IN MENTAL ARITHMETIC, UPON THE INDUCTIVE METHOD; ADAPTED TO THE BEST MODE OF INSTRUCTION IN PRIMARY SCHOOLS. BY JAMES S. EATON, M.A., INSTRUCTOR IN PHILLIPS ACADEMY, ANDOVER, AND AUTHOR OF A TREATISE ON WRITTEN ARITHMETIC. PREFACE. THE author has prepared this little book both in compliance with the solicitation of Teachers and others interested in his larger work, and with the desire to present the first principles of the science in a form to interest the youngest members of our Primary Schools. Definitions and extended explanations, being generally unintelligible, and therefore uninteresting and unprofitable, to young children, have been carefully avoided, and the simplest operations in numbers have been presented in the most familiar manner, separately or in combination, as seemed most likely to interest and benefit the pupil. No effort has been spared to make the book simple in language, varied in expression, progressive in style, and attractive in illustration; and thus, it is hoped, the little learner will form accurate habits, and unconsciously become familiar with such simple calculations as shall prepare him to enter with pleasure upon the more vigorous thinking required in WARREN COLBURN'S FIRST LESSONS. In the preparation of these Lessons, the author has received valuable aid from Teachers, eminent in their profession, and familiar with the best modes of instruction in Primary Schools. PHILLIPS ACADEMY, ANDOVER, SUGGESTIONS TO TEACHERS. A KNOWLEDGE of numerical calculation is not the only, perhaps not the most important, object to be attained in the study of a work like this. The child is to be interested; his attention secured; the power of abstraction created; his mind disciplined, in preparation for other and higher pursuits. The benefits derived in any study, preeminently in an elementary study, depend, in great measure, upon the methods employed in teaching it. These pages are designed only as specimen lessons. A large share of the instruction in Primary Arithmetic should be oral; and certainly no Teacher in this department would ever think of following, literally, the lessons of any book, however perfect the book may be. The skillful Teacher will vary the manner of presenting an idea to meet the ever-varying wants of the day, the lesson and the pupil. The golden mean between too little and too much explanation should be selected. Most teachers, especially the inexperienced, pass over first principles too rapidly. The groundwork must be carefully and thoroughly prepared, or real progress is impossible. Let the pupil repeat, and repeat again, and vary the expression, until he is perfect master of the thought. Incorporate in his very being the idea that 3 and 4 is the same as 4 and 3; that 5 times 6 is the same as 6 times 5; that 8 and 8 is identical with twice 8, etc., etc.; and his subsequent progress will be sure, and rapid, and pleasant. PRIMARY ARITHMETIC. LESSON I. JOHN has one apple in his right hand, and one apple in his left hand; how many apples has he in both hands? One apple and one apple are how many apples? How many hands has John? One hand and one hand are how many hands? Has John two feet? Count them. One, two. How many eyes has John? One eye and one eye are how many eyes? John had two apples in his left hand, but he has taken one of them in his right hand; how many has he in his left hand now? One apple taken from two apples leaves how many apples? Point to John's right hand. hand. One and one are how many? leaves how many? Point to his left One from two |