Educ T 118.46 832 VARD COLLEGE LIST GEORGE ARTHE JANDA Y 28, . Entered according to Act of Congress, in the year 1846, in the Clerk's Office of the District Court of Connecticut. N. B. A KEY to Practical Arithmetic, containing the answers, numerous suggestions, &c., is published for the use of Teachers. PREFACE. Ir has been well said, that "whoever shortens the road to knowledge, lengthens life.” The value of a knowledge of Arithmetic is too generally appreciated to require comment. When properly studied, two important ends are attained, viz: discipline of mind, and fa cility in the application of numbers to business calculations. Neither of these results can be secured, unless the pupil thoroughly understands the principle of every operation he performs. There is no uncertainty in the conclusions of mathematics; there should be no guesswork in its operations. What then is the cause of so much groping and fruitless effort in this department of education. Why this aimless, mechanical "ciphering," that is so prevalent in our schools? The present work was undertaken, and is now offered to the public, with the hope of contributing something toward the removal of these inveterate evils. Its plan is the following: 1. To lead the pupil to a knowledge of each rule by induction; that is, by the examination and solution of a large number of practical examples which involve the principles of the rule. 2. The operation is then defined, each principle is analyzed separately, and illustrated by other examples. 3. The general rule is now deduced, and put in its proper place, both for convenient reference and review; thus combining the inductive and synthetic modes of instruction. 4. The general rule is followed by copious examples for practice, which are drawn from the various departments of business, and are calculated both to call into exercise the different principles of the rule, and to prepare the learner for the active duties of life. It is believed that much of this guess-work in "figur ing," and its concomitant habits of listlessness and va cuity of mind, have arisen from the use, at first, of abstract numbers and intricate questions, requiring combinations above the capacity of children. Taking his slate and pencil, the pupil sits down to the solution of his problem, but soon finds himself involved in an impenetrable maze. He anxiously asks for light, and is directed "to learn the rule." He does it to the letter, but his mind is still in the dark. By puzzling and repeated trials, he perhaps finds that certain multiplications and divisions produce the answer in the book; but as to the reasons of the process, he is totally ignorant. To require a pupil to learn and understand the rule, before he is permitted to see its principles illustrated by simple practical examples, places him in the condition of the boy, whose mother charged him never to go into the water till he had learned to swim. These embarrassments are believed to be unnecessary, and are attempted to be removed in the following manner: 1. The examples at the commencement of each rule are all practical, and are adapted to illustrate the particular principle under consideration. Every teacher can bear testimony, that children reason upon practical questions with far greater facility and accuracy than they do upon abstract numbers. 2. The numbers contained in the examples are at first small, so that the learner can solve the question mentally, and understand the reason of each step in the opera tion. 3. As the pupil becomes familiar with the more simple combinations, the numbers gradually increase, till the slate becomes necessary for the solution, and its proper use is then explained. 4. Frequent mental exercises are interwoven with exercises upon the slate, for the purpose of strengthening the habit of analyzing and reasoning, and thus enable the learner to comprehend and solve the more intricate problems. 5. In the arrangement of subjects it has been a cardinal point to follow the natural order of the science. No principle is used in the explanation of another, until it has itself been demonstrated or explained. Common frac tions, therefore, are placed immediately after division, for two reasons. First, they arise from division, and are in fact unexecuted division. Second, in Reduction, Compound Addition, &c. it is frequently necessary to use fractions; consequently fractions must be understood. before it is possible to understand the Compound rules. For the same reason, Federal Money, which is based upon the decimal notation, is placed after Decimal Fractions. Interest, Insurance, Commission, Stocks, Duties, &c., are also placed after Percentage, upon whose principles they are based. 6. In preparing the tables of Weights and Measures, particular pains have been taken to ascertain those that are in present use in our country, and to give the legal standard of each, as adopted by the General Government.* It is well known that a great difference of weights and measures formerly existed in different parts of the country. More than ten years have elapsed since the Government wisely undertook to remedy these evils, by adopting uniform standards for the custom-houses and other purposes; and yet not a single author of arithmetic, so far as we know, has given these standards to the public. 7. The subject of Analysis is deemed so essential to a thorough knowledge of arithmetic and to business calculations, that a whole section is devoted to its development and application. The principles of Cancelation have been illustrated, and its most important applications pointed out, in their proper places. The Square and * In the year 1836, Congress directed the Secretary of the Treasury to cause to be delivered to the Governor of each State in the Union, or to such person as he should appoint, a complete set of all the Weights and Measures adopted as standards, for the use of the States respectively; to the end that a uniform standard of Weights and Measures may be established throughout the United States. Most of the States have already received them; and may we not hope that every member of this great Union will promptly and cordially unite in the accomplishment of an object so conducive both to individual and public good. Cube Roots are illustrated by geometrical figures and cu bical blocks. Such is a brief outline of the present work. It is not designed to be a book of puzzles, or mathematical anomalies; but to present the elements of practical arithmetic in a lucid and systematic manner. It embraces, in a word, all the principles and rules which the business man ever has occasion to use, and is particularly adapted to precede the study of Algebra and the higher branches of mathematics. With what success the plan has been executed remains for teachers and practical educators to decide. If it should be found to shorten the road to a thorough knowl edge of arithmetic in any degree, its highest aims will be accomplished. New Haven, Oct. 3, 1845. J. B. THOMSON. |