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.”