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child an experience, instead of presupposing one for him. Pupils become practical, not by learning forms of reasoning, but by exercising the reason upon their own plane of comprehension.
In such a spirit this ELEMENTARY ARITHMETIC has been prepared. It presents three years' work, based upon carefully graded exercises, which may be used as a means of training pupils to think, and of teaching at the same time the practical application of numbers to ordinary business transactions.
The first and hardest step in solving an arithmetical question is to determine the processes required; the second, to state the dif ferent steps of the solution in proper arithmetical forin.
It is very important that children should master the fundamental processes so thoroughly that they come to serve thought without loss of time or energy. The patient following of these graded exercises and drills should secure this result. The tables of “ Endings,” in addition (see pages 58, 61, etc.), have the same practical use as the multiplication table, and should be as thoroughly applied.
Each chapter presents, in general, division and multiplication as converse processes, followed by subtraction and addition on the same general plan. In the beginning each number is viewed as a whole, divisible into equal parts, and the parts are viewed in relation to the whole and to each other.
No formula should be taught with the thought that it will do the thinking for the pupil. Let the problem be pictured, and this followed by the expression in figures, before any formal expression in words is attempted. Give a very thorough drill, as on page 13, Article 2, before pupils are required to find these relations in con-, crete problems.
The object of picturing problems is not to teach children to make pictures (though all this work should be done with reason. able care), but to give a method of representation by which they
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can make their thoughts clear to themselves. It is a means, not an end, and should be so regarded. When problems can be stated clearly and solved correctly there is no further necessity for picture representation, except as a means of testing the pupil's comprehen. sion of spoken or written forms. Let not objective work be underrated, ho ver. It is a very necessary means, which, rightly used, will secure an accurate knowledge and use of terms, and save much time and confusion later on. Pupils should learn early to show objectively the difference between six and one-sixth of six, between one-sixth of six and one-sixth of one, etc.
Two-step and three-step problems, which may be worked out orally in the recitation, will often be found too difficult for a written test. The indiscriminate use of “miscellaneous problems” may do much harm.
All measures introduced should be learned by actual use (see page 65). The standards in common use, such as the yard, foot, ounce, pound, quart, etc., can be obtained easily, and should form a part of the regular school supplies. Exercises in estimating volume and extension train the judgment while giving practical results in knowledge, and there is no time in the course when pupils can better afford to do this work.
Having worked Part I. to learn what and how, a profitable review can be made, directing chief attention to why. Rules should be made by the pupils after the process is learned from which the rule is derived.
Long Division is one of the difficult processes for children. At first they are unable to judge how many times the divisor is contained in the dividend or partial dividend. When about to commence Long Division much mental practice should be given with small numbers, 13, 14, 15, 16, etc., — such drill as 13 in 14, 13 in 15, 13 in 16, etc., to 13 in 117; same drill with 14, 15, 16, etc.
For additional suggestions, see “ New Advanced Arithmetic,”
This book has grown from experience, and is offered to fellowteachers as a thoroughly systematic work-book.
N. C. INDIANAPOLIS, January, 1899.
T has seemed to the authors of the NORMAL COURSE
IN NUMBER that there is room for another series of Arithmetics, notwithstanding the fact that there are many admirable books on the subject already in the field.
The ELEMENTARY ARITHMETIC is the result of the experience of a supervisor of primary schools in a leading American city. Finding it quite impossible to secure satisfactory results by the use of such elementary arithmetics as were available, she began the experiment of supplying supplementary material. An effort was made to prepare problems that should be in the highest degree practical, that should develop the subject systematically, and that should appeal constantly to the child's ability to think. The accumulations of several years have been carefully re-examined, re-arranged, and supplemented, and are now presented to the public for its candid consideration.
Not the least valuable feature of this book is the careful gradation of the examples, securing thereby a natural and logical development of number work.
No space is occupied with the presentation of theory, – that side of the subject being left to the succeeding book. The first thoughts are what and how,—these so presented that the processes shall be easily comprehended and mastered. Subsequently, the why may be intelligently considered and readily understood.