PART I. child who is made to fill page after page with rows of straight marks, that look so blank and cheerless though done ever so well, has, and can have no pleasing associations with his work. The practice of beginning with making inexpressive marks, or with writing unintelligible words, bears some resemblance, in its lifelessness, to that of learning the Alphabet. Each exhales torpor and stupidity to deaden the vivacity of the worker.

"Again, I have found it an almost universal opinion with teachers of the art of writing, that children should commence with large hand rather than with fine. The reason for this, I suppose to be, that where 1 the letters themselves are larger, their differences, and peculiarities are proportionally large; hence they can be more easily discriminated, and discrimination must necessarily precede exact copying. So to speak, the child becomes acquainted with the physiognomy of the large letters more easily than with that of the small. Besides, the formation of the larger gives more freedom of motion to the hand. Now, in these respects, there is more difference between the objects used in drawing and the letters of a large hand, than between the latter and a fine hand; and therefore the argument in favour of a large hand applies with still more force in favour of drawing.

"In the course of my tour, I passed from the countries where almost every pupil in every School could draw with ease, and most of them with no inconsiderable degree of beauty and expression, to those where less and less attention was paid to the subject; and, at last, to Schools where drawing was not practised at all; and after many trials, I came to the conclusion that, with no other guide than a mere inspection of the copy-books of the pupils, I could tell whe

ther drawing were taught in School or not; so uni- PART I: formly superior was the hand-writing in those Schools where drawing was taught in connexion with it.On seeing this, I was reminded of that saying of Pestalozzi, somewhat too strong, that without drawing there can be no writing.'

"But suppose it were otherwise, and that learning to draw retarded the acquisition of good penmanship, how richly would the learner be compensated for the sacrifice. Drawing, of itself, is an expressive and beautiful language. A few strokes of the pen and pencil will often represent to the eye what no amount of words, however well chosen, can communicate. For the master architect, for the engraver, the engineer, the pattern designer, the draughtsman, moulder, machine-builder, or head mechanic of any kind, all acknowledge that this art is essential and indispensable. But there is no department of business or condition of life, where the accomplishment would not be of utility. Every man should be able to plot a field, to sketch a road or river, to draw the outlines of a simple machine, a piece of household furniture or a farming utensil, and to delineate the internal arrangement or construction of a house."

tic.

4. The importance of Arithmetic to the common Arithemeinterests of life can scarcely be over-rated. As a means of mental discipline also, being the lowest and simplest branch of mathematics, Educators have attached the highest importance to the study of it. It was a saying of Charles XII. of Sweden, that he who was ignorant of the arithmetical art, was but half a man; and Lord Bacon has said "if a man's wit be wandering let him study mathematics."Viewed either as an instrument of mental discipline or of practical utility, Teachers of the greatest ex

PART I. perience agree that it should be commenced early-as early as reading and writing.

Nay, it is held to be less difficult for a child to learn to count than to learn to read, while it contributes more than reading to strengthen and discipline the mind. But the manner in which it is too often taught, renders the study of it an insupportable task, and not unfrequently an object of bitter aversion, without imparting any useful knowledge.

There are doubtless many exceptions; but the remarks of the Author of the District School, are scarcely less applicable to Canada than to the State of New York: "From this science very little is obtained in our District Common Schools, which is of any practical use. There is much compulsive, uncertain, and laborious study of arithmetic; but it is often in vain, from the manner in which it is taught, since the scholar gets very little in return for his labour that is valuable or practical. Those who have received nothing more than a Common School education, obtain their practical knowledge of the science of numbers, not from their instructions or study in the School, but from their own invention and the rewards of experience. There is in the, country but a small part of arithmetic in use which came from the Schools; necessity has taught the people what they ought to have learned at School when young, and when they were wasting so much time and money to no purpose. The pupil learns nothing thoroughly; what he does not understand he feels little or no interest in; he sits with his slate before him most of the day, gropPerhaps scarcely any

ing, guessing, doing nothing.

two pupils are studying the same rule, or using the same book, instead of being formed in as few classes as possible."

The Teacher has not time to hear each pupil sepa- PART I. rately, and to explain and illustrate to each the nature of the rule or operation, even if he be competent and disposed to do so. The consequence is that many who have, as the phrase is, "gone through the Arithmetic," are unable to perform the simplest calculations in the transactions of business; or they do so with hesitation and uncertainty.

method.

"In Teaching Arithmetic," observes the Secretary Sensible of the British and Foreign School Society, in his much valued work on the Principles of Teaching, "nothing must be considered as done, which is not thoroughly comprehended; a meaning and 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, substract, 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? Everything 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 the child to convert this tangible arithmetic into abstractions the better."

thod.

The practice of the best Schools in other countries Intellecsuggests that children should first study Intellectual tual mearithmetic. Its influence in awakening the curiosity of pupils, in exciting their mental energies, and training them to devise means for performing more intricate exercises on the slate, can scarcely be conceived by those who have not witnessed the results. In the Model Schools attached to the Dublin Normal School

PART I. of the Irish National Board, I witnessed arithmetical operations performed by small boys and girls with the rapidity of thought, in addition, subtraction, multiplication and division, fractions, proportion, interest, discount, &c. I witnessed exercises equally surprising in Scotland, France and Germany. I will select two examples,-the one from Mr. Wood's account of the Edinburgh Sessional School; the other from Mr. Mann's Report on Prussian Schools.

How taught in Edinburgh.

Mr. Wood says: "It was in arithmetic we first succeeded in kindling that ardour, which has since diffused itself through every other department of the Institution. Arithemetic, which had hitherto been one of their dullest occupations, now became to the scholars a source of the highest interest and amusement. They, by degrees, obtained a rapidity of movement in this Art, which we should have previously accounted quite incredible, and along with that celerity a proportional accuracy in calculation. But this was not all. They obtained at the same time, what in our opinion, is infinitely more valuable than any arithmetical attainment,-that general energy and activity of mind which we find of so much service in the introduction of all our subsequent improvements, and which we doubt not has in a great measure formed the character of many of them for life." "Those who have not had an opportunity of witnessing the perfomance of our children in mental arithmetic, may form some estimate of it, when they are told, that on more than one occasion, when three or four of our best arithmeticians were employed to answer one question in every page of the 'Ready Reckoner', and selected from every variety of column in that page, (that is to say, the first question being 13 yards at a farthing, the second 54, at a half-penny,