NEW INTELLECTUAL ARITHMETIC CONTAINING AN EXTENSIVE COLLECTION OF PRACTICAL QUESTIONS WITH CONCISE AND ORIGINAL METHODS OF SOLUTION WHICH SIMPLIFY MANY OF THE MOST IMPORTANT RULES IN BY JOHN F. STODDARD, A.M. SHELDON & COMPANY, NEW YORK AND CHICAGO. Part First of this book is the Elements of Algebra; Part Second contains more difficult Test embraced in more advanced Algebra.) SHELDONS' WORD STUDIES, SHELDONS' MODERN SCHOOL READERS, SHELDONS' SUPPLEMENTARY READING. Entered, according to Act of Congress, in the year 1849, by In the Clerk's Office of the District Court of the United States for the Southern Re-entered, according to Act of Congress, in the year 1866, by In the Clerk's Office of the District Court of the United States for the Southern Copyright, 1889, by SHELDON & COMPANY, PREFACE. HAVING felt the necessity of a more extended and systematic Intellectual Arithmetic for younger, as well as more advanced pupils, the author prepared and used in manuscript, in his own school, for a number of years, such a series of questions as seemed best adapted to the purpose. The superior mental training derived from their use, and the ease with which pupils thus trained comprehended the more advanced branches of mathematics, induced him to submit them to the public in the hope that they might prove as useful to other schools as they had been to his own. The rule observed in preparing this work is: Teach but one thing, at a time, and that in its proper place. It has been his aim to keep up an intimate connection between lessons throughout the book, and from time to time, as the work progressed, to combine in review the principles illustrated in preceding sections. The scope and order of the book will be readily gathered from the Table of Contents subjoined. A series of drill exercises on the multiplication table, etc. (p. 42), has been added in the present edition. The sections treating of fractions are very full and complete, containing many original combinations of numbers, and clear and concise analyses. It is believed that they present everything that is essential both for knowledge of principles and for skill in correct reasoning and rapid and accurate combination. These are followed by a series of practical and intricate questions of various kinds, which require for their solution a thorough knowledge of the preceding sections. These problems will be of great benefit to those who are studying, or who intend to study Algebra. Percentage, with its various applications to interest, discount, profit and loss, is very fully presented, with original methods of analysis. The method presented by reducing the whole to one continued chain of reasoning, will render the rules under these heads; in Written Arithmetic (which are often incomprehensible to pupils), perfectly intelligible. This chapter, thoroughly taught, can not fail to quicken, strengthen, and develop the reasoning powers. Bringing into exercise, as thorough teaching of it will, nearly every principle taught in the twenty sections of Chapter Sixth, and also the greater part of Chapter Seventh, the pupil will acquire the habit of systematically classifying his 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, wnen 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 admit of a doubt. The following suggestions are made of such methods of teaching this important subject, as the author has found of practical value: Teach one thing at a time, thoroughly, and in its proper order. Recitations and exercises 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 generally be assigned previous to recitation, ta afford the pupils an opportunity for an examination and study of it; and during class exercise, pupils should not use the book except in rare cases of long or intricate examples. Drills, illustrations, and explanations should occupy at least onehalf 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. 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 exposing 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 deems it necessary to make a correction or an important criticism. Pupils should, as a general thing, be called upon promiscuously, and not in rotation, to take part in the recitation. Concert drills should not be employed as a regular method of reci tation, but simply to fix in the minds of pupils such tabular facts as can more readily be learned in this way to enliven the exercises, to give animation to the class, and confidence to the timid pupils. The tables should be thoroughly learned by the pupil, and both rapidity and accuracy should characterize his operations in Addition before he is required to study other parts of the subject. Special attention is called to the drill exercises on page 42. Nothing can take the place of accurate and rapid computation--indeed, the tables should be so thoroughly mastered that the pupil shall be hardly conscious of any mental effort in giving results of the various combinations. Every combination of numbers used in the tables may be illustrated when necessary with objects, such as pebbles, grains of corn, beans, so that the class may clearly understand each. A pupil thoroughly drilled in the fundamental operations of Arithmetic, will not only be able to perform them with facility and accuracy, but will have made great progress toward an easy and complete mastery of the Science of Numbers. THE preparation of new plates for this popular Intellectual Arithmetic has afforded an opportunity for careful revision, and the introduction of new matter, without departing materially either from the scope or method of a manual that has sustained its reputation in competition with the many treatises on the same subject that followed it. Its improved appearance on new type, and in a larger and open page, will be welcomed by its old friends, and it is believed gain hosts of new ones. The illustrated tables of weights and measures, and the brief but complete compend of the metric system will commend themselves to those who seek the best aids for school-room work. |