2. Was instruction in the former separated from the latter in olden times? From ancient times writing was accompanied by reading; but not until modern times, (since Graser,) has reading been connected with writing, in all its steps.

3. Is this method according to nature?

It is natural, because reading and writing are properly but two different sides of the same thing, i. e., of the written language.

4. But is it not easier, first to practice the one, and not to practice the other, until the greater difficulties of the former are mastered?

Quite the contrary. Reading and writing assist each other mutually, and experience teaches, that the first instruction in either, is made more efficient by their union.

5. In what way shall they be connected?

The teacher can either (analytically) view the spoken word as a sound, and then have it (synthetically) represented by the signs for the sounds, i. e., the letters, in which case writing is prior; or he may first view the written (printed) word as a representation of the sound, (analytically,) and then have it (synthetically) reproduced by pronouncing or reading-in which case reading is prior. We have, therefore, either a Lese (reading)-Schreib (writing)-Methode, or a Schreib-Lese-Methode,-(Writing-reading-method.)*

6. What may be said in favor of the reading-writing method?

Writing always precedes reading; the inventor of writing did it for reading's sake; he wrote first, and then he read. Hence, instruction in reading must be joined to instruction in writing.

7. What may be said in favor of the reading-writing-method?

In answering this question we take, not the place of the inventor of writing, but of him to whom he first communicated his invention; the inventor taught him first to read and then to write, and in like manner, according to nature, we must proceed now.

8. Which method is to be preferred?

It is nearly indifferent, either in regard to subject or result, whether we put the pupil in the more artificial place of the first inventor, or in the more natural place of the first pupil.

9. What rules must be observed in the adoption of either?

Reading and writing must always be intimately connected; the elements of the word must be found by analysis, and made the basis of study; and only such words and syllables must be read and written, as have a meaning for the pupil.

* Reading is always analytical, writing synthetical; but the method of teaching may be different. If reading be separated from writing, the proceeding may be

(1,) Synthetical; where the letter is given, and with it either (a) the name of the letter without the sound-buchstabirmethode, spelling method; or (b) the sound (laut) of the letter without the name-lautirmethode, phonetic method; or (c) the sound and the name of the letter, spelling and phonetic method combined, (Wilging's, Kawerau's ;) or

(2) Analytical; where the pupil reviews the written (printed) matter as a whole, that he may resolve it into its elements. The whole is (a) a proposition or sentence, (Jacotot's method;) (b) a word, (Gedike's method ;) or

(3,) Analytico-synthetical; the child, to become prepared for reading, is made to resolve sentences into words, words into syllables, syllables into sounds, and then the teacher proceeds by the combined method. See Jacobi's book on these methods; also Honcamp's "Volksschule." No. 10, p. 20.

In the Schreib-Lese Methode, (and vice versa,) it is well to give also the name of the sound and letter.

236

10. Is it not requiring too much of a child, who has not yet mastered the mechanical part of reading, to ask him to think of the contents and understand what he reads?

Not at all; for word and idea are one, and speaking and thinking are not to be disconnected. "Given the word, to think of its meaning," is not an operation which the pupil has to learn; he does it of himself and has always done it. But to speak, without joining an idea with it, the pupil has to learn, and that too in order to unlearn it afterward with much trouble.

11. Why is it important never to read meaningless syllables and unintelligible words? Because the pupil will read in future as he is taught to read; therefore, he ought to get accustomed from the beginning to seek in all that he reads a proper idea. Every thing not essential, particularly all that would embarrass the first instruction, should be put off to a later time. It is not necessary to proceed from the easier sounds to the more difficult, for the child pronounces all with equal facility; but it is good to begin with the easier letters, so far as their form is concerned, for example, o, i, s, £.

Reading by itself.

Reading may be divided into (1,) mechanical; (2,) logical, (intelligent,) and (3,) æsthetical, (feeling.)

12. Are these grades strictly to be kept asunder?

No; reading must never be merely mechanical, without regard to the understanding; with logical reading, mechanical ability ought at the same time to be advanced; nor should reading ever be without feeling; and with æsthetical reading, both the mechanical and the logical processes should be practiced. The first belongs, in a common school, to the lowest class; the second, (logical,) to the middle, and the third to the highest class, i. e., they are preeminently to be attended to in those classes.

13. Wherein consists the mechanical ability of reading?

In a quick survey of the written or printed matter, and in the ability of representing a row of letters by the right sounds, syllables and words.

14. How is this ability best acquired?

By frequent class-reading, which must alternate with single reading, so that the former is always preceded by the latter, which must serve as a model. Single words and sentences are to be repeated, until they are readily pronounced. The teacher, by his accompanying voice, directs as to right pronunciation and accentuation.

15. Wherein consists logical reading?

In that the understood contents of a piece are emphasized in conformity with that understanding.

16. When does the pupil understand the contents?

When he knows the meaning of the words, and the meaning of their relations in the sentences.

17. When does he understand the meaning of the words?

When he knows the signification of the derived and compound words by the meaning of their elements, and when he well distinguishes between the proper and the figurative meanings of the same.

18. Should the exercises in the formation of words, and such as help to understand the rhetorical figures, be practiced in the reading lesson?

They should be combined with grammar, and occur in the reading lesson only so far as is necessary for understanding the words.

19. When does the pupil understand the relations within the sentence? When he knows how one conception (of a word) refers to another; the different conceptions (words) to the speaker; one idea to another; and the different ideas to the speaker. It is sufficient for the pupil to understand these relations without having a conscious insight into them. An analysis of the conceptions and expressions belongs to the grammar, not to the reading lesson, in order not to spoil the pupil's enjoyment of the contents, etc., etc. (The rest has more particular reference to the German language.)

III. ARITHMETIC, (Rechen-Unterricht,) BY A. DIESTERWEG.

1. What has brought arithmetic into the common school?

The wants of daily life-material necessity. Its introduction was historically the first of those which caused a change in the organization of schools. (Rabanus Maurus, in the ninth century, recommended arithmetic and geometry, because they open mysteries, because the Bible speaks of cyphering and measuring, because we learn by it to measure the ark of Noah, etc.)

2. Is this the only reason why the present common school teachers retain this instruction, and consider it indispensably necessary?

Not at all. They have recognized in the right treatment of number, and of its application to daily life, an excellent discipline of the mind; the formal object is added to the material one.

3. How do they compare in value?

The formal object has the preference; in no case is it to be subordinate; the development of the mental powers is in every school the chief point. But they do not exclude one another; quite the contrary. The formal end is attained just so far as the matter to be understood is worked through.

4. What motives decide on the choice and arrangement of the matter? First, the "formal" motive; i. e., regard to the mental nature of the children, the laws of human development; and especial regard to the individual nature of the learner; next, various external circumstances-differences of place and time, and of schools. The first motive is universally the same; it dictates the management of the number; the second directs the application of the number, or calculation.

5. How far ought all to advance in arithmetic?

The maximum can not be stated; nor the minimum either, at least in regard to the degree of formal development. It remains to point out the material minimum, and this requires every child to be able to solve the common problems of every day life. It is neither necessary nor possible, that all scholars should reach the same point.

6. What is to be thought of prescribed rules and formulas?

They are to be entirely annihilated. No operation, not understood in its reasons, should be performed, or learned. The scholar must be able not to demonstrate mechanically each operation, but to give the simple reasons which justify it to the mind. The right deductions from the nature of the number and of its relations, are to prove its correctness.

7. Wherewith must instruction in arithmetic begin?

With the numbering of real objects, (cubes, little rods, fingers, etc.)

8. What inductive means are next employed, and how long is their use continued? The teacher next proceeds to the use of artificial means, as lines, points, cyphering rods, Pestalozzian tables, etc., and continues to practice the simple

changes of number with them, until the pupil has a perfectly clear idea of the numbers and of their quantities.

9. What next?

The teacher advances to the use of figures.

10. What is the treatment of the number, with and without figures?

The latter always precedes the former; the written or slate arithmetic every where follows mental arithmetic. Not only does the cultivating power of arithmetic lie in the insight into the relations of number, but also the wants of practical life demand preeminently skill in mental arithmetic.

11. Upon what chiefly depends that skill?

First on the ability in handling the decimal principle, (Zehnergesetz;) then on the ability to compare and analyze numbers.

12. How do the exercises with so-called "pure," and with applied numbers, compare?

The former always precede; application presumes ability in treating the pure number. This being attained, questions, problems and exercises follow; together with denominate numbers, and their application to life.

13. Are the exercises with numbers from 1 to 100 to come in order after the four rules, (addition, subtraction, multiplication, division?)

No. All operations ought to be performed successively with these numbers; the regulated uniformity of the operations comes later. (Grube, Schweitzer, etc.) 14. Shall fractional arithmetic be entirely separated from instruction in whole numbers?

No. No. 13 forbids it, and makes it impossible; even considered in itself it would be improper.

15. Which points must be distinguished in practical problems?

First, the understanding of the words.

Second, the relation of the question to the statement, or of the thing required to the thing given.

Third, the understanding of the way in which the unknown number depends on the number given.

Fourth, the finding of the unknown number from the given number; that is, the calculation, oral or written.

16. What has the teacher to do in these four processes, when the pupil can not proceed of his own strength?

In the first, the understanding of the words and things in their relations must be explained, and often directly given.

In the second, what is required must be well distinguished from what is given; the propriety of the question must be accurately considered.

The third point is to be brought out by means of questions from the teacher. The fourth is an affair by itself, and is the pupil's concern.

An exercise is not complete and satisfactory, until the pupil is able to explain these four points, one after another, orally, and without any aid.

The teacher leads by questions, (by analysis;) the pupil proceeds by synthesis. The former proceeds from what is sought, the latter from what is given. 17. How is talent for arithmetic to be recognized?

Besides what has been said in No. 16,-by the independent invention of new methods of solving the problems, of peculiar processes, etc.

18. In what way may uniformity in arithmetical instruction be gained? By solving each problem rationally, according to the peculiar nature of the

239 numerical relations occurring in it, and consequently, without admitting any external rule or formula, which on the contrary ought to result from the subject itself. Uniformity lies in the rational, transparent treatment, and, therefore, in the mind, not in the form. Good rules, etc., are not indifferent, but they must follow the observation of the thing.

19. Which is the most simple, natural and appropriate form of managing the problems externally?

Not the doctrine of proportions; it is too artificial, and too difficult for the common school; nor the chain rule, etc. The best form in slate arithmetic for the common school is the so-called "Zweisatz," the fractional form, (bruchform,) which every where requires reflection. (Scholz.)

20. What is the value of the so-called "proofs" and abbreviations?

The proofs are, with a rational method, superfluous; the latter are of little value. A well guided pupil finds them out himself, and if, in the highest class, some of them are pointed out to him, their origin, and thus their correctness, must be demonstrated at the same time.*

IV. GEOMETRY, (Raumlehre,) BY A. DIESTERWEG.

1. Is geometry required in the common school?

No doubt, for it teaches the forms in which every thing appears; the shape of matter and the laws of those forms; the laws of space and of extent in space; the dependence of magnitudes and forms on each other.

2. Why is such knowledge considered as a requisite for general cultivation? Because the whole mass of bodies, the universe, as well as man, exists in space; because without the knowledge of the qualities of space, man would be ignorant of that appearance of things which belong to their inmost nature; because geometry teaches how to measure lines, surfaces and bodies, which knowledge is very necessary; because without it man could not divine, that the distance and size of the sun, moon and stars, could be determined; and because he would even have no idea of the extent of his own abode, and of the mathematical, i. e., fundamental qualities of the same. All this is consequently requisite for general human cultivation, not to speak of its practical value, as well for female as male education, and therefore for the common school, the school of the people. Without it, not the most indispensable part, but an essential part, of education is wanting.

3. What elements of geometry are to be taught in the common school? and in general what parts of it may be considered there?

Space admits of "intuitive," (anschauliche,) and a demonstrative, (begriffsmaessige,) observation.

The intuitive faculty of man perceives immediately objects in space, bodies in their qualities and forms; with the sense of touch he perceives what opposes him in space, the body and its external form; the sense of sight assists him, by determining extent and distance, and by comparing and measuring them. These are operations of external intuition. The intellect abstracts the differentia of the bodies, and fixes the pure, mathematical form; and thus aids the interior pure, or mathematical intuition. Moreover, the logical intellect, perceiving the

* No school can do without an arithmetical text-book. Hence it sufficed to give here the principles. These contain the measure by which we have to judge of the value of the text-book.