and the subjects taught, together with the methods of teaching them,
should be differentiated accordingly. But here the family interposes
the interests of rank or station, and claims the right to determine by
these how much or how little instruction a boy needs.
Looked at pedagogically, each study calls for a corresponding mental
activity to be suited to the general condition of the individual. Its
success must not involve exhaustion of the pupil’s powers, nor make
demands upon them at the wrong time.
But it would be an error to argue that one who is being initiated
into one subject ought to combine with that subject a second, third,
or fourth, on the ground that subjects one, two, three, and four are
essentially interrelated. This conclusion holds for scholars, who,
so far as they are personally concerned, have long passed beyond
preliminary pedagogical considerations, and even in their case it
applies only to those branches which are intimately connected with
their specialties; it has nothing to do with the psychological
conditions by which the course of education must be governed. Only too
frequently do masses of ideas remain isolated despite the fact that
the objects corresponding to them are most intimately and necessarily
interconnected; and such isolation could not have been prevented by
merely starting work in a large web of erudition in a number of places.
The case is different where certain studies constitute the necessary
preparation for thorough knowledge of one kind or another. Here we are
right in concluding that one who cannot master the former is equally
unable to get hold of the latter.[24]
[24] These remarks upon correlation are instructive in view of later
developments of the Herbartian school in Germany. The reader is
referred to discussions in the First and Second Year-Books of the
National Herbart Society.
220. It is difficult to deal with the rare instances of tardy
development unless we find that they are due to neglected health,
or to lack of assistance in enlarging the range of experience, and
to failure to change the mode of instruction. Here an attempt may be
made to supply what is wanting. But even where the rate of progress
becomes more rapid at once, the teacher’s efforts will have turned
out favorably only when the boy gives also clear proof of a vigorous
striving for advancement.
221. To revert to fundamental ethical principles, particular mention of
the ideas of justice and equity needs to be made in this connection.
These ideas issue from reflection on human relations; they are
consequently less accessible to early childhood, which finds itself
subordinated everywhere to the family. The boy, on the other hand,
lives more among his peers, and the necessary corrections are not
always administered so promptly as to leave no time for independent
judgment. Not infrequently voluntary association takes place among
boys, personal authority plays a part, and even usurpation of power is
not rare. Now, education has to provide for clear ethical concepts and
for government and training besides. But not only that; it must also
furnish the kind of instruction that will exhibit similar but remote
relations, for purposes of unbiassed contemplation. Such instruction
must borrow its material from poetry and history.
222. To history we are referred by still another consideration. As
has already been shown (206–211), the idea of good-will points to
the necessity of religious culture; and this relies for support on
stories, old stories at that. The expansion of the pupil’s power of
thought which is here demanded must be generally attained, even though
very incompletely, in every course of instruction, that of the village
school included.
223. Another fixed goal, the importance of which exceeds even that of
reading and writing, is furnished by arithmetic, which gives clearness
to the common concepts of experience, and is indispensable in the
practical affairs of life.
224. Decimal arithmetic no pupil would be likely to think out by
himself; he would very certainly not invent Bible history. Both must
accordingly be regarded as belonging preëminently to the province of
synthetic instruction, which always involves the difficult problem of
how to assure its entrance, as a potent factor, into existing masses
of ideas. As to this, it would be a blunder to conclude that, since
Bible history and history as a whole, arithmetic and mathematics as
a whole, hang together, there is also a corresponding pedagogical
connection (219). But so much is certain, that the efficiency of
a group of ideas increases with expansion and with multiplied
association. It will be an advantage, therefore, to Bible history
and to arithmetic, if as wide a range is given to historical and
mathematical teaching as circumstances and ability permit, even if
the conditions should be such that a many-sided culture is not to be
expected.
225. The subjects next to be considered in the choice of material for
instruction are poetry and natural history, great care being taken
not to disregard the necessary sequence. The time for fables and
stories should not be curtailed; it is important to make sure that
boys do not lose the taste for them too early. The easiest and safest
facts of zoölogy will have been presented already in connection with
the picture-books of childhood. The right moment for introducing the
elements of botany has arrived when the boy is collecting plants.
Foreign languages would be assigned the lowest place, if particular
circumstances did not in many cases lend them a special importance.
The ancient classical languages, at any rate, form to such an extent
the basis of the study of theology, of jurisprudence, and of medicine,
they are so necessary to all higher scholarship, that they will
always constitute the fundamental branches of instruction in academic
preparatory schools.
It is obvious, however, that the extent of instruction depends too
much on external conditions of rank and means to permit a definite
prescription of instruction-material for all cases. Far less dependent
is the development of many-sided interest in its relation to branches
of study. If the limits set to the latter are narrow, it is still the
business of instruction to secure an approximation to many-sided
culture; while under highly favorable circumstances the very abundance
of educational help must put the teacher on his guard against losing
sight of the real aim of instruction.
226. Frequently the burden of necessary and useful studies is made
excessively heavy, a fact which the members of the teaching profession
try to conceal from themselves, but which attracts the attention of
outsiders. A few hours of gymnastics do not sufficiently counteract
such evil effects. As an offset we have at best the prevention of
the vices of idleness. From every point of view, for the mere reason
that this matter calls for special attention and that the method of
procedure has to be determined in accordance with the results of
observation, the home must do its part toward relieving that natural
strain which even good instruction exerts--and the school must not
encroach on the time necessary for that purpose. In extreme cases, to
be sure, it may be expressly demanded that the school engage the whole
of a boy’s time. But, as a rule, outside school-work should take up,
not the largest, but, on the contrary, the smallest amount of time
possible. How the remaining hours are to be employed is for parents
and guardians to decide according to individual needs, ascertained
by observation; and it is on them that the responsibility for the
consequences rests.
CHAPTER IV
=Youth=
227. Whether instruction comes to an end or is continued during
this period, all it can accomplish depends now on the fulfilment
of the condition that the young man himself regard the retention
and increase of his attainments as something valuable. Accordingly,
the interrelations of knowledge, as well as its connection with
action, must be brought before his mind with the greatest possible
distinctness. He must be furnished, also, with the strongest incentives
to reach the goal determined upon, provided the question is merely how
to overcome indolence and thoughtlessness. For it is just at this stage
that the teacher needs to fear and to prevent those wrong motives which
would issue merely in an artificial semblance of talent.
228. Moreover, the allowance made for the child and the boy can no
longer be made for the youth. His whole ability is to be put to the
test, and his position in human society determined according to the
outcome. He must experience something of the difficulty of obtaining
a foothold among men. Positions for which he does not seem quite
prepared are contested; he is surrounded by rivals, and is spurred
on by expectations, which it is often difficult to moderate when most
necessary.
229. If now the young man puts his trust in favorable circumstances,
and, in spite of all appeals, gives himself up to the pursuit of ease
and pleasure, education is at an end. It only remains to conclude with
precepts and representations which future experiences may possibly
recall.
230. If, on the other hand, the youth has his eyes fixed on a definite
goal, the form of life which he is striving to attain, and the motives
that impel him, will determine what else may be done for him. According
as the ideals of honor that he makes his own are directed more
outwardly or inwardly, they stand more or less midway between plans for
actions and maxims.
231. The youth is no longer pliant, except when his failures have made
him feel ashamed of himself. Such cases must be made use of for the
purpose of making good deficiencies. But on the whole, duty requires
that the stern demands of morality be held up to him without disguise.
Perfect frankness can hardly be looked for any longer, and to insist
on it is out of the question entirely. The reserve of the age of
adolescence marks the natural beginning of self-control.
These brief paragraphs on the development of the individual through
infancy, childhood, boyhood, and youth, mark an early interest
in what is now known as child-study, the literature of which has
become voluminous. For a dissertation on the experimental study of
children, and a bibliography of the subject, the reader is referred
to the monograph by Arthur McDonald, of the United States Bureau of
Education, entitled “Experimental Study of Children.” A smaller but
more useful bibliography has been compiled by L. N. Wilson. It is
found in _Pedagogical Seminary_ for September, 1899.
PART III
_SPECIAL APPLICATIONS OF PEDAGOGICS_
SECTION I
REMARKS ON THE TEACHINGS OF PARTICULAR BRANCHES OF STUDY
CHAPTER I
=Religion=
232. The content of religious instruction is for theologians to
determine, while philosophy bears witness that no knowledge is able to
surpass the trust of religious faith. But both the beginning and the
end of religious instruction call for remarks from the point of view of
pedagogy.
Religious instruction culminates, if it does not end, in the rite of
confirmation, and the subsequent admission to the Holy Communion. The
former is characteristic of a particular Christian denomination; the
latter, on the contrary, of the whole brotherhood of Christians.
Now the profound emotion which marks the first Communion service
should imply a conquest over the feeling of separation from other
denominations, especially since the mere admission to Communion is
conditioned on the general requirement of earnest ethical aspiration.
It is thus assumed that members of other confessions, provided they are
communicants at all, have fulfilled the same condition. Preparatory
instruction must work toward this end all the more, since with many
persons Christian love for those who differ from them in important
articles of faith belongs to the more difficult duties. Moreover, the
fact that this same instruction necessarily had to set forth clearly
fundamental denominational differences, lends additional weight to the
necessity of inculcating the virtue of Christian charity.
233. In academic schools, if Greek is begun early enough, it is
possible to deepen the impressions of Christian teaching by the
dialogues of Plato that bear on the death of Socrates, particularly
the “Crito” and the “Apology.” Being the weaker, however, impressions
of this sort should precede the time when the solemn initiation into
Christian fellowship produces its whole powerful effect.
234. Going back in thought, we find that the portion of religious
instruction which deals with characteristic denominational
distinctions, presupposes that which deals with tenets common to all
Christians, and we find that this in turn has been preceded by Bible
stories, including those of the Old Testament. But the question arises,
“Must we not go back to something more fundamental still?”
235. Religion cannot possibly be adequately presented by treating of it
merely as a perpetuation of something historical and past. The teacher
must needs make use also of the present testimony furnished by the
adjustment of means to end, in nature. But even this, for which some
knowledge of nature is prerequisite, and which leads up to the ideas of
wisdom and power, is not the first step.
236. True family feeling is elevated easily and directly to the idea
of the Father, of the father and mother. Only where such feeling is
wanting does it become necessary to make churches and Sunday observance
the starting-point as indications of humility and gratitude. An
all-pervading love, providence, and watchful care constitute the first
concept of the Highest Being,--a concept limited by the mental horizon
of the child, and expanding and becoming more elevated only by degrees.
237. The process of elevating religious concepts and purifying them
of unworthy admixtures must, however, have taken place, and the true
concepts must have been deeply impressed, before the mythological
conceptions of antiquity become known; in which case the latter will
produce the right effect by the contrast between the manifestly
fabulous and crude, and the worthy and sublime. If managed properly,
this subject presents no difficulties.
238. But there are other difficulties,--difficulties growing out of
individual peculiarities. While some would be harmed by much talk
about sin, because they would thus either become acquainted with it,
or else be filled with fantastic terror, there are others whom only
the strongest language can move, and still others who themselves
preach against the sins of the world, and, at the same time, front the
world in proud security. Then there are those who brood over ethical
problems, and who, without having heard of Spinoza, argue that what the
Highest Judge has permitted to happen he has approved of, whence might
is the practical proof of right. There are contemners of mere morality,
who think that prayers will consecrate their evil actions. Isolated
traces of such perversions may indeed be met with even in children,
especially if their glib reproduction of the sermon, or worse yet,
their praying aloud, has happened to receive praise.
Hence it is necessary to observe the effect of religious instruction on
each individual. Another task for home training.
CHAPTER II
=History=
239. The most common blunder that younger teachers of history are apt
to make is that, without intending it, they become increasingly prolix
in presentation. It is not that interest deepens, but that the network
of events lures them, now one way, now another. This of itself evinces
preparation; but mental preparation alone does not suffice; preliminary
practice, too, is necessary.
Young teachers of history, like young teachers in other subjects, are
prone to error. What the prevailing error in a given study will be,
is likely to depend upon conventional methods of presenting it. In
Germany it is customary for the teacher himself to be the historian
through whose mind all historical knowledge passes on its way to
the children. But just as good writers of history are rare, so good
teachers of history are likely to be few, since in an important sense
they are at once teachers and oral historians. Where the text-book is
depended upon for the narrative, as in the United States, a different
difficulty presents itself to the teacher. What shall he do with the
text, all the pupils having read it? Perhaps the commonest method is
to call upon them one by one to reproduce it in class. But this is a
deadening process, since it compels nineteen pupils to sit passive
while the twentieth recites the words that the nineteen could repeat
equally well. If, therefore, the besetting fault of the teacher of
history in German is prolixity, that of the American teacher is
tediousness. The German method is that of primitive man, where the
legends of the tribe are handed down from father to son by word of
mouth; the American presentation of history is modern, where all the
resources of scholarship and the advantages of the printing press are
utilized. Each method has peculiar advantages, the former having the
possible charm of first-hand narrative, the latter that of accuracy
and comprehensiveness. The narrative method is greatly superior to
that of the text-book with children whose powers of reading are
not well developed; the text-book, together with its available
accessories, is greatly to be preferred with older pupils capable
of large amounts of reading. The following sections give a vivid
description of the narrative method at its best; the commentary will
attempt to show how the printed page may be made equally attractive,
and, at the same time, much more useful.
240. If, to begin with, a purely chronological, but accurate,
outline-view of history is to be imparted, the teacher must be able
to traverse mentally the whole historical field, going with equal
readiness back, forward, or across (synchronistically). The notable
names must form definite groups and series; and the teacher must
possess facility in making the most notable names stand out clearly
from the groups, and in condensing the most salient points of a long
series into a short series.
If this mastery of subject-matter is important for the narrator, it
is equally important for the teacher who depends upon print for the
narration. Observation of current history teaching betrays the fact
that the teacher rarely becomes master of his material to such an
extent that he can throw it into new forms. As it stands in the book,
he probably knows it; but to take liberties with the facts, to expand
parts, or throw masses into brief outline, to make new groupings, or
to change a long series into a short one, usually lies beyond his
ability. This lesson the American teacher must learn through a better
mastery of his materials.
241. Again, the teacher must make himself perfectly familiar with
general notions that relate to classes of society--constitutions,
institutions, religious customs, stages of culture--and that serve
to explain events. But not only this; he must study likewise the
conditions under which he can develop them and keep them present in
the minds of his pupils. This consideration alone shuts out most
generalizations from the first lessons in history. And, accordingly,
ancient history, whose moving causes are simpler than the more modern
political factors, maintains its place in presentations of historical
material to younger pupils.
American history is better than ancient history in respect to its
richness of picturesque variety. It is, moreover, easier for children
to comprehend, since our present conditions have emerged directly
from our pioneer state. Not only are constitutions, institutions,
and religious customs to be studied, but the economic conditions of
those early times are particularly worthy of study, since they are
both important and interesting. Methods of farming, of conducting
household affairs, such as cooking, making fires, producing
clothing, securing shelter, means of transportation on land and
water, methods of communication, and many other similar topics are of
interest to the young.
242. Furthermore, due attention must be given to the difficulty of
narrating well a complex event. The very first condition is continuity
of the thought-current, in order that the thread of the story may
remain unbroken, except where there are intentional rests. This, in
turn, presupposes fluency of speech, careful cultivation of which is
indispensable to a good presentation of historical events. But mere
fluency does not suffice. There must also be resting-places, because
otherwise alternate absorption and reflection cannot be secured; and
because, without such pauses, even the formation of the series fails,
since what has preceded arrests what follows. It is therefore not
immaterial where a historical lesson begins and ends, and where the
reviews are inserted.
While the narrator can utter words in succession only, the event has,
in his mind, a very different form, which it is his business to convey
to his hearers. Nor does the form of the event resemble a level plane;
on the contrary, a manifold interest lifts some things into prominence
and lets others sink. It is essential, accordingly, to distinguish how
far, in a given instance, the narration should follow in a straight
line the succession of events, and where, on the other hand, it should
deviate to include accessory circumstances. The very language used
must possess the power to induce side-glances and retrospective views,
even without leaving the main road. The narrator must have skill to
introduce descriptions here and to linger over pictures there, but must
be able also, while moving his hearers, to retain his own self-control
and to keep his bearings.
243. There remains one other requisite of prime importance, namely, the
utmost simplicity of expression. The condensed and abstract language of
more recent historians is hardly suited even to the highest class of a
secondary school; a sentimental or witty treatment, such as that found
in modern novelists, must be avoided entirely. The only safe models are
the ancient classics.
The most serious fault with the text-book method is the barrenness
arising from condensation. To teach history solely from a single
book, even if this be among the best, is to produce an atrophy of the
historical interest. It is on this account that successful teachers
introduce large amounts of collateral reading, not of similarly
condensed books, which would be like remedying the drouth with more
dry weather, but of sections from fuller works on the same subject.
In American history the pupil is directed to read selected portions
of standard works like those of Fiske, Parkman, McMaster, Turner,
Tyler, or earlier historians. In English history he is sent directly
to such men as Gardiner, Green, Freeman, Traill, Ransome, Cunningham
and McArthur, Harrison and Macaulay. The method of copious readings
has, in turn, its disadvantages, the most conspicuous of which is
diffusiveness. It is easy for the student to become so absorbed in
a mass of details that he lose the proper sense of proportion, or
overlook the relative importance of events, or fail to fix firmly
in mind the causal series that binds all together. In the case of
either of the methods described, it is the teacher who is responsible
for order and for clearness of detail. In the one case his narrative
must have the artistic unity of the finished historian; in the other
he must so manage a wealth of given material that the golden chain
of cause and effect shall be seen binding diversity into unity. The
ability to do the first is of a much rarer order than that of the
second, for the art of teaching is not so difficult as the art of
historical composition. The remedy for the specific difficulty which
modern text-book teaching of history encounters will be discussed
under paragraph 247.
The stories of Herodotus should serve the teacher as the basis for
practice. In fact, they should actually be memorized in an accurate but
fluent translation. The effect on children is surprising. At a later
stage use may be made of Arrian and Livy. The method of the ancients of
letting the principal characters utter their views and set forth their
motives with their own lips, the narrator abstaining from reflections
of his own, should be scrupulously imitated, and should be departed
from only in the case of manifestly artificial rhetorical devices.
244. The course of preparation outlined above (240–243) having gone
hand-in-hand with a thorough, pragmatic study of history, it is
further necessary, in the exercise of the art acquired, to learn to
expand or contract, according to circumstances and the specific aims of
each occasion. Concerning this point no generally applicable rules can
be given, on account of the great variety of possible cases; but the
following suggestions should be noted:--
In general, all helps whereby historical objects may be represented to
sense--portraits, pictures of buildings, of ruins, etc.--are desirable;
maps for the more ancient times must be regarded as particularly
indispensable. They should always be at hand, and their study
should not be neglected. Among these helps must be included charts,
substantially like that by Strass entitled “The Stream of Time,” which
places before the eye not only synchronistic events, but at the same
time shows also the alternate union and division of countries. The lack
of such aids causes the loss of much time and temper over mere memory
work.
Again, attention is due to the following four aspects of the teaching
of history:--
245. (1) In the first place, even the earliest lessons in geography
give rise to the question, whenever the description of a country is
finished, “How did things look in this country formerly?” For it is
a part of correct apprehension that cities and other works of man
should not be regarded as of equal age with mountains, rivers, and
oceans. Now, although the teacher cannot stop, during the time set
apart for geography dealing with the present, to show and explain maps
illustrative of the past, it will be useful, nevertheless, to add a
few remarks about the early history of the country under discussion.
The art of narration, however, is out of place here, inasmuch as the
question, although reaching back in time, is suggested by the country.
Mention of former activity, such as migrations and wars, is made simply
for the purpose of adding life to the conception of a stationary
surface. At the beginning, the notes on by-gone periods in connection
with the geography of Germany will accordingly be as brief as possible;
gradually, however, as France, England, Spain, Italy, are being studied
in succession, these historical notes become knit together, and history
is thus, so to speak, made to loom up in the distance. How far to go
in this direction can be determined more definitely by distinguishing
between the requirements of the first, and of the second course in
geography. In the first course the most general statements may suffice,
_e.g._, that not so very long ago Germany was split up more than now;
that there were older times, when cities and neighboring princes often
made war upon each other; that the barons used to live on more or less
inaccessible heights; but that, in the interest of better order and
stricter surveillance, Germany was divided into ten districts, etc.
The second course will admit of more historical facts than the first,
although still only very few pertaining to an older epoch. Only the
more recent events can be conveniently connected with geography, except
in the case of still extant historical monuments,--such, for instance,
as the ruins in Italy, the composite language of England, the peculiar
political organization of Switzerland with its many subdivisions,
visible on the map, and its diversities of language.
If, as is sometimes recommended, the plan is adopted of preparing
the way for the study of mediæval and modern history by a separate
introductory course in short biographies, such a plan, though at best
only fragmentary in its results, becomes at least more feasible where
historical notes of the kind just mentioned are incorporated with the
lessons in geography. But in this case it is all the more essential to
have a chronological chart upon the wall, to some dates of which the
teacher must take every opportunity to refer, in order that the pupils
may obtain at least some fixed points. Otherwise scattered biographies
are liable to occasion great confusion.
246. (2) The chief basis for the earlier stages of historical teaching
will always be Greek and Roman history. It will not be inappropriate
to commence with a few charming stories from Homeric mythology, since
there is a close connection between the history of a people and their
religion. Two wrong ways, however, are to be avoided: one, that of
giving a detailed theogony or of including objectionable myths, for
the sake of completeness, which would here be devoid of a rational
purpose; the other, that of having the mythological elements memorized.
Only true history should be memorized by children. Mythology is a study
for youths or men.
Persian history must be told approximately in the sequence and setting
given by Herodotus; to it the history of Assyria and of Egypt may
be joined in the form of episodes, Greece being kept well in the
foreground. The stories from the Old Testament, on the other hand, form
a chain of lessons by themselves. The history of Rome must at first
retain its mythical beginnings.
Whatever German opinion may be regarding the beginnings of historical
instruction for their own children, American history possesses
strong claims for precedence when we come to children of the United
States. If we regard the chief intellectual purpose of history for
the student to be the understanding of the present status through
a knowledge of the historical progress that has led to it, then
the primitive and pioneer history of this country is infinitely
more valuable than any other to an American child, for in it lie
enfolded the forces that have developed our people; whereas Greece
and Rome are as distant in influence as they are in time. It is the
mythology of Greece and Rome that most attracts children; but this
belongs to literature rather than to history. Accounts of battles
are about the same the world over, but it takes more maturity of
mind to understand the Greek rage for individuality after the rise
of philosophy, than it does to understand a corresponding feeling
among the American pioneers, to say nothing of the desirability of
teaching the latter as a phase of our own development. For reasons
of simplicity, therefore, as well as for psychological nearness and
national importance, American history must take precedence over that
of Greece and Rome for American children.
247. Suppose, now, that detailed stories after the models furnished by
the ancients have won the attention of the pupils; the mere pleasure
of listening to stories can nevertheless not be allowed to determine
continuously the impression to be produced. Condensed surveys must
follow, and a few of the main facts be memorized in chronological order.
The following suggestions will be in place here. The chief events are
to attach themselves in the memory to the memorized dates in such a
way that no confusion can arise. Now, a single date may suffice for
the group of connected incidents constituting one main event; if it
seems necessary to add another, or a third, well and good, but to
keep on multiplying dates defeats the very end aimed at. The more
dates the weaker their effect, on account of the growing difficulty
of remembering them all. In the history of one country dates should
rather remain apart as far as possible, in order that the intervening
numbers may be all the more available for purposes of synchronistic
tabulation, by which the histories of different countries are to be
brought together and connected. The same sparing use should be made of
the facts of ancient geography, but those that are introduced must be
learned accurately.
Granted that the primitive method of historical narration by the
teacher is the most effective in its appeal to the beginner, it
must be maintained that the combined knowledge and literary skill
of modern historians infinitely surpass the powers of the ordinary
teacher. The modern problem is, not how to compose history, but how
to utilize that which has been composed. It is, in short, to guard
against the confusion that comes from diffuseness. Wide historical
reading may be as bad for the student as wide reading of novels. The
mind may surrender itself to the passing panorama as completely in
the one field as in the other, until the impressions made are like
those of a ship upon a sea. The remedy is the thorough organization
in the mind of the student of the knowledge gained in diverse fields.
This is secured by teacher or author, or both. Some authors secure
clearness of outline by topics, references, and research questions.
Larned’s “History of England” concludes every chapter in this way.
As an illustration we may quote from Chapter XVI, which narrates the
quarrel between King Charles and his people:--
202. _Charles I._
Topic.
1. Charles’s character and views.
References.--Bright, II, 608, 609; Green, 495; Montague, 118;
Ransome, 138, 139.
203. _Bad Faith in the Beginning of the Reign._
Topic.
1. Charles’s marriage and broken pledges.
Reference.--Bright, II, 608, 614.
204. _The First Parliament of King Charles._
Topics.
1. Charles’s designs and his treatment of Parliament.
2. Attitude of Commons and their dissolution.
3. The King’s levies.
Reference.--Gardiner, II, 502, 503.
Research Questions.--(1) What were the legal and illegal sources
of the King’s revenues? (Ransome, 151, 155). (2) What might be
said to constitute the private property of the crown? (3) What
contributed to make Charles’s court expensive? (Traill, IV, 76).
(4) How would this need for money make for parliamentary
greatness?[25]
In a similar way the remaining topics of this section of English
history are recorded, guiding the pupil in his outlines and his
readings. With suitable care on the part of the teacher to see that
the student fixes the outline firmly in mind, there is no danger of
becoming lost in a wilderness of words. At the same time the pupil’s
mind is enriched from many noble sources, instead of being limited by
the presumably meagre resources of a single teacher. By this method
the child may enjoy the benefits of modern erudition, without at the
same time being harmed by dissipation of mental energy.
Other authors reach the same ends by different means. Fiske’s
“History of the United States,” for example, concludes each chapter
with a topical outline in which cause and effect are emphasized.
At the close of Chapter X, on the “Causes and Beginning of the
Revolution,” we find the following:--
=Topics and Questions=
76. _Causes of Ill Feeling between England and her Colonies._
1. What was the European idea of a colony, and of its object?
2. What erroneous notions about trade existed?
3. What was the main object of the laws regulating trade, etc.?
77. _The Need of a Federal Union._
1. One difficulty in carrying on the French wars.
2. An account of Franklin.
3. Franklin’s plan of union, etc.
78. _The Stamp Act Passed and Repealed._
1. The kind of government needed by the colonies.
2. How Parliament sought to establish such a government.
3. The nature of a stamp act, etc.
79. _Taxation in England._
1. How Pitt’s friendship for America offended George III.
2. The representation of the English people in Parliament.
3. How the representation of the people is kept fair in the
United States.
4. How it became unfair in England.
5. Corrupt practices favored by this unfairness.
6. The party of Old Whigs.
7. The Tories, or the party of George III.
8. The party of New Whigs and its aims.
9. Why George III was so bitter against Pitt.
10. The attitude of the King toward taxation in America.
11. The people of England not our enemies, etc.
At the close of these topics there follows a list of fifteen
“Suggestive Questions and Directions,” with page references to
Fiske’s “The American Revolution,” Vol. I, the whole being concluded
by eighteen topics for collateral reading from “The American
Revolution,” and from Cooke’s “Virginia.”[26]
It is a significant fact that modern text-books for children are
being prepared by masters in the various departments of knowledge,
not a little thought being bestowed upon the highest utilization
of all modern instruments for arousing the intelligent interest of
the pupils. This being the case, it is idle to rely upon primitive
methods, however potent they may have been in the past, with pupils
who have learned to read fluently.
[25] Larned, “History of England,” Houghton, Mifflin & Co., p. 396.
[26] Fiske, John, “A History of the United States for Schools,”
Houghton, Mifflin & Co., Boston, pp. 211–215.
248. The general surveys that follow the detailed narratives have this
advantage for the pupil: he infers of his own accord, that in periods
of which not much is told, a great deal took place, nevertheless,
which the history or the teacher passes over in silence. In this way
the false impressions are prevented that would be produced by purely
compendious instruction, which indeed, at a later stage, becomes in a
measure unavoidable.
249. (3) Mediæval history derives no assistance from the study of the
ancient languages, nor is it closely related to present conditions;
there is difficulty in imparting to the presentation of it more
than the clearness obtainable through geography and chronology. But
more than this is requisite: the burden of mere memory work without
interest would become too great. The fundamental factors, Islamism,
Papacy, the Holy Roman Empire, Feudalism, must be explained and given
due prominence. Most of the facts down to Charlemagne may be made to
contribute additional touches to the panorama of the Great Migration.
With Charlemagne the chain of German history begins, and it will
usually be considered advisable to extend this chain to the end of
the Middle Ages, in order to have something to which synchronous
events may be linked later on. Yet some doubt arises as to the value
of such a plan. To be sure, the reigns of the Ottos, the Henrys, the
Hohenstaufen, together with intervening occurrences, form a tolerably
well-connected whole; but as early as the interregnum there is a
sad break, and although the historical narrative recovers, as it
were, with the stories of Rudolph Albrecht and Ludwig the Bavarian,
there is nothing in the names of succeeding leaders, from Carl IV
to Frederick III, that would make them proper starting-points and
connecting centres for the synchronism of the whole period in question.
It might be better, therefore, to stop with the excommunication of
Ludwig the Bavarian, with the assembly of the electors at Rhense,
and with the account of how the popes came to reside in Avignon.
Then--going back to Charlemagne--France, Italy, even England, may
be taken up, and greater completeness given to the history of the
crusades. Farther on, special attention might be called, in a
synchronistic way, to Burgundy and Switzerland, and to the changing
fortunes of the wars between England and France. French history may
then leave off with the reign of Charles VIII, and English history
with that of Henry VII, while German history, from Maximilian on,
is placed again in the foreground. The Hussite wars will be treated
as forerunners of the Reformation. Other events must be skilfully
inserted. Many modifications of grouping will have to be reserved for
subsequent repetitions.
250. (4) In presenting modern history, the teacher will do well to
avail himself of the fact that modern history does not cover so long
reaches of time as mediæval history does, and that it falls into
three sharply defined periods, the first of which ends with the
treaty of Westphalia, the second extends from this date to the French
Revolution, and the third, to the present. These periods should be
carefully distinguished, the leading events of each should be narrated
synchronistically, and a recital of the most essential historical facts
about each country should follow. Only after each has been handled
in this way, and the subject-matter presented has been thoroughly
impressed upon the memory by reviews, will it be well to pass on to a
somewhat fuller ethnographical account reaching back into the mediæval
history of each country and extending forward to our own times. No
harm is done by going over the same ground again for the purpose of
amplifying that which before appeared in outline only.
The chief point is, that no course of instruction which claims at all
to give completeness of culture can be regarded as concluded before it
has introduced the pupil to the pragmatic study of history, and has
taught him to look for causes and effects. This applies preëminently to
modern history, on account of its direct connection with the present;
but mediæval and ancient history, too, have to be worked over once more
from this point of view. History should be the teacher of mankind; if
it does not become so, the blame rests largely with those who teach
history in schools.
251. A well-compiled and well-proportioned brief history of inventions,
arts, and sciences should conclude the teaching of history, not only in
gymnasia, but also and especially in higher burgher schools, because
their courses of study are not supplemented by the university.
Moreover, the whole course in history is properly accompanied by
illustrative poetical selections, which, although perhaps not produced
during the different epochs, yet stand in some relation to them; and
which in some measure, even if only by illustrating ages very far
apart, exhibit the vast differences in the freest activities of the
human mind.
=Note.=--National history is not the same for each land, nor
everywhere of equal interest, and, owing to its connection with
larger events, often unintelligible to young minds when torn out
of its place and presented by itself. If its early introduction is
desired in order to kindle the heart, special pains must be taken
to select that which is intelligible and which appeals to boyhood.
CHAPTER III
=Mathematics and Nature Study=
252. Aptitude for mathematics is not rarer than aptitude for other
studies. That the contrary seems true, is owing to a belated and
slighted beginning. But that mathematicians are seldom inclined to
give as much time to children as they ought is only natural. The
elementary lessons in combination and geometry are neglected in favor
of arithmetic, and demonstration is attempted where no mathematical
imagination has been awakened.
The first essential is attention to magnitudes, and their changes,
where they occur. Hence, counting, measuring, weighing, where possible;
where impossible, at least the estimating of magnitudes to determine,
however vaguely at first, the more and the less, the larger and the
smaller, the nearer and the farther.
Special consideration should be given, on the one hand, to the number
of permutations, variations, and combinations; and, on the other hand,
to the quadratic and cubic relations, where similar planes and bodies
are determined by analogous lines.
=Note.=--This is not the place for saying much that might be said
concerning that which renders early instruction in mathematics
unnecessarily difficult. But it may be remarked in brief that
some of these difficulties arise from the terminology, some
from the teacher’s accustomed point of view, and some from the
multiplication of varying requirements.
(1) The phraseology used forms an obstacle, even to the easiest
steps in fractions. The fraction ⅔, for example, is read
two-thirds, and, accordingly, ⅔ × ⅘, two-thirds times four-fifths,
instead of, multiplication by two and by four, and division by
three and by five. The fact is overlooked that the third part of
a whole includes the concept of this whole, which cannot be a
multiplier, but only a multiplicand. This difficulty the pupils
stumble over. The same applies to the mysterious word _square
root_, employed instead of the expression: one of the two equal
factors of a product. Matters grow even worse later on when they
hear of roots of equations.
(2) Still more might be said in criticism of the erroneous
view according to which numbers are recorded as sums of units.
This is true as little as that sums are products; two does not
mean two things, but doubling, no matter whether that which is
doubled is one or many. The concept of a dozen chairs is not
made up of 12 percepts of single chairs; it comprises only two
mental products,--the general concept chair and the undivided
multiplication by 12. The concept one hundred men likewise contains
only two concepts,--the general concept man and the undivided
number 100. So, also, in such expression as six foot, seven pound,
in which language assists correct apprehension by the use of the
singular. Number concepts remain imperfect so long as they are
identified with series of numbers and recourse is had to successive
counting.
(3) In arithmetical problems the difficulty attaching to the
apprehension of the things dealt with is confounded with that of
the solution itself. Principal and interest and time, velocity and
distance and time, etc., are matters which must be familiar to
the pupils, and hence must have been previously explained, long
before use can be made of them for practice. The pupil to whom
arithmetical concepts still give trouble should be given concrete
examples so familiar to him that out of them he can create over
again the mathematical notion and not be compelled to apply it to
them.
253. The measuring of lines, angles, and arcs (for which many
children’s games, constructive in tendency, may present the first
occasion) leads over to observation exercises dealing with both planes
and spheres. Skill in this direction having been attained, frequent
application must be made of it, or else, like every other acquirement,
it will be lost again. Every plan of a building, every map every
astronomical chart, may afford opportunities for practice.
These observation exercises are to be organized in such a manner that
upon the completion of mensuration the way is fully prepared for
trigonometry, provided that besides the work in plain geometry, algebra
has been carried as far as equations of the second degree.
Extended discussions as to the place and value of the ratio
idea in elementary arithmetic are found in “The Psychology of
Number,” by McLellan & Dewey,[27] and in “The New Arithmetic,”
by W. W. Speer.[28] The former work advocates early practice in
measuring with changeable units, claiming that the child should
early acquire the idea of number as the expression of the relation
that a measured somewhat bears to a chosen measurer, and making
counting a special case of measuring. Mr. Speer makes the ratio idea
still more prominent by furnishing the school with numerous sets of
blocks of various sizes and shapes with which to drill the pupils
into instantaneous recognition of number as the ratio between two
quantities. For an extended examination of these principles the
reader may well consult Dr. David Eugene Smith’s able treatise on the
teaching of elementary mathematics.[29]
=Note.=--It is now nearly forty years since the author wrote a
little book on the plan of Pestalozzi’s A, B, C, of observation,
and he has often had it used by teachers since. Numerous
suggestions have been given by others under the title, “Study of
Forms.” The main thing is training the eye in gauging distances and
angles, and combining such exercises with very simple computations.
The aim is not merely to secure keenness of observation for objects
of sense, but, preëminently, to awaken geometrical imagination and
to connect arithmetical thinking with it. Indeed, exercises of
this sort constitute the necessary, although commonly neglected,
preparation for mathematics. The helps made use of must be concrete
objects. Various things have been tried and cast aside again;
most convenient for the first steps are triangles made from thin
hard-wood boards. Of these only seventeen pairs are needed, all
of them right-angled triangles with one side equal. To find these
triangles, draw a circle with a radius of four inches, and trace
the tangents and secants at 5°, 10°, 15°, 20°, etc., to 85°.
The numerous combinations that can be made will easily suggest
themselves. The tangents and secants must be actually measured
by the pupils; from 45° on, the corresponding figures, at first
not carried out beyond tenths, should be noted, and, after some
repetition, learned by heart. On this basis very easy arithmetical
examples may be devised for the immediate purpose of gaining the
lasting attention of the pupils to matters so simple. Observations
relating to the sphere require a more complicated apparatus,
namely, three movable great circles of a globe. It would be well
to have such means at hand in teaching spherical trigonometry.
Needless to say, of course, observation exercises do not take the
place of geometry, still less of trigonometry, but prepare the
ground for these sciences. When the pupil reaches plain geometry,
the wooden triangles are put aside, and observation is subordinated
to geometrical construction. Meanwhile arithmetic is passing beyond
exercises that deal merely with proportions, to powers, roots, and
logarithms. In fact, without the concept of the square root, not
even the Pythagorean Theorem can be fully grasped.
“Herbart’s A, B, C, of Sense Perception,” together with a number of
minor educational works, has been translated into English.[30] It
abounds in shrewd observations and ingenious devices, yet as a whole
it represents one of those side excursions, which, though delightful
to genius, is not especially useful to the world. To drill children
into the habit of resolving a landscape into a series of triangles,
may indeed be possible, but like any other schematization of the
universe, is too artificial to be desirable. Nevertheless, a limited
use of the devices mentioned in this section might tend to quicken an
otherwise torpid mind.
[27] McLellan & Dewey, “The Psychology of Number,” International
Education Series, D. Appleton & Co., New York, 1895.
[28] Speer, W. W., “The New Arithmetic,” Ginn & Co., Boston, 1896.
[29] Smith, David Eugene, “The Teaching of Elementary Mathematics,”
Ch. V, The Macmillan Co., New York, 1900.
[30] Eckoff, William J., “Herbart’s A, B, C, of Sense Perception,”
International Education Series, D. Appleton & Co., New York, 1896.
254. But now a subject comes up that, on account of the difficulties it
causes, calls for special consideration, namely, that of logarithms.
It is easy enough to explain their use, and to render the underlying
concept intelligible as far as necessary in practice--arithmetical
corresponding to geometrical series, the natural numbers being
conceived of as a geometrical series. But scientifically considered,
logarithms involve fractional and negative exponents, as also the
application of the Binomial Theorem. The latter, to be sure, is merely
an easy combinatory formula so far as integral positive exponents are
concerned, but, limited to these, is here of comparatively little use.
Now, since trigonometry in its main theorems is independent of
logarithms, but is little applied without their aid, the question
arises whether beginners should necessarily be given a complete and
vigorously scientific course in logarithms, the highly beneficial
instruction in trigonometry being postponed until after the successful
completion of such a course, or whether the practical use of logarithms
is to be permitted before accurate insight into underlying principles
has been gained.
=Note.=--The difficulty encountered in this subject--undoubtedly
one of those difficulties most keenly felt in teaching
mathematics--is after all only an illustration of the injurious
consequences of former sins of omission. If the geometrical
imagination were not neglected, there would be ample opportunity,
not only for impressing far more deeply the concept of proportion,
demanded even by elementary arithmetic, but also for developing
early the idea of function. The object lessons mentioned above
have already illustrated the dependence of tangents and secants
on angles. When these relations of dependence have become as
familiar as may be expected after a half year’s instruction, sines
and cosines also are taken up. But it is not sufficient to leave
the matter here. Somewhat later, about the time when mensuration
is introduced, the squares and cubes of natural numbers must be
emphasized, and very soon committed to memory. Next it should be
pointed out how by finding the differences of squares and cubes
respectively, and then adding these differences, the original
numbers may be obtained again. A similar treatment should be
accorded to figurate numbers.
Small wooden disks, like checker-pawns, commend themselves for the
purpose. By means of them various figures are found. The pupils
are asked to indicate how many disks they need to construct one
or the other kind of figures. A further step will be to show the
increase of squares and cubes corresponding to the increase of the
root, and to make this information serve as the preparation for
the elementary parts of differential calculus. Now the time has
come for passing on to the consideration of consecutive values of
the roots, which are found to differ by quantities of continuously
decreasing smallness as one progresses continuously through the
number system. And so, after the logarithms of 1, 10, 100, 1000,
etc., also of 1/10, 1/100, etc., have been gone over many times,
forward and backward, the conception is finally reached of the
interpolation of logarithms.
255. In schools where practical aims predominate, logarithms should
be explained by a comparison of the arithmetical with the geometrical
series, and the practical application will immediately follow. But even
where recourse is had to Taylor’s Theorem and the Binomial Theorem,
the gain to the beginner will not usually be very much greater. Not
as though these theorems, together with the elements of differential
calculus, could not be made clear; the real trouble lies in the fact
that much of what is comprehended is not likely to be retained in the
memory. The beginner, when he comes to the application, still has the
recollection of the proof and of his having understood it. Indeed, with
some assistance he would be able, perhaps, to again retrace step by
step the course of the demonstration. But he lacks perspective; and in
his application of logarithms it is of no consequence to him by what
method they have been calculated.
What has been said here of logarithms may be applied more generally.
The value of rigid demonstrations is fully seen only when one has made
himself at home in the field of concepts to which they belong.
It is customary in American schools to take up elementary algebra and
elementary geometry upon the completion of arithmetic, both algebra
and geometry being anticipated to some extent in the later stages of
arithmetic. The following paragraphs from the pen of David Eugene
Smith[31] indicate some of the advance in algebra since Herbart’s
time:--
“The great revival of learning known as the Renaissance, in the
sixteenth century, saw algebra take a fresh start after several
centuries of complete stagnation. Tartaglia solved the cubic
equation, and a little later Ferrari solved the biquadratic. By the
close of the sixteenth century Vieta had put the keystone in the
arch of elementary algebra, the only material improvements for some
time to come being in the way of symbolism. For the next two hundred
years the struggle of algebraists was for a solution of the quintic
equation, or, more generally, for a general solution of an equation
of any degree.
“The opening of the nineteenth century saw a few great additions to
the theory of algebra. The first was the positive proof that the
general equation of the fifth degree is insoluble by elementary
algebra, a proof due to Abel. The second was the mastery of the
number systems of algebra,--the complete understanding of the
negative, the imaginary, the incommensurable, the transcendent.
Other additions were in the line of the convergency of series, the
approximation of the real roots of numerical equations, the study of
determinants--all finding their way into the elements, together with
the theories of forms and groups, which must soon begin to influence
the earlier chapters of the subject.
“This hasty glance at the development of the subject is sufficient
to show how it has been revolutionized in modern times. To-day it
is progressing as never before. The higher culture is beginning to
affect the lower; determinants have found place in the beginner’s
course; graphic methods, objected to as innovations by some who
are ignorant of their prominence in the childhood of science, are
reasserting their rights; the ‘imaginary’ has become very real;
the inheritances of the algebra-teachers’ guild are being examined
with critical eyes, and many an old problem and rule must soon go
by the board. It is valuable to a teacher to see what changes have
been wrought so that he may join in the movement to weed out the
bad, to cling to the good, and to reach up into the realm of modern
mathematics to see if, perchance, he cannot find that which is good
and usable and light-shedding for the elementary work.”
The true order of elementary mathematics, according to Dr. Smith, is
substantially as follows:--
1. Elementary operations of arithmetic.
2. Simple mensuration, correlation with drawing, the models in
hand:--
Inductive geometry--the primitive form of the science.
3. Arithmetic of business and of science, using the simple equation
with one unknown quantity wherever it throws light upon the
subject.
4. Simple theory of numbers, the roots, series, logarithms.
5. Elementary algebra, including quadratic and radical equations.
6. Demonstrative plane geometry begun before the algebra is
completed and correlated with it.
7. Plane trigonometry and its elementary applications.
8. Solid geometry. Trigonometry. Advanced algebra, with the
elements of differentiation and integration.
“The student should then take a rapid review of his elementary
mathematics, including a course in elementary analytic geometry and
the calculus. He would then be prepared to enter upon the study of
higher mathematics.”
[31] Compare Smith, David Eugene, “History of Modern Mathematics,” in
Merriman & Woodworth’s “Higher Mathematics,” Wiley, New York, 1896.
256. Demonstrations taking a roundabout way through remote auxiliary
concepts are a grave evil in instruction, be they ever so elegant.
Such modes of presentation are rather to be selected as start from
simple elementary notions. For with these conviction does not depend
on the unfortunate condition requiring a comprehensive view of a
long series of preliminary propositions. Thus Taylor’s Theorem can
be deduced from an interpolation formula, and this, in turn, from
the consideration of differences, for which nothing is needed beyond
addition, subtraction, and knowledge of the permutation of numbers.
The following account of imaginary and complex numbers by
Dr. David Eugene Smith is so lucid that it is given at length:--
“The illustrations of the negative number are so numerous, so
simple, and so generally known from the common text-books that it is
unnecessary to dwell upon them.[32] Debt and credit, the scale on
the thermometer, longitude, latitude, the upward pull of a balloon
compared with the force of gravity, and the graphic illustration of
these upon horizontal and vertical lines--all these are familiar.
“But the imaginary and complex numbers have been left enshrouded in
mystery in most text-books. The books say, _inter lineas_, ‘Here
is √−1; it means nothing; you can’t imagine it; the writer knows
nothing about it; let us have done with it, and go on.’ Such is the
way in which the negative was treated in the early days of printed
algebras, but now such treatment would be condemned as inexcusable.
But there is really no more reason to-day for treating the imaginary
so unintelligently than for presenting the negative as was the
custom four hundred years ago. The graphic treatment of the complex
number is not to-day so difficult for the student about to take
up quadratics as is the presentation of the negative to one just
beginning algebra.
“Briefly, the following outline will suffice to illustrate the
procedure for the complex number:--
5 4 3 2 1 | 1 2 3 4 5
|___|___|___|___|___|___|___|___|___|___|
|
− 0 +
“1. Negative numbers may be represented in a direction opposite
to that of positive numbers, starting from an arbitrary point
called zero. Hence, when we leave the domain of positive numbers,
_direction_ enters. But there are infinitely many directions in a
plane besides those of the positive and negative numbers, and hence
there may be other numbers than these.
“2. When we add positive and negative numbers we find some results
which seem strange to a beginner. For example, if we add +4 and −3 we
say the sum is 1, although the _length_ 1 is less than the length 4
or the length −3; yet this does not trouble us because we have
considered something besides length, namely, direction; it is true,
however, that the sum of 4 and −3 is less than the absolute value
of either. This is seen to be so reasonable, however, from numerous
illustrations (as the combined weight of a balloon pulling up 3 lbs.,
tied to a 4-lb. weight), that we come not to notice the strangeness
of it; graphically, we think of the sum as obtained by starting from
0, going 4 in a positive direction, then 3 in a negative direction,
the _sum_ being _the distance from 0 to the stopping-place_.
[Illustration: Graph of 1 multiplied by √−1 twice]
“3. If we multiply 1 by −1, or by √−1 · √−1, or by √−1 twice, we
swing it counter-clockwise through 180°, and obtain −1; hence, if we
multiply it by √−1 once, we should swing it through 90°. Hence we may
graphically represent √−1 as the unit on the perpendicular axis YY′,
and this gives illustration to
√−1, 2√−1, 3√−1, ··· −√−1, −2√−1, −3√−1,
or, more briefly, ±i, ±2i, ±3i, ··· where i stands for √−1. We
therefore see that i is a symbol of quality (graphically of
direction), just as is + or −, and that −3 · 5i, i√5, etc., are just
as real as −3 · 5, √5, etc. It is impossible to look out of a window
−3 · 5 times as it is to look out −3 · 5i times; strictly, one number
is as ‘imaginary’ as the other, although the term has come by custom
to apply to one and not to the other.
“4. The complex number 3 + 2i is now readily understood. Just as
3 + (−2) is graphically represented by starting from an arbitrary
zero, passing 3 units in a positive direction (say to the right),
then 2 units in the opposite direction, calling the sum the
distance from 0 to the stopping-point, so 3 + 2i may be represented
graphically. Starting from 0, pass in the positive direction (to
the right in the figure) 3 units, then in the i direction 2 units,
calling the sum the distance from 0 to the stopping-place.
[Illustration: Graphical representation of 3 + 2i as the hypotenuse
of a right-angled triangle with sides of 3 and 2i units]
“Of course the question will arise as to the hypotenuse being the
sum of the two sides of the right-angled triangle. But the case is
parallel to that mentioned in paragraph 2; it is not the sum of
the _absolute values_, any more than is 1 the sum of the absolute
values of 4 and −3; it is the sum when we define addition for numbers
involving direction as well as length.
“A simple illustration from the parallelogram of forces is often used
to advantage.
[Illustration: Parallelogram of two forces +3 and +2i with
resultant OP]
“Suppose a force pulling 3 lbs. to the right (+3 lbs.) and another
pulling 2 lbs. upwards (+2i lbs.); required the resultant of the two.
It is evident that this is OP, _i.e._, OP = 3 + 2i.
“This elementary introduction to the subject of complex numbers shows
that the ‘imaginary’ element is easily removed, and that students
about to begin quadratics are able to get at least an intimation of
the subject. This is not the place for any adequate treatment of
these numbers: such treatment is easily accessible. It is hoped that
enough has been presented to render it impossible for any reader
to be content with the absolutely meaningless and unjustifiable
treatment found in many text-books.”[33]
[32] See Beman & Smith’s “Elements of Algebra,” p. 17.
[33] For an elementary presentation of the subject, see Beman and
Smith’s “Elements of Algebra,” Boston, 1900. For a history of the
subject, see Beman and Smith’s translation of Fink’s “History of
Mathematics,” Chicago, 1900, or Professor Beman’s Vice-Presidential
Address before the American Association for the Advancement of Science,
1898, or the author’s “History of Modern Mathematics,” already
mentioned.
257. The pedagogical value of mathematical instruction, as a whole,
depends chiefly on the extent to which it enters into and acts on
the pupil’s whole field of thought and knowledge. From this truth
it follows, to begin with, that mere presentation does not suffice;
the aim must be rather to enlist the self-activity of the pupil.
Mathematical exercises are essential. Pupils must realize how much
they can do by means of mathematics. From time to time written work in
mathematics should be assigned; only the tasks set must be sufficiently
easy. More should not be demanded and insisted on than pupils can
comfortably accomplish. Some are attracted early by pure mathematics,
especially where geometry and arithmetic are properly combined. But a
surer road to good results is applied mathematics, provided only the
application is made to an object in which interest has already been
aroused in other ways.
But the pupils ought not to be detained too long over a narrow round of
mathematical problems; there must also be progress in the presentation
of the theory. Were the only requisite to stimulate self-activity,
the elementary principles might very easily suffice for countless
examples affording the pupil the pleasure of increasing facility, and
even the delight arising from inventions of his own, without giving
him any conception of the greatness of the science. Many problems may
be compared to witty conceits, which may be welcome enough in the
right place, but which should not encroach on the time for work. There
ought to be no lingering over things that with advancing study solve
themselves, merely for the sake of performing feats of ingenuity.
Incomparably more important than mere practice examples is familiarity
with the facts of nature, and such familiarity renders all the better
service to mathematics if combined with technical knowledge.
258. Even young children may very well busy themselves with picture
books illustrating zoölogy, and later with analyses of plants which
they have gathered. If early accustomed to this, they will, with some
guidance, readily go on by themselves. At a later time they are taught
to observe the external characteristics of minerals. The continuation
of the study of zoölogy is beset with some difficulties on account of
the element of sex.
Though industriously debated, there is no field of education more
undecided both as to matter and method than nature work in the
grades. Some scientists would teach large amounts of well-classified
knowledge; others are content when they have secured a hospitable
frame of mind toward nature. If a love for flowers and birds can be
cultivated in children, the latter class are satisfied that the best
result has been attained. Thus a discussion arises as to which is the
more valuable, _attitude_ or _knowledge_.
It is feared by some that any attempt to teach real science, even
of an elementary kind, will result in a paralysis of permanent
scientific interest. To this it is replied that a sentimental regard
for æsthetic aspects of nature insures little or no true scientific
interest.
Both sides are, in large measure, wrong; for, though apparently
antagonistic in their aims, they make merely a different application
of a common principle, which, if not wholly erroneous, is at least
inadequate. Both parties assume that the end to be attained in nature
study is something only remotely related to the pupil’s practical
life. One would present nature for its own sake as scientific
knowledge; the other would offer it for its own sake as a source of
æsthetic or other feeling. The scientist often assumes that to a
pupil a scientific fact or law is its own excuse for being. He thinks
there must be a natural, spontaneous response to such a fact or law
in the breast of every properly constituted child, so that, to imbue
the mind with the scientific spirit, it is only necessary to expose
it to scientific fact.
Perhaps, unfortunately for the normal child, this view is somewhat
encouraged by the biographies of scientific geniuses. On the other
hand, those who hold the poetic view of nature assume that there must
be a native response to natural beauties in every child; so that
the true method is to expose him to nature’s beauty, when rapture is
sure to follow. Unfortunately again for the pupil, this view is also
encouraged by the influence of the nature poets. The result is that
natural science is presented as an end in itself--in the one case as
scientific knowledge, in the other as the lovable in nature.
While it may be admitted that a few children will respond now to
the one stimulus, now to the other, the great mass are not thrilled
with rapture at nature’s beauty, nor are they fettered by scientific
interest in her laws. To become an object of growing interest to
children, nature must have a better basis than natural childish
delight in the novel, or reverence for scientific law. The first of
these is evanescent, the second feeble.
We may agree with the scientist as with the poet, that both science
and poetic appreciation are desirable ends, but they cannot be
imparted to the childish mind by didactic fiat.
If there is one service greater than another that Herbart has
rendered to education, it is in bringing clearly to our consciousness
the supreme importance of the principle of apperception, or mental
assimilation, as a working basis for educative processes. So long
as a fact or a principle or system of knowledge stands as an end
in itself, just so long is it a thing apart from the real mental
life of the child. Even a formally correct method of presentation,
should it even appeal at once to all ‘six’ classes of interest, will
fail to create more than a factitious mental enthusiasm. It is like
conversation that is ‘made’ interesting; it may suffice to lighten a
tedious hour, but it awakens no vital response. When, however, the
natural love of novelty or inborn response to the true is reinforced
by a sense of warm personal relationship, when the facts of forest,
or plain, or mine, or animal life flood the mind with unexpected and
significant revelations concerning either the present or the past in
close personal touch with the learner, then instruction rests upon
an apperceptive basis. Abstractions that before were pale, beauties
that were cold, now receive color and warmth because they get a new
subjective valuation that before was impossible.
A sedate sheep nibbling grass or resting in the shade, a skipping
lamb gambolling on the green, are suitable objects of nature study.
Their pelts, their hoofs, their horns, their wool, are worthy of
note as scientific facts. A diluted interest may even be added by
recitation of the nursery rhymes about “Little Bo-Peep” and “Mary had
a Little Lamb.” But these are devices for the feeble-minded.
If the teacher can reveal to the pupil the function of wool in making
garments for the race, and can lead him to repeat the processes
by which, from time immemorial, the wool has been spun into yarn
and woven into cloth; if, at the same time, the influence of this
industry upon the home life, both of men and women, can be shown, the
study of the sheep becomes worthy the attention even of a boy who
can play foot-ball or of a girl who can cook. The literature of the
sheep is no longer infantile or fatuous. We have a gamut reaching
from Penelope to Priscilla. In the words of Professor Dewey: “The
child who is interested in the way in which men lived, the tools
they had to do with, the transformation of life that arose from the
power and leisure thus gained, is eager to repeat like processes
in his own action; to make utensils, to reproduce processes, to
rehandle materials. Since he understands their problems and their
successes only by seeing what obstacles and what resources they had
from nature, the child is interested in field and forest, ocean and
mountain, plant and animal.... The interest in history gives a more
human coloring, a wider significance, to his own study of nature.”[34]
The conclusion arising from this argument is that nature study
as an end in itself, or a thing apart from the real or imagined
experiences of the pupil, is but a faint reflection of what it may
become under a more rational treatment. In order of time, nature
study in the earliest grades may indeed rest upon the mere delight
of the childish mind in the new, the strange, the beautiful, and
especially in the motion of live creatures, and may be reinforced
by childish literature. When boyhood and girlhood begin, however,
then the industrial motive, first in the home environment, then of
primitive times, becomes the chief reliance for an abiding interest.
In the reproduction of primitive processes, there is of necessity
a historical element. When nature has attained a firm apperceptive
basis through imitation of primitive industrial processes, and has
obtained a historical background, then it may properly be further
reinforced by literary reference. The poetic value of nature will now
appeal to the mind with a potency that springs from inner life and
experience; scientific law will now have some chance of appealing to
the mind with something of the same reverence that Kant besought for
the moral law. The true order of appeal in nature study is therefore
as follows: For infancy, natural curiosity and delight in the
movements of living creatures; for the age of boyhood and girlhood,
imitation, real or imaginary, of processes depending upon natural
objects and forces, together with historical and literary reference;
secondarily, nature work may also appeal to youthful interest in
natural law or beauty.
[34] Dewey, John, “The Aim of History in Elementary Education,”
_Elementary School Record_, November, 1900, University of Chicago
Press.
259. With the foregoing should be conjoined much attention to external
nature, to the changes corresponding to the seasons, and to means of
intercommunication.
Under this head belongs, on the one hand, observation of the heavenly
bodies,--where sun and moon rise, how the latter waxes and wanes, where
the north star is found, and what arcs are described by the brighter
stars and the most conspicuous constellations.
Here belongs, on the other hand, technological knowledge, acquired
partly through direct observation, partly through lessons in
descriptive physical science. Technology ought not to be considered
merely from the side of the so-called material interests. It furnishes
very important connecting links between the apprehension of the facts
of nature and human purposes. Every growing boy and youth should learn
to handle the ordinary tools of the carpenter as well as rule and
compasses. Mechanical skill would often prove far more useful than
gymnastic exercises. The former benefits the mind, the latter benefit
the body. With burgher schools should go manual training-schools,
which does not mean that the latter must necessarily be trade schools.
Finally, every human being ought to learn how to use his hands. The
hand has a place of honor beside language in elevating mankind above
the brute.
The foregoing store of information also enters into the study of
geography; how, will appear in the next chapter.
The soundness of the foregoing remarks is witnessed by the rapid
development of manual training-schools in the last decade, and the
almost universal desire, if not practice, of providing considerable
amounts of manual training for the pupils of the grammar grades.
The girls usually have some form of sewing and cooking, while the
boys have sloyd or other similar tool work in wood. The _rationale_
of requiring girls to do carpenter work instead of the forms of
manual exercise that especially pertain to their sex is not yet
satisfactorily established.
260. On the observation of the heavenly bodies is based popular
astronomy, which provides a test as to whether the mathematical
imagination has been properly cultivated.
261. Elementary statics and mechanics will serve as an early
introduction to physics, which combines with the easiest portions
of chemistry. Long before physics is formally presented, it must be
foreshadowed by many things stimulating the attention. Notice is
directed to clocks, mills, the most familiar phenomena of atmospheric
pressure, to electrical and magnetic toys, etc. In burgher schools,
at least, so much must be said about buildings and machines as is
necessary to incite to further study in the future. The same holds for
the fundamental facts of physiology.
262. As often as a new topic for study is introduced, it is important
to give prominence to some of the salient facts, and these must be
accurately memorized. Moreover, pupils need to have practice in exact
description. Where practicable, these descriptions are corrected by
actually looking at the objects themselves.
Hasty and superficial observation of objects presented for inspection
always calls for severe criticism; else collections and experiments
become valueless. Nor should objects be shown too lavishly; pupils must
often be told beforehand what they will have to look for. Frequently
it may serve the purpose to employ successively good descriptions,
pictures, and direct observation.
CHAPTER IV
=Geography=
263. As to geography, at least two courses may be distinguished. One of
these is analytic and begins with the pupil’s immediate neighborhood,
the topography of the place, while the other starts with the globe.
Here only the former will be discussed, as the latter can be had
directly from good text-books.
=Note.=--The usual method of taking the globe as the point of
departure would be less open to criticism, if, in order to render
the conception of the earth’s sphericity more intelligible,
attention were directed to the shape of the moon, the observation
being carried on occasionally with the aid of a telescope. But
even if this is done, it still remains a blunder to substitute the
faint and vague idea of a huge ball for direct perception. Equally
injudicious is the plan of beginning with Portugal and Spain.
That spot where pupils and teacher are at the moment is the point
from which the pupils must take their bearings, and in thought
extend their horizon. It will never do to pass over the natural
starting-points provided by sense-perception.
Had the note to this section been properly heeded, we should not have
had to wait for fifty years after Herbart’s death before witnessing
the present rational methods of applying geographical science to
elementary education. It is the proud boast of the modern elementary
geography that it begins with a study of the pupil’s actual
environment. The term _home geography_ has now become a familiar one.
It signifies that the pupil is taught to observe the geographical
elements as they exist in his own neighborhood. He studies hills,
watercourses, soil, woods, lakes, together with the industrial
phenomena that come within the reach of his investigation. Upon
this primary sense-basis he rears the structure of his geographical
knowledge.
264. Geography is an associating science, and use must be made of
the opportunities it offers for binding together a variety of facts,
none of which should be allowed to remain isolated in the mind of the
learner. It is not the mathematical portion, supplemented and made
interesting by popular astronomy, that serves as the first connecting
link between mathematics and history (second course); even the
rudiments of geography may, on the basis of observation exercises,
furnish practice in the determination of triangles which occur on the
first maps used, although this step is not always necessary when once
some skill has been acquired in singling out features worthy of note.
(The determination of position by latitude and longitude is, for the
first course, as irrational as the action of a traveller in Germany
or France would be if he set about to put together the picture of the
places where he expects to remain, with the aid of their relation to
the equator and the first meridian.)
Physical geography presupposes some knowledge of nature, and furnishes
the occasion for enriching that knowledge. Political geography
designates the manner in which man inhabits and uses the earth’s
surface. It is the pedagogical aim of instruction in geography to
associate all this.
265. The teacher must cultivate the art of narration; his accounts must
resemble those of a traveller. But the narrative should conflict with
the determination of the relative position of places (by grouping them
about one principal place, and in the case of more than one by the use
of triangles) as little as, in teaching history, the story of events
should conflict with the scheme of chronology. The two go together. The
narrative is to present a clear picture, and to this end requires the
support of a few fixed points in space. On the other hand, these points
should not remain isolated; they are to be connected by the lines of
the picture.
266. It is not a matter of indifference how many unfamiliar names are
mentioned in one minute or hour. Nor is it immaterial whether they
are uttered before or after perception of the picture which the map
presents. The first requisite is that every map placed before the
pupils be conceived of as a country; three, at most four, names of
rivers, and the names of a few mountains are sufficient; completeness
is out of place here. The few names given provide ample opportunity
for fixing the position of notable points, both with reference to one
another and to the boundary lines of the country.
Due prominence having been given to these geographical features, they
should then be connected, say with the aid of a blackboard, on which
they are roughly sketched one by one, and properly joined together
afterward. In the case of the sources and outlets of rivers, this may
be done by a line to indicate the course. If now the pupils have made
good previous use of their eyes, especially if they have noticed the
fall of brooks and rivers, and have observed the slope of the ground
in a particular region,--if they have not, the deficiency must be made
good first of all,--it will not be too early to pass on to a general
description of the appearance which the country under consideration
would present to a traveller. And now the time has come for a somewhat
fuller mention of the names of rivers and mountains, but these names
must at once be gone over several times by the pupils. Doing so will
reveal whether the list of new names has been made too long; it is
often largely due to carelessness in this respect, if the study of
geography proves barren or onerous. Next in order follow detailed
descriptions of particular wonders of nature, where there are such.
Attention is then given to some of the principal cities, mention
being made of the number of inhabitants. Here the determination of
relative location comes in again, and for this the self-activity of the
pupils is indispensable. Finally, human industry and art, so far as
they relate to the products of the country, together with the little
of political organization that pupils can grasp. The names of the
provinces should ordinarily be omitted from the first course.
This section is suggestive of the old geography of the last half
century,--location, names, maps, the barren details of the science.
Geography is something richer than all this. The old geography was
political in the foregoing sense. The first break was in making it
physiographical, the last in making it social. Names as such are
nothing, and physical facts little more, but both become of value
as soon as they are brought into relation to man,--his life, his
work, his recreation. Geography is not essentially the location of
places, nor is it physiography, but it is a study of the essential
facts concerning the surface of the earth as they are related to man
himself; it is, in short, _human_ in the fullest sense. It gives a
concrete explanation of civilization; it explains the production,
the exchange, and, to some extent, the consumption of goods. It
contrasts countries, not so much by square miles, as by the number
of miles of railroads they possess. (The most momentous fact of
modern civilization is the railroad. Twelve billions of dollars are
invested in it in the United States alone. In view of these facts,
what shall be said of those recent geographies that keep the children
poring over primitive maps for years--maps without a suggestion of a
railroad in them? This is an illustration of how prone education is
to lag behind the progress of society.)
267. The reviews, which should be frequent, must steadily work toward
a growing firmness of association between names and places. Each name
is to be referred to the place it designates; hence the sequence of
names must often be reversed, and the map looked over in all directions
and from all points of view. How far to go is determined in accordance
with individual capacity. From some, only what is absolutely essential
can be demanded; from others, much more, in order that they may exert
themselves properly.
268. In the midst of other studies on which greater stress is laid,
geography is as a rule slighted by pupils and sometimes even by
teachers. This attitude merits severe criticism. Instruction in
geography may be reduced to a minimum, the first course even requires
this, but it should not be disparaged. With many pupils, geography
is the first study which gives them the consciousness that they can
learn as they are expected to learn. With all pupils, geography must
connect the remaining studies and must keep them connected. Without
it everything remains unstable. Historical events lack places and
distances; products of nature are without the regions where they are
found; popular astronomy, which is called upon so often to prevent
and dispel erroneous notions, is deprived of its very basis, and the
geometrical imagination of one of its most important incentives. If the
facts of knowledge are allowed to fall asunder in this way, instruction
endangers the whole of education.
CHAPTER V
=The Mother-tongue=
269. There would be less controversy about language teaching if
existing differences in conditions were given proper attention.
The most general distinction to make is that between understanding and
speaking. The distance between the two is a given factor at the time
when regular instruction begins. It is very great in some cases, and,
again, slight in others, according to individual aptitude and early
surroundings.
270. First of all, one’s language was acquired by hearing it spoken, by
receiving it from others, by imitation; it was refined or vulgar; it
was perceived accurately or indistinctly; it was imitated by organs,
good, bad, or indifferent. Little by little the imperfections of the
earliest stage are outgrown, where cultured persons set a daily example
and insist on correctness of speech. Sometimes, however, it takes years
to bring about such a result.
271. Another factor, and one deeply rooted in individual temperament,
is the stronger or weaker impulse toward expression through language.
This fact elevates the language of each one above mere imitation; its
improvement must start from the thoughts which it seeks to express.
Striking progress of this kind often occurs during adolescence.
The differences noted in this and the two preceding sections are
psychological, hence common to German and American children. The
problem of teaching American children their mother-tongue, assumed to
be English, is both harder and easier than to teach German to German
children. It is easier in that English is mostly uninflected, hence
unencumbered by nice distinctions in grammatical form. This same
fact, on the other hand, causes didactic difficulties, since most
teachers are at a loss as to what definite body of knowledge they
should or can impart that will train the child into a mastery of good
English speech. The last twenty years have seen a large number of
experiments on the part of authors in the effort to present a body of
information and exercises calculated to secure a good training in the
mother-tongue. These efforts have met with but partial success, owing
to the inherent difficulties of the subject. Many who can teach a
foreign language, where there is a movable fulcrum of difficulties to
be overcome, such as those found in inflection, or in the meaning of
foreign words, fail when confronted by a language that is practically
uninflected, and in which the words are easily understood.
The old recourse was technical grammar. But this is an analytical
study, calculated to lead to apprehension of subtle meanings, rather
than to an instinct for correct form. Furthermore, the grammar cannot
be successfully studied until after the habits of speech are fairly
fixed. For these reasons, it bears much the same relation to living
speech that formal logic does to real thinking. Grammar makes the
mind keen to detect formal errors of speech, just as logic trains
one to detect fallacies in reasoning.
The first important instrument for securing good English in the
early primary grades is narration by the teacher and repetition
by the children. This means, potent enough to form the speech of
any child whether from the slums or from the homes of those who
know no English, is rarely utilized up to the full measure of its
efficiency. Teachers are filled with the prepossession that they
must enable their pupils to write good English, forgetting that if
the mind is habituated to _think_ in good English first, the problem
of writing it is well-nigh solved. The requisites for successful
oral training in the mother-tongue are first, the selection of a
body of interesting and appropriate literature, and second, skill in
narration by the teacher. Given these two things, and we have the
first in great abundance, and every child will be able in a year
to give extended and correct speech within the range of his sphere
of thought to an almost unlimited extent. His tenacious memory for
forms frequently heard, together with his delight in repeating almost
word for word stories told in his presence, will produce astonishing
facility in correct speech. As much of this may be written as seems
best, but it is probable that there would not be great loss if a
child were not called upon to write a ‘composition’ before he is ten
or twelve years old. Could we be sure he would go through the high
school, formal writing might be postponed until he enters it. Not
much is ever gained by attempts to produce fruit before its natural
period for appearing.
Upon the basis of this training in correct oral speech, the children
may begin, when nine or ten years of age, to have systematic language
lessons, which should be calculated to produce two results: first, a
facile use of the pen in recording thought, special caution being
given not to weary the mind and body too much by unduly extending
the length of the written exercises; second, an inductive approach,
through brief written exercises, toward the classifications and
distinctions of technical grammar. To be of use, this latter
requirement should be clearly understood. The method of approach
is purely synthetic. It consists in devices to enable the pupil
repeatedly to use a given construction, say a relative pronoun, until
the name and construction seem natural from use alone.[35]
At the age of thirteen or fourteen the analytical study of grammar
should be begun. The essential thing here is that the pupil should
connect _words_ with the _ideas_ they express, and _sentences_ with
the _thoughts_ that give rise to them.[36] Seeing mental distinctions
clearly, he has small difficulty in their written or oral expression.
[35] For extended illustration of this point, see the “Annotator’s
Language Lessons,” the Werner School Book Co., New York, Boston, and
Chicago.
[36] This position is best exemplified by Mr. George P. Brown in his
“Essentials of English Grammar,” the Werner School Book Co., New York,
Boston, and Chicago.
272. Now such facts might seem to point to the conclusion that no
special periods of instruction are needed for the mother-tongue, or
at least not for language lessons alone. On the one hand, it might be
urged that cultured teachers will improve the language of their pupils
by their mere example, and by the occasional corrections which will of
course be necessary; while, on the other hand, the gradual progress of
mental development will shape the means of expression from within, to
the natural limits of individual capacity. But before accepting the
view here given, we need to remind ourselves, in the first place, that
for a long time the educated teacher is only imperfectly understood by
the uneducated listener, and that instruction is very much impeded if
each unusual turn of expression necessitates an inquiry as to whether
its meaning is clear.
273. But this is not all. Language is also to be read and written.
Hence, it becomes a standing object for consideration, and, to one
whose knowledge of it is deficient, a source of embarrassment.
Accordingly, the first thing for the teacher to do is to show
analytically, on the basis of what has been read or written, how
the meaning would be lost or altered if either single words were
interchanged, or the inflectional endings (especially in German) were
incorrectly chosen. That the synthesis of sentences should follow next,
advancing step by step toward greater complexity, especially by means
of various conjunctions, may be assumed to be well understood.
274. Now if all experienced equal difficulty in their reading and
writing, the language lessons designed as a remedy would commend
themselves in all cases, and might fittingly be carried to the same
extent everywhere.
But here the widest divergence appears. Accordingly, where many are
being taught together, the teacher will seek to connect language work
with other subjects. Thus, in the course of the same recitation,
analytic instruction may be directed to the language side for some
pupils, while for others it may be given a far wider scope. Moreover,
the accompanying written exercises may have a corresponding diversity.
275. The work of a recitation period will be further diversified by the
introduction of exercises in reading aloud, and in oral reproduction.
But never will it be possible to raise all pupils to the same plane of
proficiency. Here, above all, the determining power of individuality
must be acknowledged.
276. For older boys and young men, the work in the mother-tongue will
consist partly in the study of excellent examples of the various kinds
of poetry and oratory, partly in the writing of essays. Such study
will prove the more profitable, the more perfect the models, the more
suitably they are adapted to the stage of culture already attained
by the student, and the more scrupulously the teacher refrains from
forcing upon him a literary taste not congenial to his nature. The
least promising of all written exercises are those in letter-writing.
Confidential letters every one can write, each in his own way. Best of
all are written exercises with a definite and rich store of thought
to draw from and admitting of various forms of treatment. Several may
then emulate each other in handling the same theme, and the process of
correcting will awaken greater interest in consequence.
CHAPTER VI
=Greek and Latin=
277. As is well known, the exposition of grammatical distinctions
and of the many turns of expression whereby language may become an
adequate symbolization of thought, gains very materially in clearness
by a comparison of the mother-tongue with Latin and Greek. Even with
boys not more than eight years old the attempt may be made to utilize
this advantage in the teaching of English, whether it has been finally
decided, or not, that they are to take the regular classical course.
Some boys learn, without much trouble, enough of Latin inflections to
enable them soon to translate short sentences from the mother-tongue
into Latin, and _vice versa_.
The present plan in Germany is to have boys in the gymnasia begin the
study of Latin at the age of ten. The study is continued for a period
of nine years. Greek is begun three years later and continued for
six years. In the United States the prevailing plan is to postpone
the study of Latin until the pupil enters the high school at the age
of fourteen or fifteen. Good private schools and many city grammar
schools permit children to begin when some two years younger than
this. The Report on College Entrance Requirements made before the
National Educational Association in 1899 suggested the propriety
of extending the influence of the high school over the two highest
grades of the grammar school, making in effect a six-year high school
course. For students who expect to enter college or technical schools
this plan offers great advantages, since it permits the desirable
preparation to be distributed over six years instead of being
concentrated into four.
278. This experiment will not, however, be long continued; since, with
the large majority of pupils, the difficulties accumulate so rapidly as
to lead unavoidably to the admission that the burden cannot be assumed
merely for the sake of incidental advantages. Moreover, the customary
view, handed down from the time of the Reformation, of the relation of
the classical languages to the sciences, and to the needs of the age,
is undergoing a change more and more apparent from decade to decade.
The labor implied in the study of the ancient languages now pays only
where talent combines with the earnest purpose to achieve the most
complete scholarship.
This remark is prophetic of the enormous increase of instruction
in the sciences since Herbart’s day, yet Latin has also enjoyed a
phenomenal increase in popularity in American schools. According to
the Report of the National Commissioner of Education the increase of
enrollment in high schools for the years between 1890 and 1898 was
84 per cent, while the increase in the number of students pursuing
Latin was 174 per cent.[37] This surprising growth in the number
pursuing an ancient language can hardly be accounted for by increased
stringency in college entrance requirements in Latin, but must rather
be ascribed to a growing conviction among the people that the study
is indispensable in secondary education. That this must be the case
is seen by the attendant circumstances. In the first place, Latin has
become an elective in nearly all high schools; in the next place,
many rich equivalents are offered, both in science and in modern
languages; and finally our system of universal elementary education
has sent large classes of persons into the secondary schools that
have never previously been there. Yet the number of students electing
this study grows by leaps and bounds.
=Note.=--(1) The assertion is often heard that the ancient
languages supply a permanent standard by which to judge of the
progress and the decay of modern languages; also that the ancient
classics must be regarded as furnishing the models for purity and
beauty in style. These and similar contentions are undeniably
correct, and carry the greatest weight, but they are unpedagogical.
They embody the absolute requirement, but not that which younger
pupils need for _their_ culture; and the large majority of those
who are fitting themselves for official positions cannot afford to
make themselves guardians of language and style. They must take
language as it is, and acquire the manner of expression which is
adapted to the world of affairs. Those higher cares belong to
authors, but no one is educated for authorship.
(2) It is a familiar notion that the difficulty would diminish if
the ancient languages were begun later, that then the ability to
learn would prove greater. On the contrary, the older the pupil the
stronger the tendency of his thought-mass toward exclusion. Memory
work must be introduced early, especially where its usefulness
depends wholly on the acquisition of facility. It is essential to
begin early in order to make it possible to proceed slowly and to
avoid unpedagogical pressure. Four hours a week of Latin do not
hurt a healthy, bright boy, provided his other tasks are arranged
with pedagogical correctness. To put modern languages first would
be to put the cart before the horse. Useful enough, however, are
single French and English expressions relating to everyday life.
They will be of service in acquiring the pronunciation; but a few
phrases do not constitute the teaching of a language.
[37] Bennett and Bristol, “The Teaching of Latin and Greek,” Longmans,
Green & Co., New York, 1900.
279. The manner of teaching the ancient languages, where they are
regarded as a matter of necessity or conventionality, no account being
taken of pedagogical considerations, need not be discussed here. It
must rather be admitted at once that no pedagogical means whatever
exist, whereby those who live with their interests strictly confined
to the present could be brought to acquire, with genuine sympathy, the
content of the works of antiquity.
American teachers in estimating the value of Latin for the high
school student lay more stress upon training in the mastery of the
mother-tongue than upon the literary contents of the classical
writings. Professor Bennett in his treatment of “The Teaching of
Latin in the Secondary School,”[38] places in strong light the
splendid linguistic training a youth undergoes when taught by a good
teacher of this subject. In Germany, since Herbart’s time, Professor
Russell tells us that the teaching of Latin has fluctuated between
two aims--“between that view which makes the classics a purely formal
discipline, and that other view which bases the worth of such a
study on the acquisition of humanistic culture, in contact with ‘the
best thoughts of the best men of antiquity.’ In the one case it is
considered of equal value as a means of preparation for all trades
and professions dependent on intellectual acumen; in the other case
it is of worth only for those who can practically apply the technical
knowledge thereby acquired, or may have sufficient leisure to enjoy
its æsthetic qualities. It is a question of making the ancient
literature a means to an end or an end in itself.”[39]
The dogma of formal discipline as a leading aim in education has
nowhere been more discredited than among Herbartian writers. A
judicious estimate of its truth and error is made by Professor
Hinsdale.[40] His main conclusions are as follows:--
1. The degree to which power generated by education is general
depends upon the extent to which it energizes the mind, and
particularly the extent to which it overflows into congruent channels.
2. Such power is far more special than general; it is only in a
limited sense that we can be said to have a store of mobilized mental
power.
3. No one kind of mental exercise--no few kinds--can develop the
whole mind.