GENERAL KNOWLEDGE

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 ofdeduction, or by inference.

In all of the above examples, whether experienced through the senses, built up by an act of imagination, orgained 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.

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, itis said to gain a class notion, or concept; and the method by which these ideas are gained is calledconception.

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 ofinduction.

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 risingis a particular truth, butheated air risesis a general truth.The English people plunged into excesses in Charles II's reign after the removal of the stern Puritan ruleis particular, but aperiod of license follows a period of repressionis 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 aimto develop a new experiencein 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 storyMary 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.

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 ispear-shaped, yellow-skinned, soft-pulped, ofsweet taste, andaromatic 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.

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.

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.

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.

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 wayAnd 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 inChapter XXVII, which treats of the process of imagination.

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 mayinfer 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 inChapter 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.

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.

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 lessonis 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.

figure

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:

figure

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.

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.

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 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 notionnoun. 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 wordJohn, 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 wordToronto, he may note much the same except that it names a place; of the worddesk, he may note especially that it is used to name a thing and is written without a capital letter. By comparing any and all thequalities 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.

figure

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.)

figure

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.)

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.

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 wordJohn, 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.

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 andgeneralization 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.

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, inChapter XXVIII.

As further illustrations of an inductive process, the following outlines of lessons might be noted. The processesare 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.")

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?

(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.

(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.

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.Provenderis a naming word.Provenderis 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 applicationundoubtedly 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.

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 fora 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?

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 asDickens 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:

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