Copyright, 1891, by Thos. R. Vickroy. PREFACE. A Text-Book in any branch of study should be an aid to teacher and pupil. Its matter should be graded, and its form should be simple, logical and systematic. It should unfold from some fundamental idea around which all its essential facts should be grouped. Arithmetic is a means of training the will, since the material world is controlled by numbers. The intellect may think the world, but cannot change any of its forms. By his will man asserts his dominion over matter and arithmetic is the branch of study which gives him this mastery. The material world is made to serve man's purposes by counting, weighing, measuring and valuing it. Man's wealth, whether in cattle, acres, wares or dollars, is determined by counting. The products of field, workshop and mine are weighed, measured and valued. Arithmetic is therefore a practical study which deals with material things. The land on which we dwell, the houses in which we live, the clothing which we wear and the food which we eat, is determined and brought within our control through numerical processes. Arithmetic is an active force in our civilization, and its study is of fundamental importance. Number is a property of things, but numbers are expressions for things. Hence it is plain that if the child is to gain the mastery of the art of using numbers, he should derive his ideas from counting, weighing, measuring and valuing the things which come within his experience. The imagination rather than the memory should be exercised in learning the arithmetical art. The elements of arithmetic, as detailed in this book, are unfolded from this point of view. The child is led forward by easy steps to grasp arithmetical facts and afterward to use numbers to express them. His work is first oral through objects, and after the chief ideas are fixed with small numbers, he is required to deepen his knowledge through written work. The method presented here for the use of pupils of the first three years is synthetical as developed in the St. Louis Schools. Thought is awakened through material things, numbers are applied orally and by means of figures, and thus the child thinks and learns to express his thought in logical form. The analyses, rules and explanations are merely directive to aid in obtaining good form, but the live teacher will find that he can use the good things he has acquired without being hampered by a parade of “words without knowledge,” which so often prove to be serious hindrances of advancement. NOTE TO ENLARGED EDITION. The present work has been thoroughly revised and enlarged by the addition of much concrete work which the publishers feel will surely add to its value and usefulness as a text book. The subjects of Fractions and Decimals have been changed while that of Compound Numbers has been entirely re-written and greatly increased. Percentage, Interest, Bank Discount and kindred subjects, and Ratio and Proportion have been introduced and treated in a simple and objective manner. Few books of its character contain a better or more carefully graded class of examples, which fact admirably adapts it not only to graded but also to ungraded and district schools. The publishers acknowledge their obligations to MR. J. W. Hall of the St. Louis Schools, for editorial work in the revision of this edition. CONTENTS. ....... 12 ........ 15 .......... PAGE. Definitions: arithmetic, numbers, figures... Making Numbers................. Primary Combinations.............. Fundamental processes defined...... The processes with two: addition, drill cards.. 16-17 Multiplication of Twos ........... Division by TWO.... 19-20 20-22 22-27 The processes with THREE: oral drills in addition, subtraction, 30-33 33-34 Fractions of multiples of 3............. The processes with four: oral and written exercises, problems 39–41 Fractions and multiples of 4........ The processes with FIVE: oral exercises, written exercises. 42-43 The processes with sıx: oral exercises, written exercises............ 46–47 ............... ........ |