the theorem, which latter is expressed in words. The geometrical figure is the visualized expression of general principles, and can easily be employed to visualize any magnitude. In this respect we should imitate the ancients, for they represented numerical relations in meaningful constructions.1

In mathematics we should carefully visualize the actual conditions with which the problems happen to deal. These conditions should, if necessary, be explained independently of the problem, lest the subject-matter of the latter render the application of a law more difficult. The pupils must be familiar with percentage, commission, interest, discount, etc., before they solve the problems that deal with these matters, and should learn to distinguish in these problems the commercial element from the mathematical.

3. Philosophy regards the different forms in which the concrete and the abstract can appear as the proper objects of its inquiry, and this wide range of material should also influence the method of teaching this subject. The instruction in logic should abound in examples rich in variety and content. Herein lay the weakness of the older instruction with its premises concerning the mortality of all men and of Gaius in particular, and this defect has given rise to the witticism that Aristotle's logic is the best, because he was wise enough to discard all examples. The textbooks of Drobisch, Überweg, and the Erläuterungen of Trendelenburg have demonstrated how the teachings of logic can be illustrated by proper examples.

The religious instruction should turn to the Bible for the best model of how the concrete and the abstract can be combined. The parable gives body to the doctrines, without, however, materializing them, because it urges one to get at the soul of this body. It, furthermore, takes its material from the mental horizon of the masses, and in this way the sublime truths and precepts are rendered intelligible, and the heavenly doctrines are brought to bear upon the needs and conditions of everyday life. Every symbol connects some sublime content with a sensuous form. There is a relationship of mutual helpfulness between the history of the Church and the systematic treatment of her doctrines. The history of the Church illustrates her doctrines, and the doctrines convey the meaning of her history. The teacher of religion should, therefore, illustrate the commandments and doctrines by stories from the Bible; and should em

1 Supra, ch. XLIV, 3, and infra, ch. LVI.

body the didactic content of the Biblical stories, wherever possible, in brief texts from Scripture. The lives of the saints should be treated in a similar way.

The historical instruction deals with concrete facts, but these must be presented in so condensed a form as to make them. appear too abstract. Of wars, political events, revolutions, and subsequent reconstructions our young people have generally not even an idea, much less a clear picture. Only a detailed treatment and the limits to such a treatment are obvious-can visualize these matters. The chief difficulty of the teacher of history lies in discovering and maintaining the right proportion. between the detailed treatment and the outline sketch. Some educationists contend that the biographical study of history is the most elementary, because the personality of the great men, so they argue, can be visualized most easily. But against this view there is the obvious objection, that biographies are everywhere a late form of historical writing, and this is to be expected, because they necessitate the more or less artificial grouping of facts about the man whose life in under review. The biography is of all forms of historical writing farthest removed from the epic, and the latter is the first in point of historical development, and hence its methods should be adopted for the elementary historical instruction. The epic and the kindred style of historical writing furnish concrete details in sufficient quantity. The narration should draw upon the original sources, and by thus preserving, at least to some extent, the vividness of the native coloring, it will refresh the young mind tired of the dull grey of the outline sketch. Pictures will also be aids to the objectivation of the past, yet with the present deluge of historical illustrations one must insist that less pictures, if treated adequately, are more desirable, because less distracting, than a larger number. By making a drawing on the blackboard the teacher may often visualize a past event more strikingly than by exhibiting a finished picture. Blackboard sketches are valuable aids to historical instruction.

But to visualize the past is not enough, for the pupils are to obtain general views of the public and private life of the past, of the state of civilization, of cultural conditions of all kinds; and these general concepts are best imparted by using the comparative method.' History, too, is after all a school of thought, and the ancients justly called it the "mother town of philosophy.'

1 Supra, ch. XXVI, 3.

4. We have seen above1 how the teacher of geography should train his pupils to find on the map the answers to many questions. He also must be on his guard lest his pupils be distracted amid the wealth of details, and lest, in the endeavor to make geography a school of thought, the subject become dry and unattractive. The teacher of geography should have at his command a certain stock of sense-perceptions. He should, therefore, have travelled as one who carried his eyes and his itinerary along with him. It is not the extent, but the manner, of his travels that will let him reap the benefit, or, as Dr. Johnson puts it, "the use, of travelling: to regulate the imagination by reality, and, instead of thinking how things may be, to see them as they are. Riehl's Wanderbuch is a good help in the training of teachers of geography.

2

In natural history the contrast between the concrete and the abstract is found between the specimen and the species to which it belongs; in the natural sciences, between the fact and its cause, between the phenomenon and its law, between the experiment and its explanation. In the natural sciences one should not only use the sense-perceptions, but live oneself into them; and there must be an opportunity, besides, for the mind and its ideas to deal with the sensuous element. Lord Bacon has wittily likened the pure empiricists to the ants busy with collecting, the rational philosophers to the spiders spinning their web out of the juices exuded from their own bodies, and the true investigators to the bees collecting and transforming all that they collect. But in the examples that he adduces in illustration of his own method he imitates the ant, for he does no more than collect instances. Liebig has pointed out that this method is the very reverse of the experimental investigation of nature, which must be pursued along the lines of the Aristotelian induction.5

Modern experimental research takes up an individual case and examines it thoroughly, and this recalls Aristotle's doctrine regarding the activity of the intellectus agens in elaborating the concrete phantasm of the object into an intellectual concept rather than Bacon's method of accumulating instances.

Supra, ch. XLVI, 8.

2 Piozzi, Johnsoniana, 154.

3 Nov. Org., I, Aph. 95.

4 Ibid., II, Aph. 11-20.

5 Über Baco von Verulam und die Methode der Naturforschung, 1863.

Maher, Psychology, New York, 1911, p. 306.

The scientist may well lay down a certain hypothesis from which to draw conclusions, and in this he rightly imitates the spider, whose airy web is ridiculed by Bacon. The Encyclopedists of the 17th century found, like Bacon, more satisfaction in accumulating empirical materials than in entering into the nature of the sensuous materials. Witness Comenius' Orbis pictus, which presents under the caption of sense-perception, autopsy, "ocular inspection," all that can be represented in pictures, and yet allows no sense-perception to mature. Our instruction in the natural sciences inclines to the same defect, though it could be improved so easily by adopting the methods of present-day scientific research. The development of the sense-perceptions, the wise use of them, and their conversion into thought-elements are in an inverse ratio to the size of the textbooks and the quantity of didactic apparatus.

CHAPTER L.

Articulation of the Subject-Matter of Instruction.

1. We have all along regarded the content of teaching as a Lov, an organism, a whole consisting of head and members, of body and soul. This picture we had in mind both when we stated that the organization of the educational content is the chief purpose of the course of study, as well as when we demanded that each subject be adjusted to the whole course in accordance with the organico-genetic principle. And we are adhering to the same picture when insisting, in the present chapter, that the didactic technique must see to the articulation of the subject-matter of instruction.

The terms that express the organic conception of education. have gone over into the language and are employed quite generally by educationists, even by those who refuse to recognize the organic world-view and adopt instead the atomistic conception. Thus Herbart speaks of the members of interest, of the branches of study, of the articulation of instruction; though his system does not, and can not consistently, recognize any intellectual organisms. In the case of the organic world-view, however, the analogy that is the basis of these terms, is founded upon an actual relationship between the realities themselves; here the words are púσe, expressions of realities, and not mere éore,

conventional terms. The underlying purpose of all the rules we have laid down is this: all instruction should, as a whole and in its parts, on a large scale and in its minutest parts, be so conducted that the content of teaching will, in accord with the nature of the human mind, so develop and be so correlated in its parts as to be analogous to a living being. Each of the various subjects that we have dealt with, has brought out different points of this analogy. The main point in the course of study is that the various materials and studies be vivified and governed by one leading principle as by their soul. For the curriculum it is essential that all its elements be closely interrelated so as to promote the procreative progress. In actual teaching the teacher must deal with the smallest of didactic units, and here the analogy with the organic world demands that the subject-matter should out of similar parts coalesce into a connected whole; and this we call the articulation of the subject-matter of instruction.

A content of teaching is articulated if it consists of a series of points that are distinguishable from one another, yet so connected as to form a unit. If the parts of the content blend, they are like the colors that run in washing, and the pupil's reception of them will be hazy and indistinct. Yet if they are merely placed side by side, without being internally connected, some of them will be lost in the educative process. The right dividing lines are as important as the joints, and the structure of the content is best if its members are clearly distinguishable from one another, but suggest at the same time that they are parts of a whole.

2. For the purpose of obtaining a better idea of the import of articulation, we shall briefly examine it in connection with the formal steps,' because each of these shows a new phase of the subject. What the first step (reception) demands most is clearness in presenting and distinguishing the various parts or points of the subject-matter. The essential thing for the second step (comprehension) as well as for the explanation or development is that perspicuity which has all points grouped after the manner of a system to bring out their interrelation. The subjectmatter will be retained and fixed in the mind best by means of short series consisting of closely associated members. For the purpose of the third step (application) the material should consist of movable parts which admit of various combinations.

1 Supra, ch. XL, 5.