a teacher is able to assure himself that the learner's mind is really active throughout each step of the learning process. Moreover, as will be seen later, the other subsidiary methods of the developing method usually involve an accompanying use of question and answer for their successful operation. It is for this reason that the question is sometimes termed the teacher's best instrument of instruction. For the same reason, also, the young teacher should early aim to secure facility in the art of questioning. An outline of the leading principles of questioning will, therefore, be given in Chapter XVIII.

Other Forms of Development.—Notwithstanding the large part played by question and answer in the developing method, it must be observed that there are other important means which the teacher at times may use in the learning process in order to awaken clear interpreting ideas in the mind of the learner. In so far, moreover, as any such methods on the part of the teacher quicken the apperceptive process in the child, or cause him to apply his former knowledge in a more active and definite way to the problem in hand, they must be classified as phases of the developing method. Two of these subsidiary methods will now be considered.

THE OBJECTIVE METHOD

Characteristics of the Objective Method.—One important sub-section of the developing method is known as the objective method. In this method the teacher seeks, as far as possible, (1) to present the lesson problem through the use of concrete materials, and (2) to have the child interpret the problem by examining this concrete material. A child's interest and knowledge being largely centred in objects and their qualities and uses, many truths can best be presented to children through the medium of objective teaching. For example, in arithmetic, weights and measures should be taught by actually handling weights and measures and building up the various tables by experiment. Tables of lengths, areas, and volumes may be taught by measurements of lines, surfaces, and solids. Geographical facts are taught by actual contact with the neighbouring hills, streams, and ponds; and by visits to markets and manufacturing plants. In nature study, plants and animals are studied in their natural habitat or by bringing them into the class-room.

Advantages of the Objective Method.—The advantages of this method in such cases are readily manifest. Although, for instance, the pupil who knows in a general way an inch space and the numbers 144, 9, 30-1/4, 40, and 4, might be supposed to be able to organize out of his former experiences a perfect knowledge of surface measure, yet it will be found that compared with that of the pupil who has worked out the measure concretely in the school garden, the control of the former student over this knowledge will be very weak indeed. In like manner, when a student gains from a verbal description a knowledge of a plant or an animal, not only does he find it much more difficult to apply his old knowledge in interpreting the word description than he would in interpreting a concrete example, but his knowledge of the plant or animal is likely to be imperfect. Objective teaching is important, therefore, for two reasons:

1. It makes an appeal to the mind through the senses, the avenue through which the most vivid images come. Frequently several senses are brought to bear and the impressions thereby multiplied.

2. On account of his interest in objects, the young child's store of old experiences is mainly of objects and of their sensuous qualities and uses. To teach the abstract and unfamiliar through these, therefore, is an application of the law of apperception, since the object makes it easier for the child's former knowledge to be related to the presented problem.

Limitations of Objective Method.—It must be recognized, however, that objective teaching is only a means to a higher end. The concrete is valuable very often only as a means of grasping the abstract. The progress of humanity has ever been from the sensuous and concrete to the ideal and abstract. Not the objects themselves, but what the objects symbolize is the important thing. It would be a pedagogical mistake, then, to make instruction begin, continue, and end in the concrete. It is evident, moreover, that no progress could be made through object-teaching, unless the question and answer method is used in conjunction.

THE ILLUSTRATIVE METHOD

Characteristics of the Illustrative Method.—In many cases it is impossible or impracticable to bring the concrete object into the school-room, or to take the pupils to see it outside. In such cases, somewhat the same result may be obtained by means of some form of graphic illustration of the object, as a picture, sketch, diagram, map, model, lantern slide, etc. The graphic representation of an object may present to the eye most of the characteristics that the actual object would. For this reason pictures are being more and more used in teaching, though it is a question whether teachers make as good use of the pictures of the text-book, in geography for instance, as might be made.

Illustrative Method Involves Imagination.—In the illustrative method, however, the pupil, instead of being able to apply directly former knowledge obtained through the senses, in interpreting the actual object, must make use of his imagination to bridge over the gulf between the actual object and the representation. When, for example, the child is called upon to form his conception of the earth with its two hemispheres through its representation on a globe, the knowledge will become adequate only as the child's imagination is able to picture in his mind the actual object out of his own experience of land, water, form, and space, in harmony with the mere suggestions offered by the model. It is evident, for the above reason, that the illustrative method often demands more from the pupil than does the more concrete objective method. For instance, the child who is able to see an actual mountain, lake, canal, etc., is far more likely to obtain an accurate idea of these, than the student who learns them by means of illustrations. The cause for this lies mainly in the failure of the child to form a perfect image of the real object through the exercise of his imagination. In fact it sometimes happens that he makes very little use of his imagination, his mental picture of the real object differing little from the model placed before him. The writer was informed of a case in which a teacher endeavoured to give some young pupils a knowledge of the earth by means of a large school globe. When later the children were questioned thereon, it was discovered that their earth corresponded in almost every particular with the large globe in the school. The successful use of the illustrative method, therefore, demands from the teacher a careful test by the question and answer method, to see that the learner has properly bridged over, through his imagination, the gulf separating the actual object from its illustration. For this reason an acquaintance with the mental process of imagination is of great value to the teacher. The leading facts connected with this process will be set forth in Chapter XXVII.

PRECAUTIONS IN USE OF MATERIALS

In the use of objective and illustrative materials the following precautions are advisable:

1. Their use in the lesson should not be continued too long. It should be remembered that their office is illustrative, and the aim of the teacher should be to have the pupils think in the abstract as soon as possible. To make pupils constantly dependent on the concrete is to make their thinking weak.

2. The pupils must be mentally active while the concrete object or illustrative material is being used, and not merely gaze in a passive way upon the objects. It requires mental activity to grasp the abstract facts that the objects or illustrations typify. A tellurion will not teach the changes of the seasons; bundles of splints, notation; nor black-board examples, the law of agreement; unless these are brought under the child's mental apprehension. The sole purpose of such materials is, therefore, to start a flow of imagery or ideas which bear upon the presented problem.

3. The objects should not be so intrinsically interesting that they distract the attention from what they are intended to illustrate. It would be injudicious to use candies or other inherently attractive objects to illustrate number facts in primary arithmetic. The objects, not the number facts, would be of supreme interest. The teacher who used a heap of sand and some gunpowder to teach what a volcano is, found his pupils anxious for "fireworks" in subsequent geography classes. The science teacher may make his experiments so interesting that his students neglect to grasp what the experiments illustrate. The preacher who uses a large number of anecdotes to illustrate the points of his sermon, would be probably disappointed to know that the only part of his discourse remembered by the majority of his hearers was these very anecdotes. In his enthusiasm for objective teaching, the teacher may easily make the objects so attractive that the pupils fail altogether to grasp what they signify.

4. In the case of pictures, maps, and sketches, it is well to present those that are not too detailed. A map drawn on the black-board by the teacher is usually better for purposes of illustration than a printed wall map. The latter shows so many details that it is often difficult for the pupil to single out those required in the lesson. The black-board map, on the other hand, will emphasize just those details that are necessary. For the same reason the sketch is often better than the printed picture or photograph. Any one who can sketch rapidly and accurately has at his disposal a valuable means of communicating knowledge, and every teacher should strive to cultivate this power.

MODES OF PRESENTATION COMPARED

The relative clearness of different modes of presenting knowledge may be seen from the following:

If a teacher stated to his pupils that he saw a guava yesterday, possibly no information would be conveyed to them other than that some unknown object has been referred to. Merely to name any object of thought, therefore, does not guarantee any real understanding in the mind of the pupil. If the teacher describes the object as a fruit, fragrant, yellow, fleshy, and pear-shaped, the mental picture of the pupil is likely to be much more definite. If, on the other hand, a picture of the fruit is shown, it is likely that the pupil will more fully realize at least some of the features of the fruit. If the pupil is given the object and allowed to bring all his senses to bear upon it, his knowledge will become both more full and more definite. If he were allowed to express himself through drawing and modelling, his knowledge would become still more thorough, while if he grew, marketed, and manufactured the fruit into jelly, his knowledge of the fruit might be considered complete.



CHAPTER XIV

CLASSIFICATION OF KNOWLEDGE

Before passing to a consideration of the various types or classes into which school lessons may be divided, it is necessary to note a certain distinction in the way the mind thinks of objects, or two classes into which our experiences are said to divide themselves. When the mind experiences, or is conscious of, this particular chair on the platform, that tree outside the window, the size of this piece of stone, or the colour and shape of this bonnet, it is said to be occupied with a particular experience, or to be gaining particular knowledge.

ACQUISITION OF PARTICULAR KNOWLEDGE

A. Through the Senses.—These particular experiences may arise through the actual presentation of a thing to the senses. I see this chair; taste this sugar; smell this rose; hear this bell; etc. As will be seen later, the senses provide the primary conditions for revealing to the mind the presence of particular things, that is, for building up particular ideas, or, as they are frequently called, particular notions. Neither does a particular experience, or notion, necessarily represent a particular concrete object. It may be an idea of some particular state of anger or joy being experienced by an individual of the beauty embodied in this particular painting, etc.

B. Through the Imagination.—Secondly, by an act of constructive imagination, one may image a picture of a particular object as present here and now. Although never having had the actual particular experience, a person can, with the eye of the imagination, picture as now present before him any particular object or event, real or imaginary, such as King Arthur's round table; the death scene of Sir Isaac Brock or Captain Scott; the sinking of the Titanic; the Heroine of Vercheres; or the many-headed Hydra.

C. By Inference, or Deduction.—Again, knowledge about a particular individual, or particular knowledge, may be gained in what seems a yet more indirect way. For instance, instead of standing beside Socrates and seeing him drink the hemlock and die, and thus, by actual sense observation, learn that Socrates is mortal; we may, by a previous series of experiences, have gained the knowledge that all men are mortal. For that reason, even while he yet lives, we may know the particular fact that Socrates, being a man, is also mortal. In this process the person is supposed to start with the known general truth, "All men are mortal"; next, to call to mind the fact that Socrates is a man; and finally, by a comparison of these statements or thoughts, reason out, or deduce, the inference that therefore Socrates is mortal. This process is, therefore, usually illustrated in what is called the syllogistic form, thus:

All men are mortal. Socrates is a man. Socrates is mortal.

When particular knowledge about an individual thing or event is thus inferred by comparing two known statements, it is said to be secured by a process of deduction, or by inference.

GENERAL KNOWLEDGE

In all of the above examples, whether experienced through the senses, built up by an act of imagination, or gained by inference, the knowledge is of a single thing, fact, organism, or unity, possessing a real or imaginary existence. In addition to possessing its own individual unity, however, a thing will stand in a more or less close relation with many other things. Various individuals, therefore, enter into larger relations constituting groups, or classes, of objects. In addition, therefore, to recognizing the object as a particular experience, the mind is able, by examining certain individuals, to select and relate the common characteristics of such classes, or groups, and build up a general, or class, idea, which is representative of any member of the class. Thus arise such general ideas as book, man, island, county, etc. These are known as universal, or class, notions. Moreover, such rules, or definitions, as, "A noun is the name of anything"; "A fraction is a number which expresses one or more equal parts of a whole," are general truths, because they express in the form of a statement the general qualities which have been read into the ideas, noun and fraction. When the mind, from a study of particulars, thus either forms a class notion as noun, triangle, hepatica, etc., or draws a general conclusion as, "Air has weight," "Any two sides of a triangle are together greater than the third side," it is said to gain general knowledge.

ACQUISITION OF GENERAL KNOWLEDGE

A. Conception.—In describing the method of attaining general knowledge, it is customary to divide such knowledge into two slightly different types, or classes, and also to distinguish between the processes by which each type is attained. When the mind, through having experienced particular dogs, cows, chairs, books, etc., is able to form such a general, or class, idea as, dog, cow, chair, or book, it is said to gain a class notion, or concept; and the method by which these ideas are gained is called conception.

B. Induction.—When the mind, on the basis of particular experiences, arrives at some general law, or truth, as, "Any two sides of a triangle are together greater than the third side"; "Air has weight"; "Man is mortal"; "Honesty is the best policy"; etc., it is said to form a universal judgment, and the process by which the judgment is formed is called a process of induction.

Examples of General and Particular Knowledge.—When a pupil learns the St. Lawrence River system as such, he gains a particular experience, or notion; when he learns of river basins, he obtains a general notion. In like manner, for the child to realize that here are eight blocks containing two groups of four blocks, is a particular experience; but that 4 + 4 = 8, is a general, or universal, truth. To notice this water rising in a tube as heat is being applied, is a particular experience; to know that liquids are expanded by heat is a general truth. The air above this radiator is rising is a particular truth, but heated air rises is a general truth. The English people plunged into excesses in Charles II's reign after the removal of the stern Puritan rule is particular, but a period of license follows a period of repression is general.

Distinction is in Ideas, not Things.—It is to be noted further that the same object may be treated at one time as a particular individual, at another time as a member of a class, and at still another time as a part of a larger individual. Thus the large peninsula on the east of North America may be thought of now, as the individual, Nova Scotia; at another time, as a member of the class, province; and at still another time, as a part of the larger particular individual, Canada.

Only Two Types of Knowledge.—It is evident from the foregoing that no matter what subject is being taught, so far as any person may aim to develop a new experience in the mind of the pupil, that experience will be one or other of the two classes mentioned above. If the aim of our lesson is to have the pupils know the facts of the War of 1812-14, to study the rainfall of British Columbia, to master the spelling of a particular word, or to image the pictures contained in the story Mary Elizabeth, then it aims primarily to have pupils come into possession of a particular fact, or a number of particular facts. On the other hand, if the lesson aims to teach the pupils the nature of an infinitive, the rule for extracting square root, the law of gravity, the classes of nouns, etc., then the aim of the lesson is to convey some general idea or truth.

APPLIED KNOWLEDGE GENERAL

Before proceeding to a special consideration of such type lessons, it will be well to note that the mind always applies general knowledge in the learning process. That is, the application of old knowledge to the new presentation is possible only because this knowledge has taken on a general character, or has become a general way of thinking. The tendency for every new experience, whether particular or general, to pass into a general attitude, or to become a standard for interpreting other presentations, is always present, at least after the very early impressions of infancy. When, for instance, a child observes a strange object, dog, and perceives its four feet, this idea does not remain wholly confined to the particular object, but tends to take on a general character. This consists in the fact that the characteristic perceived is vaguely thought of as a quality distinct from the dog. This quality, four-footedness, therefore, is at least in some measure recognized as a quality that may occur in other objects. In other words, it takes on a general character, and will likely be applied in interpreting the next four-footed object which comes under the child's attention. So also when an adult first meets a strange fruit, guava, he observes perhaps that it is pear-shaped, yellow-skinned, soft-pulped, of sweet taste, and aromatic flavour. All such quality ideas as pear-shaped, yellow, soft, etc., as here applied, are general ideas of quality taken on from earlier experiences. Even in interpreting the qualities of particular objects, therefore, as this rose, this machine, or this animal, we apply to its interpretation general ideas, or general forms of thought, taken on from earlier experiences.

The same fact is even more evident when the mind attempts to build up the idea of a particular object by an act of imagination. One may conceive as present, a sphere, red in colour, with smooth surface, and two feet in diameter. Now this particular object is defined through the qualities spherical, red, smooth, etc. But these notions of quality are all general, although here applied to building up the image of a particular thing.

PROCESSES OF ACQUIRING KNOWLEDGE SIMILAR

If what has already been noted concerning the law of universal method is correct, and if all learning is a process of building up a new experience in accordance with the law of apperception, then all of the above modes of gaining either particular or general knowledge must ultimately conform to the laws of general method. Keeping in view the fact that applied knowledge is always general in character, it will not be difficult to demonstrate that these various processes do not differ in their essential characteristics; but that any process of acquiring either particular or general knowledge conforms to the method of selection and relation, or of analysis-synthesis, as already described in our study of the learning process. To demonstrate this, however, it will be necessary to examine and illustrate the different modes of learning in the light of the principles of general method already laid down in the text.



CHAPTER XV

MODES OF LEARNING

DEVELOPMENT OF PARTICULAR KNOWLEDGE

A. LEARNING THROUGH THE SENSES

In many lessons in nature study, elementary science, etc., pupils are led to acquire new knowledge by having placed before them some particular object which they may examine through the senses. The knowledge thus gained through the direct observation of some individual thing, since it is primarily knowledge about a particular individual, is to be classified as particular knowledge. As an example of the process by which a pupil may gain particular knowledge through the senses, a nature lesson may be taken in which he would, by actual observation, become acquainted with one of the constellations, say the Great Dipper. Here the learner first receives through his senses certain impressions of colour and form. Next he proceeds to read into these impressions definite meanings, as stars, four, corners, bowl, three, curve, handle, etc. In such a process of acquiring knowledge about a particular thing, it is to be noted that the acquisition depends upon two important conditions:

1. The senses receive impressions from a particular thing.

2. The mind reacts upon these impressions with certain phases of its old knowledge, here represented by such words as four, corner, bowl, etc.

Analysis of Process.—When the mind thus gains knowledge of a particular object through sense perception, the process is found to conform exactly to the general method already laid down; for there is involved:

1. The Motive.—To read meaning into the strange thing which is placed before the pupil as a problem to stimulate his senses.

2. Selection, or Analysis.—Bringing selected elements of former knowledge to interpret the unknown impressions, the elements of his former knowledge being represented in the above example by such words as, four, bowl, curve, handle, etc.

3. Unification, or Synthesis.—A continuous relating of these interpreting factors into the unity of a newly interpreted object, the Dipper.

SENSE PERCEPTION IN EDUCATION

A. Gives Knowledge of Things.—In many lessons in biology, botany, etc., although the chief aim of the lesson is to acquire a correct class notion, yet the learning process is in large part the gaining of particular knowledge through the senses. In a nature lesson, for instance, the pupil may be presented with an insect which he has never previously met. When the pupil interprets the object as six-legged, with hard shell-like wing covers, under wings membranous, etc., he is able to gain knowledge about this particular thing:

1. Because the thing manifests itself to him through the senses of sight and touch.

2. Because he is able to bring to bear upon these sense impressions his old knowledge, represented by such words as six, wing, shell, hard, membranous, etc. So far, therefore, as the process ends with knowledge of the particular object presented, the learning process conforms exactly to that laid down above, for there is involved:

1. The Motive.—To read meaning into the new thing which is placed before the pupil as a problem to stimulate his senses.

2. Selection, or Analysis.—Bringing selected elements of former knowledge to interpret the unknown problem, the elements of his former knowledge being represented above by such words as six, leg, wing, hard, shell, membranous, etc.

3. Unification, or Synthesis.—A continuous relating of these interpreting factors into the unity of a better known object, the insect.

B. Is a Basis for Generalization.—It is to be noted, however, that in any such lesson, although the pupil gains through his senses a knowledge of a particular individual only, yet he may at once accept this individual as a sign, or type, of a class of objects, and can readily apply the new knowledge in interpreting other similar things. Although, for example, the pupil has experienced but one such object, he does not necessarily think of it as a mere individual—this thing—but as a representative of a possible class of objects, a beetle. In other words the new particular notion tends to pass directly into a general, or class, notion.

B. LEARNING THROUGH IMAGINATION

As an example of a lesson in which the pupil secures knowledge through the use of his imagination, may be taken first the case of one called upon to image some single object of which he may have had no actual experience, as a desert, London Tower, the sphinx, etc. Taking the last named as an example, the learner must select certain characteristics as, woman, head, lion, body, etc., all of which are qualities which have been learned in other past experiences. Moreover, the mind must organize these several qualities into the representation of a single object, the sphinx. Here, evidently, the pupil follows fully the normal process of learning.

1. The term—the sphinx—suggests a problem, or felt need, namely, to read meaning into the vaguely realized term.

2. Under the direction of the instructor or the text-book, the pupil selects, or analyses out of past experience, such ideas as, woman, head, body, lion, which are felt to have a value in interpreting the present problem.

3. A synthetic, or relating, activity of mind unifies the selected ideas into an ideally constructed object which is accepted by the learner as a particular object, although never directly known through the senses.

Nor is the method different in more complex imagination processes. In literary interpretation, for instance, when the reader meets such expressions as:

The curfew tolls the knell of parting day, The lowing herd winds slowly o'er the lea, The ploughman homeward plods his weary way And leaves the world to darkness and to me;

the words of the author suggest a problem to the mind of the reader. This problem then calls up in the mind of the student a set of images out of earlier experience, as bell, evening, herd, ploughman, lea, etc., which the mind unifies into the representation of the particular scene depicted in the lines. It is in this way that much of our knowledge of various objects and scenes in nature, of historical events and characters, and of spiritual beings is obtained.

Imagination Gives Basis for Generalization.—It should be noted by the student-teacher that in many lessons we aim to give the child a notion of a class of objects, though he may in actual experience never have met any representatives of the class. In geography, for instance, the child learns of deserts, volcanoes, etc., without having experienced these objects through the senses. It has been seen, however, that our general knowledge always develops from particular experience. For this reason the pupil who has never seen a volcano, in order to gain a general notion of a volcano, must first, by an act of constructive imagination, image a definite picture of a particular volcano. The importance of using in such a lesson a picture or a representation on a sand-board, lies in the fact that this furnishes the necessary stimulus to the child's imagination, which will cause him to image a particular individual as a basis for the required general, or class, notion. Too often, however, the child is expected in such lessons to form the class notion directly, that is, without the intervention of a particular experience. This question will be considered more fully in Chapter XXVII, which treats of the process of imagination.

C. LEARNING BY INFERENCE, OR DEDUCTION

Instead of placing himself in British Columbia, and noting by actual experience that there is a large rainfall there, a person may discover the same by what is called a process of inference. For example, one may have learned from an examination of other particular instances that air takes up moisture in passing over water; that warm air absorbs large quantities of moisture; that air becomes cool as it rises; and that warm, moist air deposits its moisture as rain when it is cooled. Knowing this and knowing a number of particular facts about British Columbia, namely that warm winds pass over it from the Pacific and must rise owing to the presence of mountains, we may infer of British Columbia that it has an abundant rainfall. When we thus discover a truth in relation to any particular thing by inference, we are said to go through a process of deduction. A more particular study of this process will be made in Chapter XXVIII, but certain facts may here be noted in reference to the process as a mode of acquiring knowledge. An examination will show that the deductive process follows the ordinary process of learning, or of selecting certain elements of old knowledge, and organizing them into a new particular experience in order to meet a certain problem.

Deduction as Formal Reasoning.—It is usually stated by psychologists and logicians that in this process the person starts with the general truth and ends with the particular inference, or conclusion, for example:

Winds coming from the ocean are saturated with moisture.

The prevailing winds in British Columbia come from the Pacific.

Therefore these winds are saturated with moisture.

All winds become colder as they rise.

The winds of British Columbia rise as they go inland.

Therefore, the winds (atmosphere) in British Columbia become colder as they go inland.

The atmosphere gives out moisture as it becomes colder.

The atmosphere in British Columbia becomes colder as it goes inland.

Therefore, the atmosphere gives out moisture in British Columbia.

Steps in Process.—The various elements involved in a deductive process are often analysed into four parts in the following order:

1. Principles. The general laws which are to be applied in the solution of the problem. These, in the above deductions, constitute the first sentence in each, as,

The air becomes colder as it rises.

Air gives out its moisture as it becomes colder, etc.

2. Data. This includes the particular facts already known relative to the problem. In this lesson, the data are set forth in the second sentences, as follows:

The prevailing winds in British Columbia come from the Pacific; the wind rises as it goes inland, etc.

3. Inferences. These are the conclusions arrived at as a result of noting relations between data and principles. In the above lesson, the inferences are:

The atmosphere, or trade-winds, coming from the Pacific rise, become colder, and give out much moisture.

4. Verification. In some cases at least the learner may use other means to verify his conclusions. In the above lesson, for example, he may look it up in the geography or ask some one who has had actual experience.

Deduction Involves a Problem.—It is to be noted, however, that in a deductive learning process, the young child does not really begin with the general principle. On the contrary, as noted in the study of the learning process, the child always begins with a particular unsolved problem. In the case just cited, for instance, the child starts with the problem, "What is the condition of the rainfall in British Columbia?" It is owing to the presence of this problem, moreover, that the mind calls up the principles and data. These, of course, are already possessed as old knowledge, and are called up because the mind feels a connection between them and the problem with which it is confronted. The principles and data are thus both involved in the selecting process, or step of analysis. What the learner really does, therefore, in a deductive lesson is to interpret a new problem by selecting as interpreting ideas the principles and data. The third division, inference, is in reality the third step of our learning process, since the inference is a new experience organized out of the selected principles and data. Moreover, the verification is often found to take the form of ordinary expression. As a process of learning, therefore, deduction does not exactly follow the formal outline of the psychologists and logicians of (1) principles, (2) data, (3) inference, and (4) verification; but rather that of the learning process, namely, (1) problem, (2) selecting activity, including principles and data, (3) relating activity=inference, (4) expression=verification.

Example of Deduction as Learning Process.—A simple and interesting lesson, showing how the pupil actually goes through the deductive process, is found in paper cutting of forms balanced about a centre, say the letter X.

1. Problem. The pupil starts with the problem of discovering a way of cutting this letter by balancing about a centre.

2. Selection. Principles and Data. The pupil calls up as data what he knows of this letter, and as principles, the laws of balance he has learned from such letters as, A, B, etc.

3. Organization or Inference. The pupil infers from the principle involved in cutting the letter A, that the letter X (Fig. A) may be balanced about a vertical diameter, as in Fig. B.

Repeating the process, he infers further from the principle involved in cutting the letter B, that this result may again be balanced about a horizontal diameter, as in Fig. C.



4. Expression or Verification. By cutting Figure D and unfolding Figures E and F, he is able to verify his conclusion by noting the shape of the form as it unfolds, thus:



FURTHER EXAMPLES FOR STUDY

The following are given as further examples of deductive processes.

The materials are here arranged in the formal or logical way. The student-teacher should rearrange them as they would occur in the child's learning process.

I. DIVISION OF DECIMALS

1. Principles:

(a) Multiplying the dividend and divisor by the same number does not alter the quotient.

(b) To multiply a decimal by 10, 100, 1000, etc., move the decimal point 1, 2, 3, etc., places respectively to the right.

2. Data:

Present knowledge of facts contained in such an example as .0027 divided by .05.

3. Inferences:

(a) The divisor (.05) may be converted into a whole number by multiplying it by 100.

(b) If the divisor is multiplied by 100, the dividend must also be multiplied by 100 if the quotient is to be unchanged.

(c) The problem thus becomes .27 divided by 5, for which the answer is .054.

4. Verification:

Check the work to see that no mistakes have been made in the calculation. Multiply the quotient by the divisor to see if the result is equal to the dividend.

II. TRADE-WINDS

1. Principles:

(a) Heated air expands, becomes lighter, and is pushed upward by cooler and heavier currents of air.

(b) Air currents travelling towards a region of more rapid motion have a tendency to "lag behind," and so appear to travel in a direction opposite to that of the earth's rotation.

2. Data:

(a) The most heated portion of the earth is the tropical region.

(b) The rapidity of the earth's motion is greatest at the equator and least at the poles.

(c) The earth rotates on its axis from west to east.

3. Inferences:

(a) The heated air in equatorial regions will be constantly rising.

(b) It will be pushed upward by colder and heavier currents of air from the north and south.

(c) If the earth did not rotate, there would be constant winds towards the south, north of the equator; and towards the north, south of the equator.

(d) These currents of air are travelling from a region of less motion to a region of greater motion, and have a tendency to lag behind the earth's motion as they approach the equator.

(e) Hence they will seem to blow in a direction contrary to the earth's rotation, namely, towards the west.

(f) These two movements, towards the equator and towards the west, combine to give the currents of air a direction towards the south-west north of the equator, and towards the north-west south of the equator.

4. Verification:

Read the geography text to see if our inferences are correct.

THE DEVELOPMENT OF GENERAL KNOWLEDGE

The Conceptual Lesson.—As an example of a lesson involving a process of conception, or classification, may be taken one in which the pupil might gain the class notion noun. The pupil would first be presented with particular examples through sentences containing such words as John, Mary, Toronto, desk, boy, etc. Thereupon the pupil is led to examine these in order, noting certain characteristics in each. Examining the word John, for instance, he notes that it is a word; that it is used to name and also, perhaps, that it names a person, and is written with a capital letter. Of the word Toronto, he may note much the same except that it names a place; of the word desk, he may note especially that it is used to name a thing and is written without a capital letter. By comparing any and all the qualities thus noted, he is supposed, finally, by noting what characteristics are common to all, to form a notion of a class of words used to name.

The Inductive Lesson.—To exemplify an inductive lesson, there may be noted the process of learning the rule that to multiply the numerator and denominator of any fraction by the same number does not alter the value of the fraction.

Conversion of fractions to equivalent fractions with different denominators

The teacher draws on the black-board a series of squares, each representing a square foot. These are divided by vertical lines into a number of equal parts. One or more of these parts are shaded, and pupils are asked to state what fraction of the whole square has been shaded. The same squares are then further divided into smaller equal parts by horizontal lines, and the pupils are led to discover how many of the smaller equal parts are contained in the shaded parts.



Examine these equations one by one, treating each after some such manner as follows:

How might we obtain the numerator 18 from the numerator 3? (Multiply by 6.)

The denominator 30 from the denominator 5? (Multiply by 6.)

1x3 3 2x4 8 3x5 15 3x6 18 —- = -; —- = —; —- = —; —- = —. 2x3 6 3x4 12 4x5 20 5x6 30

If we multiply both the numerator and the denominator of the fraction 3/5 by 6, what will be the effect upon the value of the fraction? (It will be unchanged.)

What have we done with the numerator and denominator in every case? How has the fraction been affected? What rule may we infer from these examples? (Multiplying the numerator and denominator by the same number does not alter the value of the fraction.)

THE FORMAL STEPS

In describing the process of acquiring either a general notion or a general truth, the psychologist and logician usually divide it into four parts as follows:

1. The person is said to analyse a number of particular cases. In the above examples this would mean, in the conceptual lesson, noting the various characteristics of the several words, John, Toronto, desk, etc.; and in the second lesson, noting the facts involved in the several cases of shading.

2. The mind is said to compare the characteristics of the several particular cases, noting any likenesses and unlikenesses.

3. The mind is said to pick out, or abstract, any quality or quantities common to all the particular cases.

4. Finally the mind is supposed to synthesise these common characteristics into a general notion, or concept, in the conceptual process, and into a general truth if the process is inductive.

Thus the conceptual and inductive processes are both said to involve the same four steps of:

1. Analysis.—Interpreting a number of individual cases.

2. Comparison.—Noting likenesses and differences between the several individual examples.

3. Abstraction.—Selecting the common characteristics.

4. Generalization.—Synthesis of common characteristics into a general truth or a general notion, as the case may be.

Criticism.—Here again it will be found, however, that the steps of the logician do not fully represent what takes place in the pupil's mind as he goes through the learning process in a conceptual or inductive lesson. It is to be noted first that the above outline does not signify the presence of any problem to cause the child to proceed with the analysis of the several particular cases. Assuming the existence of the problem, unless this problem involves all the particular examples, the question arises whether the learner will suspend coming to any conclusion until he has analysed and compared all the particular cases before him. It is here that the actual learning process is found to vary somewhat from the outline of the psychologist and logician. As will be seen below, the child really finds his problem in the first particular case presented to him. Moreover, as he analyses out the characteristics of this case, he does not really suspend fully the generalizing process until he has examined a number of other cases, but, as the teacher is fully aware, is much more likely to jump at once to a more or less correct conclusion from the one example. It is true, of course, that it is only by going on to compare this with other cases that he assures himself that this first conclusion is correct. This slight variation of the actual learning process from the formal outline will become evident if one considers how a child builds up any general notion in ordinary life.

CONCEPTION AS A LEARNING PROCESS

A. In Ordinary Life.—Suppose a young child has received a vague impression of a cow from meeting a first and only example; we find that by accepting this as a problem and by applying to it such experience as he then possesses, he is able to read some meaning into it, for instance, that it is a brown, four-footed, hairy object. This idea, once formed, does not remain a mere particular idea, but becomes a general means for interpreting other experiences. At first, indeed, the idea may serve to read meaning, not only into another cow, but also into a horse or a buffalo. In course of time, however, as this first imperfect concept of the animal is used in interpreting cows and perhaps other animals, the first crude concept may in time, by comparison, develop into a relatively true, or logical, concept, applicable to only the actual members of the class. Now here, the child did not wait to generalize until such time as the several really essential characteristics were decided upon, but in each succeeding case applied his present knowledge to the particular thing presented. It was, in other words, by a series of regular selecting and relating processes, that his general notion was finally clarified.

B. In the School.—Practically the same conditions are noted in the child's study of particular examples in an inductive or conceptual lesson in the school, although the process is much more rapid on account of its being controlled by the teacher. In the lesson outlined above, the pupil finds a problem in the very first word John, and adjusts himself thereto in a more or less perfect way by an apperceptive process involving both a selecting and a relating of ideas. With this first more or less perfect notion as a working hypothesis, the pupil goes on to examine the next word. If he gains the true notion from the first example, he merely verifies this through the other particular examples. If his first notion is not correct, however, he is able to correct it by a further process of analysis and synthesis in connection with other examples. Throughout the formal stages, therefore, the pupil is merely applying his growing general knowledge in a selective, or analytic, way to the interpreting of several particular examples, until such time as a perfect general, or class, notion is obtained and verified. It is, indeed, on account of this immediate tendency of the mind to generalize, that care must be taken to present the children with typical examples. To make them examine a sufficient number of examples is to ensure the correcting of crude notions that may be formed by any of the pupils through their generalizing perhaps from a single particular.

INDUCTION AS A LEARNING PROCESS

In like manner, in an inductive lesson, although the results of the process of the development of a general principle may for convenience be arranged logically under the above four heads, it is evident that the child could not wholly suspend his conclusions until a number of particular cases had been examined and compared. In the lesson on the rule for conversion of fractions to equivalent fractions with different denominators, the pupils could not possibly apperceive, or analyse, the examples as suggested under the head of selection, or analysis, without at the same time implicitly abstracting and generalizing. Also in the lesson below on the predicate adjective, the pupils could not note, in all the examples, all the features given under analysis and fail at the same time to abstract and generalize. The fact is that in such lessons, if the selection, or analysis, is completed in only one example, abstraction and generalization implicitly unfold themselves at the same time and constitute a relating, or synthetic, act of the mind. The fourfold arrangement of the matter, however, may let the teacher see more fully the children's mental attitude, and thus enable him to direct them intelligently through the apperceptive process. It will undoubtedly also impress on the teacher's mind the need of having the pupils compare particular cases until a correct notion is fully organized in experience.

TWO PROCESSES SIMILAR

Notwithstanding the distinction drawn by psychologists between conception as a process of gaining a general notion, and induction as a process of arriving at a general truth, it is evident from the above that the two processes have much in common. In the development of many lesson topics, in fact, the lesson may be viewed as involving both a conceptual and an inductive process. In the subject of grammar, for instance, a first lesson on the pronoun may be viewed as a conceptual lesson, since the child gains an idea of a class of words, as indicated by the new general term pronoun, this term representing the result of a conceptual process. It may equally be viewed as an inductive lesson, since the child gains from the lesson a general truth, or judgment, as expressed in his new definition—"A pronoun is a word that represents an object without naming it," the definition representing the result of an inductive process. This fact will be considered more fully, however, in Chapter XXVIII.

FURTHER EXAMPLES OF INDUCTIVE LESSONS

As further illustrations of an inductive process, the following outlines of lessons might be noted. The processes are outlined according to the formal steps. The student-teacher should consider how the children are to approach each problem and to what extent they are likely to generalize as the various examples are being interpreted during the analytic stage.

1. THE SUBJECTIVE PREDICATE ADJECTIVE

Analysis, or selection:

Divide the following sentences into subject and predicate:

The man was old.

The weather turned cold.

The day grew stormy.

The boy became ill.

The concert proved successful.

What kind of man is referred to in the first sentence? What part of speech is "old"? What part of the sentence does it modify? In what part of the sentence does it stand? Could it be omitted? What then is its duty with reference to the verb? What are its two duties? (It completes the verb "was" and modifies the subject "man.")

Lead the pupils to deal similarly with "cold," "stormy," "ill," "successful."

Comparison, Abstraction, and Generalization, or Organization:

What two duties has each of these italicized words? Each is called a "Subjective Predicate Adjective." What is a Subjective Predicate Adjective? (A Subjective Predicate Adjective is an adjective that completes the verb and modifies the subject.)

2. CONDENSATION OF VAPOUR

Analysis, or selection:

The pupils should be asked to report observations they have made concerning some familiar occurrences like the following:

(1) Breathe upon a cold glass and upon a warm glass. What do you notice in each case? Where must the drops of water have come from? Can you see this water ordinarily? In what form must the water have been before it formed in drops on the cold glass?

(2) What have you often noticed on the window of the kitchen on cool days? From where did these drops of water come? Could you see the vapour in the air? How did the temperature of the window panes compare with the temperature of the room?

(3) When the water in a tea-kettle is boiling rapidly, what do you see between the mouth of the spout and the cloud of steam? What must have come through that clear space? Is the steam then at first visible or invisible?

The pupils should be further asked to report observations and make correct inferences concerning such things as:

(4) The deposit of moisture on the outside surface of a pitcher of ice-water on a warm summer day.

(5) The clouded condition of one's eye-glasses on coming from the cold outside air into a warm room.

Comparison, Abstraction, and Generalization, or Organization:

In all these cases you have reported what there has been in the air. Was this vapour visible or invisible? Under what condition did it become visible?

The pupils should be led to sum up their observations in some such way as the following:

Air often contains much water vapour. When this comes in contact with cooler bodies, it condenses into minute particles of water. In other words, the two conditions of condensation are (1) a considerable quantity of water vapour in the air, and (2) contact with cooler bodies.

It must be borne in mind that in a conceptual or an inductive lesson care is to be taken by the teacher to see that the particulars are sufficient in number and representative in character. As already pointed out, crude notions often arise through generalizing from too few particulars or from particulars that are not typical of the whole class. Induction can be most frequently employed in elementary school work in the subjects of grammar, arithmetic, and nature study.

INDUCTIVE-DEDUCTIVE LESSONS

Before we leave this division of general method, it should be noted that many lessons combine in a somewhat formal way two or more of the foregoing lesson types.

In many inductive lessons the step of application really involves a process of deduction. For example, after teaching the definition of a noun by a process of induction as outlined above, we may, in the same lesson, seek to have the pupil use his new knowledge in pointing out particular nouns in a set of given sentences. Here, however, the pupil is evidently called upon to discover the value of particular words by the use of the newly learned general principle. When, therefore, he discovers the grammatical value of the particular word "Provender" in the sentence "Provender is dear," the pupil's process of learning can be represented in the deductive form as follows:

All naming words are nouns. Provender is a naming word. Provender is a noun.

Although in these exercises the real aim is not to have the pupil learn the value of the individual word, but to test his mastery of the general principle, such application undoubtedly corresponds with the deductive learning process previously outlined. Any inductive lesson, therefore, which includes the above type of application may rightly be described as an inductive-deductive lesson. A great many lessons in grammar and arithmetic are of this type.



CHAPTER XVI

THE LESSON UNIT

What Constitutes a Lesson Problem.—The foregoing analysis and description of the learning process has shown that the ordinary school lesson is designed to lead the pupil to build up, or organize, a new experience, or, as it is sometimes expressed, to gain control of a unit of valuable knowledge, presented as a single problem. From what has been learned concerning the relating activity of mind, however, it is evident that the teacher may face a difficulty when he is called upon to decide what extent of knowledge, or experience, is to be accepted as a knowledge unit. It was noted, for example, that many topics regularly treated in a single lesson fall into quite distinct sub-divisions, each of which represents to a certain extent a separate group of related ideas and, therefore, a single problem. On the other hand, many different lesson experiences, or topics, although taught as separate units, are seen to stand so closely related, that in the end they naturally organize themselves into a larger single unit of knowledge, representing a division, of the subject of study. From this it is evident that situations may arise, as in teaching the classes of sentences in grammar, in which the teacher must ask himself whether it will be possible to take up the whole topic with its important sub-divisions in a single lesson, or whether each sub-division should be treated in a single lesson.

How to Approach Associated Problems.—Even when it is realized that the related matter is too large for a single lesson, it must be decided whether it will be better to bring on each sub-division as a separate topic, and later let these sub-divisions synthesise into a new unity; or whether the larger topic should be taken up first in a general way, and the sub-divisions made topics of succeeding lessons. In the study of mood in grammar, for example, shall we introduce each mood separately, and finally have the child synthesise the separate facts; or shall we begin with a lesson on mood in general, and follow this with a study of the separate moods? In like manner, in the study of winds in geography, shall we study in order land and sea breezes, trade-winds, and monsoons, and have the child synthesise these facts at the end of the series; or shall we begin with a study of winds in general, and follow this with a more detailed study of the three classes of winds?

WHOLE TO PARTS

Advantages.—The second of these methods, which is often called the method of proceeding from whole to parts, should, whenever possible, be followed. For instance, in a study of such a lesson as Dickens in the Camp, the detailed study of the various stanzas should be preceded by an introductory lesson, bringing out the leading thought of the poem, and noting the sub-topics. When, in an introductory lesson, the pupil is able to gain control of a large topic, and see the relation to it of a given number of sub-topics, he is selecting and relating the parts of the whole topic by the normal analytic-synthetic method. Moreover, in the following lessons, he is much more likely to appreciate the relation of the various sub-topics to the central topic, and the inter-relations between these various sub-topics. For this reason, in such subjects as history, literature, geography, etc., pupils are often introduced to these large divisions, or complex lesson units, and given a vague knowledge of the whole topic, the detailed study of the parts being made in subsequent lessons.

Examples.—The following outlines will further illustrate how a series of lessons (numbered I, II, III, etc.) may thus proceed from a first study of the larger whole to a more detailed study of a number of subordinate parts.

THE ST. LAWRENCE RIVER SYSTEM

I. Topic.—The St. Lawrence River:

Position, size, extent of system, other characteristics. Importance—historical, commercial, industrial.

II. Sub-topic 1.—Importance historically:

Open mouth to Europe; Open door to continent; Cartier, Champlain. System of lakes and rivers large and small gave lines of communication, inviting discovery and subsequent development and settlement.

III. Sub-topic 2.—Importance commercially:

Large tracts of valuable land, timber, etc., made available. Highway—need of such between East and West. Difficulties to be overcome, canal, ships. Competition of railways, How? Classes of goods back and forth. Avenue to and from the wheat land.

IV. Sub-topic 3.—Importance industrially:

Great commercial centres—where located and why? Water powers, elevators, manufacturing of raw materials made available in the large areas; Immigration; Fishing.

STUDY OF BACTERIA

I. Topic.—Bacteria:

What they are; relations, comparisons; other plants in same class, or those of higher orders; size, shape; where found; conditions of growth; propagation; modes of distribution; etc.

II. Sub-topic 1.—Our interest in bacteria, arising out of the injury or good they do:

(a) Injury: Decay of fruits, trees, tissues, etc., diseases—diphtheria, typhoid, tuberculosis; how developed, conditions, favourable toxins.

(b) Benefits: In soil, cheese, butter, etc.; chemical action, building new compounds and breaking up other compounds.

III. Sub-topic 2.—Our interest in controlling them; the methods based on mode and conditions of growth, etc.:

(a) Prevention: Eliminating favourable conditions; low temperature, high temperatures, cleanliness; sewerage disposal; clean cow-stables, cellars, kitchens, etc.; antiseptics—carbolic, formalin, sugar for fruit, sealing up; quarantine, vaccination, antitoxin.

(b) Cultures,—alfalfa, cheese, butter, under control.

GEOGRAPHY OF EUROPE

I. Topic.—Europe:

What interest to us; why we study it; position, latitude, near water, boundaries, size; Surface features—highlands, lowlands, drainage rivers, coast-line, etc. Climate—temperature (means, Jan., July), wind, moisture.

II. Sub-topic 1.—Products (based on above conditions):

Vegetation, animal, mineral; vary over area according to physical climatic, and geological conditions; Kinds of products of each class, in each area, etc.

III. Sub-topic 2.—Occupations (based on Lesson II):

Study of operations and conditions favourable and unfavourable under which each product is produced, gathered, and manufactured. Industries, arising from work on the raw materials.

IV. Sub-topic 3.—Trade and Commerce (based on Lessons II and III):

Transportation, producers selling and manufacturers buying raw material, distributed to homes in country and city, to factories within the region itself, to regions beyond, across oceans, etc. Manufactured products sent out, exports and imports.

V. Sub-topic 4.—Civil advantages (based on Lessons I, III, and IV):

Conditions of living—homes, dress, work and pleasure; trades, education, government, social, religious, etc.

PARTS TO WHOLE

The method of whole to parts cannot be followed in all cases even where a number of lesson units may possess important points of inter-relation. Although, for instance, simple and compound addition and addition of fractions are only different phases of one process, no one would advocate the combining of these into such a unified lesson series. In Canadian History, also, although the conditions of the Quebec Act, the coming of the United Empire Loyalists, and the passing of the Constitutional Act, have definite points of inter-relation, it would nevertheless be unwise to attempt to evolve these out of a single complex lesson unit. In such cases, therefore, the synthesis of the various parts must be made as the lessons proceed. Moreover, it is well to ensure the complete organization of the elements by means of an outline review at the end of the lesson series. The student-teacher will meet an example of this process under the topical lesson in Chapter XVII.

PRECAUTIONS

It is evident from the above considerations, that certain precautions should be observed in deciding upon the particular subject-matter to be included in each lesson topic.

1. A just balance should be maintained between the difficulty of each lesson unit and the ability of the class. Matter that is too easy requires no effort in its mastery and hence is uninteresting. Matter that is too difficult discourages effort, and is, therefore, equally uninteresting. It should be sufficiently easy for every pupil to master, and sufficiently difficult to require real effort.

2. The amount of matter included should be carefully adjusted to the length of time taken for the lesson and to the attainments of the class. If too much is attempted, there will be insufficient time for adequate drill and review, and hence there will be lack of thoroughness. If too little is attempted, time will be wasted in needless repetition.

3. Each unit of instruction in any subject should, in general, grow out of the preceding unit taken in that subject, and be closely connected with it. It is in this way that a pupil's interest is aroused for the new problem and his knowledge becomes organized. Neglect in this regard results in the possession of disconnected and unsystematized facts.

Each lesson should contain one or more central facts around which the other facts are grouped. This permits easy organization of the material of the lesson, and ensures its retention by the pupils. Further, the pupils are by this means trained to discriminate between the essential and the non-essential.



CHAPTER XVII

LESSON TYPES

The Developing Lesson.—In the various lesson plans already considered, the aim has always appeared as an attempt to direct the learning process so that the pupil may both build up a new experience and also gain such control over it as will enable him to turn it to practical use. Because in all such lessons the teacher is supposed to direct the pupils through the four steps of the learning process in such a way that they discover for themselves some important new experience, or develop it out of their own present knowledge, the lessons are spoken of as developing lessons. Moreover, the two parts of the lesson in which the new experience is especially gained by the pupils, namely the selecting and relating processes, are often spoken of as a single step and called the step of development, the lesson then being treated under four heads: Problem, preparation, development, and application.

Auxiliary Lessons.—It is evident, however, that there may be lessons in which this direct attempt to have the pupils build up some wholly new experience through a regularly controlled learning process, will not appear as the chief purpose of the lesson. In the previous consideration of the deductive lesson, it was pointed out that this type may be used to give a further mastery of general rules previously learned, rather than a knowledge of particular examples. Such would be the case in an ordinary parsing and analysis lesson in grammar. Here the primary purpose is, evidently, not to give the pupils a grammatical knowledge of the particular words and sentences which are being parsed and analysed, but rather to give them better control of certain general rules of language which they have partially mastered in previous lessons. So also a lesson in writing may seek, not to teach the form of some new letter, but to give skill in writing a letter form which the pupils have already learned. In an exercise in addition of fractions, also, the aim is not so much to have the pupil know these particular questions, as to have him gain a more complete control of the previously learned rule. In other lessons the pupils may be left to secure new knowledge largely for themselves, and the recitation be devoted to testing whether they have been able to accomplish this successfully. In still other lessons the teacher may merely outline a certain topic or certain topics, preparatory to such independent study by the pupils.

The following outlines will explain and exemplify these auxiliary lesson types.

THE STUDY LESSON

Purpose of Study Lesson.—The purpose of the Study Lesson is the mastery by the pupils of a stated portion of the text-book. Ultimately, however it is the cultivation of the power of gleaning information from the printed page, of selecting essential features, and of arranging these in their proper relationships.

The main difficulty in connection with the study lesson is the adaptation of the matter to the interests of the pupils. This difficulty is sometimes due to their inability to interpret the language of the book, and to the difficulty of their distinguishing the salient features from the non-essential. The trouble in this regard is accentuated when they approach the lesson with an inadequate preparation of mind.

The study lesson falls naturally into two parts, the assignment and the seat work.

The Assignment.—The object of the assignment is to put the pupils in an attitude of inquiry toward the new matter. It corresponds to the conception of the problem and the step of preparation in the development lesson. The most successful assignment is one in which the interest of the pupils is aroused to such a pitch that they are anxious to read more about the subject. In general it will consist of a recall of those ideas, or a statement of those facts upon which the interpretation of the new matter depends. Most of the unsuccessful study lessons are due to insufficient care in the assignment. Often pupils are told to read so many pages of the book, without any preliminary preparation and without any idea of what facts they are to learn. Under such conditions, the result is usually a very slight interest in the lesson, and consequently an unsatisfactory grasp of it.

Examples of Assignment.—A few examples will serve to illustrate what is meant by an adequate assignment. When a new reading lesson is to be prepared, the assignment should include the pronunciation and meaning of the different words, and a general understanding of the passage to be read. For a new spelling lesson, the assignment should include the pronunciation and meaning of the words, and any special difficulties that may appear in them. In assigning a history lesson on, say, the Capture of Quebec, the teacher should discuss with the class the position of Quebec, the difficulties that would present themselves to a besieging army, the character and personal appearance of Wolfe (making him stand out as vividly as possible), and the position seized by the British army, illustrating as far as possible by maps and diagrams. Then the class will be in a mental attitude to read with interest the dramatic story of the taking of the fortress. If the pupils were about to study the geography of British Columbia, the teacher might, in the assignment, ask them to note from the map of Canada the position of the province and the direction of the mountain ranges; to infer the character and direction of the rivers and their value for navigation; to infer the nature of the climate, knowing the direction of the prevailing winds; to infer the character of the chief industries, knowing the physical features and climate. With these facts in mind the class will be able to read intelligently what the text-book says about British Columbia.

The Seat Work.—However good the assignment may be, there is always a danger that there will be much waste of time in connection with the seat work. The tendency to mind-wandering is always so great that the time devoted to the preparation of lessons at seats may to a large extent be lost, unless special precautions are taken in that regard. Unfortunately every lesson cannot be made so enthralling that the pupil's mind is kept upon it in spite of distractions. To prevent this possible waste of time, suggestions have already been made in another connection (page 112 above). These will bear repetition here. Questions upon the matter to be studied might be placed on the black-board and pupils asked to prepare answers for these. The difficulty with this plan is, that, unless the questions are carefully thought out by the teacher, the pupils may get from their reading only a few disconnected facts instead of organized knowledge. The pupils might be asked to prepare lists of questions for themselves, and the one who had the best list might be permitted to put his questions to the rest of the class. The difficulty here is that most pupils have a tendency to question about what is unimportant and to neglect the important. In the higher classes, the pupils might be required to make a topical outline of the lesson studied. This requires considerable analytic ability, and the results at first are likely to be disappointing. However, it is an ability worth striving for. The individual who can readily outline what he has read has mastered the art of reading.

Use of Study Lessons.—There is a danger that the study lesson may be used too much or too little. In an ungraded school containing many classes, the teacher may be tempted to rely solely upon the study lesson as a means of intellectual advancement. Used exclusively it becomes monotonous, and the pupils grow weary of the constant effort required. On the other hand, in the graded school, where a teacher has charge of only one class, there will be a tendency to depend entirely on the oral presentation of lessons, to the exclusion of the text-book altogether. The result is that pupils do not cultivate the power to obtain knowledge from books. The study lesson should alternate with the oral lesson, so that monotony may be avoided, and the pupils will reap the undoubted benefits of both methods.

THE RECITATION LESSON

Purpose of the Recitation Lesson.—The recitation lesson is the complement of the study lesson. Its purpose is to test the pupil's grasp of the facts he has read during the study period. Incidentally the teacher clears up difficulties and corrects misconceptions on the part of the pupil. The facts of the text-book may be amplified from the teacher's stock of information. Abstract facts may be illustrated in a concrete way. The important facts may be emphasized and the unimportant ones lightly passed over. The ultimate aim of the recitation lesson is to add something to the pupil's power of interpreting and organizing facts.

Precautions.—Some precautions are to be noted in connection with the recitation lesson. (1) Care must be exercised that the pupils are not reciting mere words that have no solid basis of ideas. Young children are particularly expert at verbalizing. (2) Care must also be taken that the pupils have not merely scrappy information, but have the ideas thoroughly organized. (3) The teacher must know the facts to be recited well enough to be independent of the text-book during the recitation. To conduct the lesson with an open book before him is a confession of weakness on the part of the teacher.

CONDUCTING THE RECITATION LESSON

There are two methods of conducting the recitation lesson, namely, the question and answer method and the topical method.

A. The Question and Answer Method.—This is the easier method for the pupil, as he is called upon to answer only in a brief form detailed questions asked by the teacher. The onus of the analysis of the lesson rests largely upon the teacher. He must ask the questions in a proper sequence so that, if the answers of the pupils were written out, they would form a connected account of the matter. He must be able to detect from the pupils' answers whether they have real knowledge or are merely masquerading with words. To be able to question well is one of the most valuable accomplishments that a teacher can possess. The whole problem of the art of questioning will be considered in the next Chapter.

B. The Topical Method.—The topical recitation consists in the pupil's reporting the facts of the study lesson with a minimum of questioning on the part of the teacher. Two advantages are apparent: (1) It gives the pupil an excellent training in organizing his materials, and (2) it develops his language power. It is to be feared that the topical recitation is not so frequently used as its value warrants. The reason is probably that it is a difficult method to follow. Poor results are usually secured at first, teachers grow discouraged, they stop trying it, and thereafter put their whole faith in the question and answer recitation. This is unfortunate, for however good the latter may be, it is greatly inferior to the topical recitation in helping the pupil to institute relations among his facts, and in improving his power to use his mother-tongue effectively. Successful topical recitations can be secured only at the price of long, patient, and persistent effort. The teacher can gradually work towards them from detailed questions to questions requiring the combination of a few sentences in answer, and thence to the complete outline. In almost every lesson the pupils may be called upon to summarize some topic after it has been gone over by means of detailed questions. In such answers the pupils may reasonably be expected to state the facts in their proper connection and in good language form. In reviews, also, in such subjects as history and geography, the pupils should be frequently called upon to recite topically.

THE DRILL LESSON

Purpose of Drill Lesson.—The Drill Lesson involves the repetition of matter in the same form as it was originally learned, in order to fix it in the mind so firmly that its recall will eventually become automatic. In other words, the function of this type of lesson is habit-formation. It is necessary in those subjects that are more or less mechanical in nature, and that can be reduced to the plane of habit. The field of the drill lesson will, therefore, be largely restricted to spelling, writing, language, and the mechanical phases of art and arithmetic.

The Method.—As the purpose of the drill lesson is the formation of habit, the method will involve the application of the principles that lie at the basis of habit-formation. These are, (1) attention to the thing to be done so as to obtain a vivid picture or a clear understanding of it, and (2) repetition with attention. For instance, if the writing lesson is the formation of the capital E, the class will examine carefully a model form, note the parts of which it is composed, the relative size and position of the parts, how they are connected, etc. Then will follow the repetition of the form by the pupils, each time with careful attention to the method of making it, comparison with the model, and the noting of defects in their work. This will continue until the letter can be made correctly without attention, that is, until the method of making it has been reduced to a habit. If the lesson is on the spelling of difficult words, the first step will be to observe the pronunciation of each, the division into syllables, the difficult part of the word, and the order of the letters. Then the word will be repeated attentively until it can be spelled without effort. In a language lesson on the correct use, say, of "lie" and "lay," the pupils will first be called upon to observe the forms of each, "lie, lay, lain, lying," and "lay, laid, laying"—as used in sentences on the black-board, and the meaning of each group—"lie" meaning "to recline" and "lay" meaning "to place." The pupils will then repeat attentively the correct forms of the words in sentences, until they finally reach the stage when they unconsciously use the words correctly, or as habits of speech. The same principles apply in learning the addition and multiplication tables, and the tables of weights and measures in arithmetic; in the memorization of gems of poetry and prose; in the learning of dates, lists of events, and important provisions of acts in history; and in the memorization of lists of places and products in geography, where this is desirable. In all the cases mentioned, it must not be supposed that a single drill lesson will be sufficient for the fixing of the desired knowledge or skill. Before instant and unconscious reaction can be depended upon, repetition will be needed at intervals for some time.

Danger in Mere Repetition.—In connection with the repetition necessary in the second stage of the drill lesson, an important precaution should be noted. It is impossible for anybody to repeat anything attentively many times in succession unless there is some new element noted in each repetition. When there is no longer a new element, the repetition becomes mechanical, and hence comparatively useless so far as acquisition of knowledge or even habit is concerned. To ask a pupil who has difficulty with a combination in addition, or a product in multiplication, or the spelling of a word, to repeat it many times in succession, may be not only waste of time, but even worse, because a tendency toward mind-wandering may be encouraged. The practice of requiring pupils to write out new words, or words that have been mis-spelled in the dictation lesson, five, ten, or twenty times successively, cannot be too strongly condemned. The attention cannot possibly be concentrated upon the work beyond two or three repetitions, and the fact that pupils frequently make mistakes two or three words down the column and repeat this mistake to the end, is sufficient proof of the mechanical nature of the process. The little boy who had difficulty with the use of "went" and "gone," and was commanded by his teacher to write "I have gone" a hundred times on his slate, illustrates this principle exactly. He had been left to finish his task alone and, after writing "I have gone" faithfully forty or fifty times, grew tired of the monotony of the process. Turning the slate over, he wrote on the other side, "I have went home" and left it on the desk for the teacher's approval.

How to Overcome Dangers.—To avoid this difficulty, some device must be adopted to secure attention to each repetition until the knowledge is firmly fixed. For instance, instead of asking the pupil many times one after the other, what seven times six are, it would be better to introduce other combinations and come back frequently to seven times six. In that way the pupil would have to attend to it every time it came up. Similarly, in learning to spell a troublesome word like "separate," the best plan would be to mix it up with other words and come back to it often. Repetition is always necessary in the drill lesson, but it should always be repetition with attention.

THE REVIEW LESSON

Purpose of Review Lesson.—As the name implies, a review is a new view of old knowledge. While the drill lesson repeats the matter in the same form as it was originally learned, the review lesson repeats the matter from another standpoint or in new relations. The function of the review lesson is the organization of the material of a series of lessons into an inter-connected whole, and incidentally the fixing of these facts in the mind by the additional repetitions.

Kinds of Review.—Almost every lesson gives opportunities for incidental reviews. The step of preparation recalls old ideas in new connections, and may be properly considered a review. A lesson on the "gerund" in grammar would require a recall of the various relations in which a noun may stand, and the various ways in which a verb may be completed. It is quite probable that the pupils have never before brought these facts together in an organized way. Similarly, the step of expression affords opportunity for review. The solution of problems in simple interest confronts the pupils with new situations in which this principle can be applied. The reproduction of the matter of the history lesson requires the selection of the important facts from the mass of details given and the placing of these in their proper relationship to one another.

But besides the incidental reviews which form a part of nearly all lessons, there must be lessons which are purely reviews. Without these, the pupil, because of insufficient repetition, would rapidly forget the facts he had once learned or would never really know the facts at all, because he had not seen them in all their connections. There are two methods of conducting these reviews: (1) by means of the topical outline, (2) by means of the method of comparison.

THE TOPICAL REVIEW

Purpose of Topical Outlines.—By this method the pupil gets a bird's-eye view of a whole field. In learning the matter originally, his attention was largely concentrated upon the individual facts, and it is quite probable that he has since lost sight of some of the threads of unity running through them. The topical outline will bring these into prominence. It will enable the pupil to keep in his mind the most important headings of a subject, the sub-headings, and the individual facts coming under these. Whatever may be said against the practice of memorizing topical outlines, it must be acknowledged that unless it is done the pupil's knowledge of the subject is likely to be very hazy, indefinite, and disconnected.

Illustrations from History.—As an illustration of the review lesson by means of the topical outline, take the history of the Hudson's Bay Company. If the pupil has followed the order of the text-book, he has probably learned this subject in pieces—a bit here, another some pages later, and still another a few chapters farther on. In the multiplicity of other events, he has probably missed the connections among the facts, and a topical review will be necessary to establish these. He may be required to go through his history text-book, reading all the parts relating to the Hudson's Bay Company. He will thus get a grasp of the relationships among the facts, and this will be made firmer if an outline such as the following is worked out with the assistance of the teacher.

THE HUDSON'S BAY COMPANY

I. EARLY HISTORY:

1. Groseilliers and Radisson interest Prince Rupert in possibilities of trade in North-Western Canada. Two vessels fitted out for Hudson's Bay. Report favourable.

2. Charter granted Hudson's Bay Company by Charles II, 1670.

3. Forts Nelson, Albany, Rupert, and Hayes attacked and captured by DeTroyes and D'Iberville, 1686. Restored by Treaty of Utrecht, 1713.

II. NATURE OF FUR-TRADE:

1. Furs gathered by Indians in winter.

2. Conveyed to forts in summer, after incredible difficulties.

3. Ceremonies on arrival of Indians at forts.

4. Articles exchanged for furs at first showy and worthless, but later more useful and valuable, for example, guns, hatchets, powder, shot, blankets, etc.

III. RIVALS OF HUDSON'S BAY COMPANY:

1. Coureurs-de-bois.

2. Scottish traders—ranged from Michilimackinac to Saskatchewan. H.B. Co. built Cumberland House on Saskatchewan to compete for interior trade.

3. North-West Company, 1783-4—at first friendly to H.B. Co., but later bitter enemies.

IV. THE SELKIRK SETTLEMENT:

1. Establishment.—Lord Selkirk, a Scottish philanthropist, and a shareholder in the Hudson's Bay Co., purchased from the Company 70,000 square miles of land around Red River for Scotch colonies, 1811. About three hundred settlers came within three years. Miles Macdonell at head of the colony.

2. Trouble with North-West Company.—

(a) Suspicion of N.W. Co. that colony was established by H.B. Co. to compete for fur trade.

(b) Proclamation of Macdonell that food should not be taken out of settlement. Attack on colony by Metis Indians encouraged by N.W. Co. Withdrawal of colonists to Lake Winnipeg.

(c) Return with reinforcements under Semple. Skirmish at Seven Oaks, 1816. Semple with twenty others killed.

(d) Selkirk's descent upon Fort William. Arrest of several Nor'Westers. Colony at Red River restored.