first question in each rule is worked at full length, so that he is led forward in a gradual manner, both by precept and example; and is, it is conceived, more fully convinced of the truth of the rules, and the propriety of each operation. In this work the Table belonging to each rule is first given, that the scholar may learn the nature of the rule before he is questioned respecting it, or has sums given him for exercise. Examples for mental exercise are then given to awaken his reasoning powers, and thus prepare him to engage in each rule theoretically. The rule is then given in questions and answers, as this form, the Author believes, is better calculated to illustrate the rule, and to impress it on the mind of the pupil. Examples are then given for theoretical exercise on a slate, and one or more of these examples is worked out, and every operation fully and minutely explained. The remaining examples, not worked out, are for the exercise of the learner, until he shall become thoroughly acquainted with the theory of each rule. Immediately after these, are examples for practical exercise, consisting of a variety of miscellaneous questions, in which will be found much useful information. Most children, it is believed, experience some disgust in passing through the fundamental, or first five rules of Arithmetick, occasioned, no doubt, by the fewness of examples, and by the want of interest in those that are given. An Arithmetick should not consist, as is most generally the case, merely of an assemblage of rules and examples without EXPLANATION; So that the learner, after having committed them to memory, and learned to perform Arithmetical calculations mechanically, will leave the study totally ignorant of the principles upon which the rules are founded. Pupils are always desirous of knowing the reasons why any Arithmetical operation is performed; and if the nature and principles of the subject are clearly explained, and the rule rendered intelligible by the Author, the scholar may be able to acquire a knowledge of it without much aid from the teacher. The study would then be pleasant, and he would pursue it with delight and profit. The rules which the scholar should commit to memory are in the largest type used in the work. The examples, explanations, and exercises, are in a type of a smaller size; and the notes intended for the teacher are in the smallest type. The EXPLANATIONS should be thoroughly and carefully read by the scholar. The learner should be questioned as often as once in each day respecting the principles upon which the rules are founded; and the teacher should not permit him to commence a new sum, or engage in a new rule, until he is fully and thoroughly acquainted with the principles of the rule in which he has been working. Young scholars are generally anxious to make rapid progress. This propensity, however laudable, should not be indulged at the expense of a partial knowledge of the subject. No. 1, contains only the five fundamental rules of Arithmetick. These rules have been treated of more largely than is customary, from the belief that most pupils pass from these to the more difficult rules before they are thoroughly acquainted with them. Fractions, and the Compound Rules, are entirely omitted in No. 1, until the learner is well acquainted with the working of whole numbers. No. 1, is also made small that the young learner may not be disheartened by having a large volume put into his hands; and that the parent shall not be under the necessity of purchasing a larger and more expensive book for his child before he shall require it. No. 2, commences with the Compound Rules, and includes all that is necessary of every other rule in Arithmetick for practical purposes, and the transactions of business. In No. 2, the EXPLANATIONS of the nature and principles of each rule are also fuily and minutely given. No. 2, likewise, contains a Practical System of Book-Keeping. Tradesmen, without number, the most industrious and meritorious of men, often carry on their business with great difficulty, and many of them become involved and ruined, merely from the want of a simple system of keeping their accounts. Such a system is, therefore, given at the close of No. 2. One very important advantage of this work is, that all, or nearly all, the questions for practical exercise are in dollars and cents. The Author of the following work appeals, without apprehension or reluctance, to that publick, whose candour and liberality he has often experienced, to decide upon this attempt to render the elementary rules of Arithmetick both practical and popular, and also beneficial to the youth of this country, LYMAN COBB. New York, Jan. 25, 1832. |