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regard, however, to changed conditions-the customs of our forbears.1

The application of the heuristic method must be considered in outlining the course of study as well as in didactic technique. But we shall here consider it only in its bearing on the curriculum, reserving the other aspect for later treatment. There are certain branches whose matter is, in the main, not new and hence needs only to be elaborated, while in other branches the heuristic element is important enough to affect the whole field of study so as to call for consideration in connection with the didactic formation. But in a third class of subjects the heuristic element occurs so rarely that it can be left to the discretion of the individual teacher, i. e., to didactic technique. We shall here deal only with the first category of studies, among which we find the elementary instruction in the mother-tongue, mathematical form study, and geography.

6. The mother-tongue is familiar to the pupil; its laws and rules govern his speech, though he is not aware of it. It is the function of instruction to, complete this half-knowledge and make it conscious. This is done thetically when a foreign language is made the subject of instruction, and the forms and inflections of this language are then the fixed points around which the respective equivalents of the mother-tongue assemble, so that little more need be done to bring home to the pupil the structure of the latter. Though this road is actually a roundabout way, it is not so easily missed as the other, that of the heuristic method, which makes the mother-tongue the direct object of study, so that the pupil is taught to attend closely to his speech. This method to use a comparison we employed before demonstrates language like a machine in operation." The pupil's language consciousness is the source of knowledge; spoken sentences must be the object of analyses, comparisons, and generalizations; and grammatical categories must be developed successively on the ground of the material that has been thus obtained. This method, it is true, is more attractive than the thetic. But the teacher who would adopt it, must consistently apply the underlying principle throughout and must beware of zigzagging between the two methods; for this would lead the pupil to believe that nothing new was to be learned,

1 For suggestions how this can be done, cf. Kirsch, Thoroughness in the Teaching of Language, Cath. Educational Review, May, 1913, pp. 398 ff. 2 Supra, ch. XVII, 5.

that there was nothing in his mother-tongue that he did not already know.

To illustrate the difference between this false procedure and the heuristic method, we shall take the treatment of the subjunctive in English. It would be wrong to proceed from the verbs whose subjunctive form differs least from the indicative. To apply the heuristic method we must, on the contrary, select a verb which shows strikingly the difference in the forms of the two moods. In order to bring home the idea that the indicative has a variant—and as such the subjunctive must be conceived-we should place side by side, not: I praised—if I praised, but rather: I am if I be, I was-if I were, and other forms that exhibit, like these, obviously different formations. These forms should naturally be taken from sentences, and preferably from such as let one conceive the indicative forms as parallel. Indirect speech, which employs both the indicative and the subjunctive, is best adapted to this purpose. Consequently, the transposition of direct speech into indirect furnishes the basis for obtaining the subjunctive.

7. Like grammar, mathematics meets with unconscious knowledge and skill in reference to the relationships of magnitude. The heuristic method must introduce, step by step, what is unconscious into the consciousness. Here, too, a more simple method may be adopted: that of letting the pupils operate freely with the known relationships, and this will prepare for the full comprehension of the relationships of magnitude. Especially in the case of forms of bodies is it advisable to have them drawn or represented in other concrete ways. Thus the way will be prepared for the study of geometry. The teacher will obtain still better results by giving systematic explanations about the forms of bodies represented by the pupils. This combination of the technical with the theoretical is the characteristic feature. of form study.' Form study is heuristic in nature, and this fact should never be lost sight of. It should be neither elementary nor thetic, though geometrical objectivation generally has both these qualities. Form study should train the pupils first to make and observe forms of bodies and then to express in words the results of their observation. It should deal partly with such forms as present, because of their regularity, few, if any, difficulties as the square, the circle, and symmetrical figures of all kinds-and partly with such as will, because of

1 Supra, ch. XXXVI, 4.

their variability, hold the attention for a longer time as angles with revolving sides, figures with sliding sides, etc. The works of nature and art have different figures and so will occasion a different kind of search and discovery.

8. There are two considerations which should encourage the application of the heuristic method to geographical instruction. The first is the circumstance that home geography should, as we recommend, precede the geography of the world at large. Home geography is here understood to embrace all the accessible environment of the pupil; and this environment may prove to him. a valuable source of geographical data and concepts, which should not be lost amid the wealth of the subject-matter of geography. What the pupil can perceive with his senses, may be made, on the one hand, the point of correlation and, on the other, the point of comparison. In geographical instruction the following questions must ever be at hand: What is the relationship between the respective foreign country and us? What were the relations formerly? What objects of our environement have been imported from that country? What products do we furnish to this country in return? How do we get there? How could we get there? and so forth. A second series of questions suggests the comparison of home and foreign conditions: What have we in our home town to illustrate what we have learned of foreign conditions? Is there anything in our present environment to assist the imagination in picturing foreign conditions? Is there anything familiar to us that might serve to explain this or that foreign custom that appears so strange to us?

These and similar questions should never be omitted in geographical instruction, and hence they belong not only to didactic technique, but also to the course of study. The discussions resulting from them are introductory and should be followed by the subject-matter proper, primarily by the map, because it visualizes so much geographical knowledge. This is the second opportunity for applying the heuristic method: the map is to be made a source of knowledge. At present, the map is used merely for verifying the statements of the textbook; it is considered only of secondary importance, whereas it ought to be the primary instrument of instruction; and the pupil should be trained to glean from it as much knowledge as possible, so that the descriptive text would be merely supplementary. Peschel says: "Maps are philosophers' stones, and so if the philosophers be missing, they are naught but stones; they are symbols which speak to us in words full of mystery, and hence

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it should be the chief duty of the teacher of geography to ensure a clear understanding of their symbolical language.' It is on the same grounds that Sydow demands that the teacher make his "pupils read and explain the map; the teacher's questions must be methodical, so that the reading and explanation be correct. . . . The nomenclature of the map should not be taught dogmatically, but the pupil should learn to find the terms on the map, and thus he will be obliged to interrelate the terms with the concepts obtained from the drawing of the map.

The same viewpoints that govern the reading of a text by virtue of its organic nature,2 should govern the study of maps. What can be read from the map should not be drawn from another source; but what must be drawn from other sources, should be correlated as closely as possible with what is given. The parallels running through a country allow us to infer facts about its seasons. Its meridians allow us to compare its day time with ours. From the degrees of longitude and latitude we can figure out the size of the country. The hatching or coloring indicates the relative altitudes. From the elevation and lay of the valleys one can infer their probable temperature. The grouping of the cities shows the lines of trade and commerce; and it is interesting to learn from the map what influences the rivers and mountain ranges had on the divisions of a country. From the place-names we can conclude what race or races inhabited the country. Thus the place-names on the map of Spain are either of Roman, or Germanic, or Arabic origin; and the placenames of England reveal an analogous historical stratification.

Historical maps admit of a similar application of the heuristic method. And by making proper use of such maps, historical instruction not only obtains a solid basis, but can also economize by saving the time now spent in imparting that information. which could easily enough be gleaned from the map. We shall illustrate this by an example, in chapter LII.

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IV.

DIDACTIC TECHNIQUE.

CHAPTER XLVII.

The Educative Process of the Individual.

1. The organization of the content of education and the didactic formation of the subject-matter of instruction are only indirect factors in the educative process and must be supplemented by the personal element of the teacher, i. e., by the didactic technique. The Latin proverb says, "Viva vox alit plenius." Indeed, only the living voice can impart the full mental food, because it gives to the dead material something of its life. It is only when a living person is actively engaged in transmitting the intellectual treasures of the race that the corresponding faculties of the young are called into being and into active co-operation. Without a teacher the course of study is only a score without an orchestra, a digest of laws without a judge.

The didactic technique deals with the learner and with the details of the content of teaching; and this relationship determines the twofold scope of our inquiry. We must, on the one hand, treat the educative process of the individual as the field. or domain of the didactic technique, and, on the other hand, examine how the principles laid down for the course of study are to be applied to the smaller didactic units, viz., lessons, daily tasks, and exercises. Each of these two subjects should be treated, first, in a general way, and then, in detail. But the educative process of the individual may be treated partly with regard to the stages of his development and partly with regard to his individuality, i. e., with regard to the differences in ability. The second field may be specialized with regard either to the branches of study or the forms of instruction (presentation, explanation, development, etc.). It is impossible for us to treat in this work all these phases of the subject, and we shall content ourselves with treating the educative process of the individual in general, the psychological and logical elements of the didactic

I Quint., Inst., II, 2, 8.

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