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NEW REVISED EDITION,
AN EXTENSIVE COLLECTION OF PRACTICAL QUESTIONS
ON THE GENERAL PRINCIPLES OF ARITHMETIC.
WHICH SIMPLIFY MANY OF THE MOST IMPORTANT RULE Ir
JOHN F. STODDARD, A.M.,
SHELDON & COMPANY
NEW YORK AND CHICAGO
OLNEY'S HIGHER MATHEMATICS.
OLREY'S INTRODUCTION TO ALGEBRA
COMPLETE SCHOOL "
Entered, according to Act of Congress, in the year 1849, by
JOHN F. STODDARD, in the Clerk's Office of the District Court of the United States for the Southern
District of New York.
Re-entered, according to Act of Congress, in the year 1866, by
SHELDON & COMPANY, Ein the Clerk's Office of the District Court of the United States for the Southery
District of New York,
HAVING felt the necessity of a more extended and systematie Intellectual Arithmetic for younger, as well as more advanced pupils, I prepared and used in manuscript, in my own school, for a number of years, such a series of questions as I deemed best adapted to the purpose. After observing the superior mental training derived from their use, and the ease with which pupils thus trained comprehended the more advanced branches of mathematics, I venture to submit them to the public in the following pages, hoping that they may prove as useful to other schools as they bave to my own.
The rule which I have observed in preparing this work is: Tell but one thing at a time, and that in its proper place.
Although in many particulars the work differs from other “ Mental ” Arithmetics, as an examination of the “ questions' will show, mention of these differences is omitted, and the following exposition of its arrangements of subjects is presented.
Chapters First, Second, Third, and Fourth, from Lesson I to Lesson XV, treat respectively of Addition, Subtraction, Mul. tiplication, and Division of simple numbers ; each of which is rendered familiar by an extensive collection of practical questions. Lesson VII consists of questions which combine Addition and Subtraction; Lesson IX, of questions combining Addition, Sabtraction, and Multiplication ; Lesson XIII, of questions combining the twelve previous Lessons; and Lesson XIV, of questions in Proportion. Thus, an intimate connection between Lessons and even Chapters is kept up through the entire work, with the exception of Chapter Fifth, Lesson XIV to Lesson XXVII, which contains some of the most important Tables of Weights and Measures; each of which is illustrated with appropriate questions.
Chapter Sixth, from Lesson XXVI to Lesson XLVI, is devoted to the subject of Fractions, in which twenty lessons are many original combinations of numbers and concise analyses..
Chapter Seventh, from Lesson XLVI to Lesson LIX, consists of practical and intricate questions of various kinds, which require for their solution a thorough -nowledge of the preced
ing Chapters. This Chapter (perhaps not contained in any similar work), when understood, will be of great benefit to those who are studying, or who intend to study Algebra.
Chapter Eighth, from Lesson LIX to the end, includes Interest, Discount, and Per Cent., in their various modifications. The method of treating these subjects is original; and renders the rules under these heads, in Written Arithmetics (which are often incomprehensible to pupils), perfectly intelligible, by reducing the whole to one continued train of reasoning.
This Chapter, thoroughly taught, can not fail to quicken, strengthen, and develop the reasoning powers. Bringing into exercise, as thorough teaching or it will, nearly every principle taught in the twenty lessons of Chapter Sixth, and also the greater part of Chapter Seventh, the pupil will acquire the habit of systematically classifying was knowledge, and be enabled to call to his aid such portions of it as will assist in illustrating or demonstrating the subject under consideration.
That Intellectual Arithmetic, when properly taught, is better calculated, than any other study, to invigorate and develop the reasoning faculties of the mind, to produce accurate and close discrimination, and to enable the pupil to acquire a knowledge of the Higher Mathematics with greater ease, can scarcely knit of a doubt.
J. F. STODDARD. NES EQRK. ngust 1, 1860.
.UBLISHERS NOTE.—A new edition of this popular Intelectual Arithinetic, carefully revised by the author, is here presented in new and larger type, and on larger pages, without any changes which might interfere with its use in the same classes with previous editions. The “Lessons” are numbered, in regular order, throughout the book. In Lesson XXVI are full Tables of Metrical Weights and Measures on the Decimal System, the simplicity of which is an important consideration for instructors of youth.
Prof. Stoddard's new Key to this book, containing his Methods af Teaching Intellectual Arithmetic, is now published
SUGGESTIONS TO TEACHERS.
For the benefit of those whose experience in teachiug Ven tal Arithmetic is limited, the following suggestions are made of such methods of teaching this important subject, as may prove best suited to fix the attention, strengthen the memory, develop the reasoning powers, and secure rapid and accurate computation.
One thing at a time should be taught, thoroughly, and in its proper order.
Recitations and exercises for children should be short, and during their continuance the careful attention of each member of the class should be secured, and thereby animation and promptness will be encouraged.
The lesson should be assigned previous to recitation, to afford the pupils an opportunity for an examination and study of it; and during class exercise, pupils should not use the hook.
Drills, Illustrations, and Explanations should occupy at least one half of the time devoted to each recitation for children.
Care should be taken that the positions of children should be good, and that the language used be strictly correct in articulation, pronunciation, and construction, and addressed to the person asking the question. Both listlessness and hurried solutions should be avoided ; in the latter, pupils not unfrequently pronounce and, if, what, costs, quarts, as follows, an, ef, wat, coss, quats. By careful attention to these particulars, lessons in Intellectual Arithmetic will be valuable exercises in address, elocution, grammar, rhetoric, and logic, and pupils will acquire both a ready command of their thoughts, and a fluency of language in expressing them.
A Question should be read slowly and distinctly, and a pupil be required to repeat it accurately, and analyze it thoroughly, according to the forms given. There should be no interruption, except when the teacher cleems it necessary to make a correction or an important criticism