LIPPINCOTT'S SCHOOL TEXT SERIES EDITED BY WILLIAM F. RUSSELL, PH.D. DEAN, COLLEGE OF EDUCATION, STATE UNIVERSITY OF IOWA APPLIED ARITHMETIC THE THREE ESSENTIALS BY N. J. LENNES, B.S., M.S., Ph.D. PROFESSOR OF MATHEMATICS, UNIVERSITY OF MONTANA AND FRANCES JENKINS PROFESSOR OF ELEMENTARY EDUCATION, UNIVERSITY OF CINCINNATI, AND SUPERVISOR OF ELEMENTARY PREFACE THIS book is the first of a three-book series, and is intended to cover the work in Arithmetic of the second, third, and fourth grades. The principles which have guided the authors may be grouped under three main heads: 1. Selection and Organization of Subject Matter. Recent discussion and practice, as revealed in the literature and in published curricula, seem to show substantial agreement as to what topics should be included in the earlier part of a course in Arithmetic, while there is yet considerable difference of opinion as to topics to be included in the later parts. All topics whose inclusion or exclusion is now being debated are placed among the supplementary topics at the end of Books II and III. The main body of each book furnishes a minimum course, which may be studied without break in continuity. At points noted in the text supplementary topics may be taken up. It is believed that in this respect these books will serve each of many different needs just as effectively as if they were prepared to meet each need exclusively. The business of the maker of text books is to furnish teachers and supervising officers effective instruments for carrying out their purposes, rather than to seek to impose rigidly his own personal predilections or whims. It has been the purpose of the authors to arrange the subject matter in such a manner that the greatest simplicity of treatment may be attained. In the first book this is exemplified by the relating of the fundamental combinations, as shown on pages 17, 31, 34 for the addition and subtraction combinations, and on pages 20, 29, 36, 48, 56, 98, 100, 101, 133 for the multiplication and division combinations. In order to simplify the development, effort has been made to break up larger difficulties into smaller constituent difficulties. On this point see the development of addition, pages 72 to 86; the development of subtraction, pages 92 and 113 to 117; the development of multiplication, pages 126 and 148 to 152; and the development of long division, pages 231 to 239, and 252 and 253. In the later books this unifying and simplifying of the subject matter has been carried out in many ways. 2. Derivation and Application. It is commonplace to remark that the elementary facts of Arithmetic should be derived from the child's own experiences. But practice has not been in uniform accord with this commonplace. Too frequently use has been made of material that actually comes within the experience of a comparatively small number of children. Thus, manual training may furnish most excellent sources for number work, provided the child has had experience with just that kind of manual training; otherwise it is very bad material. The authors believe in these books the elementary facts of Arithmetic are derived from situations which are within the range of experience of nearly all normal children. Not infrequently books have been based on work done in some one very excellent school or system of schools, where the children have been subjected to special experiences, such as construction work. When such books are placed in the hands of children not subjected to these particular experiences, the result is disastrous. The applications of Arithmetic should likewise be made to things of general child interest. The most effective applications of Arithmetic can be made only when considerable local material is brought in. Such material is most effective PREFACE when brought in by the child itself. For these reasons there are throughout these books many suggestions for the making of problems by the children. On this point see the pages referred to in the index under the heading, "Making New Problems." 3. Motivation. The subject matter of Arithmetic can be motivated most effectively only when the freest possible use is made of the child's many spontaneous interests. The authors have not neglected any opportunity that has occurred to them to interest the child in the subject matter itself and its manifold applications. They have recognized, however, that it is possible so to connect the learning of Arithmetic with other activities which in themselves are of compelling interest to the child, that the combination will be a source of joy and life when the Arithmetic elements alone would lead to sadness and forced labor. For this reason systematic use has been made of games of group competition and many simpler games. On this point see the pages referred to in the index under the heads, "Games used in drills in Addition," "Games used in drills in Subtraction," and so on. Some other points may be mentioned. The best existing information on the relative difficulties that children have in learning and retaining the various fundamental combinations has been made use of, and the more difficult combinations have been repeated more frequently in drills and reviews. Moreover, each child is encouraged to make lists of combinations of exceptional difficulty, and to study them separately. See pages referred to in the index under the title, "Difficult Combinations." The formal setting out of each new number fact as it is first learned should help to create definite responsibility on the part of the child for the important things he is to learn. |