land is north, east, west, or south from them. They should take such views on the globe, that they will know at once the direction or point of compass of any place on the earth. If the teacher will direct the attention of the class to this particular point, they will learn the relative situation of countries in a short time. This is necessary to be known on many accounts. News is coming from every quarter every day; and when a place is mentioned, the position and direction should be instantly conceived. I have often seen scholars, who had been "through the geography," and yet did not know whether Maine was east or south; Virginia, south or west. This ignorance of direction is great, and should have the especial attention of the teacher. The distances of places, likewise, should be taught; the length and breadth of the state; the number of miles to the most noted places, and the distances between them should be familiar to the pupil. This is seldom the case; but it is useful and important knowledge. The boundaries of the states should be so familiar to the mind that the position of each one would occur immediately. A map of all the countries in Europe should be drawn, and the geography of each attentively studied, as the scholar may have time. Asia should come next, followed by Africa. The particular attainments and age of the pupil must direct the discriminating teacher. No directions but those which are very general can be given.

I would, however, earnestly recommend the inductive method which I have described. I am satisfied, that from the constitution of the mind, and the nature of the study, it is the best. It is likewise adopted by our most experienced teachers; and I hope will soon be received wherever geography is taught.

SECTION XIV.

THE BEST METHOD OF TEACHING ARITHMETIC.

FROM this science very little is obtained in our district 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 but 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 school, but from their own invention, and the rewards of experience. There is in the country but a small quantity 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. After making such observations as justify these assertions, and reflecting on the misapplication of so much time and effort, it is natural to inquire why this is so.

Are the books in use filled with unintelligible rules and impracticable examples? Do the teachers omit the practical application of the principles they teach? or do the scholars but half know what they have the credit of having learned? To each of these inquiries we may reply, to a great extent, in the affirmative. Books now in use at a little distance from cities and large villages, in which, indeed, some improvements have appeared within a few years, are blind and difficult to the scholars, and present the art of calculating by numbers in an unnatural, discouraging form. The magnitude of the examples is so great that the child forms no correct idea of the numbers which constitute them. The reasoning from them, therefore, the child cannot comprehend. These examples, likewise, are abstract numbers. The child's mind is not prepared for perceiving abstract numbers and quantities with sufficient clearness and distinctness to be able to connect them with practical examples, the only use any one can make of them which is of any value. The pupil's mind is perplexed and wearied with these large, unmeaning examples, which he considers altogether useless, and without any practical connexion whatever. This is the first idea

which is obtained from the arithmetic; and it generally goes along with them until they relinquish the unpleasant study. In most cases the figures are new to the child, and the quantities they represent he can form no conception of; and a darker, more disagreeable study, the pupil hopes he never will have to undertake. Such is the commencement (from the nature of the first lessons of the books now in use) of the study of arithmetic. What the child dislikes at first, it seldom becomes fond of afterwards.

The first step being but imperfectly understood, the pupil is not fitted to take the second, and consequently, from being unable to help himself, requires the aid of the teacher. The teacher's explanations do not assist him, for he is not prepared for them on this point-he does not understand the first step. The instructer supposes the pupil stupid, and the pupil thinks that he has attempted what is too difficult for him to comprehend. The third step is tried, but with less success, for in the science of numbers the after steps always require a knowledge of those which have gone before. In this manner the scholar is forced a short distance into the arithmetic without knowing where he is, or what he is doing. The whole is a mystery, for in reality nothing has been learned.

The teacher requires the scholars to commit the rules to memory, but never gives or demands a single reason for one of them. The pupil has not understood the examples-knows nothing about

Q

the facts upon which the rules are founded; and of course does not understand the rule, or see any direction or application in it. The teacher is peremptory for the memoriter recitation of the rule, and the scholar, after many accusations of his memory, and much protracted labour, is able (from the mere association of words, for he has not, during the hundred readings, got an idea) to repeat the rule without the book. I have frequently met with some of the larger scholars who could promptly and accurately repeat every rule in the arithmetic, and yet not able to apply in practical life the most simple one, nor did they know one reason for any of them. How can they expect that such knowledge will be of any use? The great thing aimed at with teachers, seems to be the ready recitation of the rule from memory, rather than the ready application of it to practical pur

poses.

The tables, also, which ought to be committed before any progress is attempted, are either entirely overlooked, or less than half learned. The child is at work in the rule of multiplication, and does not know how many four multiplied by four make. Every time he multiplies he is sent to the multiplication table. This constant reference to that which he ought to know, interrupts his operations-he forgets the last step he took, and on examination the sum is wrong. In this manner he goes through the rule; and still ignorant of the table. He is, perhaps, ciphering in the compound