OF ELEMENTARY ARITHMETIC; INCLUDING ORAL, SLATE, AND WRITTEN EXERCISES, AND A COMPLETE METHOD OF PRESENTING EACH SUBJECT. BY MALCOLM MACVICAR, PH.D., LL.D., PRINCIPAL STATE NORMAL SCHOOL, POTSDAM, N. Y. PUBLISHED BY TAINTOR BROTHERS, MERRILL & CO. NEW YORK. Copyright, 1880, by Taintor Brothers, Merrill & Co. ELECTROTYPED BY SMITH & MCDOUGAL, TEACHERS' MANUAL. THE INTRODUCTION. HE Teachers' Manual of Elementary Arithmetic has been prepared for the purpose of avoiding the injurious plan of introducing into the pupil's book hints and suggestions intended exclusively for the use of the teacher. In using this Manual, the following should be carefully noted: 1. The elementary work in Arithmetic should make the pupils, first, accurate and expert in reading and writing numbers, and in adding, subtracting, multiplying, and dividing; second, accurate and expert in finding, and in stating in good form upon paper, the solution and explanation of simple practical examples. These two objects are kept constantly in view in the method of presentation and drill suggested for each subject. 2. The various exercises given have been arranged with strict reference to the laws of the pupil's mind. In every step of the work indicated, it is assumed as a fundamental principle, that the pupil's mind can be properly developed and furnished only as its experiences are the direct products of its own effort, and as these experiences are, by its own effort, transformed into systematic knowledge. 3. The instructions regarding the method of presentation and drill in each subject had, of necessity, to be made definite, |