Third Year in Arithmetic.

AIMS.

I. To teach all the fundamental operations of numbers to one hundred.

The operations to this limit should be absolutely mastered, and the pupils should be able to prove their knowledge in written as well as in oral exercises. Certainty of knowledge is the end to be sought. Never be satisfied until it is gained.

II. To teach notation and numeration through two periods.

Arabic notation is meant of course, but Roman notation should be extended to one hundred, and the values of D and M. may be given. See that every pupil is able to read and write the numbers in those two periods with the utmost readiness.

III. To teach the tables of common weights and measures not yet learned.

In addition to the tables of Avoirdupois, Troy and Apothecaries' Weight, and Long, Square and Cubic Measures, the denominations of United States and English money, and the terms dozen, gross, hand, fathom and chain, should be taught. A clear conception of the meaning and use of the various units of magnitude must be acquired before the tables are memorized.

IV. To teach the reduction of the simple fraction already learned. Give the pupils exercises requiring halves to be changed to fourths, sixths, eighths and tenths; thirds, to sixths and ninths; fourths, to eighths; fifths, to tenths; and the reverse. Continue the use of objects until the fractions are clearly understood.

V. To teach the multiplication table to one hundred and forty-four. In the beginning require pupils to make their own multiplication tables, and test their knowledge of them every day. Both oral and written drills on these tables must be continued until the pupils can recite any table, regularly and promiscuously, and give the product of any two single numbers without the slightest hesitation."

VI. To teach a concise form of analysis of the problems solved. Power to reason clearly and logically, as well as to calculate accurately and rapidly, must be developed. Pupils should be trained to explain and illustrate to the teacher, rather than the teacher to them. What is done for a pupil is known by what he can do for himself.

STEPS.

1. Finding the product of any two single numbers by addition; for example, the product of four and six is, 6+6+6+6, or 4+4 +4+4+4+4, or 24.

2. Memorizing the product of any two single numbers, so it can be recalled instantly.

3. Showing that division is the inverse of multiplication; for example, 4 X 3 = 12; 12÷3=4.

4. Learning to explain in a clear and logical manner each step taken in the solution of a problem.

METHODS.

1. Have constant drills in adding 2's, 3's, 4's, etc., and numbers in vertical and horizontal columns. Introduce examples in this order: First, those consisting of three, four, five, etc.; numbers of one place each, as 9+8 +7, 8+3+6+ 9, etc.; second, one number of two places, and one by one, as 16+8; and third, numbers of two and three places, as 21+ 34, 312+243, etc.

2. Teach subtraction, step by step, by taking up examples in the following order: Finding the difference, first, between single numbers, as 95; second, when there is no "borrowing," as 45-32; third, when there is "borrowing," as 14-9; and fourth, when there are ciphers in the minuend, as 600—498.

3. Multiplication and division may be taught in the following

4. Limit the multipliers and divisors to numbers consisting of one figure each.

5. Use addition and subtraction in the same examples as soon as it can be safely done.

6. Devices for drill, like the following, can be used with profit: 9, 4, 1, 3, 0, 6, 5, 8, 2, 7.

Add 4 to each of the above numbers, add 5, add 1 X 7, add 21÷3. Subtract each from 12, from 8 X 2, from 20. Multiply each by 3, by

7. by 4+ 5. Divide 36 by each. Tell what number must be added to each to produce a given number. How much more to one than to another?

DIRECTIONS.

1. Give frequent drills in rapid calculations.

2. Demand neatness and exactness in blackboard work.

3. Give a large number of examples to test what has been taught. 4. In writing numbers require units to be separated from thousands by a comma.

5. Arouse every mind to its fullest activity.

CAUTIONS.

1. Don't fail to give plenty of slate-work.

2. The analysis of examples should be short and clear. 3. Remember that unnecessary help always weakens. 4. See that all perceptions are clear and accurate. 5. Frequent reviews of previous work must be given. SUPT. T. J. MITCHELL.

Charlotte, N. C.

Cultivating the Power to Think.

Special attention has been given to the training of pupils to the habit of close and continued application. In those schools in which there are two or more grades each grade recites by itself. If a school has only one grade it is divided into sections, and each section recites separately. If it be a grammar grade, it is divided into two sections; if a primary grade, it is divided into two or more sections. Thus the pupil is given more time for study, for patient personal endeavor, for wrestling with difficulties single-handed, for overcoming obstacles alone and unassisted; in short, for learning to think, and, above all, for feeling the intense satisfaction and exquisite delight that come from the consciousness of personal effort persistently put forth and successfully directed. We learn to think by thinking, and to the attainment of this object no royal road has yet been discovered. The old-time ungraded district school had one advantage that did much to compensate for the disadvantages of such an organization. It compelled the pupil to do his own thinking. The teacher had not time to do it for him. To teach a child to think is no easy task. It is much easier to do the thinking for him. And just here, in my judgment, is the danger to our modern system of

graded schools. And the more complete the grading the greater is the danger. There is a constant temptation to the teacher to substitute the pouring-in process, with its shallow and ephemeral results for the substantial and enduring work of mind-training. No teacher of a single grade is ever free from this temptation. It is a constant obstacle to the achievement of the highest success. Years of careful observation have confirmed me in this judgment. The difficulty may be remedied in two ways. Two grades, or two divisions of different grades may be assigned to each teacher, or schools of a single grade may be divided into two sections. Both of these plans of organization are now in operation in our schools, and we shall have abundant opportunity to observe them and make choice between them.-Supt. Thomas Emerson, Newton, Mass.

A boy cannot be noisy, and ill-bred, and careless in his manners all through his youth and then suddenly blossom but into a proper gentleman as he becomes a man. Good manners come to no one in a day. They are the result of long cultivation and much painstaking.

THE STUDY OF THE CLASSICS.-A well-known educator, in a recent paper before the Teachers' Association of this State, on the "Use of Studying the Ancient Classics," maintains, and truly, that in studying Latin and Greek the student is learning to express his thought clearly, exactly, and forcibly. He says: "The very element he works in is thought; his daily tasks are a constant familiarizing of his mind with the instruments which thought must use, the laws which thought must obey in all its operations in every conceivable sphere. He is learning not merely the language which is before him and its several parts; in a most important sense he is also learning to think." He further holds: "It were scarcely an exaggeration to say that the chief object of education is to enable a man to think clearly and to express his thought forcibly. The educated man is largely distinguished from the uneducated by correct thought, and clear, forcible speech. * * * Such training," he concludes, " is, therefore, elementary and practical in the highest degree. It subserves the purposes of human life always and everywhere. The scientist needs, above all things, this very precision of thought and expression, both to guide him in his researches and to aid him in conveying to others the results of his researches. The business man needs this facility

rightly to lay and adjust his plans, and successfully to enlist the cooperation of others to secure his end. And he who has the most of this acquired power will succeed the best.-Educational Notes.

A MIGHTY SENTENCE.-The opening sentence of the Bible, "In the beginning God created the Heaven and the earth," contains five great universal terms, and speaks of as many boundless totalities— God, Heaven, earth, creation and the beginning. It is, perhaps, the most weighty sentence ever uttered, having the most gigantic members. In its comprehensive sweep it takes in all past time, all conceivable space, all known things, all power and intelligence, and the most comprehensive act of that intelligence and power. This sentence is a declaration on nearly all the great problems now exercising scientists and philosophers.-The Independent.

THE BACK SEAT.-In a back seat sits a young miss whose poor scholarship has won her that position; a position where such an unenviable standing is best preserved; a position full of temptations, and quite removed from that magnetic circle which surrounds the teacher's desk, and throws a strong protective influence about the elect.-E. E. Kenyon.

It is comparatively easy to control the outward behavior of children and compel them to seem intent upon their work; but subtle indeed is the power that will chain their thoughts to labor.

THE greatest man is he who chooses the right with invincible resolution; who resists the sorest temptations from within and without; who bears the heaviest burdens cheerfully; who is the calmest in storms, and whose reliance on truth, on virtue, on God, is most unfaltering. Channing.

EDITORIAL PARAGRAPHS.

THE STATE NORMAL SCHOOL at Farmville.-We have received the catalogue of this institution for the session 1885-6. It shows the school under the control of Hon. W. H. Ruffner, Principal, and a corps of nine teachers. The number of pupils in attendance foots up 172-97 in the normal school proper, 36 in the preparatory