PUBLISHED BY ROBERT S. DAVIS & CO. NEW YORK: D. APPLETON & Co., AND MASON BROTHERS. 1857. KC 11391 Entered according to Act of Congress, in the year 1845, by BENJAMIN GREENLEAF, In the Clerk's Office of the District Court of the District of Massachusetts. Entered according to Act of Congress, in the year 1851, by In the Clerk's Office of the District Court of the District of Massachusetts. Entered according to Act of Congress, in the year 1857, by In the Clerk's Office of the District Court of the District of Massachusetts. 1. PRIMARY ARITHMETIC; OR, MENTAL ARITHMETIC, upon the Inductive Plan; designed for Primary Schools. Improved edition, 72 pp. 2. INTELLECTUAL ARITHMETIC, upon the Inductive Plan; designed for Common Schools and Academies. Improved edition. 3. COMMON SCHOOL ARITHMETIC; OR, INTRODUCTION TO THE NATIONAL ARITHMETIC. Improved stereotype edition, 324 pp. 4. HIGHER ARITHMETIC; OR, THE NATIONAL ARITHMETIC, for advanced scholars in Common Schools and Academies. New electrotype edition, with additions and improvments: 444 pp. 5. PRACTICAL TREATISE ON ALGEBRA, for Academies and High Schools, and for advanced Students in Common Schools. Fifteenth improved stereotype edition. 360 pp. 6. ELEMENTS OF GEOMETRY, for Academies and High Schools, and for Advanced Students in Common Schools. [In preparation, and will soon be published, to form a volume of about 300 pp., 12mo.] COMPLETE KEYS TO THE INTRODUCTION, AND NATIONAL ARITHMETIC, AND THE PRACTICAL TREATISE ON ALGEBRA, containing Solutions and Explanations, for Teachers only. In 3 volumes. ELECTROTYPED BY HOBART & ROBBINS, BOSTON. !!VERSITY PREFACE LIBRARY THE object of this primary book is to teach the pupil how to think, and to enable him, by an almost imperceptible gradation of thought, to advance from the simplest forms of reasoning to the more vigorous exercises of the mind. Hence, no arbitrary rules have been introduced, and only such hints and suggestions, with occasional formulas of reasoning, as were considered absolutely necessary for the profitable study of the lessons. In order that the reasoning of some of the principal processes might be the more apparent to the beginner, pictures of objects have been, to some extent, introduced. After these, counters are employed, as unit marks; and then follow lessons without any such aids, that the learner may early acquire the habit of depending upon mental resources alone for the solution of problems. This arrangement is deemed not only the most simple and progressive, but that which is confirmed, by the experience of teachers, as the best suited to produce a normal mental development. Several pages of written arithmetic have been introduced, at the close of the work, which can be used while the pupil is advancing in the mental department, or omitted until that is finished. BRADFORD, MASS., July, 1857. (3) SUGGESTIONS TO TEACHERS. THE lessons assigned to the learner should never be longer than will admit of being thoroughly prepared for recitation. The better to secure the attention of each member of the class, and elicit earnestness of thought, the questions should be read to the whole class, and each pupil taught to be in readiness, in whatever order called upon, to give promptly the solution required. such forms The solutions should be uniformly according to as are deemed by the teacher the neatest and best. The greatest care should be observed to have them always expressed in language entirely accurate, and pronounced in a clear and distinct manner. Frequent reviews, especially of the tables, will alone give thoroughness. In general, with a lesson in advance, it will be advantageous to assign some portion previously gone over, as a review. The exercises for the slate may, if thought best, be performed in connection with those that are purely mental; but the slate should not be allowed to be used in the performance of the latter. Every term, or process, connected with any of the lessons, which the beginner may be likely not readily to understand, the intelligent teacher will not need to be reminded, should be clearly explained to the pupil, before assigning the lesson. MENTAL ARITHMETIC. LESSON I 1. IF you wish to know how many fingers you have, what must you do? ANSWER. I must count them. 2. What, then, is counting? ANS. Finding the number of things. 3. In counting, what is a single thing called? ANS. A unit, or one. 4. What, then, is a number? ANS. A unit, or a collection of units. 5. Count the cups in each of the above rows. |