How to Teach
by
George Drayton Strayer and Naomi Norsworthy
Part 4 out of 5
from her class, and of the pupil who said that she would not stay in
school if she had to go to that teacher, by telling them both to take
time to think it through and decide how they would reconcile their
differences, is a case in point. What we need is not the punishment
which follows rapidly upon our feeling of resentment, but rather the
wisdom of waiting and accepting the mistake or offense of the pupil as
an opportunity for careful consideration upon his part and as a possible
means of growth for him.
There has been considerable discussion during recent years concerning
the obligation of the school to teach children concerning matters of
sex. Traditionally, our policy has been one of almost entire neglect.
The consequence has been, on the whole, the acquisition upon the part of
boys and girls of a large body of misinformation, which has for the most
part been vicious. It is not probable that we can ever expect most
teachers to have the training necessary to give adequate instruction in
this field. For children in the upper grades, during the preadolescent
period especially, some such instruction given by the men and women
trained in biology, or possibly by men and women doctors who have made a
specialty of this field, promises a large contribution to the
development of the right attitudes with respect to the sex life and the
elimination of much of the immorality which has been due to ignorance or
to the vicious misinformation which has commonly been spread among
children. The policy of secrecy and ignorance cannot well be maintained
if we accept the idea of responsibility and the exercise of judgment as
the basis of moral social activity. In no other field are the results of
a lack of training or a lack of morality more certain to be disastrous
both for the individual and for the social group.
QUESTIONS
1. How satisfactory is the morality of the man who claims that he does
no wrong?
2. How is it possible for a child to be unmoral and not immoral?
3. Are children who observe school rules and regulations necessarily
growing in morality?
4. Why is it important, from the standpoint of growth in morality, to
have children form socially desirable habits, even though we may not
speak of this kind of activity as moral conduct?
5. What constitutes growth in morality for the adult?
6. In what sense is it possible for the same act to be immoral, unmoral,
and moral for individuals living under differing circumstances and in
different social groups? Give an example.
7. Why have moral reformers sometimes been considered immoral by their
associates?
8. What is the moral significance of earning a living? Of being prompt?
Of being courteous?
9. What are the instincts upon which we may hope to build in moral
training? What instinctive basis is there for immoral conduct?
10. To what extent is intellectual activity involved in moral conduct?
What is the significance of one's emotional response?
11. What stages of development are distinguishable in the moral
development of children? Is it possible to classify children as
belonging to one stage or the other by their ages?
12. Why is it true that one's character depends upon the deliberate
choices which he makes among several possible modes or types of action?
13. Why is it important to have positive satisfaction follow moral
conduct?
14. How may the conduct of parents and teachers influence conduct of
children?
15. What is the weakness of direct moral instruction, e.g. the telling
of stories of truthfulness, the teaching of moral precepts, and the
like?
16. What opportunities can you provide in your class for moral social
conduct?
17. Children will do what is right because of their desire to please,
their respect for authority, their fear of unpleasant consequences,
their careful, thoughtful analysis of the situation and choice of that
form of action which they consider right. Arrange these motives in order
of their desirability. Would you be satisfied to utilize the motive
which brings results most quickly and most surely?
18. In what sense is it true that lapses from moral conduct are the
teacher's best opportunity for moral teaching?
19. How may children contribute to the social welfare of the school
community? Of the larger social group outside of the school?
20. How may pupil participation in school government be made significant
in the development of social moral conduct?
* * * * *
XII. TRANSFER OF TRAINING
Formal discipline or transfer of training concerns itself with the
question as to how far training in one subject, along one line,
influences other lines. How far, for instance, training in reasoning in
mathematics helps a child to reason in history, in morals, in household
administration; how far memorizing gems of poetry or dates in history
aids memory when it is applied to learning stenography or botany; how
far giving attention to the gymnasium will insure attention to sermons
and one's social engagements. The question is, How far does the special
training one gets in home and school fit him to react to the environment
of life with its new and complex situations? Put in another way, the
question is what effect upon other bonds does forming this particular
situation response series of bonds have. The practical import of the
question and its answer is tremendous. Most of our present school
system, both in subject matter and method, is built upon the assumption
that one answer is correct--if it is false, much work remains to be done
by the present-day education.
The point of view which was held until recent years is best made clear
by a series of quotations.
"Since the mind is a unit and the faculties are simply phases
or manifestations of its activity, whatever strengthens one
faculty indirectly strengthens all the others. The _verbal_
memory seems to be an exception to this statement, however,
for it may be abnormally cultivated without involving to any
profitable extent the other faculties. But only things that
are rightly perceived and rightly understood can be _rightly_
remembered. Hence whatever develops the acquisitive and
assimilative powers will also strengthen memory; and,
conversely, rightly strengthening the memory necessitates the
developing and training of the other powers." (R.N. Roark,
Method in Education, p. 27.)
"It is as a means of training the faculties of perception and
generalization that the study of such a language as Latin in
comparison with English is so valuable." (C.L. Morgan,
Psychology for Teachers, p. 186.)
"Arithmetic, if judiciously taught, forms in the pupil habits
of mental attention, argumentative sequence, absolute
accuracy, and satisfaction in truth as a result, that do not
seem to spring equally from the study of any other subject
suitable to this elementary stage of instruction." (Joseph
Payne, Lectures on Education, Vol. I, p. 260.)
"By means of experimental and observational work in science,
not only will his attention be excited, the power of
observation, previously awakened, much strengthened, and the
senses exercised and disciplined, but the very important habit
of doing homage to the authority of facts rather than to the
authority of men, be initiated." (_Ibid_., p. 261.)
The view maintained by these writers is that the mind is made up of
certain elemental powers such as attention, reasoning, observation,
imagination, and the like, each of which acts as a unit. Training any
one of these powers means simply its exercise irrespective of the
material used. The facility gained through this exercise may then be
transferred to other subjects or situations, which are quite different.
The present point of view with regard to this question is very
different, as is shown by the following quotations:
"We may conclude, then, that there is something which may be
called formal discipline, and that it may be more or less
general in character. It consists in the establishment of
habitual reactions that correspond to the form of situations.
These reactions foster adjustments, attitudes, and ideas that
favor the successful dealing with the emergencies that arouse
them. On the other hand, both the form that we can learn to
deal with more effectively, and the reactions that we
associate with it, are definite. There is no general training
of the powers or faculties, so far as we can determine."
(Henderson, 10, p. 307 f.)
"One mental function or activity improves others in so far as
and because they are in part identical with it, because it
contains elements common to them. Addition improves
multiplication because multiplication is largely addition;
knowledge of Latin gives increased ability to learn French
because many of the facts learned in the one case are needed
in the other. The study of geometry may lead a pupil to be
more logical in all respects, for one element of being logical
in all respects is to realize that facts can be absolutely
proven and to admire and desire this certain and
unquestionable sort of demonstration...." (Thorndike, '06, pp.
243-245, _passim_.)
"Mental discipline is the most important thing in education,
but it is specific, not general. The ability developed by
means of one subject can be transferred to another subject
only in so far as the latter has elements in common with the
former. Abilities should be developed in school only by means
of those elements of subject-matter and of method that are
common to the most valuable phases of the outside environment.
In the high school there should also be an effort to work out
general concepts of method from the specific methods used."
(Heck, '09, Edition of '11, p. 198.)
"... No study should have a place in the curriculum for which
this general disciplinary characteristic is the chief
recommendation. Such advantage can probably be gotten in some
degree from every study, and the intrinsic values of each
study afford at present a far safer criterion of educational
work than any which we can derive from the theory of formal
discipline." (Angell, '08, p. 14.)
These writers also believe in transfer of training, but they believe the
transfer to be never complete, to be in general a very small percentage
of the special improvement gained and at times to be negative and to
interfere with responses in other fields instead of being a help. They
also emphasize the belief that when the transfer does occur, it is for
some perfectly valid reason and under certain very definite conditions.
They reject utterly the machine-like idea of the mind and its elemental
faculties held by the writers first quoted. They hold the view of mental
activity which has been emphasized in the discussion of original
tendencies and inheritance from near ancestry, _i.e._, that the physical
correlate of all types of mental activity is a definite forming of
connections between particular bonds-these connections, of course,
according to the laws of readiness exercise, and effect, would be
determined by the situation acting as a stimulus and would, therefore,
vary as the total situation varied. They believe in a highly specialized
human brain, which reacts in small groups of nerve tracts--not in gross
wholes. They would express each of the "elemental" powers in the plural
and not in the singular.
The basis of this change of view within the last fifteen or twenty years
is to be found in experimental work. The question has definitely been
put to the test as to how far training in one line did influence others.
For a full description of the various types of experiments performed the
reader is referred to Thorndike's "Psychology of Learning," Chapter 12.
Only an indication of the type of work done and the general character of
the results can be given here. Experiments in the effect of cross
education, in memorizing, in observing and judging sensory and
perceptual data, and in forming sensori-motor association habits have
been conducted in considerable numbers. A few experiments in special
school functions have also been carried out. Investigations in the
correlation between various parts of the same subject and between
different subjects supposed to be closely allied also throw light upon
this subject. The results from these different lines of experiment,
although confusing and sometimes contradictory, seem to warrant the
belief stated above. They have made it very clear that the question of
transfer is not a simple one, but, on the contrary, that it is extremely
complex. They make plain that in some cases where large transfer was
confidently expected, that little resulted, while, on the other hand, in
some cases when little was expected, much more occurred. It is evident
that the old idea of a large transfer in some subtle and unexplained way
of special improvements to a general faculty is false. But, on the other
hand, it would be equally false to say that no transfer occurred. The
general principle seems to be that transfer occurs when the same bonds
are used in the second situation to the extent that the alteration in
these particular connections affects the second response. Both the
knowledge of what bonds are used in various responses and to what extent
alteration in them will affect different total responses is lacking.
Therefore, all that is at present possible is a statement of conditions
under which transfer is probable.
In general, then, transfer of training will occur to the extent that the
two responses use the same bonds--to the extent, then, that there is
identity of some sort. This identity which makes transfer possible may
be of all degrees of generality and of several different types. First,
there may be identity of content. For instance, forming useful
connections with six, island, and, red, habit, Africa, square root,
triangle, gender, percentage, and so on, in this or that particular
context should be of use in other contexts and therefore allow of
transfer of training. The more common the particular responses are to
all sorts of life situations, the greater the possibility of transfer.
Second, the identity may be that of method or procedure. To be able to
add, to carry, to know the method of classifying an unknown flower, to
have a definite method of meeting a new situation in hand-work, to know
how to use source material in history, to have gained the technique of
laboratory skill in chemistry, to know how to study in geography, should
be useful in other departments where the same method would serve. Some
of these methods are, of course, of much more general service than
others. In establishing skill in the use of these various procedures,
two types of responses are needed. The learner must form connections of
a positive nature, such as analyzing, collecting material, criticizing
according to standard, picking out the essential and so on, and he must
also form connections of a negative character which will cause him to
neglect certain tendencies. He must learn not to accept the first idea
offered, to neglect suggestions, to hurry or to leave half finished, to
ignore interruptions, to prevent personal bias to influence criticism,
and so on. These connections which result in neglecting certain elements
are quite as important as the positive element, both in the production
of the particular procedure and in the transfer to other fields. Third,
the identity may be of still more general character and be in terms of
attitude or ideal. To learn to be thorough in connection with history,
accurate in handwork, open-minded in science, persistent in Latin,
critical in geometry, thorough in class and school activities; to form
habits of allegiance to ideals of truth, cooeperation, fair play,
tolerance, courage, and so on, _may_ help the learner to exhibit these
same attitudes in other situations in life. Here again the connections
of neglect are important. To neglect selfish suggestions, to ignore the
escape from consequences that falsehood might make possible, to be dead
to fear, to ignore bodily aches and pains, are quite as necessary in
producing conduct that is generous, truthful, and courageous as are the
positive connections made in building up the ideal.
In the discussion of transfer because of identity, it was emphasised
that the presence of identity of various types explained cases of
transfer that exist and made transfer possible. In no case must it be
understood, however, that the presence of these identical elements is a
warrant of transfer. Transfer _may_ take place under such conditions,
but it need not do so. Transfer is most sure to occur in cases of
identity of substance and least likely in cases of identity of attitude
or ideals. To have useful responses to six, above, city, quart, and so
on, in one situation will very likely mean responses of a useful nature
in almost all situations which have such elements present. It is very
different with the ideals. A child may be very accurate in handwork, and
yet almost nothing of it show elsewhere; he may be truthful to his
teacher and lie to his parents; he may be generous to his classmates and
the reverse to his brothers and sisters. Persistence in Latin may not
influence his work in the shop, and the critical attitude of geometry be
lacking in his science. Transfer in methods holds a middle ground. It
seems that the more complex and the more subtle the connections
involved, the less is the amount and the surety of the transfer.
In order to increase the probability of transfer when connections of
method or attitudes are being formed, first, it should be made
conscious, and second, it should be put into practice in several types
of situations. There is grave danger that the method will not be
differentiated from the subject, the ideal from the context of the
situation. To many children learning how to study in connection with
history, or to be critical in geometry, or to be scientific in the
laboratory, has never been separated from the particular situation. The
method or the ideal and the situation in which they have been acquired
are one--one response. The general elements of method or attitude have
never been made conscious, they are submerged in the particular subject
or situation, and therefore the probability of transfer is lessened. If,
on the other hand, the question of method, as an idea by itself, apart
from any particular subject, is brought to the child's attention; if
truth as an ideal, independent of context, is made conscious, it is much
more likely to be reacted to in a different situation, for it has become
a free idea and therefore crystallized. Then having freed the general
somewhat from its particular setting, the learner should be given
opportunity to put it in practice in other settings. To simply form the
method connections or the attitude responses in Latin and then blindly
trust that they will be of general use is unsafe. It is the business of
the educator to make as sure as he can of the transfer, and that can
only be done by practicing in several fields. These two procedures which
make transfer more sure, i.e., making the element conscious and giving
practice in several fields, are not sharply divided, but interact.
Practice makes the idea clearer and freer, and this in turn makes fresh
practice profitable. It is simply the application of the law of analysis
by varying concomitants.
In all this matter of transfer it must be borne in mind that a very
slight amount of transfer of some of these more general responses may be
of tremendous value educationally, provided it is over a very wide
field. If a boy's study of high school science made him at all more
scientific in his attitude towards such life situations as politics,
morals, city sanitation, and the like, it would be of much more value
than the particular habit formed. If a girl's work in home economics
resulted in but a slight transfer of vital interest to the actual
problems of home-making, it would mean much to the homes of America. If
a boy's training in connection with the athletics of his school fosters
in him an ideal of fair play which influences him at all in his dealings
with men in business, with his family, with himself, the training would
have been worth while. To discount training simply because the transfer
is slight is manifestly unfair. The kind of responses which transfer are
quite as important as the amount of the transfer.
The idea that every subject will furnish the same amount of discipline
provided they are equally well taught is evidently false. Every school
subject must now be weighed from two points of view,--first, as to the
worth of the particular facts, responses, habits, which it forms, and
second, as to the opportunity it offers for the formation of connections
which are of general application. The training which educators are sure
of is the particular training offered by the subject; the general
training is more problematic. Hence no subject should be retained in our
present curriculum whose only value is a claim to disciplinary training.
Such general training as the subject affords could probably be gained
from some other subject whose content is also valuable. Just because a
subject is difficult, or is distasteful, is no sign that its pursuit
will result in disciplinary training. In fact, the psychology of play
and drudgery make it apparent that the presence of annoyance, of
distaste, will lessen the disciplinary value. Only those subjects and
activities which are characterized by the play spirit can offer true
educational development. The more the play spirit enters in, the greater
the possibility of securing not only special training, but general
discipline as well. Thorndike sums up the present attitude towards
special subjects by saying, "An impartial inventory of the facts in the
ordinary pupil of ten to eighteen would find the general training from
English composition greater than that from formal logic, the training
from physics and chemistry greater than that from geometry, and the
training from a year's study of the laws and institutions of the Romans
greater than that from equal study of their language. The grammatical
studies which have been considered the chief depositories of
disciplinary magic would be found in general inferior to scientific
treatments of human nature as a whole. The superiority for discipline of
pure overapplied science would be referred in large measure to the fact
that pure science could be so widely applied. The disciplinary value of
geometry would appear to be due, not to the simplicity of its
conditions, but to the rigor of its proofs; the greatest disciplinary
value of Latin would appear in the case, not of those who disliked it
and found it hard, but of those to whom it was a charming game."
QUESTIONS
1. It has been experimentally determined that the ease with which one
memorizes one set of facts may be very greatly improved without a
corresponding improvement in ability to memorize in some other field.
How would you use this fact to refute the argument that we possess a
general faculty of memory?
2. How is it possible for a man to reason accurately in the field of
engineering and yet make very grave mistakes in his reasoning about
government or education?
3. What assurance have we that skill or capacity for successful work
developed in one situation will be transferred to another situation
involving the same mental processes of habit formation, reasoning,
imagination, and the like?
4. What are the different types of identity which make possible transfer
of training?
5. How can we make the identity of methods of work most significant for
transfer of training and for the education of the individual?
6. Why do ideals which seem to control in one situation fail to affect
other activities in which the same ideal is called for?
7. Under what conditions may a very slight amount of transfer of
training become of the very greatest importance for education?
8. Why may we not hope for the largest results in training by compelling
children to study that which is distasteful? Do children (or adults)
work hardest when they are forced to attend to that from which they
derive little or no satisfaction?
9. Which student gets the most significant training from his algebra,
the boy who enjoys work in this field or the boy who worries through it
because algebra is required for graduation from the high school?
10. Why may we hope to secure more significant training in junior high
schools which offer a great variety of courses than was accomplished by
the seventh and eighth grades in which all pupils were compelled to
study the same subjects?
11. Why is Latin a good subject from the standpoint of training for one
student and a very poor subject with which to seek to educate another
student?
* * * * *
XIII. TYPES OF CLASSROOM EXERCISES
The exercises which teachers conduct in their classrooms do not commonly
involve a single type of mental activity. It is true, however, that
certain lessons tend to involve one type of activity predominantly.
There are lessons which seek primarily to fix habits, others in which
thinking of the inductive type is primarily involved, and still others
in which deductive thinking or appreciation are the ends sought. As has
already been indicated in the discussion of habit, thinking, and
appreciation in the previous chapters, these types of mental activity
are not to be thought of as separate and distinct. Habit formation may
involve thinking. In a lesson predominantly inductive or deductive, some
element of drill may enter, or appreciation may be sought with respect
to some particular part of the situation presented. These different
kinds of exercises, drills, thinking (inductive or deductive), and
appreciation are fairly distinct psychological types.
In addition to the psychological types of exercises mentioned above,
exercises are conducted in the classroom which may be designated under
the following heads: lecturing, the recitation lesson, examination and
review lessons. In any one of these the mental process involved may be
any of those mentioned above as belonging to the purely psychological
types of lessons or a combination of any two or more of them. It has
seemed worth while to treat briefly of both sorts of lesson types, and
to discuss at some length, lecturing, about which there is considerable
disagreement, and the additional topic of questioning, which is the
means employed in all of these different types of classroom exercises.
_The Inductive Lesson_. It has been common in the discussion of the
inductive development lesson to classify the stages through which one
passes from his recognition of a problem to his conclusion in five
steps. These divisions have commonly been spoken of as (1) preparation;
(2) presentation; (3)comparison and abstraction; (4) generalization; and
(5) application. It has even been suggested that all lessons should
conform to this order of procedure. From the discussions in the previous
chapters, the reader will understand that such a formal method of
procedure would not conform to what we know about mental activity and
its normal exercise and development. There is some advantage, however,
in thinking of the general order of procedure in the inductive lesson as
outlined by these steps.
The step of preparation has to do with making clear to the pupil the aim
or purpose of the problem with which he is to deal. It is not always
possible in the classroom to have children at work upon just such
problems as may occur to them. The orderly development of a subject to
be taught requires that the teacher discover to children problems or
purposes which may result in thinking. The skill of the teacher depends
upon his knowledge of the previous experiences of the children in the
class and his skill in having them word the problem which remains
unsolved in their experience in such a way as to make it attractive to
them. Indeed, it may be said that children never have a worthy aim
unless it is one which is intellectually stimulating. A problem exists
only when we desire to find the answer.
The term "presentation" suggests a method of procedure which we would
not want to follow too frequently; that is, we may hope not simply to
present facts for acceptance or rejection, but, rather, we want children
to search for the data which they may need in solving their problem.
From the very beginning of their school career children need, in the
light of a problem stated, to learn to utilize all of the possible
sources of information available. Their own experience, the questions
which they may put to other people, observations which they may
undertake with considerable care, books or other sources of information
which they may consult, all are to be thought of as tools to be used or
sources of information available for the solution of problems. It cannot
be too often reiterated that it is not simply getting facts, reading
books, performing experiments, which is significant, but, rather, which
of these operations is conducted in the light of a problem clearly
conceived by children.
The step of presentation, as above described, is not one that may be
begun and completed before other parts of the inductive lesson are
carried on. As soon as any facts are available they are either accepted
or rejected, as they may help in the solution of the problem;
comparisons are instituted, the essential elements of likeness are
noticed, and even a partial solution of the problem may be suggested in
terms of a new generalization. The student may then begin to gather
further facts, to pass through further steps of comparison, and to make
still further modifications of his generalization as he proceeds in his
work. At any stage of the process the student may stop to apply or test
the validity of a generalization which has been formed. It is even true
that the statement of the problem with which one starts may be modified
in the light of new facts found, or new analyses instituted, or new
elements of likeness which have been discovered.
In the conduct of an inductive lesson it is of primary importance that
the teacher discover to children problems, the solutions of which are
important for them, that he guide them in so far as it is possible for
them to find all of the facts necessary in their search for data, that
he encourage them to discuss with each other, even to the extent of
disagreeing, with respect to comparisons which are instituted or
generalizations which are premature, and above all, that he develop, in
so far as it is possible, the habit of verifying conclusions.
_The Deductive Lesson._ The interdependence of induction and deduction
has been discussed in the chapter devoted to thinking. The procedure in
a deductive lesson is from a clear recognition of the problem involved,
through the analysis of the situation and abstraction of the essential
elements, to a search for the laws or principles in which to classify
the particular element or individual with which we are dealing, to a
careful comparison of this particular with the general that we have
found, to our conclusion, which is established by a process of
verification. Briefly stated, the normal order of procedure might be
indicated as follows: (1) finding the problem; (2) finding the
generalization or principles; (3) inference; (4) verification. It is
important in this type of exercise, as has been indicated in the
discussion of the inductive lesson, that the problem be made clear. So
long as children indulge in random guesses as to the process which is
involved in the solution of a problem in arithmetic, or the principle
which is to be invoked in science, or the rule which is to be called to
mind in explaining a grammatical construction, we may take it for
granted that they have no very clear conception of the process through
which they must pass, nor of the issues which are involved. In the
search for the generalization or principle which will explain the
problem, a process of acceptance and rejection is involved. It helps
children to state definitely, with respect to a problem in arithmetic,
that they know that this particular principle is not the one which they
need. It is often by a process of elimination that a child can best
explain a grammatical construction, either in English or in a foreign
language. Of course the elimination of the principle or law which is not
the right one means simply that we are reducing the number of chances of
making a mistake. If out of four possibilities we can immediately
eliminate two of them, there are only two left to be considered. After
children have discovered the generalization or principle involved, it is
well to have them state definitely the inference which they make. Just
as in the inductive process we pass almost immediately from the step of
comparison and abstraction to the statement of generalization, so in the
deductive lesson, when once we have related the particular case under
consideration to the principle which explains it, we are ready to state
our inference. Verification involves the trying out of our inference to
see that it certainly will hold. This may be done by proposing some
other inference which we find to be invalid, or by seeking to find any
other law or principle which will explain our particular situation. Here
again, as in the inductive lesson, the skillful teacher makes his
greatest contribution by having children become increasingly careful in
this step of verification. Almost any one can pass through the several
stages involved in deductive thinking and arrive at a wrong conclusion.
That which distinguishes the careful thinker from the careless student
is the sincerity of the former in his unwillingness to accept his
conclusions until they are verified.
_The Drill Lesson._ The drill lesson is so clearly a matter of fixing
habits that little needs to be added to the chapter dealing with this
subject. If one were to attempt to give in order the steps of the
process involved, they might be stated as follows: (1) establishing a
motive for forming the habit; (2) knowing exactly what we wish to do, or
the habit or skill to be acquired; (3) recognition of the importance of
the focusing of attention during the period devoted to repetitions; (4)
variation in practice in order to lessen fatigue and to help to fix
attention; (5) a recognition of the danger of making mistakes, with
consequent provision against lapses; (6) the principle of review, which
may be stated best by suggesting that the period between practice
exercises may only gradually be lengthened.
Possibly the greatest deficiency in drill work, as commonly conducted,
is found in the tendency upon the part of some teachers to depend upon
repetition involving many mistakes. This is due quite frequently to the
assignment of too much to be accomplished. Twenty-five words in
spelling, a whole multiplication table, a complete conjugation in Latin,
all suggest the danger of mistakes which will be difficult to eliminate
later on. The wise teacher is the one who provides very carefully
against mistakes upon the part of pupils. He assigns a minimum number of
words, or a number of combinations, or a part of a conjugation, and
takes care to discover that children are sure of themselves before
indulging in that practice which is to fix the habit.
In much of the drill work there is, of course, the desirability of
gaining in speed. In this field successful teachers have discovered that
much is gained by more or less artificial stimuli which seem to be
altogether outside of the work required to form a habit. In drill on
column addition successful work is done by placing the problem on the
board and following through the combinations by pointing the pointer and
making a tap on the board as one proceeds through the column. Concert
work of this sort seems to have the effect of speeding up those who
would ordinarily lag, even though they might get the right result. The
most skillful teachers of typewriting count or clap their hands or use
the phonograph for the sake of speeding up their students. They have
discovered that the same amount of time devoted to typewriting practice
will produce anywhere from twenty-five to one hundred per cent more
speed under such artificial stimulation as they were in the habit of
getting merely by asking the students to practice. These experiences, of
course, suggest that drill work will require an expenditure of energy
and an alertness upon the part of teachers, and not merely an assignment
of work to be done by pupils.
_Appreciation Lesson._ The work which the teacher does in securing
appreciation has been suggested in a previous chapter. It will suffice
here briefly to state what may be thought of as the order of procedure
in securing appreciation. It is not as easy in this case to state the
development in terms of particular steps or processes, since, as has
already been indicated in the chapter on appreciation, the student is
passive rather than active, is contemplating and enjoying, rather than
attacking and working to secure a particular result. The work of the
teacher may, however, be organized around the following heads: (1) it is
of primary importance that the teacher bring to the class an enthusiasm
and joy for the picture, music, poetry, person, or achievement which he
wishes to present; (2) children must not be forced to accept nor even
encouraged to repeat the evaluation determined by teachers; (3)
spontaneous and sincere response upon the part of children should be
accepted, even though it may not conform to the teacher's estimate; (4)
children should be encouraged to choose from among many of the forms or
situations presented for their approval those which they like best; (5)
the technique involved in the creation of the artistic form should be
subordinated to enjoyment in the field of the fine arts; (6) throughout,
the play spirit should be predominant, for if the element of drudgery
enters, appreciation disappears.
Teachers who get good results in appreciation secure them mainly by
virtue of the fact that they have large capacity for enjoyment in the
fields which they present to children. A teacher who is enthusiastic,
and who really finds great joy in music, will awaken and develop power
of appreciation upon the part of his pupils. The teacher who can enter
into the spirit of the child poetry, or of the fairy tale, will get a
type of appreciation not enjoyed by the teacher who finds delight only
in adult literature. It is of the utmost importance to recognize the
fact that children only gradually grow from an appreciation or joy in
that which is crude to that which represents the highest type of
artistic production. It is important to have children try themselves out
in creative work; but the influence of a teacher may be far greater than
that of the attempts of the children to produce in these fields.
_Lecturing_. Among the various types of methods used in teaching there
is probably no one which has received such severe criticism as the
so-called lecture method. The result of this criticism has been,
theoretically at least, to abolish lecturing from the elementary school
and to diminish the use of this method in the high school, although in
the colleges and universities it is still the most popular method.
Although it is true that the lecture method is not the best one for
continual use in elementary and high school, still its entire disuse is
unfortunate. So is its blind use by those who still adhere to the old
ways of doing things.
The chief criticisms of the method are, first, that it makes of the
learner a mere recipient instead of a thinker; second, that the material
so gained does not become part of the mental life of the hearers and so
is not so well remembered nor so easily applied as material gained in
other ways; third, that the instructor has no means of determining
whether his class is getting the right ideas or wholly false ones;
fourth, the method lacks interest in the majority of cases. Despite the
truth of these criticisms, there are occasions when the lecture or
telling method is the best one--in fact the only one that can accomplish
the desired result.
First, the lecture method may sometimes take the place of books. Often,
even in the elementary school, there is need for the children to get
facts,--information in history or geography or literature,--and the
getting of these facts from books would be too difficult or too
wasteful. In such a case telling the facts is certainly the best way to
give them. A teacher in half a period can give material that it might
take the children hours to find. By telling them the facts, he not only
saves waste of time, but also retains the interest. Very often
discouragement and even dislike results from a prolonged search for a
few facts. Of course in the higher schools, when the material to be
given is not in print, when the professor is the source of certain
theories, methods, and explanations, lecturing is the only way for
students to get the material. It must be borne in mind that human beings
are naturally a source of interest, particularly to children, and
therefore having the teacher tell, other things being equal, will make a
greater impression than reading it in a book.
Second, the lecture method is valuable as a means of explanation.
Despite the fact that the material given may be adapted to the child's
level of development, still it often happens that it is not clear. Then,
instead of sending the child to the same material again, an explanation
by teacher or fellow pupil is much better. It may be just the inflection
used, or the choice of different words, that will clear up the
difficulty.
Third, the telling method should be used for illustration. Very often
when illustration is necessary the lecture method is supplemented by
illustrative material of various types--objects, experiments, pictures,
models, diagrams, and so on. None of this material, however, is used to
its best advantage unless it is accompanied by the telling method. It is
through the telling that the essentials of the illustrative material
gain the proper perspective. Without such explanation some unimportant
detail may focus the attention and the value of the material be lost. It
has been customary to emphasize the need for and the value of this
concrete illustrative material. Teachers have felt that if it was
possible to have the actual object, it should be obtained; if that was
not possible, why then have pictures, but diagrams and words should only
be used as a last resort. There can be no doubt as to the value of the
concrete material, especially with little children--but its use has been
carried to an extreme because it has been used blindly. For instance,
sometimes the concrete material because of its general inherent
interest, or because of its special appeal to some instinct, attracts
the attention of the child in such a way that the point which was to be
illustrated is lost sight of. Witness work in nature study in the lower
grades, and in chemistry in the high school. The concrete material may
be so complex that again the essential point is lost in the
mass of detail. No perspective can be obtained because of the
complexity--witness work with principles of machines in physics and the
circulation of the blood in biology. Sometimes the diagram or word
explanation with nothing of the more concrete material is the best type
of illustration. A fresh application of the principle or lesson by the
teacher is another means of illustration and one of the best, for it not
only broadens the student's point of view and gives another cue to the
material, but it may also make direct connection with his own
experience. Illustrations in the book often fail to do this, but the
teacher knowing his particular class can make the application that will
mean most. Telling a story or incident is another way of illustration.
The personal element is nearly always present in this means, and is a
valuable spur to interest.
Illustrations of all kinds, from the concrete to the story form, have
been grossly misused in teaching, so that to-day teachers are almost
afraid to use any. The difficulty has been that illustrations have been
used as a means of regaining wandering attention. It has been the
sugar-coating. The illustration, then, has become the important thing
and the material nonimportant. The class has watched the experiment or
listened to the story, but when that was over the attention was gone
again. Illustrations should not be the means of holding the attention;
that is the function of the material itself. If the lesson cannot hold
the interest, illustrations are worse than useless. Illustrations, then,
of all kinds must be subordinated to the material--they are only a means
to an end, and that end is a better understanding of the material.
Illustrations, further, should have a vital, necessary connection with
the point they are used to make clearer. Illustrations that are dragged
in, that are not vitally connected with the point, are entirely out of
place. If illustrations always truly illustrated, then children would
not remember the illustration and forget the point, for remembering the
illustration they would be led directly to the point because of the
closeness of the connection.
Fourth, telling or lecturing is the best way to get appreciation. This
was discussed in the chapter on appreciation, so need only be mentioned
here. The interpretation by the teacher of the character, the picture,
the poem, the policy, or what not, not only increases the understanding
of the listener, but also calls up feeling responses. It is in this
telling that the personality of the teacher, his experiences, his
ideals, make themselves felt. One can often win appreciation of and
allegiance to the best in life by the use of the telling method in the
appropriate situations.
Fifth, the lecture method should sometimes be used as a means of getting
the desired mental attitude. The general laws of learning emphasize the
importance of the mind's set as a condition to readiness of neurone
tracts. Five or ten minutes spent at the beginning of a subject, or a
new section of work, in introducing the class to it, may give the
keynote for the whole course. A whole period may be profitably be spent
this way. Not only will the telling method used on such occasions give
the right emotional attitude towards a subject, but also the right
intellectual set as well.
It is evident then that the lecture or telling method has its place in
all parts of the educational system, but its place should be clearly and
definitely recognized. The danger is not in using it, but in using it at
the wrong time, and in overusing it. Bearing in mind the dangers that
adhere to its use, it is always well, whether the method is used in
grades or in college, to mix it with other methods or to follow it by
another method that will do the things that the lecture method may have
left undone.
_The Recitation Lesson._ As has been suggested in the opening of this
chapter, the recitation lesson is not a type involving any particular
psychological process. It is, rather, a method of procedure which may
involve any of the other types of work already discussed. When the
recitation lesson means merely reciting paragraphs from the book with
little or no reference to problems to be solved or skill to be
developed, it has no place in a schoolroom. When, however, the teacher
uses the recitation lesson as an exercise in which he assures himself
that facts needed for further progress in thinking have been secured, or
that habits have been established, or verbatim memorization
accomplished, this type of exercise is justified. It is well to remember
that the thought process involved in the development of a subject, or
the solution even of a single problem, may extend over many class
periods. The recitation lesson may be important in organizing the
material which is to be used in the larger thought whole. Again, this
type of exercise may involve the presentation of material which is to be
used as a basis for appreciation in literature, in music, in art, in
history, and the like. The organization of experiences of children,
whether secured through observations, discussions, or from books, around
certain topics may furnish a most satisfactory basis for the development
of problems or of the gathering of the material essential for their
solution. A better understanding of the conditions which make for
success in habit formation, in thinking, and the development of
appreciation, will tend to eliminate from our schools that type of
exercise in which teachers ask merely that children recite to them what
they have been able to remember from the books which they have read or
the lectures which they have heard.
_The Examination and Review Lessons._ In the establishment of habits,
the development of appreciation, or the growth in understanding which we
seek to secure through thinking, there will be many occasions for
checking up our work. Successful teaching requires that the habit that
we think we have established be called for and additional practice given
from time to time in order to be certain that it is fixed. In like
manner, the development of our thought in any field is not something
which is accomplished without respect to later neglect. We, rather,
build a system of thought with reference to a particular field or
subject as a result of thinking, and rethinking through the many
different situations which are involved. In like manner, in the field of
appreciation the very essence of our enjoyment is to be found in the
fact that that which we have enjoyed we recall, and strengthen our
appreciation through the revival of the experience. The review is, of
course, most successful when it is not simply going over the whole
material in exactly the same way. In habit formation it is often
advisable to arrange in a different order the stimuli which are to bring
the desired responses, for the very essence of habit formation is found
in the fact that the particular response can be secured regardless of
the order in which they are called for. In thinking, as a subject is
developed, our control is measured by the better perspective which we
secure. This means, of course, that in review we will not be concerned
with reviving all of the processes through which we have passed, but,
rather, in a reorganization quite different from that which was
originally provided.
The examination lesson is classified here as of the same type as the
review because a good examination involves all that has been suggested
by review. The writer has no sympathy with those who argue against
examinations. The only proof that we can get of the success or failure
of our work is to be found in the achievement of pupils. It is not
desirable to set aside a particular period of a week devoted entirely to
examinations, because examinations in all subjects cannot to best
advantage be given during the same period. There are stages in the
development of our thinking, or in the acquiring of skill, or in our
understanding and appreciation which occur at irregular intervals and
which call for a summing up of what has gone before, in order that we
may be sure of success in the work which is to follow. It is, of course,
undesirable to devote a whole week to examinations on account of the
strain and excitement under which children labor. It is entirely
possible to know of the achievements of children through examinations
which have been given at irregular intervals throughout the term. It
would be best, probably, never to give more than one examination on any
one day, and, as a rule, to devote only the regular class period to such
work. In another chapter the discussion of more exact methods of
measuring the achievements of children will be discussed at some length.
In all of the lesson types mentioned above, one of the most important
means employed by teachers for the stimulation of pupils is the
question. It seems wise, therefore, to devote some paragraphs to a
consideration of questioning as determining skill in teaching.
_Questioning_. The purpose of a question is to serve as a situation
which shall arouse to activity certain nerve connections and thus bring
a response. Questions, oral or written, are the chief tools used in
schools to gain responses. In some situations it is the only means a
teacher may have of arousing the response. Psychologically, then, the
value of the question must be judged by the response.
Questions may be considered from the point of view of the kind of
response they call for. Probably the most common kind of question is the
one that calls for facts as answers. It involves memory--but memory of a
rote type. It does not require thinking. All drill questions are of this
type. The connections aroused are definitely final in a certain order,
and the question simply sets off the train of bonds that leads directly
to the answer. Another type of question involving the memory process is
the one which initiates recall, but here thought is active. The answer
cannot be gained in a mechanical way, but selection and rejection are
involved. The answer is to be found by examining past experience, but
only in a thoughtful way. Questions which call for comparison form
another type. These may vary from those which involve the comparison of
sense material to those which involve the comparison of policies
or epochs. Words, characters, plots, definitions, plans,
subjects--everything with which intellectual life deals is open to
comparison. Comparison is one of the steps in the process of reasoning,
and hence questions of this type are extremely important. Then there are
the questions which arouse the response of analysis. These questions
vary among themselves according to the type of analysis needed, whether
piecemeal attention or analysis due to varying concomitants. The former
drives the thinker through gradual recognition and elimination of the
known elements to a consciousness of the only partly known. The latter,
by attracting the attention to unvarying factors in the changing
situations, forces out the new and until then unknown element. Some
questions require judgment as a response. The judgment may be one
concerning relationships, or concerning worth or value, or be merely a
matter of definition--all questions calling for criticism are of this
type. In any case this type of question involves the thought element at
its best. The question requiring organization forms another type. There
is no sharp line of division between these types of questions. No one of
them should be used exclusively. Some of them imply operations of a
simple type as well as the particular response demanded by that form.
For instance, some of the questions involving analysis imply comparison
and recalling. A judgment question might call for all the simple
processes noted above and others as well. The responses then vary in
complexity and difficulty. The order of advance in both complexity and
difficulty of the response is from the mere drill question to the
judgment question.
Another type of question is the one which desires appreciation as a
response. This question is one of the most difficult to frame, for it
must tend to inhibit the critical attitude and by means of the
associations it arouses or its own suggestive power get the appreciative
response. Questions of this type often call for constructive imagery as
a means to the desired end. Some questions are directive in their
tendency. They require as response an attitude or set of the mind. They
set the child thinking in this direction rather than that. In a sense
they are suggestive, but they suggest the line of search rather than the
response. A final type of question is akin to the one just
discussed--the question whose response is further questions. Here again
the response desired is an attitude, but in this case it is more than an
attitude, it is also a definite response that shall come in the form of
questions. The questions of a good teacher should result in students
asking questions both of people and of books. These last three types of
questions are perhaps the most difficult of all. Because of their
complexity and subtlety they often miss fire and fail of their purpose.
Properly handled they are among the most powerful tools a teacher has.
The type of question used must vary, not only with the particular group
of children, and the type of lesson, but also with the subject.
Questions that would be the best type in mathematics might not be so
good for an art lesson. The kinds of questions used must be adapted to
the particular situation.
Psychologically a question is valuable not only in accordance with the
kind of response it gets, but also in proportion to the readiness of the
response. A question that is of such a character that the response is
hazy, stumbling, hesitating--a question that brings no clear-cut
response because the child does not understand what is wanted, is a poor
question. This does not at all mean that the right response must always
come immediately. Some of the best questions are put with the intention
of forcing the child to realize that he can't answer--that he doesn't
know. If that type of response comes to that question, it is the best
possible answer. Nor need the whole answer come immediately. For
instance, in many of the judgment questions the thinking process aroused
may take some time before the judgment is reached, and meanwhile several
partial answers may be given. But if the question asked started the
process, without waste of time in trying to find out what it meant, the
question is good. With these explanations, then, the second
qualification of a good question is that it secures the appropriate
response readily. In order to do this, these factors must be considered:
First, the principle of apperception must be recognized. Every question
must deal with material that is on a level with the stage of development
of the one questioned. Not only so, but the question must connect
somewhere with the learner's experience. This means a recognition also
of individual differences. The question must also be couched in language
that can be understood easily by the one questioned. To have to try to
understand the language of the question as well as the question, results
in divided attention and delayed responses. Second, the question should
be clear and definite. A question that has these characteristics will
challenge the attention of the class. It is directed straight at the
point at issue, and no time will be lost in wondering what the question
means, or in trying two or three tentative answers. Third, the younger
the child, the simpler the question must be. With little children, to be
good a question may involve only one idea, or relationship. The amount
involved in the question, its scope and content, must be adapted to the
mental development of the learner. It is only a mature thinker who can
carry simultaneously two or three points of issue, or possibilities.
Fourth, the question to gain a ready response must be interesting. Not
only must the lesson as a whole be interesting, but the questions
themselves must have the same quality. Dull questions can kill an
otherwise good lesson. The form of the question is thus a big factor in
gaining a ready response. All the qualities which gain involuntary
attention can be used in framing an interesting question--novelty,
exaggeration, contrast, life, color, and so on.
The third point to be considered in determining a good question is
whether or not it satisfies the demands of economy. This demand is a
fair one both from the standpoint of the best use of the time at the
disposal of the learner, and also from the standpoint of the best means
of gaining the greatest development on the part of the learner in a
given time. The number of questions asked thus enters in as a factor.
When a teacher asks four or five questions when one would serve the same
purpose, she is not only wasting time, but the child is not getting the
opportunity to do any thinking and therefore is not developing. Recent
studies on the actual number of questions asked in a recitation point to
the conclusion that economy both of time and in development is being
seriously overlooked. Economy in response may also be brightened by
preserving a logical sequence between questions. It is a matter of fact
in psychology that associations are systematized about central ideas; it
is also a fact that the set of the mind, in this direction rather than
that, is characteristic of all work. Logical sequence, then, makes use
of both these facts--both of the systematization of ideas and of the
mental attitude.
The fourth test of good questioning is the universality of its appeal.
Some questions which are otherwise good appeal but to comparatively few
in the class. This, of course, means that responses are being gained but
from few. The best questioning stimulates most of the class; all members
of the class are working. In order to secure this result the questions
must be properly distributed over the class. The bright pupils must not
be allowed to do all the work; or, on the other hand, all the attention
of the teachers must not be given to the dull pupils. Not only should
the questions be well distributed, but they must vary according to the
individual ability of the particular child. This has already been
emphasized in dealing with readiness of response. Many a lesson has been
unsuccessful because the teacher gave too difficult a question to a dull
child, and while she was struggling with him, she lost the rest of the
class. The reverse is also true, to give a bright child a question that
requires almost no thinking means that a mechanical answer will be given
and no further activity stimulated. The extent to which all the class
are mentally active is one measure of a good question.
QUESTIONS
1. Give an example of a lesson which you have taught which was
predominantly inductive. Show how you proceeded from the discovery of
the problem to your pupils to the solution attained.
2. What is involved in the "step" of presentation?
3. Why may we not consider the several "steps" of the inductive lesson
as occurring in a definite and mutually exclusive sequence?
4. In what respect is the procedure in a deductive lesson like that
which you follow in an inductive lesson?
5. Show how verification is an important element in both inductive and
deductive lessons.
6. Give illustrations of successful drill lessons and make clear the
reason for the degree of success achieved.
7. What measures have you found most advantageous in securing speed in
drill work?
8. What are the elements which make for success in an appreciation
lesson?
9. Upon what grounds and to what extent can lecturing be defended as a
method of instruction?
10. What may be the relation between a good recitation lesson and the
solution of a problem? Growth in power of appreciation?
11. For what purposes should examinations be given? When should
examinations be given?
12. When are questions which call for facts justified?
13. Why are questions which call for comparisons to be considered
important?
14. Why is it important to phrase questions carefully?
15. Why should a teacher ask some questions which cannot be answered
immediately?
16. What criteria would you apply in testing the questions which you put
to your class?
17. Write five questions which in your judgment will demand thinking
upon some topic which you plan to teach to your class.
* * * * *
XIV. HOW TO STUDY
The term study has been used very loosely by both teachers and children.
As used by teachers it frequently meant something very different from
what children had in mind when they used it. Further, teachers
themselves have often used the term in connection with mental activities
which, technically speaking, could not possibly come under that head.
Much confusion and lack of efficient work has been the result. Recently
various attempts have been made to give the term study a more exact
meaning. McMurry defines it as "the work that is necessary in the
assimilation of ideas"--"the vigorous application of the mind to a
subject for the satisfaction of a felt need." In other words, study is
thinking. Psychologically, what makes for good thinking makes for good
study. Study is controlled mental activity working towards the
realization of a goal. It is the adaptation of means to end, in the
attempt to satisfy a felt need. It involves a definite purpose or goal,
which is problematic, the selection and rejection of suggestions,
tentative judgments, and conclusion. The mind of the one who studies is
active, vigorously active, not in an aimless fashion, but along sharply
defined lines. This is the essential characteristic of all study.
There are, however, various types of study which differ materially from
each other according to the subject matter or to the type of response
required. Some study involves comparatively little thinking. The
directed activity must be present, but the choice, the judgment, may
need to be exercised only in the beginning when methods of procedure
need to be selected, and later on, perhaps, when successes or failures
need to be noted and changes made in the methods accordingly. Another
type of study needs continual thinking of the most active sort all the
way through the period. Just the proportion of the various factors
involved in thinking which is present at any given study period must be
determined by the response. A type of study which would be completely
satisfactory for one subject needing one response, would be entirely
inadequate for another subject needing another response. To illustrate,
in some cases the study must deal with habit formation. The need felt is
to learn a mechanical response of a very definite nature to this
situation; the problem is to get that response. The thinking would come
in in deciding upon the method, in watching for successes, in
criticizing progress, and in judging when the end was obtained. A large
part of the time spent in study would, however, need to be spent in
repetition, in drill. Of such character is study of spelling, of
vocabularies, of dates; study in order to gain skill in adding, or speed
in reading, or to improve in writing or sewing. Much of habit formation
goes on without study--in fact, to some it may seem to be ludicrous to
use the word "study" in connection with the formation of habits. It is
just because the study elements in connection with responses of this
type have been omitted that there has been such a tremendous waste of
time in teaching children to form right habits. This omission also
explains the poor results, for the process has been mechanical and blind
on the part of the student. At the other extreme in types of study is
that which can be used in science and mathematics, in geography and
history, when the major part of the time is given to selecting and
rejecting suggestions and seems required by the goal. In this type the
habituation, the fixing of the material, comes largely as a by-product
of the factors used in the thinking.
Study may, then, be classified according as the response required is
physical habit, memory, appreciation, or judgment. These types overlap,
no one of them can exist absolutely alone, but it is possible to name
them according to the response. Study may also be classified into
supervised study, or unsupervised study, into individual or group study.
We might also classify study as it has to do with books, with people, or
with materials. The term has been rather arbitrarily applied to
activities that dealt with books, but surely much study is accomplished
when people are consulted instead of books, and also when the sources of
information or the standards are flowers, or rocks, or textiles.
Study, then, is a big term, including many different varieties of
activities, of varying degrees of difficulty and responsibility. It
cannot possibly be taught all at once, according to one method, at one
spot in the school curriculum. Power to study is of very gradual growth.
It must proceed slowly, from simple to complex types. From easy to
difficult problems, from situations where there is close supervision and
direction to situations where the student assumes full responsibility.
Knowing how to study is not an inborn gift--it does not come as a matter
of intuition, nor does it come in some mysterious way when the child is
of high school age. It is governed by the laws of learning, or
readiness, exercise, and effect, just as truly as any other ability is.
If adults are to know how to study, if they are to use the technique of
the various kinds of study efficiently, children must be taught how. Nor
can we expect the upper grammar grade or the high school teachers to do
this. Habits of study must be formed just as soon as the responses to
which it leads are needed. Beginning down in the kindergarten with study
in connection with physical and mental habits, the child should be
taught how to study. The type must gradually become more complex; he
must pass from group to individual study, from supervised to
unsupervised, but it must all come logically, from step to step. True,
it is not easy to teach how to study. A careful analysis of the various
types with their peculiar elements should be a help. First, however,
there are some general principles that underlie all study which must be
discussed.
Study must have, as has already been stated, a purpose. The individual,
in order to exercise his mind in a controlled way, must have an aim. The
clearer and more definite the aim, whether it be little or big, the
better the study will be. From the beginning, then, children must be
taught to make sure they know what they are going to do before beginning
to study. It may be necessary to teach them in the early grades to say
to themselves or to the class just what they are going to accomplish in
the study. Teach them when the lesson is assigned to write down in their
books just what the problem for study is. Warn them never to begin study
without definitely knowing the aim--if they don't know it, make them
realize that the first thing to do is to find out the purpose by asking
some one else. Better no study at all than aimless or misdirected
activity, because of lack of purpose.
No study worthy of the name can be carried on without interest. The
child who studies well must be brought to realize this. The value of
interest can be brought home to him by having him compare the work he
does, the time he spends, and how he feels when studying something in
which he has a vital interest with the results when the topic is
uninteresting. Of course, as will be pointed out later, much of the
gaining of interest lies in the hands of the teacher necessarily, but if
the child realizes the need of it in efficient study, some
responsibility will rest on him to find an interest if it is not already
there. No matter how expert the teacher may be, because of individual
differences no problem will be equally interesting to all pupils in
itself, and no incentive will have an equal appeal to all children.
Therefore children should be taught to find interest for themselves.
Certain devices can be suggested, such as working with another child and
competing with him, "making believe" in study, and finding some
connection with something in which he is interested, working against his
own score, and the like.
Not only do the demands of economy require that the topic of study
receive concentrated attention, but the results themselves are better
when such is the case. Half an hour of concentrated work gives much
better results than an hour of study with scattered attention. An hour
spent when half an hour would do is thus not only wasteful of time, but
is productive of poorer results and bad habits of study as well.
Children need to be taught this from the beginning. Much time is wasted
even by mature university students when they suppose themselves to be
studying. Children can be taught to ignore distractions--to train
themselves to keep their eyes on the book, despite the fact that the
door is opened, or a seat mate is looking for a book. They should be
encouraged to set themselves time limits in various subjects and adhere
to them. It is economical to follow a regular schedule in study--either
in the school or at home. Let each child make out his study schedule and
keep to it. Teach children that the best work is done when they are calm
and steady. That either excitement or worry is a hindrance. Therefore
they should avoid doing their studying under those conditions, and
should do all they can to remove such conditions. Training children to
do their best and then not to worry would not only improve the health of
many upper grammar grade and high school children, but would also
improve their work.
Study requires a certain critical attitude, a checking up of results
against the problem set. In order to be efficient in study a child
should know when he has reached the solution, when the means have been
adapted to the end, when he has reached the goal. This checking up, of
course, means habits of self-criticism and standards. Sometimes all that
is necessary is for the child to be made conscious of this fact so that
he can test himself, for instance, in memory work, or in solving a
problem in mathematics. On the other hand, sometimes he will have to
compare his work with definite standards, such as the Thorndike
Handwriting Scale, or the Hillegas Composition Scale.[19] In other
instances, he will have to search for standards. He will need to know
what his classmates have accomplished, what other people think, what
other text-books say, and so on. Gradually he must be made conscious
that study is a controlled activity, and unless it reaches the goal, and
the correct one, it is useless. He must be made to feel that the
responsibility to see that such results are reached rests on him.
These, then, are the general factors involved in all types of study, and
therefore are fundamental to good habits of study: a clear purpose;
vital interest of some kind; concentrated attention, and a critical
attitude. There are further additional suggestions which are peculiar to
the special type of study.
In study which is directed to habit formation, the student should be
taught the danger of allowing exceptions. He should know the possibility
of undoing much good work through a little carelessness. Preaching won't
bring this home to him--it must come through having his attention
attracted to such an occurrence in his own work or in that of his mates.
After that knowledge of the actual experiences of others, athletes,
musicians, and others will help to intensify the impression. The value
of repetition as one of the chief factors in habit formation must be
emphasized. The child should be encouraged to make opportunities for
practice both in free minutes during the school program, and outside of
school. He must be taught in habit formation to practice the new habit
in the way it is to be used: practicing the sounds of letters in words,
the writing movements in writing words, swimming movements in the water,
and so on. Practicing the whole movements, not trying to gain perfection
in parts of it and then putting it together. It is important also that
the learner be taught to keep his attention on the result to be
obtained, instead of the movements. He should attend to the swing of the
club, the lightness of the song, the cut the saw is making, the words he
is writing, instead of the muscle movements involved. In breaking up bad
habits it is sometimes necessary to concentrate on a part or a movement,
when that is the crux of the error, but in general it is a bad practice
when forming a new habit. The child must also learn to watch the habit
of skill he is forming for signs of improvement and then to try to find
out the reason for it. It has been proved experimentally that much of
the improvement in habits of skill comes unconsciously to the learner,
and necessarily so, but that in order for the improvement to continue
and be effective, it must become conscious. Of course, at the beginning
and for a long time it must be the teacher's duty to point out the
improvement and to help the child to think out the reasons for it, but
if he is to learn to study by himself the child must finally come to
habits of self-criticism which will enable him to recognize success or
failure in his own work. In all this discussion of teaching children to
study it must be constantly borne in mind that it is a gradual
process--and only very slowly does the child become conscious of the
technique. Which elements can be made conscious, how much he can be left
to himself, must depend on his maturity and previous training. In time,
however, he should be able to apply them all--for only by so doing will
he become capable of independent study.
When the study is primarily concerned with memory responses, all the
elements which have just been discussed in connection with habit apply,
for, after all, memory is but mental habit. There are other factors
which enter into and which should be used in this type of study. First,
the child should realize the need for understanding the material that is
to be learned, before beginning to memorize it. He will then be taught
to read the entire assignment through--look up difficult words and
references, master the content, whether prose or poetry, whether the
learning is to be verbatim or not, before doing anything further.
Second, he will need to know the value of the modified whole method of
learning, as well as its difficulties. If in the supervised periods of
study and in class work, this method has been followed, it is very easy
to make him conscious of it and willing to adopt it when he comes to do
independent study. Third, he must be taught to distribute his time so
that he does not devote too long a stretch to one subject. The value of
going over work in the morning, after having studied the night or two
nights before, should be emphasized. Also the value of beginning on
assignments some time ahead, even if there is not time to finish them.
Fourth, the child should be taught not to stop his work the minute he
can give it perfectly. The need for overlearning, for permanent
retention, must be made clear. How much overlearning is necessary, each
child should find out for himself. Fifth, the value of outlining
material as a means of aiding memory must be stressed. Sixth, the child
should be taught to search for associations, connections of all types,
in order to help himself remember facts. He might even be encouraged to
make up some mnemonic device as an aid if these measures fail. If
instead of simply trying to hammer material in by mere repetition
children had been taught in their study to consciously make use of the
other elements in a good memory, much time would be saved. But the
responsibility should rest finally on the child to make use of these
helps. The teacher must make him conscious of them, sometimes from their
value by experiment, and then teach him to use them himself.
Much less can be done as a matter of conscious technique when the
occasion of study is to further appreciation. A few suggestions might be
offered. First, the child should be taught the value of associating with
those who do appreciate in the line in which he is striving for
improvement. He should be encouraged to consciously associate with them
when opportunities for appreciation come. Second, he should know the
need for coming in contact with the objects of appreciation if true
feeling is to be developed. It is only by mingling with people, reading
books, listening to music, that appreciation in those fields can be
developed. Third, the value of concrete imagery and of connections with
personal experience in arousing emotional tone should be emphasized. The
child might be encouraged to consciously call up images and make
connections with his own experience during study.
Study, when the object is to arrive at responses of judgment, is the
type which has received most attention. This type of study includes
within itself several possibilities. Although judgment is the only
response that can solve the problem, still the problem may be one of
giving the best expression in art or music or drama. It may be the
analysis of a course of action or of a chemical compound. It may be the
comparison of various opinions. It may be the arriving at a new law or
principle. It is to one of these types of thinking that the term "study"
is usually applied. Important as it is, the other three types already
discussed cannot be neglected. If children are taught to study in
connection with the simpler situations provided by the first two types,
they will be the better prepared to deal with this complex type, for
this highest type of study involves habit formation often and memory
work always.
In the type of study involving reasoning, because of its complexity, and
because the individual must work more independently, the child must
learn the danger of following the first suggestion which offers itself.
He must learn to weigh each suggestion offered with reference to the
goal aimed at. Each step in the process must be tested and weighed in
this manner. To go blindly ahead, following out a line of suggestions
until the end is reached, which is then found to be the wrong one,
wastes much time and is extremely discouraging. No suggestion of the way
to adapt means to end should be accepted without careful criticism. The
pupil should gradually be made conscious of the technique of reasoning,
analysis, comparison, and abstraction. He must know that the first thing
to do is to analyze the problem and see just what it requires. He must
know that the abstraction depends upon the goal. The learner should be
taught the sources of some of the commonest mistakes in judgment. For
instance, if he knows of the tendency to respond in terms of analogy,
and sees some of the errors to which accepting a minor likeness between
two situations as identity lead, he will be much more apt to avoid such
mistakes than would otherwise be true. If he knows how unsafe it is to
form a judgment on limited data,--if from his own and his classmates'
thinking first, and later from the history of science, illustrations are
drawn of the disastrous effect of such thinking, he will see the value
of seeking sources of information and several points of view before
forming his own judgment. In his study the child should be taught not to
be satisfied until he has tested the correctness of his judgment by
verifying the result. This is a very necessary part of studying. He
should check up his own thinking by finding out through appeal to facts
if it is so; by putting the judgment into execution; by consulting the
opinion of others, and so on.
Study may be considered from the point of view of the type of material
which is used in the process. The student may be engaged on a problem
which involves the use of apparatus or specimens of various kinds, or he
may need to consult people, or he may have to use books. So far as the
first type is concerned, it is obviously unwise to have a student at
work on a problem which involves the use of material, unless the
technique of method of use is well known. Until he can handle the
material with some degree of facility it is waste of time for him to be
struggling with problems which necessitate such use. Such practice
results in divided attention, poor results from the study, and often bad
habits in technique as well. Gaining the technique must be in itself a
problem for separate study.
Children should be taught to ask questions which bear directly on the
point they wish to know. If they in working out some problem are
dependent on getting some information from the janitor, or the postman,
or a mason, they must be able to ask questions which will bring them
what they want to know. Much practice in framing questions, having them
criticized, having them answered just as they are asked, is necessary.
Children should be aware of the question as a tool in their study and
therefore they must know how to handle it. In connection with this
second type of material, the problem of the best source of information
will arise. Children must then be made conscious of the relative values
of various persons as sources of a particular piece of information.
Training in choice of the source of information is very important both
when that source is people and also when it is books.
Teaching children to use books in their study is one of the big tasks of
the teacher. They must learn that books are written in answer to
questions. In order to thoroughly understand a book, students must seek
to frame the questions which it answers. They must also know how to use
books to answer their own questions. This means they must know how to
turn from part to part, gleaning here or there what they need. It means
training in the ability to skim, omitting unessentials and picking out
essentials. It means the ability to recognize major points, minor
points, and illustrative material. Children must be taught to use the
table of contents, the index, and paragraph headings. They must, in
their search for fuller information or criticism, be able to interpret
different authors, use different language, and attack from different
angles, even when treating the same object. Children must in their
studying be taught to use books as a means to an end--not an infallible
means, but one which needs continual criticism, modification, and
amplification.
Study may be supervised study, or unsupervised study. To some people the
requirements in learning to study may seem too difficult to be possible,
but it should be remembered that the process is gradual--that one by one
these elements in study are taught to the children in their supervised
study periods. These periods should begin in the primary grades, and
require from the teacher quite as much preparation as any other period.
Many teachers have taught subjects, but not how to study subjects. The
latter is the more important. The matter of distributed learning
periods, of search for motive, of asking questions, of criticizing
achievement, of use of books; each element is a topic for class
discussion before it is accepted as an element in study. Even after it
is accepted, it may be raised by some child as a source of particular
difficulty and fresh suggestions added. Very often with little children
it is necessary for the teacher to study the lesson with them. Teachers
need much more practice in doing this, for one of the best ways to teach
a child to study is to study with him. Not to tell him, and do the work
for him, but to really study with him. Later on the supervised study
period is one in which each child is silently engaged upon his own work
and the teacher passes from one to the other. In order to do this well,
the teacher needs to be able to do two things. First, to find out when
the child is in difficulty and to locate it, and second, to help him
over the trouble without giving too much assistance. Adequate
questioning is needed in both cases. It is probably true that
comparatively little new work should be given for unsupervised study.
There is too much danger of error as well as lack of interest unless a
start is given under supervision.
Studying, especially unsupervised, may be done in groups or
individually. The former is a stepping-stone to the latter. There is a
greater chance for suggestions, for getting the problem worded, for
arousing interest and checking results, when a group of children are
working together than when a child is by himself. Two things must be
looked after. First, that the children in the group be taught not to
waste time, and second, that the personnel of the group be right. It is
not very helpful if one child does all the work, nor if one is so far
below the level of the group that he is always tagging along behind.
More opportunities for group study in the grammar grades would be
advantageous.
When it comes to individual study, the student then assumes all
responsibility for his methods of study. He should be taught the
influence of physical conditions or mental reactions. He will therefore
be responsible for choosing in the home and in the school the best
possible conditions for his study. He will see to it that, in so far as
possible, the air and light are good, that there are no unnecessary
distractions, and that he is as comfortable bodily as can be. He must
think not only in terms of the goal to be reached, but also with respect
to the methods to be employed. He should be asked by the teacher to
report his methods of work as well as his results.
QUESTIONS
1. Are children always primarily engaged in thinking when they study?
2. What type of study is involved in learning a multiplication table, a
list of words in spelling, a conjugation in French?
3. How would you teach a pupil to study his spelling lesson?
4. In what sense may one study in learning to write? In acquiring skill
in swimming?
5. How would you teach your pupils to memorize?
6. Show how ability to study may be developed over a period of years in
some subject with which you are familiar. Reading? Geography? History?
Latin translation?
7. Is the boy who reads over and over again his lesson necessarily
studying?
8. Can one study a subject even though he may dislike it? Can one study
without interest?
9. How can you teach children what is meant by concentration of
attention?
10. How have you found it possible to develop a critical attitude toward
their work upon the part of children?
11. Of what factors in habit formation must children become conscious,
if they are to study to best advantage in this field?
12. How may we hope to have children learn to study in the fields
requiring judgment? Why will not consciousness of the technique of study
make pupils equally able in studying?
13. What exercises can you conduct which will help children to learn how
to use books?
14. How can a teacher study with a pupil and yet help him to develop
independence in this field?
15. How may small groups of children work together advantageously in
studying?
* * * * *
XV. MEASURING THE ACHIEVEMENTS OF CHILDREN
The success or failure of the teacher in applying the principles which
have been discussed in the preceding chapters is measured by the
achievements of the children. Of course, it is also possible that the
validity of the principle which we have sought to establish may be
called in question by the same sort of measurement. We cannot be sure
that our methods of work are sound, or that we are making the best use
of the time during which we work with children, except as we discover
the results of our instruction. Teaching is after all the adaptation of
our methods to the normal development of boys and girls, and their
education can be measured only in terms of the changes which we are able
to bring about in knowledge, skill, appreciation, reasoning, and the
like.
Any attempt to measure the achievements of children should result in a
discovery of the progress which is being made from week to week, or
month to month, or year to year. It would often be found quite
advantageous to note the deficiencies as well as the achievements at one
period as compared with the work done two or three months later. It will
always be profitable to get as clearly in mind as is possible the
variation among members of the same class, and for those who are
interested in the supervision of schools, the variation from class to
class, from school to school, or from school system to school system.
For the teacher a study of the variability in achievement among the
members of his own class ought to result in special attention to those
who need special help, especially a kind of teaching which will remove
particular difficulties. There should also be offered unusual
opportunity and more than the ordinary demand be made of those who show
themselves to be more capable than the ordinary pupils.
The type of measurement which we wish to discuss is something more than
the ordinary examination. The difficulties with examinations, as we have
commonly organized them, has* been their unreliability, either from the
standpoint of discovering to us the deficiencies of children, or their
achievements. Of ten problems in arithmetic or of twenty words in
spelling given in the ordinary examination, there are very great
differences in difficulty. We do not have an adequate measure of the
achievements of children when we assign to each of the problems or words
a value of ten or of five per cent and proceed to determine the mark to
be given on the examination paper. If we are wise in setting our
examinations, we usually give one problem or one word which we expect
practically everybody to be able to get right. On the other hand, if we
really measure the achievements of children, we must give some problems
or some words that are too hard for any one to get right. Otherwise, we
do not know the limit or extent of ability possessed by the abler
pupils. It is safe to say that in many examinations one question may
actually be four or five times as hard as some other to which an equal
value is assigned.
Another difficulty that we have to meet in the ordinary examination is
the variability among teachers in marking papers. We do not commonly
assign the same values to the same result. Indeed, if a set of papers is
given to a group of capable teachers and marked as conscientiously as
may be by each of them, it is not uncommon to find a variation among the
marks assigned to the same paper which may be as great as twenty-five
per cent of the highest mark given. Even more interesting is the fact
that upon re-marking these same papers individual teachers will vary
from their own first mark by almost as great an amount.
Still another difficulty with the ordinary examination is the tendency
among teachers to derive their standards of achievement from the group
itself, rather than from any objective standard by which all are
measured. It is possible, for example, for children in English
composition to write very poorly for their grade and still to find the
teacher giving relatively high marks to those who happen to belong to
the upper group in the class. As a result of the establishment of such a
standard, the teacher may not be conscious of the fact that children
should be spurred to greater effort, and that possibly he himself should
seek to improve his methods of work.
Out of the situation described above, which includes on the one hand the
necessity for measurement as a means of testing the success of our
theories and of our practice, and on the other hand of having objective
standards, has grown the movement for measurement by means of standard
tests and scales. A standard test which has been given to some thousands
of children classified by grades or by ages, if given to another group
of children of the same grade or age group will enable the teacher to
compare the achievement of his children with that which is found
elsewhere. For example, the Courtis tests in arithmetic, which consist
of series of problems of equal difficulty in addition, subtraction,
multiplication, and division may be used to discover how far facility in
these fields has been accomplished by children of any particular group
as compared with the achievements of children in other school systems
throughout the country. In these tests each of the problems is of equal
difficulty. The measure is made by discovering how many of these
separate problems can be solved in a given number of minutes.[20]
A scale for measuring the achievements of children in the fundamental
operations of addition, subtraction, multiplication, and division has
been derived by Dr. Clifford Woody,[21] which differs from the Courtis
tests in that it affords opportunity to discover what children can
achieve from the simplest problem in each of these fields to a problem
which is in each case approximately twice as difficult as the problems
appearing on the Courtis tests. The great value of this type of test is
in discovering to teachers and to pupils, as well, their particular
difficulties. A pupil must be able to do fairly acceptable work in
addition before he can solve one problem on the Courtis tests.
Considerable facility can be measured on the Woody tests before an
ability sufficient to be registered on the Courtis tests has been
acquired. In his monograph on the derivation of these tests Mr. Woody
gives results which will enable the teacher to compare his class with
children already tested in other school systems. In the case of all of
these standard tests, school surveys and superintendents' reports are
available which will make it possible to institute comparisons among
different classes and different school systems. One form of the Woody
tests is as follows:
* * * * *
SERIES A
ADDITION SCALE
BY CLIFFORD WOODY
Name......................
When is your next birthday?...... How old will you be?.....
Are you a boy or girl?....... In what grade are you?......
(1) (3) (5) (7) (9) (10) (11) (12) (13) (15) (16)
2 17 72 3+1= 20 21 32 43 23 100 9
3 2 26 10 33 59 1 25 33 24
-- -- -- 2 35 17 2 16 45 12
30 -- -- 13 -- 201 15
(2) (4) (6) (8) 25 -- 46 19
2 53 60 2+5+1= -- --- --
4 45 37 (14)
3 -- -- 25+42=
--
(17) (19) (21) (22) (23) (26) (29)
199 $ .75 $8.00 547 1/3+1/3= 121/2 4 3/4
194 1.25 5.75 197 621/2 2 1/4
295 .49 2.33 685 (24) 121/2 5 1/4
156 ----- 4.16 678 4.0125 371/2 -----
--- .94 456 1.5907 ---
6.32 393 4.10 (30)
(18) (20) ----- 525 8.673 (27) 2 1/2
2563 $12.50 240 ------ 1/8+1/4+1/2= 6 3/8
1387 16.75 152 3 3/4
4954 15.75 --- -----
2065 ------ (25) (28)
---- 3/8+5/8+7/8+1/8= 3/4+1/4=
(31) (33) (34) (35) (36) (37)
113.46 .49 1/6+3/8= 2ft. 6in. 2yr. 5mo. 16 1/3
49.6097 .28 3ft. 5in. 3yr. 6mo. 12 1/8
19.9 .63 4ft. 9in. 4yr. 9mo. 21 1/2
9.87 .95 --------- 5yr. 2mo. 32 3/4
.0086 1.69 6yr. 7mo. ------
18.253 .22 ---------
6.04 .33
-------- .36 (38)
1.01 25.091+100.4+25+98.28+19.3614=
(32) .56
3/4+1/2+1/4= .88
.75
.56
1.10
.18
.56
----
* * * * *
SERIES A
SUBTRACTION SCALE
BY CLIFFORD WOODY
Name......................
When is your next birthday?......How old will you be?.....
Are you a boy or girl?.......In what grade are you?.......
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
8 6 2 9 4 11 13 59 78 7-4= 76
5 0 1 3 4 7 8 12 37 60
-- -- -- -- -- -- -- -- -- --
(12) (13) (14) (15) (16) (17) (18) (19) (20)
27 16 50 21 270 393 1000 567482 2 3/4-1=
3 9 25 9 190 178 537 106493
-- -- -- -- --- --- ---- ------
(21) (22) (23) (24) (25) (26)
10.00 3 1/2-1/2= 80836465 8 7/8 27 4yd. 1ft. 6in.
3.49 49178036 5 3/4 12 5/8 2yd. 2ft. 3in.
----- -------- ----- ------ --------------
(27) (28) (29) (30)
5yd. 1ft. 4in. 10-6.25 75 3/4 9.8063-9.019=
2yd. 2ft. 8in. 52 1/4
-------------- ------
(31) (32) (33) (34) (35)
7.3-3.00081= 1912 6mo. 8da. 5/12-2/10= 6 1/8 3 7/8-1 5/8=
1910 7mo. 15da. 2 7/8
--------------- -----
* * * * *
SERIES A
DIVISION SCALE
BY CLIFFORD WOODY
Name...............................
When is your next birthday?....... How old will you be?......
Are you a boy or girl?.......... In what grade are you?......
(1) (2) (3) (4) (5) (6)
__ ___ ___ __ ___ ___
3)6 9)27 4)28 1)5 9)36 3)39
(7) (8) (9) (10) (11) (12)
4 / 2 = __ __ 6 x __ = 30 ___ 2 / 2 =
9)0 1)1 2)13
(13) (14) (15) (16) (17)
______________ _____ 1/4 of 128= _____ 50 / 7 =
4)24 lbs. 8 oz. 8)5856 68)2108
(18) (19) (20) (21) (22)
______ 248 / 7 = _____ _____ ______
13)65065 2.1)25.2 25)9750 2)13.50
(23) (24) (25) (26)
____ ________ _______ _____
23)469 75)2250300 2400)504000 12)2.76
(27) (28) (29) (30)
7/8 of 624 = ______ 3 1/2 / 9 = 3/4 / 5 =
.003).0936
(31) (32) (33)
5/4 / 3/5 = 9 5/8 / 3 3/4 = _____
52)3756
(34) (35) (36)
62.50 / 1 1/4 = ______ ______________
531)37722 9)69 lbs. 9 oz.
* * * * *
SERIES A
MULTIPLICATION SCALE
BY CLIFFORD WOODY
Name......................
When is your next birthday?...... How old will you be?.....
Are you a boy or girl?....... In what grade are you?.......
(1) (2) (3) (4) (5) (6) (7)
3 x 7 = 5 x 1 = 2 x 3 = 4 x 8 = 23 310 7 x 9 =
3 4
-- ---
(8) (9) (10) (11) (12) (13) (14) (15)
50 254 623 1036 5096 8754 165 235
3 6 7 8 6 8 40 23
-- --- --- ---- ---- ---- --- ---
(16) (17) (18) (19) (20) (21) (22)
7898 145 24 9.6 287 24 8 x 53/4
9 206 234 4 .05 21/2
---- --- --- --- --- --
(23) (24) (25) (26) (27) (28) (29)
11/4 x 8 = 16 7/8 x 3/4 = 9742 6.25 .0123 1/8 x 2 =
2 5/8 59 3.2 9.8
------ ---- ---- -----
(30) (31) (32) (33) (34)
2.49 12 15 6 dollars 49 cents 2-1/2 x 3-1/2 = 1/2 x 1/2 =
36 -- x -- 8
---- 25 32 ------------------
(35) (36) (37) (38) (39)
9873/4 3ft. 5in. 21/4 x 41/2 x 11/2 = .0963 1/8 8ft. 91/2in.
25 5 .084 9
---- --------- --------- ----------
* * * * *
A series of problems in reasoning in arithmetic which were given in
twenty-six school systems by Dr. C.W. Stone furnish a valuable test in
this field, as well as an opportunity for comparison with other schools
in which these problems have been used.[22] A list of problems follows.
Solve as many of the following problems as you have time for;
work them in order as numbered:
1. If you buy 2 tablets at 7 cents each and a book for 65
cents, how much change should you receive from a two-dollar
bill?
2. John sold 4 Saturday Evening Posts at 5 cents each. He kept
1/2 the money and with the other 1/2 he bought Sunday papers
at 2 cents each. How many did he buy?
3. If James had 4 times as much money as George, he would have
$16. How much money has George?
4. How many pencils can you buy for 50 cents at the rate of 2
for 5 cents?
5. The uniforms for a baseball nine cost $2.50 each. The shoes
cost $2 a pair. What was the total cost of uniforms and shoes
for the nine?
6. In the schools of a certain city there are 2200 pupils; 1/2
are in the primary grades, 1/4 in the grammar grades, 1/8 in
the High School, and the rest in the night school. How many
pupils are there in the night school?
7. If 3-1/2 tons of coal cost $21, what will 5-1/2 tons cost?
8. A news dealer bought some magazines for $1. He sold them
for $1.20, gaining 5 cents on each magazine. How many
magazines were there?
9. A girl spent 1/8 of her money for car fare, and three times
as much for clothes. Half of what she had left was 80 cents.
How much money did she have at first?
10. Two girls receive $2.10 for making buttonholes. One makes
42, the other 28. How shall they divide the money?
11. Mr. Brown paid one third of the cost of a building; Mr.
Johnson paid 1/2 the cost. Mr. Johnson received $500 more
annual rent than Mr. Brown. How much did each receive?
12. A freight train left Albany for New York at 6 o'clock. An
express left on the same track at 8 o'clock. It went at the
rate of 40 miles an hour. At what time of day will it overtake
the freight train if the freight train stops after it has gone
56 miles?
A different type of measurement is accomplished by using Thorndike's
scale for measuring the quality of handwriting.[23] A typical
distribution of the scores which children receive on the handwriting
scale reads as follows: For a fourth grade one child writes quality
four, two quality six, five quality seven, seven quality eight, eight
quality nine, three quality ten, two quality eleven, two quality twelve,
one quality thirteen, one quality fourteen. In a table the distributions
of scores in penmanship for a large number of papers selected at random
show the following results:
============================================================
| GRADES
SCORES +------+------+------+------+------+------+-----
| 2 | 3 | 4 | 5 | 6 | 7 | 8
------------+-------------+------+------+------+------+-----
0 | -- | -- | -- | -- | -- | -- | --
1 | -- | -- | -- | -- | -- | -- | --
2 | -- | -- | -- | -- | -- | -- | --
3 | -- | -- | -- | -- | -- | -- | --
4 | 5 | 2 | -- | -- | -- | -- | --
5 | 22 | 2 | 3 | 3 | -- | 1 | --
6 | 21 | 21 | 16 | 3 | 2 | -- | 1
7 | 29 | 44 | 24 | 12 | 1 | 3 | 3
8 | 28 | 86 | 42 | 56 | 20 | 15 | 7
9 | 42 | 41 | 55 | 61 | 25 | 29 | 11
10 | 7 | 8 | 20 | 16 | 9 | 11 | 1
11 | 29 | 13 | 21 | 17 | 32 | 25 | 23
12 | 5 | 2 | 15 | 15 | 44 | 12 | 21
13 | 7 | 2 | 2 | 6 | 17 | 19 | 9
14 | -- | -- | 3 | 4 | 10 | 16 | 9
15 | -- | -- | 1 | -- | 9 | 6 | 15
16 | 1 | -- | -- | 1 | 10 | 12 | 17
17 | -- | -- | -- | -- | 6 | 2 | 3
18 | -- | -- | -- | -- | 3 | 1 | --
------------+------+------+------+------+------+------+-----
Total papers| 196 | 221 | 202 | 194 | 188 | 152 | 124
============================================================
* * * * *
A SCALE FOR HANDWRITING OF CHILDREN IN GRADES 5-8
The Unit of the Scale Equals approximately One-Tenth of the Difference
between the Best and Worst of the Formal Writings of 1,000 Children in
Grades 5-8. The Differences 16-15, 15-14, 14-13, etc., represent Equal
Fractions of the Combined Mental Scale of Merit of from 23-55 Competent
Judges.
Sample 140, representing zero merit in handwriting. Zero merit is
arbitrarily defined as that of a handwriting, recognizable as such, but
yet not legible at all and possessed of no beauty.
[Illustration: qual0.png: ]
Quality 4.
[Illustration: qual4.png: ]
Quality 5.
[Illustration: qual5.png: ]
Quality 6.
[Illustration: qual6.png: ]
Quality 7.
[Illustration: qual7.png: ]
Quality 8.
[Illustration: qual8a.png: ]
[Illustration: qual8b.png: ]
Quality 9.
[Illustration: qual9a.png: ]
[Illustration: qual9b.png: ]
[Illustration: qual9c.png: ]
Quality 10.
[Illustration: qual10.png: ]
Quality 11.
[Illustration: qual11a.png: ]
[Illustration: qual11b.png: ]
[Illustration: qual11c.png: ]
Quality 12.
[Illustration: qual12a.png: ]
[Illustration: qual12b.png: ]
[Illustration: qual12c.png: ]
Quality 13.
[Illustration: qual13a.png: ]
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