MYERS ARITHMETIC ELEMENTARY BY GEORGE WILLIAM MYERS PROFESSOR OF THE TEACHING OF MATHEMATICS AND ASTRONOMY CHICAGO SCOTT, FORESMAN AND COMPANY 1909 09.5 MARVARD COLLEGE LIBRAKY PRERLIN COLLEGE LIBRARY COPYRIGHT, 1898, 1903, 1905, 1908, 1909 BY SCOTT, FORESMAN AND COMPANY PREFACE Recent years have seen many substantial gains in both theory and practice in elementary education. Arithmetic has gained largely from this general advance. In teaching the elements of mathematical science we have learned of late many practicable ways of attaining the larger educational aims; viz., strengthening the judgment and the will, and fostering the power to think and to do. PLACE FOR There is no school subject in which foreshortened views and distorted perspective work more harm than in elementary mathematics. Children, as well as adults, learn new ideas by meeting them first in simple forms, intermingled with familiar ideas and fairly well-understood uses of the new ideas. After a little, the new idea makes itself felt as something new. This is the time to differentiate it for formal study, to learn what it really is. This is the stage for the study of process and for drill enough to impress it and to make its use easy and facile. The learner then desires to experience the added power the mastery of the process has given him, and this calls for the application stage. The treatment of new ideas, processes, and topics in this book is accordingly arranged on this three-fold plan of (1) its informal use, (2) its formal study, and (3) its application. Examples of this plan may be seen in the teaching of the tables. The arrangement of number work for the grades must be in accordance with the natural unfolding of the child's mind. Too often this important fact is lost sight of in the logic of the subject itself. Strictly speaking, there can be no contradiction between the demands of the child's DEVELOP MENT. mental development and the logical requirements of the subject. It is only when logic is construed to mean the procedure of adult mind that the demands of ORDER OF logic become mischievous in the elementary school. Rightly understood, logic means the natural procedure of the learning mind in mastering a subject. Recent work of educational experts has proved that the best nurture for the child as a child remains always the best nurture he could have had. In the language of biological science, while the frog is a tadpole, whatever is best for the tadpole will eventuate in the most perfect frog. This doctrine is now generally accepted by all students of education. It has done much toward the general accrediting of childhood at its true worth. It has given flat and final denial of the right to quarrel with the child because he is not something else, by attempting to force upon him the logic of the adult. This modern doctrine is accepted by this book. It is believed the book has unified the interests of logic with those of the child by making its logic the logic of the learner at the stage he has reached. MATERIAL. The ideas of number and of the numerical processes must be derived from the concrete. Form and number are the two main developments of quantity. The process of numbering in its varied aspects is very closely paralleled in the physical world by the process of measuring in its varied applications. This does not imply that numbering and measuring are one and the same process, or set of processes. What it does imply is that numbering is the mental side of the same problem of adjustment of activity that has its physical expression in in measurement. It means that measurement is the most direct and certain route to correct notions of number, for one who has not yet acquired them. The MYERS ELEMENTARY ARITHMETIC organizes the material of modern elementary school mathematics into four parts. Each part after Part I, contains a full year's work for a public school of average possibilities for arithmetic work. Part I is an introduction of a dozen pages of exercises and simple, practical problems about every-day affairs. They are drawn from sources with which the pupil's experiences, in and out of school, have familiarized him in an indefinite way, and for the right understanding of which the use of numbers and of arithmetical processes is needed. These introductory pages will perform three important services to arithmetic teaching, viz: (1) They start the notions of number and its processes as apt ways of expressing mental needs, inwardly demanded, rather than outwardly impressed. (2) They bring together and put into the child's control the scattering items of number knowledge, that have been gleaned, in school and out, through the first and second grades, and digest these facts into a sort of system. (3) They assist the teacher to know what the pupil has already learned and how and where to begin the next advance. These pages are not a full year's work. They are rather a body of detailed suggestions, readily capable of being amplified into an entire year's work for the second grade. Part II is for the third grade. It begins by impressing the pupil with the need for estimating and measuring, by giving him considerable work in indefinite comparison, leading to definite comparison, measurement, and numbering. This work, while interesting in itself to children, is done not so much for its own sake, as to supply a rich groundwork of number judgments for arithmetical number and process. The year's work includes many of the uses of number that gather about the common standards and processes of measurement, and makes a |