IN ALGEBRA BY FLETCHER DURELL, PH.D. HEAD OF MATHEMATICAL DEPARTMENT, THE LAWRENCEVILLE SCHOOL AND E. E. ARNOLD, M.A. SUPERVISING PRINCIPAL, THE PUBLIC SCHOOLS OF FORMERLY SPECIALIST IN MATHEMATICS, THE Educ T 129.19.342 HARVARD COLLEGE LIB? GIFT OF GINN & COMPANY MARCH 17, 1927 COPYRIGHT, 1919, BY CHARLES E. MERRILL CO. PREFACE THIS book has been written to meet the changes in High School work which have developed in recent years. For instance, most pupils now entering High School are younger and more immature than such pupils were even a decade ago. A majority of them also study only first year algebra and do not take the later more advanced course. Hence a demand has arisen that the first year in Algebra be simplified and made as directly practical as possible. The outstanding features of this book are as follows: I. A simplification of subject matter. Among the omissions are the involved use of the parenthesis, the larger part of factoring, complex fractions, special devices in the solution of equations, the method of comparison in solving simultaneous equations, the square root of complicated expressions, all treatment of fractional, negative, and literal exponents, and most of radicals. II. Increased and systematic use of the graph. The omissions just specified make possible, among other things, an enlarged and systematized use of the graph. At the outset, the scales to be used on the axes and also partial diagrams for graphs are supplied. The other various stages by which the pupil proceeds from the simple to the more complex cases have been carefully developed. The pupil thus acquires an organized and comprehensive grasp and a power both to construct and to interpret graphs, giving a disciplinary training equal and perhaps superior to that conferred by the more technical algebraic topics omitted, and far exceeding them in vocational and cultural values. III. Increased use of the formula. A like development has been made of the formula. In particular, almost every topic in arithmetic is stated, reviewed, and further developed by aid of the formula. IV. Improved treatment of written problems. Particular attention is called to the new method of dealing with written problems, shown on pp. 4-7, and used throughout the book. Teachers agree that the written problem is the most difficult topic in algebra. It is believed that the method here presented meets this fundamental difficulty, just as the group method used in the authors' text on geometry has overcome the difficulty in teaching pupils to work originals in that subject. V. Large amount of oral exercise work in the use of algebraic language. Each exercise in written problems is preceded by an oral exercise in the use of algebraic language. In certain of the examples of these sight drills, the more difficult written problems which follow in the next exercise are analyzed. VI. Organization of the chapters into Parts I and II. In Part I of each chapter, the simple elements of the new topic are presented with as little theory as possible. It is intended that the class shall study in a first course or semester Part I of all the chapters in succession, and then return to the beginning of the book, and study the Parts II in order, reviewing each Part I, before taking up the Part II which follows it. The arrangement of material, however, is such that if the teacher prefers all the subject matter can be studied consecutively. It is strongly recommended, however, that the method of first studying all of the Parts I be followed. VII. Relation to syllabi. As a whole the book covers the ground specified by the new syllabus adopted by the State of New York, and is in close accord with the syllabus recently formulated by the Association of Mathematical Teachers of New Jersey. Used in connection with a second algebra which is to follow it, the book will meet the specifications in Elementary Algebra of the College Entrance Examination Board. It is generally understood that the most difficult problem in mathematical pedagogy is the transition from arithmetic to algebra. It is felt that the new departures in this book make a distinct contribution toward the solution of this problem. |