_The Logical Presupposition or Method._
§ 103. The logical presupposition of instruction is the order in which
the subject-matter develops for the consciousness. The subject, the
consciousness of the pupil, and the activity of the instructor,
interpenetrate each other in instruction, and constitute in actuality
one whole.
§ 104. (1) First of all, the subject which is to be learned has a
specific determinateness which demands in its representation a certain
fixed order. However arbitrary we may desire to be, the subject has a
certain self-determination of its own which no mistreatment can wholly
crush out, and this inherent immortal reason is the general foundation
of instruction.
--To illustrate; however one may desire to manipulate a language in
teaching it, he cannot change the words in it, or the inflections of the
declensions and conjugations. And the same restriction is laid upon our
inclinations in the different divisions of Natural History, in the
theorems of Arithmetic, Geometry, &c. The theorem of Pascal remains
still the theorem of Pascal, and will always remain so.--
§ 105. (2) But the subject must be adapted to the consciousness of the
pupil, and here the order of procedure and the exposition depend upon
the stage which he has reached intellectually, for the special manner of
the instruction must be conditioned by this. If he is in the stage of
perception, we must use the illustrative method; if in the stage of
conception, that of combination; and if in the stage of reflection that
of demonstration. The first exhibits the object directly, or some
representation of it; the second considers it according to the different
possibilities which exist in it, and turns it around on all sides; the
third questions the necessity of the connection in which it stands
either with itself or with others. This is the natural order from the
stand-point of the scientific intelligence: first, the object is
presented to the perception; then combination presents its different
phases; and, finally, the thinking activity circumscribes the restlessly
moving reflection by the idea of necessity. Experiment in the method of
combination is an excellent means for a discovery of relations, for a
sharpening of the attention, for the arousing of a many-sided interest;
but it is no true dialectic, though it be often denoted by that name.
--Illustration is especially necessary in the natural sciences and also
in æsthetics, because in both of these departments the sensuous is an
essential element of the matter dealt with. In this respect we have made
great progress in charts and maps. Sydow's hand and wall maps and
Berghaus's physical atlas are most excellent means of illustrative
instruction; also Burmeister's zoölogical atlas.--
§ 106. The demonstrative method, in order to bring about its proof of
necessity, has a choice of many different ways. But we must not imagine,
either that there are an unlimited number, and that it is only a chance
which one we shall take; or that they have no connection among
themselves, and run, as it were, side by side. It is not, however, the
business of Pedagogics to develop different methods of proof; this
belongs to Logic. We have only to remember that, logically taken, proof
must be analytic, synthetic, or dialectic. Analysis begins with the
single one, and leads out of it by induction to the general principle
from which its existence results. Synthesis, on the contrary, begins
with a general which is presupposed as true, and leads from this through
deduction to the special determinations which were implicit in it. The
regressive search of analysis for a determining principle is
_Invention_; the forward progress of synthesis from the simple elements
seeking for the multiplicity of the single one is _Construction_. Each,
in its result, passes over into the other; but their truth is found in
the dialectic method, which in each phase allows unity to separate into
diversity and diversity to return into unity. While in the analytic as
well as in the synthetic method the mediation of the individual with the
general, or of the general with the individual, lets the phase of
particularity be only subjectively connected with it in the dialectic
method, we have the going over of the general through the particular to
the individual, or to the self-determination of the idea, and it
therefore rightly claims the title of the genetic method. We can also
say that while the inventive method gives us the idea (notion) and the
constructive the judgment, the genetic gives us the syllogism which
leads the determinations of reflection back again into substantial
identity.
§ 107. (3) The active mediation of the pupil with the content which is
to be impressed upon his consciousness is the work of the teacher, whose
personality creates a method adapted to the individual; for however
clearly the subject may be defined, however exactly the psychological
stage of the pupil may be regulated, the teacher cannot dispense with
the power of his own individuality even in the most objective relations.
This individuality must penetrate the whole with its own exposition, and
that peculiarity which we call his _manner_, and which cannot be
determined _à priori_, must appear. The teacher must place himself on
the stand-point of the pupil, i.e. must adapt himself; he must see that
the abstract is made clear to him in the concrete, i.e. must illustrate;
he must fill up the gaps which will certainly appear, and which may mar
the thorough seizing of the subject, i.e. must supply. In all these
relations the pedagogical tact of the teacher may prove itself truly
ingenious in varying the method according to the changefulness of the
ever-varying needs, in contracting or expanding the extent, in stating,
or indicating what is to be supplied. The true teacher is free from any
superstitious belief in any one procedure as a sure specific which he
follows always in a monotonous bondage. This can only happen when he is
capable of the highest method. The teacher has arrived at the highest
point of ability in teaching when he can make use of all means, from the
loftiness of solemn seriousness, through smooth statement, to the play
of jest--yes, even to the incentive of irony, and to humor.
--Pedagogics can be in nothing more specious than in its method, and it
is here that charlatanism can most readily intrude itself. Every little
change, every inadequate modification, is proclaimed aloud as a new or
an improved method; and even the most foolish and superficial changes
find at once their imitators, who themselves conceal their insolence
behind some frivolous differences, and, with laughable conceit, hail
themselves as inventors.--