THE INDUCTIVE LESSON
We are skeptical to-day of that sort of teaching which aims mainly
to equip children with a body of accepted knowledge in order that
they may some time find use for this body of information in later
life. We emphasize, rather, the control of mental activity which
makes for the discovery of truth and the avoidance of error. Thinking
of this sort is purposeful. We control or direct our ideas toward
some end, toward the solution of some problem. One great purpose of
teaching must be to provide the opportunity and the stimulus for this
kind of thinking. We may not be able to lay down any fixed order of
procedure, nor to devise any set of rules whereby children may be
trained to be good reasoners; but we can consider what is involved
in the process, point out the possibilities of interference, and
suggest some of the means to be employed in encouraging this type of
mental activity on the part of children. In this chapter we shall
confine ourselves to that type of reasoning which we call inductive.
This type of schoolroom exercise has usually been treated as composed
of five steps; namely, preparation, presentation, comparison and
abstraction, generalization, and application. We shall employ this
classification to guide us in our discussion of the process.
_Preparation_: To prepare a child to reason in a given situation from
the data in hand to the conclusions which must of necessity follow,
it is first of all necessary that he should see that the situation
presents a problem. We reason only when we have some aim or purpose
which can be satisfied by the process. But if consciousness of aim or
problem is at the foundation of this type of thinking, and if we are
to deal with children in groups, it is essential that the situation
which involves the problem be made the common possession of all.
The step of preparation presents these two problems to the teacher:
(1) to find a basis in experience already had, or to provide the
experience which involves the problem to be considered; (2) to make
the children feel the necessity for the solution, _i.e._ to make the
problem vital to them.
In considering the necessity for common experience as a basis
for discovering the problem to children, we are dealing with the
principle of apperception. Briefly stated, it is this,—that any
object or situation has meaning for us only as it connects itself
with and is interpreted by our previous experience. Suppose, for
example, that a group of first-grade children were asked to tell what
made seeds grow. It is possible that some of them would not know,
could not interpret from past experience, the meaning of seeds. If
the class were at work in a large city, we could be sure that many
had never been conscious that growing plants had any connection with
seeds, and there would be few, if any, who had ever noticed the
conditions under which such growth takes place. The first problem for
the teacher in this case would be solved only when, through recall
of past experiences, observations, or experiments, the experience
“seeds growing” became the common possession of the group. This is
an extreme case, one in which the experience which involves the
problem is entirely wanting. At the other end of the series, we may
have a problem for consideration, the basis for which is found in
experiences common to all children. But even though this be the case,
there will still be need for the recall of the experience and for
making prominent some factor heretofore unnoticed before the children
will be ready to reason. We may suppose that all children have
had experience with streets or roads, but we shall want to recall
many of these experiences in order to make significant the problem
of transportation which we wish to consider in the class in home
geography.
The step of preparation has only partially accomplished its purpose
when the experience necessary to the realization of the problem has
been recalled or provided. Still greater skill is required in making
the child conscious of the problem. Indeed, it may well be argued
that in the curriculum as it is at present organized, very many of
the problems that we ask children to solve are problems for them
only because we, as teachers, require that that certain piece of
work be done. Often the child’s problem consists mainly in avoiding,
as far as possible, the work which we require, which has little or
no significance for him. Children would do much more thinking if
we were only more careful to give them childish problems to solve.
Too frequently the organization of knowledge which we impose is
influenced exclusively by our adult logical conceptions. Not that
children should be illogical, but rather that child logic and the
child’s ability to reason depend upon his ability to appreciate
problems, upon his experience, and upon his ability to interpret that
experience. When we impose our adult point of view upon him, when
we ask him to take _our_ problem and with the data that _we_ supply
ask him to work out our solution, whatever else may be said of the
exercise, it may not be called an exercise in reasoning by children.
If we do respect the child’s experience and point of view, the
task still remains of making all of the group of children we teach
conscious of the aim as _their_ problem. There is no greater test of
teaching skill than this. Can the teacher, after having brought to
mind the experiences which are relevant to the work she wishes the
children to do, make them conscious of a lack in this experience;
can she awaken the need for further consideration of past experience
and a desire to reconstruct and to amplify it? In proportion as she
is able to accomplish this result, we may be sure that children
are reasoning upon problems which are vital to them, and that the
motive has been provided which will secure the maximum of controlled
intellectual activity on their part. The best single test of the
accomplishment of this ideal is to require that the statement of
aim be made by the children themselves as a result of the guidance
we have given. This conception of the meaning and significance of
the aim suggests the solution of the difficulty which some people
find in harmonizing the idea of instruction with the doctrine of
self-activity.
Instruction, when properly conducted, does not impose the ideas, the
problems, or the conclusions of adults upon children. Rather we are
concerned in instruction with the child’s experience, his tendency
to react, his need of adjustment; and our function as teachers is
to guide him, to stimulate him to his own best efforts, to insure
the maximum of self-activity while we guide this activity toward the
accomplishment of ends which are desirable. The difficulty is, of
course, that the problem for solution at any given time may not be
equally vital to every member of the group. Here is where the element
of control enters somewhat in opposition to the self-activity of
the individual. But this condition of affairs is necessarily true
both in school and out of it, for society sets up for us certain
norms or standards of experience which must be realized by all, and
we must for the sake of economy handle children in groups. If the
problem is not beyond the child’s comprehension, if it deals with
situations which are significant to him, if the solution derived has
some bearing on his future action, if he has carefully scrutinized
his experience in the light of the problem stated and has brought to
bear those elements which are significant for its solution, we may be
confident that the activity resulting is closely akin to that which
is found in the controlled thinking of men the world over.
In order that it may be more easy for children to focus their
attention upon the problem in hand, there is considerable advantage
in a clear, concise, concrete, and preferably a brief statement of
the aim.[7] A problem is half solved when one can state it clearly.
So long as the problem is not sufficiently well defined to admit of
accurate statement on the part of pupils, there is danger that there
may be much wandering in its consideration. One of the great lessons
to be taught in work of this sort is the need of examining the ideas
as they suggest themselves to see whether or not they are relevant.
The argument as it has been stated above points to the statement of
aim as the culmination of the step of preparation. This does not
mean that a considerable period must always elapse in the conduct
of an exercise of this type before the aim can be stated. There
are occasions, and when the teaching has been good they should
be frequent, when the lesson should begin with the statement of
the problem discovered in a previous lesson and made clear in the
assignment of work. In other cases the same aim may hold for several
days; _i.e._ until the problem is solved. In general, as we advance
through the grades, the ends for which children work should become
relatively more remote, and the achievement of these ends should
require a longer period of work. There is an advantage in setting up
subsidiary aims which will make steps of progress in the realization
of the larger purpose.
Another distinction that it is well to keep in mind concerns the
development of intellectual interests on the part of children.
The characteristic aim for a first-grade child may make its
appeal chiefly to his desire for satisfaction, which has little
intellectual significance; but education fails if it does not make
for an increase of interest in intellectual activity. For example,
a first-grade boy may be led to count because he wants to be able
to tell how many marbles he has, or how to measure the materials
he uses in constructive work; while the mathematician may work
night and day upon a problem of mathematics because of a purely
speculative interest in the result. We may not hope to produce the
great mathematician in the elementary school, but we may hope after
a certain point has been reached in our study of arithmetic that a
boy will recognize the necessity for drill in addition simply because
he realizes that in the ordinary affairs of life this knowledge is
required.
_Presentation_: The full realization of the problem to be solved
involves a consideration of data already at hand in experience. When
we have the problem clearly in mind, we examine this experience more
carefully to see what bearing it may have upon the solution, or we
gather further data, observe more critically or more extensively,
or experiment in such a manner as to involve the solution of our
problem. What is the function of the teacher during this part of the
process? There is no single answer to this question. Sometimes the
work of the teacher will consist almost wholly in helping children to
recall their past experience and to apply it to the question at hand.
At another time, when experience is lacking, the teacher must direct
children to the sources of data, guide them in their observations
or experiments, or even give them outright all of the data that she
can bring to bear on the situation. It will not always be economical
to wait for children to gather the data for themselves, just as
it is not _always_ feasible to require them to reach conclusions
for themselves. There are times when the best teaching consists in
demonstration, and occasions arise when the only feasible course for
the teacher is to literally flood the children with data from which
they may draw their conclusions.
Again the problem of gathering data becomes the problem of memory. We
want children to think, and we should insist that they gather facts
with reference to the solution of some problem; but the _solution_
may not always be immediate. We may suspend judgment while we
gather further facts and organize them. The facts gathered for one
purpose, when rearranged with reference to a new problem, take on
a new meaning. If this be true, we may not in our zeal for clear
thinking neglect the tools with which we work. There may be some
people who have a great many facts and who reason little, but no one
can reason without data. Our ability to think logically upon any
topic is conditioned by our ability to see facts in new relations, to
reorganize our data with reference to new problems; but facts we must
have, and a memory stored with facts is one of the greatest aids to
thinking.
One of the means mentioned above for the gathering of data was
observation. It is necessary that we appreciate the fact that
observation involves something more than having the thing present to
the senses. Our observations are significant for our thinking when
we have clearly in view the problem which the observations are to
help solve. Teachers sometimes make the mistake of supposing that
when children have objects with which to work they have a problem. It
is not unusual to hear teachers speak of objective work as concrete
work. Now the concreteness of a situation is not at all dependent
upon the presence of objects. Logically a situation may be concrete,
and yet present no objects to the senses. On the other hand, objects
may be present, children may be directed to use them, and yet in the
absence of any real problem the work done may be of the most abstract
sort. Objects help to make a situation concrete when the problem
under consideration demands their presence, or when they help to make
clear the situation under consideration. For example, children may
have peas or beans in solving problems in addition; they serve to
present objectively the reality which is symbolized by the teacher
or pupils in their written work, but this does not make the work in
addition concrete. The concreteness of these exercises will depend
upon the need which children feel of the ability to find the sum of
two or more numbers. The beans will be significant, beyond their
use as objects, to illustrate the one-to-one correspondence between
symbolic representation and reality, only if the problem of summation
which at that time engages their attention concerns the sum of
certain numbers of beans. Indeed, it may be claimed that the use of
one set of objects continuously to illustrate a process in arithmetic
hinders rather than helps the child in his ability to reason in this
situation, since he may come to consider this chance relationship of
beans and addition as essential. He may think that he ought always to
add when he is given beans.
A good illustration of the necessity for a well defined problem for
guidance when observations are to be made is found in the futility
of much work that is done, or rather left undone, when children are
taken on excursions. The directions which follow for the conduct
of excursions are those which should be followed whenever work in
observation is required, those which have reference to the handling
of a large group of children in the field being added.
1. The teacher must have clearly defined in her own mind the purpose
of the observation. If the teacher has not definitely formulated the
problem, the observation of the children will surely be purposeless.
2. It is not enough that the teacher know just what data she expects
the children to gather toward the solution of a particular problem;
she must know exactly what data are available under the conditions
governing the observation.
3. The preliminary work must have prepared children for their
observations by giving them very definite problems to solve. Often it
will be advantageous to have these problems written in notebooks.
4. Children not only need to want to see, but also need to be
directed while they are observing. Nothing is easier than to look and
not see that which is essential.
5. It is always advisable to test the success of the observations
while they are being made. There is nothing more difficult than
to correct a misconception growing out of careless or inadequate
observations.
6. It is well to remember that not merely number of observations
counts in the solution of a problem. It is rather observations
under varying conditions which give weight to our conclusions. One
intensive observation may be worth a thousand careless ones.
7. When children are taken on excursions, great care must be
exercised to keep them under proper guidance and control. The
organization of children into smaller groups with leaders who are
made responsible for their proper observance of directions will help.
These leaders should have been over the ground with the teacher
before the excursion. The assistance of parents, teachers, or of
older pupils will at times be necessary.
8. There should be definite work periods during the excursion, just
as in the schoolroom or laboratory.
9. A whistle, as a signal for assembling at one point, will help in
out-of-door work, provided it is clearly understood that this signal
must be obeyed immediately, and under all circumstances.
_Comparison and abstraction_: With the problem clearly defined and
the data provided, the next step consists of comparison and the
resulting abstraction of the element present in all of the cases
which makes for the solution of the problem. In the ordinary course
of our thinking the sequence is as follows: We find ourselves in a
situation which presents a problem which demands an adjustment; we
make a guess or formulate an hypothesis which furnishes the basis
for our work in attempting to solve the problem; we gather data in
the light of the hypothesis assumed, which, through comparison and
abstraction, leads us to believe our hypothesis correct or false; if
the hypothesis seems justified by the data gathered, it is further
tested or verified by an appeal to experience; _i.e._ we endeavor to
see whether our conclusion holds in all cases; if this test proves
satisfactory, we generalize or define; and lastly this generalization
or definition is used as a point of reference or truth to guide in
later thinking or activity.
There is danger that we may overlook the very great importance of
inference in this process. We cannot say just when this step in the
process will be possible, but it is possibly the most significant
of all. A situation presents a problem. Our success in solving the
problem depends upon our ability to infer from the facts at our
command. Often many inferences will be necessary before we succeed
in finding the one that will stand the test. Again with the problem
in mind we may be conscious of a great lack of data and may postpone
our inference while we collect the needed information. There is
one fallacy that must be carefully guarded against in dealing
with children, as also with adults; namely, the tendency once the
inference has been made to admit only such data as are found to
support this particular hypothesis.
It is this ability to infer, to formulate a workable hypothesis,
which distinguishes the genius from the man of mediocre ability.
It is the ability to see facts in new relations, the giving of new
meaning to facts which may be the common possession of all, that
characterizes the great thinker. Other people knew many of the
facts; but it took the mind of a Newton to discover the relationship
existing among these data which he formulated in the law that all
bodies attract each other directly in proportion to their weight and
inversely in proportion to the square of the distance separating
them. As we teach children we should encourage the intelligent
guess. We would not, of course, encourage mere random guessing,
which may be engaged in by children to have something to say or to
blind the teacher. A child who offers a guess or hypothesis should
be asked to give his ground for the inference, should show that his
guess has grown out of his consideration of the data in hand. It is
fallacious to suppose that this kind of thinking is beyond the power
of children. They have been forming their inferences and testing them
in action from the time that they began to act independently.
There is one element in the consideration of the step of comparison
which cannot be too much emphasized, and that is that it is not the
comparison of things or situations which present striking likenesses
which gives rise to the highest type of thinking. To look at a dozen
horses and then to conclude that all horses have four legs is
merely a matter of classification; to observe that the sun, chemical
action, electricity, and friction produce heat, and to arrive at the
generalization from these cases, apparently so unlike, that heat is
a mode of motion is the work of a genius. In general, it is safe to
say that we would greatly strengthen our teaching if we were only
more careful to see to it that our basis for generalization is found
in situations presenting as many variations as possible. For example,
if we want to teach a principle in arithmetic, the way to fix it and
to make it available for further use by our pupils is not to get a
number of problems all of which are alike in form and statement;
but rather we should seek as great a variety as is possible in
the language used or symbols employed that is compatible with the
application of the principle to be taught. In an interesting article
on reasoning in primary arithmetic, Professor Suzzallo has pointed
out the fact that children’s difficulty in reasoning is often one
of language.[8] The trouble has been that teachers have always used
a set form, or a very few forms of expression, when they described
situations which involved any one of the arithmetical processes.
Later when the child is called upon to solve a problem involving
this process he does not know which process to apply because he is
unfamiliar with the form of expression used. To succeed in teaching
children when to add involves the presentation of the situations
which call for addition with as great a variation as is possible,
_i.e._ by using not one form, but all of the words or phrases which
may be used to indicate summation. In like manner in other fields
the examples for comparison will be valuable in proportion as they
present variety rather than uniformity in those elements which
are not essential. Equally good illustration can be had from any
other field. If we want pupils to get any adequate conception of
the function of adjectives, we should use examples which involve a
variety of adjectives in different parts of sentences. In geography
the concept “river” will be clear only when the different types
of rivers have been considered and the non-essential elements
disregarded.
_Generalization_: When we feel that we have solved the problem,
we are ready to state our generalization. There is considerable
advantage in making such a statement. One can never be quite sure
that he has solved his problem until he finds himself able to state
clearly the results of his thinking. To attempt to define or to
generalize is often to realize the inadequacy of our thought on the
problem. Children should be encouraged to give their own definition
or generalization before referring to that which is provided by the
teacher or the book. Indeed, the significance of a generalization
for further thinking or later action depends not simply upon one’s
ability to repeat words, but rather upon adequate realization of
the significance of the conclusion reached. The best test of such
comprehension is found in the ability of the pupil to state the
generalization for himself.
There is very great danger, if definitions or generalizations are
given ready-made to children, that they will learn to juggle with
words. The parrot-like repetition of rules of syntax, or principles
of arithmetic, never indicates real grasp of these subjects. Children
think most when the requirement for thinking is greatest, and none
are readier than they to take advantage of laxness on the part of the
teacher in this respect. It is not only when the formal statement of
principles or definitions is called for that the teacher needs to be
on her guard. At any stage of the process, if the teacher will only
take their words and read meaning into them, some children will be
found ready to substitute words for thought. It is really a mistake
to tell a child that you know what he means even though he did not
say it. Language is the instrument which he employs in thinking, and,
if his statement lacked clearness or definiteness, the chances are
very great that his thinking has failed in these same particulars.
Instead of encouraging children in loose thinking by accepting any
statement offered, it would be much better to raise the question
of the real significance of the statement, to inquire just what was
meant by the words used. Such procedure will help to make children
more careful in expressing themselves, and will inevitably tend to
clearer thinking.
_Application_: Whatever conclusions we have reached, whatever truths
we have satisfactorily established, influence us in our later
thought and action. But even though this is true, there is a decided
advantage in providing for a definite application of the results
of the thinking which children have done as soon as possible and
in as many different ways as is feasible. In the first place, such
application makes clearer the truth itself, and helps to fix it in
mind. Again, the conclusion arrived at to-day is chiefly significant
as a basis for our thinking of to-morrow, and it is as we apply
our conclusions that new problems arise to stimulate us to further
thought. Then, too, the satisfaction which comes when one feels
his power over situations as a result of thinking is the very best
possible stimulus to further intellectual activity. Finally, we need
to show children the application of that which they have learned to
the life which they live outside of the school. We are not apt to
err on the side of too frequent or too varied application of the
generalizations we have led children to make. Rather we shall have to
study diligently to provide enough applications to fix for the child
the habit of verification by an appeal to experience.
A few words by way of caution concerning the inductive lesson may not
be out of place.
_First_: Not all school work can be undertaken on this general plan.
There are times when the end to be accomplished is distinctly not the
discovery of some new truth, but rather the fixing of some habit.
There are exercises which are distinctively deductive, some which aim
to produce habits, and others which seek to secure appreciation. But
more of this is in the succeeding chapters.
_Second_: Even when we seek to establish truth, we cannot always
develop it by an appeal to the experience of children nor to
observations which they can make. We shall have, on some occasions,
to supply the data, and in still other cases it will be most
economical to demonstrate the truth of the position which we desire
to have them take. There are occasions when the solution of the
problem is not possible for children. In this last instance we shall
have to provide the authoritative statement. Indeed, it may be argued
that one of the lessons which we all need to learn is respect for
the expert. We cannot settle all of the problems which arise, but we
may choose from among those who profess to have found a solution.
Our education ought to help us to avoid the quack and the charlatan.
The habit of logical thinking on the part of children, and expert
knowledge in some field, however small, is the only protection which
the school can give against the pretensions of those who represent
themselves as the dispensers of truth.[9]
_Third_: There is a grave danger that we may help children too much.
Some teachers interpret the inductive development lesson to mean
that each step in the thinking required must be carefully prepared
for and quickly passed. They consider that they have taught the
best lesson when there has been no hitch in the progress from the
statement of aim to the wording of the generalization. The suggestive
question which makes thinking on the part of children unnecessary is
a favorite measure employed. If we stop to consider what thinking
means, we cannot fail to see the fallacy of such work. We all do our
best thinking, not when the problem to be solved is explained by some
one else and all of the difficulties removed, but rather when we find
the problem most difficult of solution.
If children are at work on problems which are vital to them, we may
expect them to continue to work even though they make mistakes.
Indeed, the best recitation may be the one that leaves the children
not with a solution skillfully supplied for them by the teacher, but
rather with a keen realization of the problem, and with a somewhat
clearer idea of the direction in which the solution may be sought.
It is the teacher’s work to help the child to see the problem,
and, seeing the problem herself from the child’s point of view, to
stimulate the child to his best effort. The teacher must know not
only the pupil’s attitude of mind toward the problem and how his
mind is most likely to react, but also the mental activity required
to master properly the issue that has been raised. On the one hand,
the teacher’s equipment consists of a knowledge of the minds of
the children whom she teaches, and on the other a knowledge of the
subject to be taught, not simply as a body of knowledge more or less
classified or organized, but as a mode of mental growth.[10] What
the teacher needs is a clear realization of the difficulties which
the pupils must meet, and the way in which childish minds may best
overcome these obstacles. When such sympathy exists between teacher
and pupil, we may expect that pupils will constantly grow stronger in
their ability to think logically, instead of becoming more and more
dependent upon the teacher. And this is our great work as teachers,
to render our services unnecessary.
_Fourth_: No teacher should attempt to outline her work on the basis
of the steps indicated in the discussion of the inductive method
without a clear realization of the fact that these steps cannot be
sharply differentiated, that they are not mutually exclusive. To
define a problem adequately may mean that we have passed through
the whole process. At any step in the process after the problem is
defined, and some hypothesis formed, we may wish to verify our guess
by an appeal to known facts, and often we shall find it necessary
to abandon the hypothesis already formed and provide another as a
basis for further thinking. It is true that the natural movement
of the mind is roughly indicated by the steps named; but it must be
remembered that no mind can possibly arrive at the solution of a real
problem by adhering to a fixed order of procedure. We do not by our
teaching create the power of logical thought; we rather guide a mind
that naturally operates logically. We can never teach children to
reason, but we can provide the occasion for logical thinking, and can
guard against the common fallacies. Our success will depend upon a
clear realization of the possibilities of the child mind and of the
subjects we teach as part of their growth and development.
_Teaching by Types_: Teaching by means of types is sometimes
discussed as a separate method, while in reality it is simply one
form of the inductive process. As was indicated in our discussion of
observation above, there are times when the consideration of a single
situation or object in detail may be worth more than a thousand
careless observations. It is especially true that a thoroughly
adequate knowledge of one object or case of a class prepares in the
best possible way for future observations of members of the same
class. Familiarity with the life history of one animal or plant will
help us greatly to understand other animals and plants, because that
which is most essential in all has been carefully observed in the
case considered. Now let us suppose that several plants and animals
have been studied. If the cases which are considered are truly
typical, it may be possible for the student to appreciate not simply
the individuals belonging to the classes studied, but also something
of the interrelation of the several classes. This illustration,
given because it represents in a general way something of the method
followed in the study of science, represents a very common method
of procedure in the ordinary affairs of life. None of us can hope
to support our conclusions by a careful scrutiny of all possible
cases. We take something on authority; namely, that the individual
case considered is representative of a large group, then after we
have investigated the one case we apply our conclusions to the whole
group. Of course there is one great danger. We may be overhasty in
our generalizations. No fallacy is more common than the emphasis
placed upon non-essentials by those whose observations have been
limited. The stories of the traveler who generalizes, after seeing
one red-headed child or after eating at one hotel, concerning the
children and hotels of the country visited, are too common to need
repetition here. Where observations are necessarily limited, the
important consideration is to get cases that seem as different as
possible in order that that which is essential may be differentiated
from the non-essential or accidental.
Teaching by types in our ordinary school work has been applied most
frequently to the subject of geography. Applying the principle stated
above, we shall be careful in teaching rivers, mountains, cities,
commerce, or any other geographical notion to see to it that the
individual cases considered are as widely different as possible.
To teach New York City, Philadelphia, and Chicago only would give
children a very erroneous idea of the concept “city.” They are all
exceptionally large, all American, all modern. There are cities
smaller, with peculiarities due to age, to location, and to the
ideas and resources of the people building them. A better selection
would be New York City, London, Tokyo, Venice, Cairo, and Munich.
Objection could still very well be offered that this list is too
short to include all classes. There can be no doubt that to have
taught any city carefully will aid greatly in understanding the
notion “city” and in appreciating other cities, but manifestly any
final generalization concerning cities must wait until our knowledge
of geography has been widely extended. The same conclusion would
be reached were any other notion of geography, or any other study,
subjected to the same test. There is, however, no harm in forming
tentative judgments. Indeed, we must all do this every day of our
lives. The main issue is to see to it that there is no mistake as
to the tentative character of the conclusions reached, that the
open-minded attitude be preserved.
FOR COLLATERAL READING
C. A. and F. M. McMurry, _The Method of the Recitation_, Chapters
VI to IX inclusive.
John Dewey, _How We Think_, Chapters XII to XV inclusive.
_Exercises._
1. What is the purpose of the step of preparation in the inductive
lesson? When would you begin an inductive lesson with a statement
of aim or problem? What value is there in having children state the
aim of a lesson? When during the lesson should the aim be referred
to?
2. How would you hope to have country children get a clear idea of
a city? Could you develop this idea with sufficient definiteness by
asking questions?
3. What preparation would you think necessary for a class that were
taking their first trip to a dairy?
4. What was wrong in the class where, after a trip to the country,
a small child said, “A cow is a small animal with four legs that
likes to live in the mud and grunt”?
5. Would you allow a boy to perform an experiment in nature study
that you knew would result unsatisfactorily?
6. A teacher used the following sentences in her attempt to teach
the function of an adjective; criticize the list given.
The red apple is sweet.
The green grass is soft.
The yellow house is large.
The tall man is sick.
The largest horse is fast.
Suggest a better list of sentences for the purpose indicated.
7. In what sense is it true that an induction begins with a
generalization? How do you proceed when you modify a generalization
which you once held as true?
8. A pupil defined a river as a stream of water flowing through the
land. How would you hope to secure a more accurate generalization
from him?
9. What is the function of a lecture on Germany to a group of
children studying the geography of Europe? Do you think such a
lecture would be as valuable as a lesson in which the pupils are
asked to find out why German commerce has developed so rapidly
during the past twenty years?
10. Under what conditions would you require children to commit to
memory the definitions found in their textbooks?
11. If your pupils were reading Kipling’s _Jungle Book_, would you
try to make your lessons inductive?
12. What difficulties would you encounter in trying to teach
children who live in the Mississippi Valley the meaning of the term
_mountain_? How could you hope to overcome these difficulties?
13. The following illustrative problems were used by a teacher who
was presenting the subject of percentage to a class for the first
time. Can you improve the list?
A man who had $10,000 lost 25 per cent of his money. How much did
he lose?
A horse which cost $250 was sold at a loss of 10 per cent. How much
did the owner lose?
A house which cost $25,000 was burned. It was insured for 50
per cent of its value. How much did the owner receive from the
insurance company?
A suit of clothes which cost the dealer $18 was sold at a gain of
25 per cent. How much did the dealer gain on the suit?
14. Which would be better, to tell a group of children of a trip
which you took to a cattle ranch, show them pictures, and possibly
read a description of ranch life, or spend the same amount of time
questioning these same children in the hope of developing some
adequate idea of this type of life? If you follow the first method,
could you be sure that children had derived accurate ideas from
your description?
15. Write a series of questions which you would use in developing
the generalization, “Men who live in cities are dependent upon
those who live in the country for the necessities of life.”
16. How would you defend the following statement: It is more
important that a pupil should have worked out the solution of a
single problem in which he is interested, than that he should have
learned, without solving the problems for himself, the answers to a
dozen problems from books which he is asked to read.
17. Why do most lessons in which pupils recite from the material
assigned in textbooks require little thinking? How can such lessons
be made to stimulate thinking?
18. Would you ever allow children to accept an incomplete
generalization as a result of their own experience and thought? An
incorrect generalization?