The copies and writing books should always be prepared by the instructer out of school; a particular hour should be set apart every day for writing; and neither teacher nor pupils should attend to any thing else while the writing is going forward.

Although it may cost considerable time and attention at first, it will ultimately occasion a great saving of both, to teach children to make their own pens.

ESSAY VI.

Arithmetic.

"Arithmetic is the easiest, and consequently the first sort of abstract reasoning which the mind bears or accustoms itself to; and is of so general use in all parts of life and business, that scarce any thing is to be done without it."

Locke.

There appears to be a difference of opinion among teachers, at the present time, as to the best mode of instructing in arithmetic. One class proposes to lay aside all the rules found in our common books of arithmetic, and solve every question by what they call mental arith, metic, or by an equation. They pronounce even the rule of proportion to be an useless incumbrance, and such rules as Barter, Loss and Gain, &c., as worse than useless. Others are for retaining all the old rules, rejecting mental arithmetic and all compendious modes of solv, ing questions, and performing every operation with the slate and pencil according to the letter of the rules. The former bring philosophy and science to support their opinions, and the latter affirm, that for the practical purposes of business, their method is the best. We are inclined to believe that the truth lies between the two extremes. Mental arithmetic is an excellent exercise for the reasoning powers, and is necessary for a complete education; and on the

other hand, the old fashioned rules furnish many applications of the principles of arithmetic which are useful for the practical purposes of life.

In proposing a system of instruction in this branch of education, we would by all means recommend the explanatory method; on which we have already offered some remarks. This may be used with very young children; and a person who has never seen it attempted would be surprised to find what progress may be made at a very tender age.

In the first stage of instruction, it is necessary to have recourse to sensible objects. Beans or counters will answer tolerably well, but the Abacus, or Numerical Frame, is more convenient. This instrument consists of a square wooden frame with ten horizontal wires, and ten sliding balls of wood on each wire, as represented in the following figure:

operations in the simple rules, to those children who are too young to form an abstract idea of number, without the assistance of sensible objects. When they have become in some measure familiarized with the simplest operations, and begin to remember their results, they should be exercised with operations on abstract numbers, and required to retain their results in the memory. In other words, they should acquire a perfect knowledge of the tables of Addition, Subtraction, Multiplication, and Division; and the contrivances and operations already mentioned, furnish the means for acquiring this knowledge in an easy and highly interesting manner, instead of the irksome labour of committing it to memory from a single piece of paper, divided into squares, and marked with figures.

When the pupil has become tolerably familiar with easy operations in the simple rules, he should be exercised with a variety of applications of these rules mentally, i. e. without the use of the slate. He should then be taught to read and write numbers, and required to perform the same operations on the slate.

He should next be taught the operations in Vulgar Fractions mentally, and afterwards with the slate. The same method may be pursued with great advantage through the compound rules, and indeed through all the rules contained in our common arithmetics.

The system of interrogation and explanation on all the principles and applications of arith

metic should be thoroughly pursued, with reference to the development of the faculties of reasoning and observation; and the old custom of keeping a manuscript should by no means be laid aside, while it is important to cultivate habits of method in business, and systematic arrangement of knowledge.

Instructers should attach great importance to arithmetic, as a discipline for the mental powers. They should read the best authors, in order to become thoroughly acquainted with the subject; and they should carefully examine and train their pupils in the principles and reasons, the why and the wherefore, of every rule and operation. It It is not enough that the pupil should be able to do this or that sum in the book, or to say that he has done any number of sums; but he should be so thoroughly versed in each and every principle of the science, as to refer any given operation to its proper rule or principle, and solve it without referring to the book or the teacher.

Arithmetic, taught in this manner, is one of the happiest means of training the mind to "clearness of thought and force of reasoning." "The mathematical sciences," says Dr. Watts, "and particularly arithmetic, geometry, and mechanics, abound with these advantages; and if there were nothing valuable in them, for the uses of human life, yet the very speculative parts of this sort of learning are well worth our study; for, by perpetual examples, they teach us to conceive with clearness, to connect