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Examples for Addition.

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an incorrect result; for that you can do without any attempt at adding the several columns. Rapidity and accuracy together will be very desirable. You may now write.” (Dictate either of the following :) 2 4 8 7 5

7 8 5 64 9 5 6 2 8

9 6 8 7 5 7 6 4 39

6 3 9 8 7 8 7 5 4 2

4 9 5 6 3 9 4 3 87

87 45 9 62 9 5 4

9 5 3 8 6 457 68

7 4 3 2 1 89541

9 7 487 9 7 8 6 5

7 8 9 6 5

As soon as you have repeated the last line, say, distinctly, “Add,and be ready, with your watch in hand, to note down the time required, by each, in obtaining an answer. After all have performed the work, call for answers, and then name the time occupied by each. If you have a liberal supply of blackboard, let a class occasionally take chalk, and perform similar operations upon the board. This will afford you a better opportunity for pointing out defects in figures and columns.

Exercises like the above will yield good results. If you will devote six or eight minutes, daily, for ten days, at the expiration of the time you will find that most of your pupils will obtain correct answers in about one half the amount of time at first required. When you commence, the time used in

Do not render too much Aid.

obtaining the answer to a sum having as many figures as there are in the examples given, will vary from one to three minutes; but at the end of the time named, you will find that many will be able to perform similar examples in thirty seconds, and less. And, moreover, you will find that the skill and accuracy gained here will be of service in all the more difficult operations of the Arithmetic. Of course, the number of figures and columns may be varied from time to time. It will be well, often, to give a single column, of some twenty or more figures, for the double purpose of giving discipline in addition, and training the eye in making straight columns of figures. The same general method may be adopted with examples in division, subtraction, multiplication, fractions, etc.

Do not be satisfied with the mere verbatim repetition of the rules of the Arithmetic, and the mechaical performance of the questions under the several rules. Vary the questions, and ask many not contained in the book. Do not abandon one rule or principle, and pass to another, until the former is perfectly clear. Move “ step by step,” never forgetting that practice tends to make perfect.

Do not render too much Help in the Performance of Problems. It will be necessary for you to exer cise much judgment and discretion on this point. Some aid you must render; but be very careful and not give too much or too soon. One prominent object, in all school exercises, should be to train pupils

Give Encouragement.

to overcome difficulties, to surmount obstacles. In no branch will this hold more true than in that under consideration. It will scarcely ever be well for you to solve a difficult problem for a pupil. Give him one or two hints in the right direction, and then encourage him to persevere. If you can once succeed in arousing a true spirit of perseverance, you will find but little difficulty. “My teacher says I can do very hard problems if I will try long enough,” said James Diligent, “and if I can, I know I will; for I can try as hard and as long as any one." With such a feeling, but very few insurmountable obstacles will be found. Give to your pupils as mottoes, Labor omnia vincit, and Nil desperandum.

Encourage your Pupils. - Utter words of cheer and expressions of kindly interest, and lead your pupils to feel that you are their sincere friend, and that you require them to learn hard lessons because you know it will do them good to learn such lessons. The following incident illustrates the power of encouraging words.

The teacher of a large school had a little girl under her care who was exceedingly backward in her lessons. She was at the bottom of the class, and seemed to care but little about what had passed in it.

During the school hours, singing was sometimes employed as a relaxation, and, noticing that this girl had a very clear, sweet voice, her teacher said

Illustrative Anecdote.

to her: “Jane, you have a good voice, and you may lead in the singing.”

She brightened up, and from that time her mind seemed more active. Her lessons were attended to, and she made steady progress. One day, as the teacher was going home, she overtook Jane and one of her schoolmates.

“ Well, Jane," said she, "you are getting on very well at school. How is it that you do so much better now than you did at the beginning of the half

year ?"

“I do not know why it is,” replied Jane.

"I know what she told me the other day,” said her companion.

66 And what was that?" asked the teacher. “Why, she said she was encouraged."

Yes, there was the secret, — she was encouraged. She felt she was not dull in everything; she had learned self-respect, and thus she was encouraged to self-improvement.

Take the hint, dear friend, and try to reach the intellect through the heart. Endeavor to draw out the dormant faculties of your scholars by discriminating culture and well-timed commendation. Give them the credit whenever you can, and allure them with hopeful words. Many a dull-minded child has been made irretrievably stupid by constant faultfinding or ungenerous sarcasm. And, on the other hand, how often has a genial smile or an approving remark awakened into new life some slow-learning pupil.

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Make Explanations Clear.

Make your Explanations plain and intelligible. It is not unfrequently the case, that teachers fail to make their explanations sufficiently simple. At all times strive to awaken or impart ideas, and not merely to give words. Said a child to her teacher, “ Will you please tell me why I carry one for every ten ? "

“ Certainly,” said the teacher, pleasantly, “it is because numbers increase from right to left in a decimal ratio.” The child went to her seat, and, with a sad expression, sat repeating the words just quoted. She did not comprehend the answer of her teacher, and felt disappointed. The words 66 decimal ” and “ ratio” she did not understand. She sat thinking for a while, and then, utterly discouraged, she put aside her book, saying, “I do not like arithmetic ; I cannot understand it."

See to it, my friend, that your pupils do not suffer in this way. When you give illustrations or explanations, have them such that they will convey to the pupil's mind the ideas or information intended by you and desired by them. As far as may be, use illustrations for the eye. . Long measure, square measure, cubic measure, etc. may be illustrated by drawings and blocks. Let me suppose you ask a pupil the difference between ten square miles and ten miles square. A word answer may be given without conveying any clear idea ; but if you go to the board and draw a figure, you may make all plain and clear. Let the following be used, considering each square the representative of a square mile :

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