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Exercises like the following—in which the whole
school may take part — will be found of great value, and a few minutes of daily practice will, in a short time, lead to a wonderful degree of rapidity and accuracy in mental operations. In these exercises, the pupils are expected to follow the dictation of the teacher, so that they will be able to give the answer the instant he pauses. The terms plus, minus, and square should be well understood.
The above may be varied and extended almost indefinitely. I merely give the hint. In treating of written arithmetic it will not be necessary for me to go fully into the details of teaching the various rules and principles. Most of the modern textbooks on this subject usually contain good formulas and a sufficient number of rules. I have sometimes thought that the rules and explanations, the formulas and directions, were too numerous, – leaving too little for the pupils to accomplish, and thus failing to secure that mental growth which is so essential to true progress.
* In dictating this, the teacher would say, Square 5, add (or plus) 6, multiply by 3, divide by 2, subtract (or minus) 5, divide by 8, add 6, multiply by 5, – how many ?
Avoid undue Haste.
It will be my aim to caution you against two or three of the common errors of teachers, in relation to arithmetic, and, in passing, to give a few hints touching miscellaneous exercises that may be found useful, for the purpose of general drill and review.
Avoid undue Haste. — Many teachers seem to think that, if they can only say they have “taken a class through the text-book,” they will have accomplished all that is required, - and under this impression they “take ’’ their pupils along at a surprisingly rapid gait. Scholars, too, seem to imagine that the degree of their proficiency will be augmented by every new page “gone over’’ in the textbook, and they “hurry on,” impatient of delay. And, in addition to this, parents and committees often “harp on the same string,” so that, with all, the amount “passed over * is made the only criterion of the teacher's ability or of the pupil’s progress.
I once visited a school in which the feeling just spoken of greatly prevailed. It was a showy school, and, to a superficial observer, might present a good appearance. The teacher was one of your wordy men. He blew his own trumpet loud enough, and long enough, and, I am sorry to say, he deceived many whose ears had never been properly tuned to such blasts. Many supposed he kept an excellent school, and his pupils considered themselves of the ne plus ultra order. In speaking of his first class, he said: “This is the finest class you ever
A Visit to a School.
saw. I have taken this class over more ground than any other class was ever taken in the same time. I took them through Davies's Arithmetic in three months, and they can do anything within the covers of that book.” This was said in that positive manner which would be sure proof to some that the statement made was true. Without in the lea: ; Questioning the truth of what had been said, I remarked: “That is a very intelligent class, and they must have been well trained to accomplish so much.” “O yes, I have done well by them, and they have done well for themselves.” “Are you willing to have me ask them a few questions : ” said I. Somewhat “taken aback ’’ by the question, he hesitated a moment, and then said: “Why, yes, I have no objection, but I don’t know how they will get along with questions from a stranger.” “My questions shall not be difficult,” said I; “I do not wish to puzzle or trouble them.” I then proceeded to ask a few questions on the ground rules, and the answers were mostly wrong or very defective. I gave them a few examples in addition, subtraction, etc. These were performed very slowly, and not more than one in ten gave the correct answers; and not a single one could give a clear reason for what he did. I passed to fractions, and there found a total lack of knowledge. The same was true of interest, discount, mensuration, &c. They actually knew less than any intelligent boy of the same age would know after a week’s proper instruction; and yet they really felt that they were quite expert in arith
metical operations. The teacher undertook to console himself, and satisfy me, by attributing their seeming ignorance to diffidence before a stranger; but a more self-conceited class I never saw. The pupils seemed to feel almost insulted that I should question them in the simple rules, and yet the result showed that they had not been properly or thoroughly drilled on those rules. Surely, thought I, you have been “taken through '' the book; and a hard task will it be to take self-conceit away, and cause you to see your true position as arithmetical “know-nothings.” Now, my friend, let me say to you, “Make haste . slowly.” Be thorough. Teach one thing at a time, and be careful that you teach it properly, and that your teaching is understood. Be not ambitious to “take your pupils through the book,” but rather aim so to teach and train them that they will be able, if necessary, to complete the book without the aid of a teacher, after they have been fairly started upon the right track. .
Be sure that the simple or ground Rules are thoroughly comprehended. — Most teachers pass over these too rapidly. We frequently meet with persons who can, somewhat readily, perform many of the more difficult problems of arithmetic, and yet are very moderate and unreliable in adding columns of figures. I would recommend that you devote a few minutes nearly every day to some gen
eral exercises, for the entire school, in the elemen
tary rules. The results of a little daily practice will be highly satisfactory. If the maxim, “Practice makes perfect,” is ever true, it is strictly so in relation to operations in arithmetic. I would advise you to have daily exercises in notation, numeration, addition, multiplication, subtraction, division, fractions, &c. In such exercises, let all who are sufficiently advanced take part, and insist on promptness and energy in the performance of the work. I will give you an example or two, as a specimen for the general exercise alluded to, and the same plan may be adopted in reference to the other rules. Calling for the attention of your pupils, you address them somewhat as follows: “Scholars, I wish you to give your entire attention to an exercise I
am about to give. It is a simple exercise, – one in
which all who have ciphered can take part. It is only a sum in simple addition. But in performing the example, I wish you to aim to excel in three or four particulars: —
1. Make your figures plain.
2. Put them down in straight columns.
3. Add accurately.
4. Add rapidly. As I dictate the figures, you will write them; and when I say, “Add,' you will all commence. The pupil who first obtains an answer will speak distinctly and say, ‘No. 1'; the second, ‘No. 2'; and so on. I will note the time in which each performs the example, and will read to you the result. But remember that there will be no merit in obtaining