SANTA CLARA COUNTY TEACHERS' LIBRARY 7111-16 DEPARTMENT OF RECEIVED OCT 2 5 1919 LELAND STANFORD JUNIOR UNIVERSITY FIRST LESSONS IN ARITHMETIC ON THE INDUCTIVE PLAN INCLUDING ORAL AND WRITTEN EXERCISES. BY WILLIAM J. MILNE, PH. D., LL. D., PRINCIPAL OF THE STATE NORMAL SCHOOL, GENESEO, N. Y. JONES BROTHERS & COMPANY: CINCINNATI, PHILADELPHIA, 1881. CHICAGO, THIS book is designed to teach the principles of Arithmetical Science as far as they are involved in the elementary processes, and to secure a reasonable degree of accuracy and rapidity in expressing numbers and computing results. The pupils for whose use this book is intended can not be expected, at the outset, to explain processes, give definitions, or assign reasons, though their notions of all of them may be quite correct; much less should they be expected to grasp the principles of a science by committing to memory statements which are the deductions and generalizations of persons entirely familiar with the subjects treated. And, therefore, this work has been prepared upon the inductive and objective methods, so that the pupil may obtain his knowledge of arithmetic from actual work with numbers, rather than from the stereotyped statements of the book. The true method of awakening in the child a clear idea of numbers is through a perception of objects, or by pictures or other representations of them. After he has become familiar with things and their names, the name will signify to him all that he needs to know about the objects so far as number is concerned; and it is no longer necessary that the objects should be present before him. The necessity, too, of associating the same numbers with such a variety of things, causes him at length to cease to regard them in connection with any particular thing, or as any thing more than abstractions. (iii) |