THE DEDUCTIVE LESSON
The complete process of thought involves both induction and
deduction. Every general principle, unless it is self-evident,
must either be arrived at through the process of induction, or be
accepted without any attempt at verification. Having formed our
generalizations, we use them as a basis for further thinking. If
we find that the principle always holds, we are satisfied with
its validity. In this testing of the generalization tentatively
made, the process of thought is deductive. The fact is that in the
process which we designate as induction, deduction enters to verify
our inference. In the face of the problem which can be settled
only by reference to some established principle, we find ourselves
questioning the generalizations formerly accepted, and the process
of thought in solving our problem will involve induction as well as
deduction. For convenience we treat the problems of teaching under
the two heads, the inductive and the deductive lesson, according as
one or the other type of thought seems to predominate in reasoning
required to solve the problem involved.
Every one thinks deductively who has had sufficient experience to
form any generalizations. In the early life of the child we find
the psychological basis for deduction in the tendency to act in
accordance with ideas. Children define things in terms of their
function. Thus a hat is something to wear on the head; a drawer
something to pull out and push in; a shovel something to move the
sand with; and so for the other objects in the child world. A child
makes a dog in clay, draws a picture of a flower, makes a house
of his blocks—and in this way tests his ideas. Not all deductive
thinking ends in motor activity; but we can never be satisfied with
our deductions until we have established them experimentally. The
question concerning our ideas always is, will they work?
Whenever we offer an explanation of our ideas or of our actions,
the process of thought is deductive. Not that either adults or
children often state the general principle upon which they base their
statement or action. We are all only too prone to assume the general
principle. The foolish answers which children give may be logical
enough. From his very limited experience a boy may have generalized
that grass is something to look at and not to be walked on, and that
people always live in houses from four to ten stories high, with
many families in a house. Now, if such erroneous generalizations
have been developed, the way to handle the boy is not to laugh at
his deductions from these premises, but rather to require him to
state the generalizations upon which he has based his thinking, and
to lead him to discover their inadequacy. It matters not what group
of children one works with, this same need for a declaration of the
principle upon which the argument is based, the generalization which
covers the situation under consideration, will be found essential.
That teacher does much for the children who frequently pushes them
back to a statement of what they assume to be true. This statement
is not always easy to make. Even with adults it is very common to
explain action by reference to some feeling or attitude which it
is assumed has some basis in reason. Some instinctive tendency, or
a mode of feeling, thinking, or acting which has become habitual,
frequently explains, but fails to justify our actions. The ability
to state clearly what one assumes, and to claim as valid only such
conclusions as are based on premises which are admitted to be true,
is the mark of the man of unusual rationality.
There is no set of rules which a teacher may follow in order to make
the children she teaches logically minded. On the other hand, all of
her activity tends in some degree to encourage or to eliminate the
logical habit of mind. The teacher who dogmatizes continually in her
teaching can do little to overcome a like tendency in the children
by conducting exercises logically correct. The wrong emphasis on
correctness of the result, instead of correctness of the method
employed in getting the result, encourages much illogical work and
develops careless habits of thought. And it is just as true that an
open-minded attitude on the part of the teacher will be reflected
in the children. The teacher who insists upon the verification of
generalizations, who asks children frequently to give the ground for
the statements which they make, and who encourages reflection, will
engender logical habits of thought.
To recognize the wide application of the deductive method in our
thinking, one has only to consider what is meant by reflection.
It is well also in this connection to remember that the habit of
reflection distinguishes the educated from the uneducated man. It
is not the number of experiences which makes the difference between
men, but rather the use that has been made of those experiences.
When we reflect, we think over, organize, and relate our past
experiences. Suppose, for example, that some one makes the statement
that corporal punishment should be banished from all schools. If
you reflect upon such a thesis, you bring to bear your experiences,
whether of action, observation, or thought stimulated by reading
what some one else has said; and, as a result of your thinking, you
consciously or unconsciously assume a general principle under which
you feel satisfied that this question of discipline falls; and then
you will refer all of your experiences to this principle, testing its
validity by seeing whether or not it does uniformly hold. The process
of thinking which you have employed is essentially deductive. If
stated in the form of a syllogism, it might be expressed somewhat as
follows:—
1. Any action which tends to brutalize either pupil or teacher should
not be permitted in any school.
2. Corporal punishment tends to brutalize both teacher and pupil.
3. Hence corporal punishment should be banished from all schools.
The process of thought employed has led you to search for a general
principle which you accept as true and which offers an explanation
of the position which you take in agreeing that corporal punishment
should be banished. If you are really reflecting, you will not stop
with this reference to a generalization apparently true. Rather you
will inquire whether in your experience the infliction of corporal
punishment has tended to brutalize you. You will also ask yourself
whether this is true of others, and to what degree. You will recall
specific cases of punishment of this sort, and will try to decide
whether the disadvantages or evil outweighed the good. Only after
such careful thought is the process of reflection complete, and it
is only then that you can feel satisfied of the soundness of the
position which you have taken. It will be noted that the process of
thought has been both inductive and deductive.
If children are to learn to reflect, they must have leisure to think
over their past experiences. There is danger that in our desire for
more knowledge and more activity on the part of our pupils, we may
give them little time for reflection. To ask a child to state the
significance of what he has done, to encourage him to examine every
assumed truth in the light of his experience, and to state somewhat
formally the result of his reflection is worth much more than the
new experiences which might have been gained in the same length of
time. The habit of reflection will be developed only when sufficient
time is given for children to stop and take account of the experience
which they have had, when respect is accorded the experiences of
the individual, and when the teacher requires such work and guides
children in the process.
An attempt has been made in the preceding pages to indicate in a
general way the significance of the deductive method in our school
work. It remains to indicate briefly the method of procedure in the
conduct of class exercises which are essentially deductive in their
nature. Such exercises will be found in any subject in which there is
developed a body of general principles. For example, the real test
of a pupil’s knowledge of a principle of arithmetic is found, not in
familiarity with the process of induction by which the principle is
derived, nor in his ability to apply this principle to the problems
given in the book, immediately following the rule, all of which fit
the generalization, but rather in his ability, when a miscellaneous
list of problems is given, to pick out the principle which applies
to this one case. The test of one’s knowledge of geography is found
not simply in the facts which he knows, but also in his ability to
explain phenomena or to anticipate situations by reference to a body
of general principles.
_The problem_: From what has already been said it is clear that in
deductive thinking, as well as when the process is inductive, the
occasion for thought is found in a problem to be solved. We wish
to know why a certain region is arid or what the possibilities of
agriculture are in another, and we, therefore, recall our knowledge
of the principles of geography in order to solve our problem. A moral
situation confronts us; we need to act; and in response to this
necessity we endeavor to refer the situation to some norm or standard
of conduct which we accept as fundamental. The success of our work in
securing clear thinking by children will always be conditioned by our
success in enabling them to realize the significance of the problem
presented for solution.
_Finding the generalization or principles_ which fit the situation
to be accounted for or explained is the next step. In order to
accomplish this part of the process successfully one must be able to
discover that which is essential and to neglect the non-essential in
the problem to be solved. Suppose, for example, that the problem is:
Why has the greater part of Africa not been settled by civilized men?
The factor which is significant is the climate of this region, and it
will be of no use for the pupil to recall the size of the continent,
the color of its inhabitants, the fact that Livingstone made a
journey across it, except that by eliminating these facts he may be
brought to realize that none of them determine the situation, and
hence he need no longer pay any attention to them. It is the function
of the teacher to suggest to the pupil a number of alternatives
and then to guide him in his search for the determining factor.
For example, the teacher might ask: Is it because of the savage
inhabitants, because of a lack of means of transportation, because
the country is overrun by dangerous wild animals, or because of
climate? Each of these classes of facts may be known to the pupils,
and each in turn may be eliminated as non-determining factors until
he comes finally to the last. He must then, provided he decides that
climate may determine the availability of a region as a habitation
for civilized man, discover under what condition of climate civilized
man fails to make advance. He has thus fitted his situation, his
problem, to the generalization under which it falls, and has, in
fact, taken the next step in the process.
_Inference_: The inference that the greater part of Africa is not
inhabited by civilized men because of adverse climatic conditions
is arrived at just as soon as the pupil settles upon climate as
the essential factor. Just as in the inductive process we pass
immediately from the step of comparison and abstraction to the
statement of the generalization, so in the deductive lesson, when
once we have related the particular case under consideration to
the principle which explains the situation, we are ready to state
our inference. There is real value in making such a statement. The
further process of verification depends upon a clear and definite
statement of the inference; and the best test we have of the
completion of the preceding step is the ability which the pupil shows
to state his inference.
_Verification_: When the inference has been made, we have yet to
satisfy ourselves concerning the validity of our reasoning by an
appeal to known facts. Following the illustration already used,
we should ask ourselves what has happened in the past to civilized
men who have gone to Central Africa. We will be satisfied that our
reasoning has been correct, only if all of the facts we are able to
discover point unmistakably to the conclusion that the climate of the
larger part of Africa is unendurable by civilized men.
The element which needs most emphasis in deductive teaching is the
realization on the part of the teacher that the success of the
process is directly proportional to the independence with which
the pupil discovers for himself that which is essential in the
situation under consideration, his attempt to fit or relate the
particular case to the principle or generalization by which it will
be explained, and his willingness, when he discovers his error by
an attempted verification, to repeat the process. We do not think
logically by having some one else do our thinking for us, nor is our
growth measured by the uniformity with which we hit upon the correct
solution of the problem at the first attempt. Rather we may measure
success by the power of our pupils to criticize the reasoning which
appears plausible until carefully scrutinized, and by their readiness
to retrace their steps and to search for firmer ground when they have
of their own accord given up a scheme of reasoning which has proved
invalid.
FOR COLLATERAL READING
W. C. Bagley, _The Educative Process_, Chapter XX.
I. E. Miller, _The Psychology of Thinking_, Chapter XVIII.
_Exercises._
1. A class is engaged in deriving inductively the generalization
that multiplying the numerator of a fraction by any number
multiplies the fraction by that number; will there be any occasion
for deductive thinking as the work proceeds?
2. A history teacher has tried to develop the generalization that
taxation without representation is tyranny. A girl in the class
says that this proves that women should have the right to vote.
Analyze the process of thought by which the girl arrived at her
conclusion. Was the process essentially inductive or deductive?
3. Some people pride themselves upon the fact that they never
change their minds. What comment would you feel justified in making
concerning their processes of thought?
4. Why can the leader of a mob influence his followers to most
unreasonable action?
5. An eighth-grade boy remarked that he thought that we should
forbid all foreigners to come to the United States. How would you
lead such a boy to change his point of view by means of his own
thought on the subject?
6. A class in grammar was required to commit to memory fifty rules
of syntax and later to correct sentences in which the mistakes in
syntax were covered by the rules already learned. Could you suggest
a better way to teach English syntax?
7. What is the value of the miscellaneous problems given at the end
of each section of the arithmetic? A teacher of arithmetic went
through one of these lists and had the class indicate opposite each
problem the case, or rule, which was involved. Was this a good
thing to do?
8. What sort of reasoning is demanded of a class in parsing?
9. Do you consider your teaching of arithmetic, in so far as it
involves reasoning, mainly inductive or deductive?
10. In what sense is it true that in deduction we begin with
a particular rather than with a generalization? Compare the
significance of the problem in induction and deduction.
11. In some textbooks in geometry, the problem is stated, and then
the proof is presented step by step with a reference wherever need
be to the principles involved in developing the proof; what is the
weakness of this sort of an exercise?
12. How can the teacher best help children who are unable to refer
a problem in arithmetic to any one of the principles which have
been learned?
13. Children often make mistakes in reasoning which seem ridiculous
to teachers; how can teachers be most helpful in such situations?
14. Do you think it possible to teach children the meaning and
significance of reflection? How would you attempt to secure such
insight?
15. Why would it be valuable for us many times to write the reasons
for our action before carrying into effect our plans?
16. What can you do as a teacher that will stimulate children to do
their best thinking? Is it possible that you may actually interfere
or discourage them in this part of their work? How?