should be studied first, as it affords much aid to the general explanation of maps.' The elements of astronomical geography should also be taught in the elementary school, at least in so far as to explain those changes in the heavens that can be observed locally. The elementary school should restore to the masses at least so much of this knowledge as was a common possession, before printed calendars came into general use, when the man in the street was familiar with the time of the rising of certain stars and other signs of the change of the seasons. But at present this knowledge seems to be found only among the people living on the coast. The noting down of the changes in the heavens, vivid descriptions, interesting narratives, short memory lines resembling proverbs-these are the best media for imparting this knowledge, for if we would popularize the subject, we must avoid anything savoring of scientific form or terminology. Hebel's Schatzkästlein points the way to the correct treatment of the subject. 3. The teaching of reading, writing, and arithmetic is a primary object of the elementary school. The elementary school is evaluated by the men of practical affairs as well as by the higher schools according to its success in teaching these three subjects. And success can not be attained but by diligence and persistent effort on the part of teacher and pupils. Rational and improved methods may make the instruction more interesting and more educative, but can not dispense with the slow and patient work. It has been said that the pupils wrote better in former times, when the teachers talked less of methods of writing, and that there was also better figuring done in the schools, when the multiplication table was the only help known. But for this poor showing we may not blame the more rational methods. On the contrary, the greater interest centering in the improved methods has led the teachers to scorn the drudgery that is after all inseparable from elementary school instruction. The right thing is to add the improved methods to painstaking and unwearying care: the latter produces positive results, and the improved methods are an important factor in formal education. We have seen that the instruction in writing contributes materially to formal education.2 Connected with it is the in 1 More extensive use should be made of the topographic maps published and sold at a nominal price by the United States Geological Survey, Washington, D.C.; cf. Press Bulletin of the United States Geological Survey, Washington, April, 1913. 2 Supra, ch. XVI, 2. struction in grammar, whose primary aim is the development of the mind. But the grammatical instruction of the elementary school should be reformed in accordance with the principles of the science of education and of linguistics. Grammar suggests of itself the application of analytic and heuristic methods, which fact is quite generally overlooked.' A further mistake in method is made in analyzing sentences, if the categories of the parts of a sentence and of the parts of speech are treated as a fixed framework, for this practice ignores the interrelation between the two and fails to show the organic nature of language. This mistake can be corrected only by treating both categories according to the genetic method. Again, amid the many exercises in sentence analysis the teacher does not give sufficient attention to the variability of expressing and coloring thoughts, although this variability shows the co-operation between the logical and the grammatical element of language much better than does the analyzing of sentences. Similarly, the subject of word study does not receive sufficient attention; whereas it is just the study of word-formation, of the means employed to this end, of the various meanings of words, of synonyms and antonyms, etc., that will elicit the children's interest, compel them to think, and increase their vocabulary. 2 Elementary language instruction should follow the formal steps as described in Ch. L, 8. The heuristic method should be employed first, for the respective language form should be discovered in the pupil's language consciousness and thence brought to light. After this the form will have to be shown in so many variants or instances as to arouse the pupil's attention and to hold it until the form is received into his mind. Thence the pupil proceeds to the step of comprehension by understanding and expressing in his own words the analogy, i. e., the grammatical rule governing the respective language form. What has been thus understood must finally be committed to memory, and the respective rule must be applied to similar cases, first in a narrow field and, then in a broader. 4. The formal steps will also prove helpful for the rational instruction in arithmetic, with this difference, however, that the steps are to be followed not so much in the single lesson as in the arrangement of the whole course. The first object must be the obtaining of the concept of number, and this had best be 1 Ch. XVII, 5 and ch. XLVI, 6. 2 Ch. XLIII. done by visualization. Objects that can be seen should be added together, subtracted, multiplied, etc.; and in this way the idea of number and of the arithmetical operations should be made plain.' Hence the teacher should, in the beginning, confine himself to such a number of objects as can be controlled with the pupil's eyes. The aim to be kept in view in this preliminary work is to illustrate the law of formation, that is, the manner in which the work of addition, subtraction, multiplication, etc., is to be done under certain circumstances, e. g., by completing ten, as with 8+4, or by taking away from ten, as with 12-4, or by adding the same number, which will, because of the completing of the tens, result in a continual decrease of the units, as in the series 9, 18, 27, 36...8, 16, 24, 32, etc. After this has been understood, it will no longer be necessary to confine the problems to what is perceived by the pupil, for the principle, once it is comprehended, is elastic enough to start the figuring without the aid of sense-perception. But this increase in mental skill does not dispense with the memorization, for the operations, even after they are understood, must be fixed permanently in the mind by means of the different arithmetical tables, among which the multiplication table is the most important. Arithmetic offers a practically unlimited field for varying the problems, and hence the teacher should never be at a loss for material to apply what has been comprehended. The problems, however, should not be creations of the wild fancy, but should be taken from real life and should, as far as possible, be interrelated with each other; and the rules that we laid down for algebra problems should be applied here also.2 For object lessons in arithmetic Pestalozzi recommended a square to be divided off into a hundred smaller squares, and it is to be regretted that this method is no longer in use. There is no doubt that arithmetic can be taught much better if each pupil has the didactic material before him than if the teacher alone uses it for demonstration, as is the case with the different forms of the abacus. If the pupils themselves represent the numbers with peas or small sticks of wood placed on a checkerboard, they will readily understand the laws of formation and get a clear idea, especially of the principle underlying the columns of the multiplication table. 1 Supra, ch. XLIV, 3. 2 Ch. LVI, 4 f. 3 Ch. XLIV, 5. Form study will combine formal education with useful skill, if it trains the eye and the hand, cultivates taste, and develops the faculty of combination. It is advisable to let the children construct, as early as possible, different figures and to let them vary these in every possible way. The stigmographic chart ("stigmographisches Blatt") is the simplest help for such work, and, besides being obviously related to the abacus, it has the advantage of familiarizing the pupil with the idea of co-ordination, which is important for the later study of mathematics. More extensive experiments should be made with this chart, for with it many exercises connected with the Fræbelian gifts can be made without these gifts themselves. Form study should prepare also for industrial training; and we have seen how the industrial training can be given a general character while remaining correlated with the special trades.' CHAPTER LXX. The Training of Teachers. 1. Though the normal school is generally conceived as being related to the elementary school alone, we can not here restrict it to so narrow a field, because there can be no unity of the teaching profession' unless all the training schools for teachers are examined from a viewpoint common to them all. Natural gifts, practice, and understanding are, as we have seen," the prerequisites on the part of the pupils for successful study, and they are also the prerequisites for successful teaching. The prospective teacher must have a natural talent for teaching; he must through practice acquire skill in teaching; and by diligent study he must acquire knowledge. The practice and studies of the prospective teacher must deal with a double content: on the one hand, with the matter which the teacher must impart to his pupils and, on the other hand, with the process of this imparting. Hence the candidate for the teaching profession must acquire four things: (1) material skill, i. e., mastery of the arts ("Fertigkeiten") which are the subjects of instruction; 1 Supra, ch. XXXII, (2) material knowledge, i. e., comprehension of the theoretical materials of instruction; (3) didactic skill, i. e., familiarity with the technique of instruction; (4) didactic knowledge, i. e., an understanding of the educative process. The training school for teachers must presuppose in its students the talent for teaching, the donum didacticum. However, the training schools should take greater care to exclude all those that lack the natural ability for teaching. The apprentice who would learn a trade for which he is unfit, is soon discharged because of his obvious awkwardness. But with the long course of theoretical preparation a teacher's unfitness is often discovered only after he has entered upon his professional duties. A practical test of a candidate's professional fitness would be to have the normal school admit him only after he has been tried out in the schoolroom as an assistant (even if only for very elementary work) to an experienced teacher. If this practical test were applied by all normal schools, the number of misfits in the teaching profession would become decidedly smaller. As the natural talent for teaching is always more or less one-sided, it admits of many variations. He who is a good teacher is not necessarily a good instructor, and the aptitude for a special method of teaching more often excludes than includes the aptitude for other methods. Herbart has connected some individual forms of the donum didacticum with the conditions of many-sidedness, clearness, association, system, and method. "Some teachers," he says, "lay great stress on the explication, step by step, of the smaller and smallest components of the subject, and insist on a similar reproduction on the part of the pupils. Others prefer to teach by conversation, and allow themselves and their pupils great freedom of expression. Others, again, call especially for the leading thoughts, but demand that these be given with accuracy and precision, and in the prescribed order. Others, finally, are not satisfied until their pupils are self-actively exercising their minds in systematic thinking. "1 This classification, however, ignores that kind of teacher whose forte lies in presenting, narrating, and describing, and whom most pupils would call a good teacher. But the punctilious teacher, who is more intent on fixing the subject-matter in the minds by means of many exercises, is appreciated by his 1 Outline of Educational Doctrine, transl. by A. F. Lange, London, 1913, PP. 52-53, § 67. |