At first, the children write with a pencil on slate, the pencil being inserted in a tin or steel case, to give it the length of an ordinary pen. The plan of using a short pencil without a case is most injurious to the handwriting, on account of the cramped manner in which the hand must necessarily be held. It is difficult to teach children to hold even a long pencil well, from its want of elasticity; they are almost obliged to bend the forefinger in order to obtain sufficient force to make a distinct mark on the slate. Hence it would be extremely desirable, were it not for the additional expense, to use pen, ink, and paper from the first. In ordinary National Schools, however, about half the children write on paper.

The mechanical plan of teaching children to write solely by imitation has been superseded in many schools by a more rational and intellectual system. The method newly introduced was the invention of M. Mulhäuser, of Geneva.

"The method of Mulhäuser consists in the decomposition of the written characters into their elements, so that they may be presented to the child in the order of their simplicity, and that it may copy each of them separately. The synthesis, or recomposition of these elements into letters and words, is the process by which the child learns to write. The method enables the child to determine, with ease, the height, breadth, and inclination of every letter."

Although it is impossible for an ordinary National schoolmaster, on account of his multifarious duties, to carry out the method of Mulhäuser in all its details, yet it is most desirable that he should adopt its principles as the basis of his writing-lessons, and as far as possible instruct his pupils in the theory of caligraphy by frequent oral explanations, the practice in their copy-books

being taken as a sort of examination upon the lessons they have received.

The points upon which oral instruction should be given are such as the following:

(a) The posture of the body.

(b) The position of the book or slate.

(c) The manner of holding the pen.

:

(d) The rules which relate to the distances, form, inclination, and height of letters in the different hands. The following are a few of the most necessary rules:1. All letters to be equally distant from each other. 2. All letters (capitals and compounds excepted) to be of the same width.

3. All downstrokes to be uniform in thickness.

4. All upstrokes in small hand to be carried from the bottom of the preceding letter; in larger hands from the middle of the letter.

5. Loop letters to be of the same height above the line as capitals.

6. Loop letters below the line (as y, g, &c.) to be made the same length as capitals and loop letters above the line.

7. The letter d, and those letters which are sometimes made without loops, to be one-third lower than capitals. 8. The letters t and p to be half the height of capitals.

9. At least one-eighth of an inch to be left between words.

10. At least three-quarters of an inch to be left between sentences.

CHAPTER VIII.

ON TEACHING ARITHMETIC.

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No person in these days will attempt to deny the usefulness of arithmetic as a science, or its importance as a mental discipline for schools. Number," says Dr. Mayo, "presents a most important field in which to develop and strengthen the minds of children. Its obvious connexion with the circumstances surrounding them, the simplicity of its data, the clearness and certainty of its processes, the neatness and indisputable correctness of its results, adapt it, in an eminent degree, for early instruction. Arithmetical exercises tend to give clearness, activity, and tenacity to the mind: many an intellect that has not power enough for geometry, nor refinement enough for language, finds in them a department of study, on which it may labour with the invigorating consciousness of success."

The many advantages here described are however not to be realised under the old system of teaching arithmetic, which included nothing more than the mere enunciation of rules for the mechanical performance of certain operations with figures. Indeed it is only of late years that works have appeared in which the reasons for the processes have been explained; and it is therefore not much to be wondered at that teachers, whose business rarely goes beyond the using of such educational books as are provided for them, have not given that attention to the subject which it deserves. The want of good textbooks explanatory of the principles of arithmetic cannot however, at the present time be urged. On this subject

it will suffice to mention the names of the excellent works of De Morgan, Hunter, Hind, Colenso, &c.

To enter fully into the details of teaching any branch of National School instruction is not the object of this book. All that is aimed at is to direct attention to the broad principles of method, leaving inexperienced teachers to find their own way, after they have, as it were, been once placed in the road. With respect to the subject now under consideration, this remark must apply with greater force than almost to any other. The principles of arithmetic, as investigated in Professor De Morgan's valuable work, occupy above 200 pages of closely-printed matter; it may hence be imagined how small, as compared with the whole, that portion must be which can be treated of in a single chapter. A few only of the most striking points connected with teaching the principles of arithmetic can be mentioned here.

The child's first exercise in number used to be counting, that is, repeating the words one, two, three, &c., in succession. Sometimes he was required to do this mentally, with abstract numbers only; at other times it was his task to count either his fingers or other objects which might be near him, pointing to the objects and using the words one, two, three, &c., as before. Thus he was often taught to attach to some particular object the name which it received in his counting, and in this way erroneous ideas as to the principles of number were instilled into his mind. The plan now adopted in the best infant schools is far more rational and interesting. An instrument called the Arithmeticon is generally employed, which consists of a wooden frame, traversed by twelve wires, on each of which are twelve sliding balls. Other contrivances are sometimes used, as collections of counters, beans, cubes, &c., but the Arithmeticon ap

pears to be upon the whole most convenient for the teacher's purpose, although it might be advisable for the sake of variety to adopt occasionally other modes of illustration.

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The manner in which the Arithmeticon is used may be briefly explained. The teacher moves one ball to some distance from the others, and pointing to it says ball;" the children repeat after him, one ball." Then he moves up another to its side, using the phrase, “two balls," which being duly repeated, another is added, and so on up to ten. By a similar process he is made to count up to one hundred, which is sufficiently high for the comprehension of a very young child. To make him the more familiar with the different numbers he is frequently called upon to move the balls for himself. To give him the notion of ordinal as well as cardinal numbers, he is required to change the phrase one ball, two balls, &c., to first ball, second ball, &c.

As soon as the child can count up to ten by this method, he is ready to commence addition and subtraction. Every possible combination in which the result will not exceed ten may be introduced to his notice by means of the balls, and the reverse processes of subtraction may also to the same extent be solved before his eyes. When he has become familiar with the addition and subtraction of these numbers, he may proceed gradually to higher ones, the teacher being careful that he does not get involved in calculations which are above his comprehension. When a question in addition has been proposed, the corresponding question in subtraction should follow. Thus after the question, How many are three and four? should follow the question, If three be taken from seven, how many remain? And if four be taken from seven, how many remain? Other combinations besides three and four, which make seven, may