be treated like any other breach of order. The natural punishment for the child who has written badly is to detain him and make him write well-though, as a general rule, it is unwise to set writing for punishment.

10. There is a 'personal equation' in writing as in other things. Hence a pen which has been used by one hand fails often to suit another exactly, and it is a good plan Pens

to let each pupil have his own pen. The nibs, however, should be uniform, and selected by the teacher. II. When the lesson is over, the pen should be carefully cleaned not on the pupil's clothes, or on his neighbour's. Cleaning Where slates are used, each child has (or ought to pens

have) a sponge, and the pen can be wiped on this. If slates are not used each child should be required to have a pen-wiper. Another method is to have the pens placed, as collected, point downwards in a jam pot or jar containing about half an inch of water, and then to have them wiped by a monitor. 12. There should be a piece of blotting paper in every copy-book, and the children should be made to employ it for two purposes only-to lay under the hand in order to keep the paper clean, and, when turning over the leaf, or at the end of the lesson, to dry the last lines written. The habit which some children have of employing the blotting paper for every few words is due to the carelessness of the teacher, or his inability to exact obedience. 'Smudging' is due to ignorance of the proper method of using.

Blotting paper

APPENDIX

MULHÄUSER'S SYSTEM OF TEACHING WRITING

Mulhäuser's method, though now little employed, deserves some mention as a serious and successful attempt to reduce the teaching of writing to a system. Mulhäuser, being appointed

inspector under the Geneva Commission of Primary Schools, found the writing very unsatisfactory, and came to the conclusion that it would continue to be very unsatisfactory, till the custom of imitating a complete copy was abandoned for something which deserved to be called a plan of instruction. Recognising that children cannot be expected to reproduce a complex whole till they have learned to reproduce the simple constituents, he carefully resolved the small letters into the following elements :—

1. The right line, down and up. 2. The curve, down and up.

3. The loop, down and up.

4. The crotchet (at the end of v, &c.).

The paper was ruled with horizontal lines crossed by parallel lines at an angle of sixty degrees. These rhomboids regulated the length, breadth, and slope of each letter, so that nothing was left to caprice or chance.

The small letters were taught in the following order :-i, u, t, l, n, m, h, p, c, o, e, a, d, q, i, g, y, b, f, r, v, w, k, s, x, z. (The capitals were not analysed.)

The teaching was divided into two parts, 'the study at the circles' and 'study at the desks.' In the first the elements were taught orally and illustrated on the blackboard ; in the second came the actual practice on paper.

ARITHMETIC

an art

EDUCATIONAL VALUE

ARITHMETIC is a science setting forth the general properties of numbers, and an art showing the application of those properties to computation. Studied as a science it is an Arithmetic a science and admirable training in abstraction, judgment, and reasoning. Practised as an art it enters into the daily life of nearly every civilised being, from the boy who sells matches in the street to the minister who controls the finances of a nation. It has, therefore, two incontrovertible claims to form part of any scheme of education. So strong did Plato consider one of them, that in his 'Republic' he advocates making the teaching of Arithmetic compulsory. He somewhat disparages the art, as being useful to merchants and shopkeepers only, but holds the science to be worthy of the highest powers of the philosopher.

We hold the science to be worthy of the highest powers of merchants and shopkeepers also, and of all who have dealings with merchants and shopkeepers. To treat Arithmetic as nothing more than a body of rules is a grave error, for the rules themselves can be applied with greater certainty and intelligence when the reasons for them are understood,' and the main business of teachers is to produce not 'lightning calculators,' but men and women with symmetrically developed minds.

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'En arithmétique surtout comprendre c'est apprendre,'

Arithmetic is of extreme value as a mental discipline

because

Its value as a mental discipline

1. It deals with pure abstractions.

2. Its operations are the simplest examples of perfect deductive reasoning; while under skilful guidance the learning of the rules is a good exercise in inductive reasoning.

3. It is absolutely independent of every other science.

4. The processes can be arranged in a logical chain, each link firmly connected with that which goes before and with that which comes after.

5. It induces a habit of concentrated attention. Allowing the thoughts to wander for an instant is like letting go the crank of a windlass; the work must be begun all over again. 'More haste less speed' does not apply to computation.

6. It induces a habit of accuracy. If there is a single mistake made all subsequent (and, indeed, all previous) labour is wasted.

7. It creates self-confidence. In many departments of thought there is no immutable standard; there is room for difference of opinion, but in Arithmetic a result is absolutely right or absolutely wrong, and the youngest child who reasons correctly and computes correctly may defend his answer against a senior wrangler.

8. It teaches to distinguish between what is essential and what is accidental. One problem may take a thousand forms, but the student must recognise the identity under every disguise.

ABSTRACTION

Of the foregoing reasons the weightiest is the first: Arithmetic is the simplest and most perfect of the Abstraction means readily available for training children to deal with abstractions, but in order that the means may be employed

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