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An Imaginary Journey.
fine your attention to either of those which consists partly of water. I shall wish you to describe the course, tell where you leave the steamer for the cars, the prominent places through which you pass, and about how long it will require to make the journey. At another time, we will make the return over a route wholly by railroad.” The idea you will readily see, and also the extent to which this course may be carried.
If the interesting volumes of Dr. Kane have been read, his perilous travels, daring adventures, and many hardships, may be made to invest many a geography lesson with an interest before unthought of. Let the various points spoken of be pointed out upon the map, and let the members of your class be called on to state all the incidents that may occur to them as worthy of note. This course will tend to awaken a spirit of attention and investigation in relation to their reading.
I would again advise that you make the drawing of maps a prominent exercise; and, if rightly conducted, it will prove a very pleasant and profitable one. If the lesson is about a certain country, let its outlines be drawn upon the blackboard, together with the prominent features, mountains, rivers, etc. Frequent and careful. practice will give results highly useful and satisfactory.
As a valuable aid to you in the department of map-drawing, I would call your attention to a small work just published, entitled “Elements of Mapdrawing, with Plans for Sketching Maps by Trian
A New Work.
gulation, and Improved Methods of Projection. The author is Cornelius S. Cartée, a successful instructor in Charlestown, Mass. The work is a valuable one, and original in its plan.
Your sincere friend,
LETTER X VII.
MY DEAR FRIEND:I NOW come to consider the subject of Arithmetic. This has been made a very prominent branch, in most of our schools. In this age of money-getting and calculation, there is a strong tendency to give it an undue prominence. I have sometimes thought it did receive more than its just share of time and attention. It is urged that the science of numbers is deserving of special consideration, on account of the mental discipline it will give. This may be urged in favor of other branches, though, it may be, not to the same extent. The amount and quality of mental drill and development depend more upon the teacher's manner of teaching, and the pupil's habits of learning, than upon the mere subject taught.
Let me say, at the outset, that it will be hardly possible for you to overestimate the value of mental arithmetic. This should be commenced at an early period in the child's education, and be continued through a series of years. Indeed, it would be well
if the pupils in all our schools and academies should be required to devote a short time, daily or weekly, to operations in mental arithmetic. A little daily practice, in the right way, will secure results of the most satisfactory nature. I have heard children of the age of nine or ten years perform mental operations with a degree of rapidity and accuracy far greater than most adults could perform similar exercises with the use of slate and pencil. If, then, you wish to have your pupils make true progress in numbers, give them frequent and thorough drilling in mental arithmetic. If you devote an hour, daily, to the study of arithmetic, give at least one half of it to mental operations. I have no hesitation in saying that a lad, who has been thoroughly and properly trained in all the exercises in Colburn's First Lessons, or in those of the mental Arithmetics of Davies, Thompson, Greenleaf, Stoddard, or any other well-prepared book of the kind, without having received an hour's training in written arithmetic, that such a lad will be better fitted for any common business, so far as arithmetic is concerned, than he would be if he had devoted months merely to written arithmetic, without giving any attention to mental exercises.
In teaching mental arithmetic, the Numeral Frame will be found almost invaluable. No primary or intermediate school should be without one of these simple articles of apparatus. It is alike useful in teaching the little ones to count, and in illustrating operations in addition, subtraction, di
Bishop Potter quoted.
vision, and also in explaining fractions. It will prove worth tenfold its cost in the hands of any active and judicious teacher. A set of blocks and solids for the illustration of square and cubic measure will be found very useful, both in mental and written arithmetic.
In the performance of mental exercises, it will be well to require the pupils to recite without the book. Read the question distinctly, and let the pupils give the answer and explain the process, - giving the reason for every step. This course will tend to secure attention, and prove a more desirable mental discipline. From the beginning, cause your pupils to feel that they must recite the lesson without your aid. You may, of course, solve one or two problems, as a specimen of the mode in which you wish to have them solved. It is often the case that much of the benefit of such examples is lost by the careless and immethodical manner of performing them. Then let me urge you to train your pupils to be accurate and self-reliant. Train them to think and act for themselves. Says Bishop Potter : “If I were to reduce to a single maxim the concentrated wisdom of the world on the subject of practical education, I should enunciate a proposition, which, I think, is not incorporated as it should be into the practices of schools and families. That principle is, that, in educating the young, you serve them most effectually, not by what you do to them or for them, but by what you teach them to do for themselves. This is the true secret of educational development.”