INCIDENTAL TEACHING, by which I mean the practice of communicating general knowledge in an incidental and unsystematic manner, although not liable to the same abuse, still needs to be imparted with judgment and caution. It should never be forgotten, that in science, as well as in religion, there are many things which a "babe" in knowledge is "not able to bear." Some teachers, in the plenitude of their zeal to impart, or rather perhaps in their anxiety to display, are accustomed to cram mere children with a kind of food which their tender minds can never digest. This is on every account highly objectionable. The mere accumulation of facts in the memory is of trifling value, if unaccompanied by the development and training of the faculties. A mind filled with the results of other men's research, and unacquainted with the steps and processes of the proof, may, as Beattie remarks, fitly enough be compared to a well-filled granary, but bears no resemblance to the fruitful field, which multiplies that which is cast into its lap a thousand fold.

WRITING. On this subject a very few hints must suffice. 1. Bear in mind, that your pupil's success mainly depends upon the attention paid to him when first beginning to write. It is then that habits are formed, which he will find it afterwards almost impossible to alter. 2. Let writing on slate precede the use of. pen and paper. The forms and combinations of letters will most read

ily be attained in this way; and when that is done, no great difficulty will be found in accustoming the pupil to the use of the pen. 3. Let not the pupil attempt what is termed "small hand," until he can write a good bold text hand with neatness and accuracy. 4. When he comes to learn the current or running hand, let him be taught that neither legibility nor elegance will do without expedition. Accustom him, therefore, to write

freely from dictation.

The most approved rules for preserving a right position of the body, for holding the pen, and for effecting the various movements and combinations by which the letters are to be executed, though highly important for you to know, would yet be out of place here. For these particulars you must study the best treatises on the art of penmanship.

The only other points to which it is necessary for me to allude, are these. 1. Materials for writing should be of good quality,—it is not economical to use inferior articles. Steel pens, which may now be purchased at a very reasonable rate, are in every respect preferable to those which are made from quills; they are cheaper, they need no mending, and they execute the letters with greater neatness and precision. 2. Every line should be examined as it is written. The habit which prevails in some schools, of writing a page before examination, is highly pernicious; quality

in writing should at all times be regarded rather

than quantity. ARITHMETIC. In teaching arithmetic, regard must be had to the same great principles which have already been laid down in relation to other branches of knowledge. Nothing must be considered as done, that is not thoroughly comprehended; a meaning and a reason, must be attached to every step of the process. Begin, therefore, first of all, by referring the pupil to sensible objects, and teach him to compute what he can see, before you perplex him with abstract conceptions. A mere infant may in this way be taught to add, subtract, multiply, and divide, to a considerable extent. Apparatus for this purpose, of various kinds, is already in use; but what need have you of apparatus? Every thing around you and about you may be made subservient to this end.

It will not do, however, to stop here. The mind must before long be accustomed to abstractions, and therefore the sooner you can teach a child to convert this tangible arithmetic into abstractions, the better. You will do this to some extent, by drawing its attention to what has been called, aptly enough, "the process of disentanglement."

"You take a skein of ruffled thread; and, if you can find the end, you carefully draw it through all its loops and knots, and in a few minutes it is unravelled.

Now just in this manner must the minds of children be exercised in finding out the truth of some abstract proposition. To a mind not so exercised, a very simple question will be extremely formidable. How often have not only children, but their elders, been puzzled by the simple question, 'What is two-thirds of three-fourths of any thing?' Now to get at the truth required here, it will be seen how necessary it is to get at that part of the proposition that can be laid hold of; that is to say, the part to which the mind can attach, from its being something known: it would in this case, of course, see first that three-fourths were three-quarters; and then it would soon discover that two quarters, the two-thirds of them, must be half. We give this and other illustrations, to show that, by applying the analytic process properly, a very small quantity of real knowledge will produce a very large proportion of arithmetical power; therefore it is not so much the knowledge that may be fixed dogmatically in the mind, that will serve your purpose, as that which the mind itself evolves in its process of elaboration. It will be the business of the teacher to help the mind to create its own strength, and this he will do by subjecting it to wholesome and judicious exercise."*

Take care that your pupil never proceeds to a second example in any rule, until you are quite sure that he thoroughly understands the first. No matter what time may be consumed upon this introductory effort,―he must not be allowed to go on with

*Educational Magazine.-Method of Teaching Mental Arith

metic.

partial and inaccurate notions of what he is about. You will often be deceived in this particular. It is necessary, therefore, when a result is obtained, to require an explanation of every step by which it has been reached; to demand why that particular course, in preference to any other, should have been pursued; and to ascertain whether the pupil so far understands the reasons of the process, that he could, if he chose, in conformity with those reasons, adopt other modes of arriving at the same conclusion.

"Two persons never have exactly the same associations of ideas; they never associate their ideas in exactly the same order. The consequence is, that no two persons think of the same proposition alike. Hence, a proposition expressed in certain terms, may be very clear and intelligible to one person, and very obscure, or altogether unintelligible, to another; and perhaps, with a very slight change of terms, the case would be entirely changed. It would be intelligible to the latter, and unintelligible to the former. An explanation which is very clear and lucid to one, will often convey no idea at all to another. When a proposition is made for two persons to reason upon, they will often take it up and manage it very differently in their minds. When the subject is such as to admit of demonstration, as is the case with mathematics, they will generally come to the same conclusions. But on other subjects their conclusions will sometimes agree and sometimes not. There are several valuable practical results to be derived from this. First, it is very important that the teacher should