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of Arion's rescue, that he kept him hid in order to surprise the
sailors by producing him before them; but Ovid concludes his
account with the marvelous journey. It is plainly Ovid's pur-
pose to demonstrate the power of song and music, and thus he
attributes to Arion those wonderful results, which are in other
classics related of Orpheus and Amphion (lines 84-90).

The ancients and this leads over to the discussion of the
moral elements of the tal ascribed to poetry and music a
power over nature akin to that which they exert over man.
With the Romans the one word "carmen" signified song, incan-
tation, and hymn of consecration. Ancient legends relate that
singers and musicians stopped the warring of brutes; and at the
bottom of all such tales is the belief that this warfare was not
the primitive state and that it would again have to give way
to universal peace. Vergil tells us, in his fourth eclogue, that
when the Golden Age returns to the earth, the lion will no longer
be feared of the herds, and that the serpent will die; and there
is an unmistakable similarity between his words and the prophe-
cy of Isaias (ch. XI.) concerning the kingdom of the Messias:
"The wolf shall dwell with the lamb; and the leopard shall lie
down with the kid; the calf and the lion and the sheep shall
abide together, and a little child shall lead them. "

After this a comparison of modern versions (by A. W. v.
Schlegel and Tieck) with the ancient model will be in order,
and such a comparison should prove a suitable subject for com-
position work. The teacher may also examine into the deeper
significance of the tale: Arion, the inventor of the dithyramb
(the choric hymn, sung in honor of Dionysos and usually by
revellers to flute accompaniment), was preserved from prema-
turely descending to Hades, just as Orpheus, the priest of the
Chthonian gods, was allowed to return from Hades to earth.



364 DIDACTIC TECHNIQUE.

The dolphin is both in pagan and Christian symbolism the
kind guide of the dead; on ancient tombs it is represented as
carrying Eros on its back; and on articles of ornament a butter-
fly, representing the soul returning home, is frequently shown
hovering above a dolphin.

There is some similarity between the tale of Arion and the
Homeric hymn, "Dionysos or the Pirates." The young Dio-
nysos was kidnapped by pirates, and the pilot of their ship is
the only "one who recognizes the god, the rest of the crew being
blind with greed and avarice. The god lets grapevines and ivy
grow on the ship and frightens the pirates by producing a lion
and a bear, whereupon they throw themselves into the sea and
are changed into dolphins, the pilot alone being saved and
blessed by Dionysos. This version shows the point of contact
with the mysteries: it is only the initiated, /'. e. } those who have
through the mysteries become acquainted with the soul's guide,
the Xvcrtos 6eo<s, who journey safely on the ship of life to the
haven, while the uninitiated succumb to the forces of nature,
the lion symbolizing the heat, and the northern constellation of
the Great Bear or Dipper symbolizing the cold.

6. The antiquarian explanation must deal, first, with the
poet's rich dress (which was twice dyed in purple), with his
lute, and the dithyramb, which he sings to the accompaniment
of the lute. The following matters pertain to mythology: the
owl is sacred to Minerva; the swan, to Apollo; and the dolphin
is sacred to Poseidon and Apollo. The dolphin should be treated
in its aspect to natural history also. The dolphin that Ovid
speaks of seems to be the Delphinus Delphis, the common
dolphin usually called porpoise by sailors, which usually be-
comes about seven feet long, and has on the middle of its back
a fin a foot and a half in height. Dolphins feed on fish and
swim in large schools, and when at play they often leap entirely
out of the water. When not disturbed, they are fond of fol-
lowing and playing about vessels; and perhaps they do enjoy
music, as the ancients claim. But there is little probability to
the riding on a dolphin's back, though there are several legend-
ary accounts of this, but. all these date from ancient times.
The hero of one of these accounts is Taras, the founder of Taren-
tum, the port where Arion embarked; and this circumstance
may indicate some connection between the two tales. The
struggle between the crows and owl (line 89) should also be
touched upon; and it may be illustrated by the custom that
obtains even to-day among hunters of building huts in which



EXAMPLES OF EXPLANATORY INSTRUCTION. 365

an owl is kept, for the purpose of alluring the crows to within
range of the rifle.

The poetico-rhetorical explanation should note the double
apostrophe in the poet's addresses to Arion and the pilot (lines
97-98 and 101-102), the parallelism in line 83: "quod mare non
novit, qua nescit Ariona tellus?" This parallelism may be il-
lustrated by Scriptural quotations, for instance, "Whatsoever
the Lord pleased He hath done, in heaven, in earth, in the sea,
and in all the deeps" (Ps. 134, 6). The teacher should also
draw attention to the repetition: " scepe sequens scepe avidum
scepe canes" (lines 85-87) and to the like endings (6/txotoreXeirrov)
in line 105: " dant veniam videntque moram, capit ille coronam."
Note should be taken of the poetical use of the adjective for
the genitive: "fraterni modi" (1. 92), " nomen Arionium" (1. 94),
" ' lyrici soni" and " Ausonis ora" (1. 94); of the synecdoche in
"puppis" used for ship (1. 95), as well as in " penna" used for
arrow (1. no); and of the epitheta ornantia: " loquax comix"
(1. 89), "puppis dubia" (1. 101), " ccerula puppis" (1. 112), and
" tergum recurvum" (1. 113).

Of individual words, the adjective "voca/is," used in line 91
in the sense of poet, is noteworthy, because in grammar the
term has various meanings. In order to show the connection
between the different usages, one may examine such terms as
" aves cantu vocales" and " verb a vocalia." It may be added
that "vocales" in low Latin means musicians. The Greek word-
formation in "Ausonis" should not be overlooked. The signifi-
cance of the term swansong is clear in the light of lines 109-110.
The synonyms "modi" (1.92) and " numeri" (1. 109) should be
compared with each other. The poetical usage of "referre"\r\ the
sense of recite is akin to the prose meaning of " relata refero."

Points of etymology are recalled by "puppis," which is one
of the words allowing im in the accusative, and by "delphina"
which has the form of the Greek accusative. Points of syntax
will be suggested by the poetical construction of "forsitan"
with the indicative (1. 97), where in prose the subjunctive would
be required. The accusative of limitation is used after the
Greek manner (accusations Grcecus) in " pectora trajectus" (1. no).
The pupils should note the apposition " cant at pretium vehendi"
(1. 115). From the viewpoint of style, the following phrases
are interesting: "Quid tibi cum gladio?" (1. 101), "mortem non
deprecor" (1. 103), " constricto ense consistere" (1. 99), "navem
regere" (1. 101), "in medias undas desilire" (1. in), 'fide majus"

(1. ii3)-



366 DIDACTIC TECHNIQUE.

CHAPTER LV.
Developmental Instruction.

i. By developmental instruction we mean the method em-
ployed by the teacher when developing before and with his
pupils a content of teaching. We, therefore, give an objective
meaning to the term, while others attach to it the subjective
signification of the development of the mental faculties. In this
second sense both presentative and explanatory instruction are
developmental. But the development of the mental faculties
will be furthered in a special way by the instruction that de-
velops an object, and hence our term developmental instruction,
though implying primarily the objective development, connotes
the subjective element also.

Developmental instruction meets the two requirements of
imparting knowledge and of exerting thereby an educational
influence, and it is particularly the stimulating of the under-
standing and the exercise it affords in thinking that distinguish
this form of instruction. But it must meet a third requirement,
that of correlating all the results with one harmonious whole;
and this is the more urgent, as the abstract materials, which
are the specific matter for the application of developmental
instruction, might create the impression of their being entirely
independent and complete in themselves witness the isolation
of mathematics whereas it is just these materials that must
be connected with the concrete and correlated with the mental
horizon. The course of the development itself should, indeed,
be spontaneous and without any artificial deflections. Still a
skilful preparation, if it is heuristic and if it visualizes and re-
views what went before, may prevent the isolation of the sub-
ject-matter; and the varied application at the end should aim
at the same object.

To find the points of contact and the methods of application,
is the function of the inventio. But as the subject-matter is
homogeneous, the inventio is less difficult in developmental in-
struction than in presentative instruction. Greater care must
be given to the dispositio, for the purpose of insuring order and
perspicuity. The pupil must be able to follow the thread of
the development, and to pursue it to the centre of the argu-
mentation, and to establish the proper relationship between the
starting-point and the end of the development, between the



DEVELOPMENTAL INSTRUCTION. 367

question and its answer, and the problem and its solution.
Consequently, we must eliminate all secondary and subsidiary
matters and choose the shortest path. In respect to the elocutio^
we must distinguish the development proper from the final
statement of it: the former demands at times eloquence and
variety of expression; but the latter had best imitate the brevity
of the formula and system.' The actio^ i. e., the pupil's co-
operation, is less free than in presentative instruction. In de-
velopmental instruction the best co-operation of the pupils con-
sists in following, without a break, the teacher's course of de-
velopment; and of this co-operation the teacher can assure him-
self by interspersing such brief questions as can be answered in
a few words.

In the development the given is either traced back to the
general or is derived thence. In the first case, the development
is analytical; and in the second, synthetical (ch. XLI, 2). But
in instruction, analysis and synthesis are not confined to the
sphere of development, for they occur whenever anything ab-
stract is illustrated by something concrete, or when anything
concrete is treated speculatively (ch. XLIX, i). But there is
question of a development only when these operations are ap-
plied to a whole, which involves the extension of the mental
operations also to a larger field. The development can be ap-
plied to empirical as well as to rational materials. In the first
case, its object is the connected speculative treatment; and in
the second, the purpose is .the acquiring of new knowledge from
what is already in the mind.

2. With regard to the development of empirical materials,
one must see to it that these be sufficiently prepared for the
application of the developmental method. If the analytical
process is to be applied, the concrete must offer a solid enough
basis for supporting the abstract; the facts must be plain enough,
before one can proceed from them to the causes. This holds,
in the first place, for the instruction in the natural sciences.
The teacher should not attempt to develop a genus before the
pupils have grown familiar with a series of species, as the basis
for the process of abstraction would otherwise be too narrow.
In physics observation should come first, and its results should
be accepted without attempting an explanation, and the seeking
for the causes should come last. We had an analogous develop-
ment, in the field of astronomy, when dealing, in ch. XLII, 7,
with climatic differences. The wording of a definition also neces-
sitates an analytical process, and in finding a definition the



368 DIDACTIC TECHNIQUE.

teacher may generally employ the heuristic form of teaching.
All such analyses must lead the pupils to appreciate the value
of the general concept and of the explanatory cause; but they
miss their purpose if the general and the cause be conceived as
an increase merely of the subject-matter of instruction, /. ^., as
an increase of the burden of the school, whereas they should be
regarded as levers, /. e., as means for increasing one's strength.

It is a defect of empirico-analytical developments that they
can rarely furnish all the presuppositions needed for generalizing
and rinding the causes, but must content themselves with ex-
amples. The more mature pupils should be reminded of this
circumstance and should be dissuaded from attempting though
only the most talented among them will be tempted to do so
the analytical development independently of the teacher.

3. Before taking up the synthetical development of an em-
pirical matter, it is necessary that the single parts of the process
be familiar, and that the results of the synthesis be recognized
as the outcome of previous analyses and syntheses. This form
of development is applied most in language instruction. The
connected treatment of grammar, poetics, and rhetoric should
be that of a synthetical development, which is in place after
the pupils have, by the analytical method, become familiar with
the single parts of the subject-matter. The finding of the parts
of speech and of the parts of the sentence, all of which can be
developed from the basic relationship of subject and predicate
(ch. XLIII, 2), is an example of synthetical development. The
elements of the metrical system of the ancients afford another
good illustration of synthetical development: the feet, verses,
and stanzas developed from the two kinds of time duration,
diplasic and isomeric, 1 which were modified and added together,
as is clearly and convincingly shown in J. Methner's Grundzuge
der Metrik und Rhythmik, 1881. The analytical method is the
most natural for teaching the grammar of the mother-tongue
and the art of language. 2 The theory of the art of language
can also be taught analytically, viz., by searching for definitions.
The classification or division, the reverse of the definition, is a
special form of synthesis that can be used with empirical ma-
terials. The systematic development of a definition or division,
with the pupils co-operating, is one of the most pleasant tasks
of the teacher.



dnrXdffiov and 7^"s frof, cf. John J. White, The Verse of Greek
Comedy, London, 1912.
2 Cf. supra, ch. XLVI, 6.



EXAMPLES OF DEVELOPMENTAL INSTRUCTION. 369

Familiarity with the materials is likewise a prerequisite for
the development of a rational content. If the material must
first be obtained with great labor, it is vain to expect any elas-
ticity in the mental operations. The abstract matter renders
it particularly difficult to follow the course of development, and
hence key-words or other distinctive marks should be used for
showing the various stages in this course. The long demon-
strations of mathematics, if unavoidable, should be divided into
several; and the presuppositions of problems should be treated
separately, and should be united only after the pupils have
been familiarized with them. The process of solving problems
and of proving theorems is analytical; but the synthetical method
is used in rinding problems and in drawing conclusions from a
theorem proved. It is an advantage of mathematics that it
alternates the two methods. In some cases it admits of the
application of analysis and synthesis to one arid the same object,
and such cases are well adapted for familiarizing the pupils with
the methods themselves.



CHAPTER LVI.
Examples of Developmental Instruction.

i.. To illustrate the analytical and synthetical development
of an empirical matter and to demonstrate, at the same time,
how a system 1 is to be established and applied, we shall select
the tense-formation in Greek, which is one of the most compli-
cated problems of school grammar. The Greek conjugation has
two formations, thematic and athematic, one with, and the
other without, the thematic vowel. Accordingly, the old gram-
marians distinguished two principal conjugations, the one of the
verbs ending in <o and the other of the verbs ending in /LU, and
this division has, for practical reasons, been retained ever since.
Yet, in point of fact, the two methods of formation and the
two principal conjugations do not coincide at all. The /u
conjugation forms athematically only the present, the imperfect,
and the strong aorist; but all the other tenses are formed the-
matically. On the other hand, the (a conjugation forms athe-
matically the perfect and the pluperfect of the passive and the
passive aorists, to which can be added some isolated analogous
formations of the aorist and the perfect. Modern grammarians
undertook to remedy the defect by dividing the conjugations

1 Supra, ch. L, 3.
24



37O DIDACTIC TECHNIQUE.

according to the tense-stems. But this would necessitate that
LcrrrjiML and the analogous forms be treated along with the pres-
ent stem, and ecmrjv, along with the strong aorist stem, which
arrangement would disproportionately increase the matter of
the respective parts. Consequently, the traditional division still
commends itself to most teachers. Lest the pupils, however,
forfeit what constitutes no mean part of the educational value
of Greek, 1 viz., an insight into the laws that govern the forma-
tion of the Greek verb, the teacher and pupils should, after
having finished the conjugations, reunite what they have torn
asunder and set aright what they have dislocated; and to show
how this can be done, is the purpose of the following.

The starting-point should be the comparison of the two
principal conjugations, as this will clearly show the difference
between the thematic and athematic formations. In the two
formations we perceive the further difference that the ending
is joined either directly to the stem or to the thematic vowel
added to the stem. Hence we have four different formations:
i. athematic formation on the pure stem, (jyrj-fii; 2. athematic
formation on the enlarged stem, Beue-w-fM; 3. thematic forma-
tion on the pure stem, Xv-cu; 4. thematic formation on the en-
larged stem, TVTT-T-O)- Now we must inquire whether the other
tenses have a similar formation. The imperfect, being derived
from the present stem, need not be considered. Of the aorists,
the pupils will readily place eoTTj-v beside tfrtj-pL, tXiir-ov beside
XV-GJ, eXv-cr-a beside TVTT-T-O); and they will also perceive, without
any difficulty, the analogy between ekv-drj-v and Sei/e-vv-/u-
Of the perfects to which the pluperfect also belongs such
formations of the active as ia - ^ev and others and the whole
perfect passive belong to the first division. None belong to
the second. The perfects ending in a belong to the third di-
vision; and those ending in KO,, to the fourth. All futures are
thematic formations on the enlarged stem, and belong, there-
fore, to the fourth division.

The following system embodies the results of this com-
parison:



Xu-o> eXiTT-ov XeXoiTT-a

TVTT-T-O) \v-cr-a XeXv-/c-a \v-cr-t

1 5/>ra,ch. XX, i.



EXAMPLES OF DEVELOPMENTAL INSTRUCTION. 37!

This system should be written on the blackboard, and the
pupils should then copy and explain it. They should also give
the proper headings for the horizontal and the vertical rows.
They should, in brief, learn to know how much is condensed
into the thirteen words; and one member of the class should
discuss the scheme connectedly. Hitherto the method applied
was analytical, since it ascended from the individual and specific
to the generic; and now that the latter has been found, it will
be well to proceed synthetically, /. e., group the particular under
the categories obtained. In the first place, we should supple-
ment what is suggested by the system. Active and medial
forms should be placed beside the passive, and the reduplicated
forms should be given; e^rjva should be placed beside eXv<ra;
<j>ava), beside Xvcrw; specimens of contract verbs, beside Xvw;
and specimens of the other classes of verbs ending in w, beside
TVTTTO). The athematic formations on the pure stem may be
grouped, as in grammar, according to the final letters of the
stem, etc. What has been grouped together in the system,
should be compared with what is said in the grammar, as this
brings out the relation between the two principal conjugations:
the verbs in /LU are represented by </>i7/ou, SeLKWfu, and eo-Tyv,
and these forms may be separated from the others by a broken
line. The system is applied by letting the pupils find forms that
will "fit into it, and to this end they should propose questions
to one another. A further application of the insight into the
formation of the verb would be to compare the corresponding
Latin forms. It is not difficult to demonstrate the analogy
between (17/41 and fers, ferf, etc.; between Xv<y and lego; be-
tween TVTTTO) and flecto; eKiirov and legi\ eXvcra and scripsi\ and
Xvtrw and amabo.

Another method of applying what has been found, is to
reflect upon the way which has led to the discoveries; and this
will prove a preparation for the study of logic. In the present
case the divisions have been applied most. The four divisions
are based on the crossing of the following concepts: athematic,
thematic, formation on the pure stem, formation on the en-
larged stem. And these concepts themselves fall under the
concept of formation-media. In the system itself the two con-
cepts, kind of formation and tense, are crossed.

2. To illustrate the method of applying analytical develop-
ment in the instruction in logic, we shall develop the concepts
analysis and synthesis. We have, in ch. XLI, 2, developed
these concepts synthetically, but we shall now, for the purpose



372 DIDACTIC TECHNIQUE.

of practical instruction, show their analytical derivation. This
will, at the same time, give us an opportunity to illustrate
how logic can be correlated with the other branches of the
curriculum. 1

The ascending thought-process of analysis and the descend-
ing one of synthesis are understood most easily in their applica-
tion to concepts, in the form, consequently, of abstraction and
determination. In the first place, the teacher should illustrate
how new concepts are obtained from the old, namely, on the
one hand, by abstraction, and, on the other, by determination.
Examples taken from grammar are particularly appropriate.
The discovery that Greek, Latin, German, English, and other
languages are cognate, gave rise to the new and higher concept
of the Indo-Germanic languages. On the other hand, the study
of the history of the English language and of its dialects gave
rise to a number of lower and narrower concepts: Old English,
Middle English, Yorkshire dialect, etc., so that from the one
concept, English language, there has been an ascending and a
descending process, in the direction of the genus as well as of
the species. Natural history, too, on the one hand, groups the
species under the genus and, on the other, divides the species
into families, and thus offers a large number of illustrations.
Witness, on the one hand, the concepts of classes: canis, felis,
mammalia, ruminantia, etc. which had in many cases to be
expressed by new terms and, on the other hand, the concepts
of the families within the species.

A similar process of ascending and descending can be ob-
served in judgments, theorems, and cognitions. The theorem
of Pythagoras, for instance, is the generalization of what has
been observed in certain right triangles with commensurable
sides. These angles are known as the Pythagorean triangles,
whose sides are in the proportion of 3 : 4 : 5, of 6 : 8 : 10, of
5 : 12 : 13, etc. The theorem of Pythagoras, however, can be
amplified in a double way. First, the relation which it expres-
ses between squares, is true of all similar figures, so that all
similar polygons constructed upon the legs are equal to the
similar polygon constructed upon the hypotenuse. Secondly, its
formula: c 2 = a* + b* in the changed form: c 2 = a 2 4. b 2 lab cos y
can be applied to all triangles. The theorem of Pythagoras will
then appear as only a special case of more general theorems.
Every application of the theorem for example, to apply it to



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