Chapter 20: Logic in the Class Room

=1. THOUGHT IS KING.=

“Our habits make or unmake us.” “In a thoughtless hour a groove is imbedded in the nerve substance, and thereafter, nine-tenths of the life flows through that groove.” Habit is, indeed, a most powerful and a most tyrannical master; and yet it has come within the observation and even the experience of many, that _thought is even more masterful than habit_. Appearing at the psychological moment and in a pedagogical way, a thought may be made to possess the mind with force sufficient to break almost any habit. From an ethical point of view, the exceptions to this are due to an inability to arouse thought of sufficient strength. Moreover, mental reactions which result in habit are originally brought about through some thought process. Speaking in general terms, it may be affirmed that thought _makes habit_ and if sufficiently strong _breaks habit_. That our habits make or unmake us may be true, but is it not likewise true that our thoughts make or unmake our habits?

Thought is king; thought has made man king of the animal kingdom, and if thought has figured so largely in the evolution of the human animal in past ages, may we not assume that it will sway the future ages in like manner? Thought is a product of the class room. Here thoughts which _make_ habits, and thoughts which _break_ habits have full sway. As the children of the American schools think to-day, so will the men of American life think on the morrow; and as America _thinks_ so will she ultimately _do_. This lends vital import to any object which may either inspire or regulate thought.

=2. SPECIAL FUNCTION OF INDUCTION AND DEDUCTION.=

As commonly treated logic is a _regulative_ subject. This implies the two aspects of _direction_ and _correction_. Logic directs by means of the _laws_ and _forms_ of thought, and corrects by means of the _rules_ of right thinking. To a certain degree both departments of logic are directive as well as corrective; but it is worthy of remark that inductive logic emphasizes the former, while deductive logic lays stress upon the latter. It is inductive logic which shows how man has acquired _new_ knowledge; inductive logic explains the mode of procedure adopted by the discoverer and the inventor. On the other hand, deductive logic is distinctly a science of criticism. Induction _directs_ to new truth; deduction aims to _modify_ and _correct_ new truth.

=3. TWO TYPES OF MIND.=

Though there are many _special_ forms of thought, yet there are but two _general_ forms; namely, induction and deduction. Inductive thought seeks the new; deductive thought corrects the old. Similarly, there are two types of mind: the inductive type and the deductive type. The former _reaches out for new things_, the latter is satisfied with _ordering the old_. In politics the man with the inductive type of mind becomes a “Liberal” or a “Progressive”; while the man with the deductive type of mind becomes a “Conservative” or a “Standpatter.” It must be conceded that _both are needed in the development of the best form of Democracy_. We need an _unfettered_ freedom as advocated by Jefferson; but we also need an _ordered_ freedom as taught by Hamilton.

=4. TOO MUCH CONSERVATISM IN SCHOOL ROOM.=

Since the beginning these two mental types have been in evidence――the liberal who wants to _do_ things, and the conservative who wants to _weigh_ things. With the liberal, it is fight whether or no; with the conservative, it is fight provided the enemy is not too formidable. The one _dares_; the other _cautions_: both are needed to balance the world.

Liberalism and conservatism may be fostered in the school room, and to maintain a true balance each must receive its share of attention. Is such the case? The passing of “district-school-individualism” and the coming of “graded-school-collectism” has transferred the emphasis from liberalism to conservatism――from the inductive type to the deductive type. In this day it seems to be more important to have the child’s work _orderly_, than to have it _original_. In the main, examination papers call for correct knowledge and not for thought; in the main, promotions are based on _accuracy_, not on _initiative_. The conservative type being in control, the schools are sending out too many “Deductives,” not enough “Inductives.” The world needs more Columbuses and Edisons.

=5. THE METHOD OF THE DISCOVERER.=

A change must come. The methods of instruction are too didactic and not sufficiently inspirational. Greater attention must be given to the spirit of discovery and less to the spirit of correction. _The teacher must lead less and follow more; must correct less and suggest more; must tell less and direct more._ If we are to give greater attention to the training of discoverers, logic may aid in this crusade by calling attention to the common mode of procedure which the discoverers of the past have adopted. This is a legitimate topic for the logician, since _induction_, _deduction_, _hypothesis_, and _proof_ have ever been common tools in the discoverer’s workshop. With a view to becoming better acquainted with the common mode of procedure of the man who seeks for new truth, let us study two typical instances:

(1) The Discovery of Neptune.

The discovery of Neptune was a double one. Early in the present
century it was found that Uranus was straying widely from his
theoretic positions, and the cause of this deviation was for
a long time unsuspected. Two astronomers, Adams in England and
Leverrier in France, the former in 1843 and the latter in 1845,
undertook to find out the cause of this perturbation, on the
supposition of an undiscovered planet beyond Uranus. Adams
reached his result first, and the English astronomers began
to search for the suspected planet with their telescopes, by
first making a careful map of all the stars in that part of the
sky. But Leverrier, on reaching the conclusion of his search,
sent his result to the Berlin observatory, where it chanced
that an accurate map had just been formed of all the stars
in the suspected region. On comparing this with the sky, the
new planet, afterward called Neptune, was at once discovered,
23d September, 1846.

(2) Bees are guided in their flight by a knowledge of their
surroundings, not by a general sense of direction.

“M. Romanes took a score of bees in a box out to sea, where
there could be no landmarks to guide the insects home. None of
them returned home. Then he liberated a second lot of bees on
the seashore and none of these returning, he liberated another
lot on the lawn between the shore and the house. None of these
returned, although the distance from the lawn to the hive was
not more than two hundred yards. Lastly he liberated bees in
different parts of the flower garden on either side of the house,
and these at once returned to the hive.” (Hibben.)

A multiplication of instances would only give stronger evidence to the fact that the mode of procedure adopted by the discoverer and inventor conforms to these three general steps: (1) antecedent facts, (2) forming an hypothesis, (3) verification. It will be to our advantage to study somewhat in detail these three steps.

(1) Antecedent facts.

In the discovery of Neptune the _decisive_ or _crucial fact_ was the knowledge that Uranus deviated from his true path about the sun. This knowledge was obtained through observation and mathematical calculation. But the hypothesis of the existence of another planet could not have been formed had it not been for the _more fundamental facts_ of inertia, gravitation, falling bodies, etc. For the sake of definiteness antecedent facts may thus be divided into _foundation_ facts and _crucial or decisive_ facts. The latter are an outgrowth of the former. The _foundation_ fact of the second illustration is Romanes’ knowledge of animal instinct; while the _crucial fact_ is, no doubt, the observation that bees fly in a circle before starting for home. In the case of Newton’s discovery of the law of gravitation, the falling of the apple was the crucial fact; while his knowledge of terrestrial gravity proved to be the vital foundation fact.

_A crucial fact is one which leads immediately to the formation of a reasonable hypothesis._ It is not to be inferred from this that the same fact becomes a crucial one to _all_ alike. The falling of the apple was only crucial to a genius like Newton. With the average only _extraordinary_ facts become crucial; but with the genius any _ordinary_ fact may become crucial. Both the scholar and the genius may have the foundation facts, but only the latter may be able to read into a dry fact or event, a new world of truth.

(2) Forming an Hypothesis.

From the viewpoint of logical correctness, the matter of hypothesis has received due attention in an antecedent chapter; we need now to look at the subject through the eyes of the discoverer, not the logician. The crucial fact at first creates an intellectual perplexity which is accompanied with an uneasy, dissatisfied state of mind. This unsatisfied feeling drives the intellect to protracted thought. As a final result some hypothesis is constructed which seems to explain the crucial fact. Here is where analogy functions in a most vital manner. No hypothesis is forthcoming unless it resembles the crucial fact. It has been remarked elsewhere that analogy is the basic element in the forming of hypotheses. So it transpires, that the protracted thought referred to, is virtually a mental effort to detect significant resemblances between the well known crucial fact, and some hypothetical fact which the imagination may picture. To put it differently: The crucial fact arouses a mental state of unrest which in turn drives the mind to a “still hunt” for _relations_. The establishment of the hypothesis is simply a makeshift, designed to satisfy this “mental urge.” In the discovery of Neptune the crucial fact, the deviation of Uranus, produced a state of uneasiness in the minds of the astronomers. Surely something was wrong. This urged them to further meditation, which finally resulted in the hypothesis that there must be an unknown planet beyond the orbit of Uranus. They assumed, of course, that the relation between this supposed planet and Uranus was analogous to the relation between any two of the known planets. In the case of Newton the falling apple stirred his astute mind to the assumption that the same force which pulled the apple, likewise pulled the moon towards the earth. Here we have again (1) the crucial fact, (2) the mental urge, (3) the analogous hypothesis.

(3) Verification.

Forming an hypothesis only partly fulfills the demands of an unsatisfied intellect. The true discoverer, being possessed with a passion for truth, seeks for “the truth, the whole truth, and nothing but the truth.” In consequence the hypothesis is subjected to tests which may lead to its confirmation, its rejection, or its modification.

The two possible modes of verification are recourse to experience and appeal to reason; or _empirical_ proofs and _rational_ proofs. In the former the hypothesis is compared with facts by means of further observation and experiment. M. Romanes’ experience with the bees is a fair illustration of this form. Possibly the student has already noted that Romanes’ mode of procedure conforms to the “joint method of agreement and difference.” In the case of rational proofs the hypothesis is subjected to deductive demonstration, either of the form of syllogistic argument or mathematical calculation. A fair sample of this kind of verification is Newton’s discovery of universal gravitation. When he decided that the moon and the apple might be controlled by the same universal force, he undertook to establish his hypothesis by mathematical calculation. At first his figures seemed to disprove his theory, but after a wait of ten years, new data relative to the diameter of the earth, removed the apparent discrepancy. In the case of the discovery of Neptune, the verification was both rational and empirical. Mathematical (rational) calculation led to the assumption that the new planet must be at such a point. With this knowledge the observer was enabled to turn his telescope to the spot indicated and there, true to the calculations, was Neptune (empirical).

To summarize: The method of the discoverer involves a knowledge of certain fundamental facts; the observation of crucial facts; a mental unrest; the constructing of an hypothesis through analogy; and finally verification by either appeal to experience, or mathematical demonstration.

=6. THE REAL INDUCTIVE METHOD OR DISCOVERER’S METHOD NOT IN VOGUE
IN CLASS ROOM WORK.=

It has been remarked elsewhere that there are two general mind types, the liberal and the conservative. Also that the natural method of thought animating the former is inductive; while the natural method of thought of the latter is deductive. The “liberal” is the apostle of _new_ truth; the “conservative” an apostle of _safe_ truth. Both types are needed; the one to balance the other. In consequence both methods are of service in the class room; here each should be given its proportionate place. That this condition does not obtain may not be apparent, since much attention is being given to certain inductive forms, such as “proceeding from the concrete to the abstract,” “from the particular to the general,” “from the known to the related unknown,” etc. Likewise the courses of study and the various text books, claim to advocate the use of the inductive process. Seemingly these facts point toward a very general observance of the inductive tenets. This is true with one vital exception: Induction is the natural method of the discoverer. With it he _acquires_ knowledge; but in the class room induction is used to _impart_ knowledge. In life the discoverer takes the initiative, thinks his own thoughts first hand; but in the school room, above the kindergarten, the child is not allowed to take the initiative, not even in his play. All is planned for him, all doled out, not in the raw, but partially made over. The teacher must impart a certain amount of knowledge in a given time, and consequently she must “set the pace” in this race for _second hand facts_. To allow the child to lead; to give him the benefit of his own individuality; to permit him to use the God given spirit of discovery which clamors for recognition; would be suicidal according to our present standards. If the plan of the discoverer were followed, the course of study could not be covered; children would fail of promotion; and criticism would be forthcoming from both principal and parent.

_In the average class room of the day the inductive FORM prevails but the SPIRIT is not in evidence._ Like a wolf in sheep’s clothing induction has entered the class room to devour that primal force in the child’s make-up, which has raised his race above his simian ancestors. Our class room methods, being inductive in form but deductive in spirit, may train the youngster to be a _camp follower_ but never a _leader_ in thought and action. The call of the day is for more initiative; for more originality; for more individuality; for more enthusiasm. There is too much form without the spirit; so much that bespeaks system and refinement without those native impulses and native abilities which mark one child from another. Like the books of a library our children are classified and labeled, and when more come in the others are dusted and placed on the next higher shelf. How many more centuries must we wait before the schools will adopt, in spirit as well as in form, the pedagogical principles of life? Will the time ever come when it may be said _that all our leaders in thought and action are college graduates_?

=7. AS A METHOD OF INSTRUCTION DEDUCTION IS SUPERIOR TO INDUCTION.=

The inductive method is pre-eminently the method of the discoverer only when it involves both the _form_, which he follows, and the _spirit_, which he evinces. The so-called method of the school room is _inductive in form_, as the procedure is from particular facts to general truths; but _deductive in spirit_, as it is used to _impart_ knowledge. If it were inductive in spirit, the child would be allowed to _acquire knowledge entirely through his own initiative_. Deduction is the method of _instruction_, whereas induction is the method of _discovery_. That the child of the school is _instructed_ or better “deducted” and _not generally allowed to discover_, is a situation so apparent that we need not labor the point further.

Because the inductive process has been made a method of instruction, it has been robbed of its chief advantage over deduction. Indeed, as a method of instruction, deduction is really the superior method. It requires less time, demands greater concentration, often arouses more interest, and creates situations which are less involved.

=8. CONQUEST NOT KNOWLEDGE THE DESIDERATUM.=

In all great inventions, man has taken his cue from nature. In inventing the telescope, his model was the eye; in building his house, his inspiration was the cave. In reality man has accepted nature’s suggestions, and then attempted to improve upon them. In this he has met with success. From the crab apple tree, he has developed the northern spy; from the _wild_ hen which laid 25 eggs a year, he has evolved the modern hen which produces 225 eggs a year. Moreover, man has attained his greatest successes by _enlarging_ upon the thoughts of nature and not by _unmixed substitutions_. Burbank, through a long process of years, has changed the color of a flower, but in accomplishing this did he not use some hidden tendency of nature? Burbank, with all his wisdom, cannot give a flower color unaided by “Dame Nature.”

When man commenced to study nature’s mode of education, he saw that fearful sacrifices were entailed, both in time and in energy as well as in life itself; and so he evolved a _more economical way_ of leading the child through the experiences of the race. In consequence, he has developed the present splendid system of education.

In the evolution of all great institutions, there are in evidence crucial weaknesses, and in the evolution of man’s educational system it appears that he has erred in adopting nature’s _form of education_ without her _spirit of education_. In his anxiety to have the young acquire as much as possible, man has overshot nature’s true purpose. For example, the big word in man’s educational system is _knowledge_; but the big word in nature’s educational system is _conquest_. Nature gives man knowledge simply to reward him _for his effort_; but man would give to his fellow the reward _without the effort_. According to nature, the strongest men are those who _overcome_ most; according to man, the strongest men are those who _know_ most. The common educational principles, such as, “From the concrete to the abstract and from the known to the related unknown,” etc., are interpreted by man from the viewpoint of _knowledge_; whereas nature would teach that these are a feasible way to develop _power――to grow manhood_. It is seen that nature uses knowledge only as a means to an end, and therefore when man uses knowledge as an end only, he is trying to substitute a plan of his own for nature’s plan. _The best results can be secured only when man co-operates with nature in developing, and at the same time regulating, the spirit of conquest._

=9. MOTIVATION AS RELATED TO THE SPIRIT OF DISCOVERY.=

It has been remarked in this chapter, that the “crucial fact” serves to stir the mind of the natural born discoverer to an activity raised to the nth power of effectiveness. Naturally, the intent of such activity is to _solve the mysteries_ which the crucial fact may suggest. This passion of the mind to “know more about it” is appropriately termed “the mental urge.” From the viewpoint of the pedagogue, the “mental urge” is simply an intrinsic interest in the situation at hand; an interest born of an innate or acquired passion to know the truth.

With the average child, the “mental urge” is strong only when the situations appeal to some immediate need or vital experience. The attempt to make the school work concrete and vital; to make it answer the child’s natural curiosities and real necessities, is dignified with the name “_motivation_.” It is obvious that this is a new term for an old condition. To motivate the work, means to give to it an attractiveness which _any_ situation might have for the true born discoverer and inventor. _If we would use the discoverer’s method successfully, we must learn the art of motivating the work._ This may be accomplished by appealing to the play instincts, to the business instincts, and to the vital interests of every day life.

=10. DISCOVERER’S METHOD OR THE REAL INDUCTIVE METHOD ADAPTED TO
CLASS ROOM WORK.=

A revolt has already set in against this insatiate desire to teach _knowledge_, rather than to teach the _child_. Many schools are permitting a study of those topics which vitally concern every day life. Less attention is being given to formal discipline, and more attention to self activity. Gradually will the scheme of education be directed toward fitting the school work to the child, rather than fitting the child to the school work. When this new thought in education is fully upon us, then will every device and method be directed toward giving full scope to the _spirit of inquiry_, which so completely possesses every normal child.

It now remains for us to indicate ways in which the spirit of inquiry, or the “discoverer’s method,” may be adapted to school room work. In the first illustration, we shall outline the topic as it is generally given in the average school where attention is paid to development work. This will then be followed by a second outline which may be suggestive of the discoverer’s mode of procedure.

First illustration. _School Room Method._

I. Aim: To teach addition of business fractions.

II. Preparation: (Only type examples given).

(1) (2) (3)
3 bushels 3 parts Rule: Only like numbers
+ 5 bushels + 5 parts can be added.
――――――――――― ―――――――――
8 bushels 8 parts

III. Presentation:

(1) (2) (3) (4)
3 ninths 3/9 2/3 = 4/6 2/3 = 8/12
+ 5 ninths + 5/9 1/6 = + 1/6 3/4 = + 9/12
―――――――――― ――――― ――――――――――― ――――――――――――
8 ninths 8/9 5/6 17/12

IV. Summary:

(1) Only like fractions can be added.

(2) Change unlike fractions to like fractions.

(3) Add the numerators, placing the sum over the common denominator.

V. Application:

Examples and problems involving similar and dissimilar fractions.

Before undertaking to illustrate the discoverer’s method, it may be well to designate in order the evident steps as they would appear to the pedagogue:

(1) Motivate the topic to be presented.

(2) Bring to mind appropriate “foundation facts.”

(3) Make evident the “crucial fact.”

(4) Lead to the forming of an hypothesis through analogy.

(5) Afford ample opportunity to prove the hypothesis.

_Discoverer’s Method Adapted._

Lesson Plan.

I. Aim: (1) _By playing upon the curiosity or by exposing a vital need, create a strong desire to know how to add business fractions._ (Motivate the topic.)

Curiosity: “We all know what a fraction is and we know, too, how to change fractions to higher or lower terms.” “Now I wonder how many know how to _add_ fractions, such as 2/5 and 1/5?” “Don’t you tell any one, Mary, but just write your answer on a piece of paper and show it to me.” (Mary’s answer shows that she has thought correctly, but figured incorrectly. John, after having raised his hand, shows his answer to the teacher.) “John has the right answer.” “That’s fine, but let us keep the secret, John.” “I wonder how many others there are in this class who will find the right way?” etc., _or_

Vital need: Discuss with the class the various occupations of life and secure expressions of preference. Some may plan to be real estate agents, others contractors or book keepers, etc. “George, you plan to be a book keeper.” “Let us suppose that I have given you the job of book keeper in my factory.” “Show that you are worth your wages by adding these numbers: 124¾, 647⅔.” “What! can’t do it?” “Then I don’t want you!” etc.

II. Preparation:

(2) Bring to the foreground the necessary _foundational knowledge_. Suggestions:

4 bushels 8 parts
+ 3 bushels + 2 parts
――――――――――― ―――――――――
7 bushels 10 parts

III. Presentation:

(3) Make evident the _crucial fact_. Suggestions:

Add 2 fifths 3 eighths 3/8
+ 1 fifth + 1 eighth + 1/8
―――――――――― ――――――――――― ―――――
3 fifths 4 eighths

(4) Without further suggestion, give the young discoverer suitable opportunity for finding the sum of 3/8 and 1/8. In the act of discovering, an implicit _hypothesis_ takes form in the mind through analogous reasoning. This point marks the climax of the lesson――the supreme moment, when the skill and tact of the teacher is assessed to the limit. Just here the child must have a comfortable environment where perfect concentration is possible. Nothing must be forced; and there should be nothing suggestive of disgrace or shame, if the youthful Columbus is unsuccessful. The first attempt should be without books. If more help is needed, access to books may be given. If the investigation is still without definite result, then _as a last resort_ the teacher may, in the presence of the child, _add fractions_, solving _with deliberation_ example after example, until the child believes he has discovered the process.

(5) Stimulate a desire to _verify the facts discovered_.

Suggestions leading to verification: Afford opportunity for mathematical demonstration. Illustrations: The fractions 1/4 and 3/8 have been added in this way――

1/4 = 2/8
3/8 = + 3/8
―――
5/8

Use is now made of the crucial fact, when the example assumes this form――

2 eighths
+ 3 eighths
―――――――――――
5 eighths

_Or_ if the class has been trained in the use of the diagram the following may be the form of proof:

{ ━━━━━━━━━━
1/4 { ──────────
{ ━━━━━━━━━━
──────────
━━━━━━━━━━
{ ──────────
3/8 { ━━━━━━━━━━
{ ──────────
{ ━━━━━━━━━━

Explanation from diagram. I see that 1/4 equals 2 parts and 3/8 equals 3 parts; the sum of 3 parts and 2 parts are 5 parts. But the name of the part is eighths; hence the answer 5 parts may be written 5 eighths, or 5/8. Thus the final form is

2 parts
+ 3 parts
─────────
5 parts = 5/8

Give opportunity to consult answers in text books as further verification.

The _summary_ and _application_ of adding fractions according to the “discoverer’s method,” are virtually the same as the corresponding steps in the “school room method.”

_Second Illustration of Discoverer’s Method._

David P. Page in his Theory and Practice of Teaching well illustrates the discoverer’s method in conducting a general exercise in nature study. We cannot do better than to quote from him:

“It is the purpose of the following remarks to give a specimen
of the manner of conducting exercises with reference to _waking
up the mind_ in the school and also in the district. Let us
suppose that the teacher has promised that on the next day,
at ten minutes past ten o’clock, he shall request the whole
school to give their attention five minutes to something that
he may have to show them. This very announcement will excite an
interest both in school and at home (playing upon the curiosity);
and when the children come in the morning they will be more
wakeful than usual till the fixed time arrives. At the precise
time, the teacher gives the signal agreed upon, and all the
pupils drop their studies and sit erect. When there is perfect
silence and strict attention by all, he takes from his pocket
an ear of corn and in silence holds it up before the school.
The children smile, for it is a familiar object (foundational
knowledge already in hand); and they probably did not suspect
they were to be fed with corn.”

Teacher. “Now, children,” addressing himself to the youngest,
“I am going to ask you only one question about this ear of corn.
If you can answer it, I shall be very glad. As soon as I ask the
question, those who are under seven years old, and think they
can give an answer, may raise their hand. _What is this ear of
corn for?_”

Several of the children raise their hands, and the teacher
points to one after another in order, and they rise and give
their answers.

Mary. It is to feed the geese with.

John. Yes, and the hens, too, and the pigs.

Sarah. My father gives corn to the cows.

Laura. It is good to eat. They shell it from the cobs and send
it to the mill, and it is ground into meal. They make bread of
the meal and we eat it.

“I am sorry to tell you that none of you have mentioned the use
I was thinking of, though, I confess, I expected it every minute.
I shall now put the ear of corn in my desk, and no one of you
must speak to me about it till to-morrow. You may now take your
studies.”

The consequence of this would be that various families, father,
mother and older brothers and sisters, would resolve themselves
into a committee of the whole on the ear of corn: and by the
next morning several children would have something further to
communicate on the subject. The hour would this day be awaited
with great interest and the first signal would produce perfect
silence.

The teacher now takes the ear of corn from the desk and displays
it before the school; and quite a number of hands are instantly
raised as if eager to be the first to tell what other use they
have discovered for it.

The teacher now says pleasantly, “The use I am thinking of you
have all observed, I have no doubt; it is a very important use,
indeed; but as it is a little out of the common course (crucial
facts) I shall not be surprised if you cannot give it. However,
you may try.”

“It is good to boil,” says little Susan, almost springing from
the floor as she speaks. “And it is for squirrels to eat,” says
little Samuel. “I saw one carry away a whole mouthful yesterday
from the cornfield.”

Others still mention other uses. Perhaps, however, none
will name the one the teacher has in his own mind; he should
cordially welcome the answer if perchance it is given.
(Supposing that it has not been given.) “I have told you
that the answer I was thinking of was a very simple one; it
is something you have all observed and you may be a little
disappointed when I tell you. The use I have been thinking of
for the ear of corn is this: _It is to plant._ _It is for seed_,
to propagate that species of plant called corn.” (Verification.)
Here the children may look disappointed as much as to say, We
knew that before. The teacher continues: “And this is a very
important use for the corn; for if for one year none should be
planted, and all the ears that grew the year before should be
consumed, we should have no more corn. The other uses you have
named were merely secondary. But I mean to make something more
of my ear of corn. My next question is: _Do other plants have
seed?_” Here is a new field of inquiry, etc., etc.

From the standpoint of “the greatest amount of knowledge in the shortest possible time,” this mode of presentation consumes an inexcusable amount of time and is, therefore, “impracticable.” But when viewed from the ground of interest, originality, initiative, and conquest――the watchwords of the “new thought in education”; there is no real waste in either time or energy. _The spirit and method of the discoverer will no doubt be the educational slogan of the future age._

Epitome of Discoverer’s Method, adapted to the class room:

(1) Motivate the topic to be presented.

(2) Bring to mind, if necessary, the “foundational facts.”

(3) Make evident the “crucial fact.”

(4) Furnish every opportunity for a first-hand discovery of the
“lesson-point” (establishing hypothesis through analogy).

(5) Let the hypothesis be verified.

_The entire situation must be one of freedom, zeal, originality, and initiative._

=11. THE QUESTION AND ANSWER METHOD NOT NECESSARILY ONE OF DISCOVERY.=

No one mode of presentation is more universally used than the “question and answer.” The advantages of this mode are many and the teacher who is an adept in the art of questioning, from the standpoint of knowledge, is generally efficient. The common error, however, incident to much questioning, is that of asking “telling questions.” By the use of such, the class is forced along the desired channel of thought so rigorously as to have a condition _where the spirit of inquiry is entirely wanting_. It is possible to conform to the rules of good questioning, and yet rob the class of all originality and initiative. From the teacher’s viewpoint, the discoverer’s method demands few questions; it is the method of _suggestion_ rather than one of questions. Avowedly in this method, the children should ask and answer their own questions. Viewed from the ground of discovery there are three modes of presentation which may represent a progressive series. These are (1) the lecture mode, (2) the question and answer mode, (3) the mode by suggestion. In the first there is _little_ of the spirit of the discoverer; in the second there is a trifle more of the spirit of the discoverer; while in the third there is _much_ of this spirit. The student is advised to select some class room topic with a view to illustrating these three modes of presentation.

=12. OUTLINE.=

LOGIC IN THE CLASS ROOM.

(1) Thought is king.

(2) Special functions of induction and deduction.

(3) Two types of mind.
Inductive or liberal.
Deductive or conservative.

(4) Too much conservatism in school.

(5) The method of the discoverer.
Three steps

1. Antecedent { 1. Foundational
facts { 2. Crucial

2. Forming { 1. “Mental urge”
hypothesis { 2. Analogy

3. Verification { 1. Empirical
{ 2. Rational

(6) The real inductive method or Discoverer’s Method not in vogue in
class room work.

(7) As a method of instruction, deduction is superior to induction.

(8) Conquest, not knowledge, the desideratum.

(9) Motivation as related to the spirit of discovery.

(10) Discoverer’s method or the real inductive method adapted to
class room work.
School room method.
Discoverer’s method.
Epitome.

(11) Question and answer method not necessarily one of discovery.

=13. SUMMARY.=

(1) Thought is king in that it is the ruling factor in the making and breaking of habit. This lends import to logic, which is the science of thought.

(2) The chief function of induction is to discover new truth; whereas deduction aims at clarifying and correcting new truth. Inductive logic makes known the special forms of thought which the discoverer uses; while deductive logic tends to show how he verifies the truth thus obtained.

(3) Just as there are two general forms of thinking, inductive and deductive; so there are two general types of mind, the inductive and the deductive; the former leads to liberalism, the latter to conservatism. Both types are needed to maintain a safe balance.

(4) The schools of the day are emphasizing the deductive phase of work to the sacrifice of the inductive. They are neglecting the Columbuses and the Edisons of the class. The course of study makes for a conservatism, which “nips in the bud” any marked tendency to discover and invent.

(5) Logic may aid in the crusade against the ultra conservative tendency of class method, by giving emphasis to the method of the discoverer and inventor. An analysis of this method reveals these three steps: antecedent facts, forming an hypothesis and verification. Antecedent facts may be divided into foundational and crucial. A crucial fact leads immediately to the formation of the hypothesis; whereas the foundational facts represent that body of knowledge which makes it possible to interpret the crucial fact. The crucial fact creates an unsatisfied state of mind, which, in turn, urges the discoverer to construct some satisfactory hypothesis. Inference by analogy is the process used in such a construction. The two modes of verification are recourse to experience, or empirical; and appeal to reason, or rational.

(6) In the class room, induction is used in form, not in spirit; in consequence we are neglecting the generals for the camp followers.

(7) The inductive method is logically the method of discovery, while the deductive method is the method of instruction. In the class room, both methods have been devoted to the matter of instruction. Because of this, induction has been robbed of its chief advantage over deduction.

(8) Man has attained his greatest success by _enlarging_ upon the thoughts of nature and not by an _absolute substitution_. In enlarging upon nature’s way of educating the child, man has adopted her form of procedure, but has lost her spirit of work. In his scheme of education, man’s watchword is _knowledge_, while nature’s is _conquest_. To seek knowledge without inspiring the spirit of conquest is man’s way; whereas nature’s way is to encourage the spirit of conquest by using knowledge as a reward. Man must co-operate with nature, if the best results are to be secured.

(9) In the case of the true discoverer, it is not necessary to endow the object of his thought with added attractiveness; but with the child enthusiasm may need to be stimulated by “motivating” the subject in hand. This may be accomplished by appealing directly to the vital needs, worldly necessities, and innate cravings of the child mind.

(10) A revolt is in evidence against that insatiate desire to teach knowledge, which has been so marked in the past. Already schools are introducing departments of work which look toward _conquest_ rather than _knowledge_.

When adapted to the school room the discoverer’s method naturally resolves itself into these five steps:

(1) “Motivate” the topic for presentation.

(2) Bring to mind “foundational facts.”

(3) Vividly make evident the “crucial fact.”

(4) Lead to discovery of “lesson-point.”

(5) Afford opportunity for verification.

(11) The question and answer method of presenting work, does not necessarily give full scope to the spirit of inquiry as emulated by the true born discoverer.

As a matter of affording opportunity for the development of the spirit of discovery, there are three modes of presentation which may be arranged in a progressive series:

(1) The lecture mode in which there is little opportunity for
discovery.

(2) The question and answer mode which permits some opportunity for
discovery.

(3) The mode by suggestion which permits ample opportunity for
discovery.

=14. REVIEW QUESTIONS.=

(1) Show that thought may be made to make and break habit.

(2) “Induction directs to new truth, deduction aims to modify and
correct new truth.” Explain and illustrate this.

(3) Relate radicalism and conservatism to induction and deduction.

(4) Show that in the present day school situations, the spirit of
deduction prevails.

(5) Describe a discovery which is a typical illustration of the
_discoverer’s method_.

(6) Indicate with explanation the general steps in the discoverer’s
method.

(7) Show by illustration the difference between “foundational facts”
and “crucial facts.”

(8) Explain how the “crucial fact” leads to the construction of an
hypothesis.

(9) Explain and illustrate the two ways of verification.

(10) Distinguish between the inductive method as it is used in the
class room, and the inductive method as used by the discoverer.

(11) Show that in his inventions, man enlarges upon the thoughts of
nature.

(12) Explain “motivation” and show that it is a new name for an old
situation.

(13) In adapting the discoverer’s method to class work, what are the
successive steps to be followed?

(14) Show by illustration that the question and answer method is not
necessarily one which encourages the spirit of discovery.

=15. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=

(1) “Our pet thoughts control us.” Discuss this.

(2) Select some class room experience for the purpose of showing that
induction is especially _directive_ in nature, whereas deduction
is more or less _corrective_ in nature.

(3) “There are just two kinds of people in the world, the
_Inductives_ and the _Deductives_.” Explain.

(4) Are the schools sending out too many _Deductives_? Argue the
question.

(5) “It is the business of the teacher to teach himself out of the
business.” Explain.

(6) Look up the discovery of the laws of the pendulum, with a view
of showing that the event well illustrates the fact of the three
general steps in the discoverer’s method.

(7) “With the average, only extraordinary facts become crucial; but
with the genius any ordinary fact may become crucial.” Make this
clear.

(8) Explain “mental urge.” Illustrate.

(9) Illustrate “empirical proof,” also “rational proof.”

(10) Show by illustration that the inductive method as used in the
class room, falls far short of being the method of the discoverer.

(11) Indicate by citing historical examples, that conquest rather than
knowledge makes for manhood.

(12) Show how you would motivate a topic in geography.

(13) Outline a plan for teaching some topic in nature according to the
discoverer’s method.

(14) Select a topic in arithmetic, for the purpose of giving a
comparative illustration of the “question and answer mode” of
presentation, and the “mode by suggestion.”