JUNIOR HIGH SCHOOL MATHEMATICS BY WALTER W. HART, A.B. ASSISTANT PROFESSOR OF MATHEMATICS UNIVERSITY OF WISCONSIN SCHOOL OF EDUCATION Book Two D. C. HEATH & CO., PUBLISHERS BOSTON NEW YORK J CHICAGO PREFACE THIS book is the second of a series presenting a reorganized course in mathematics. It is designed for grade eight or the middle year of the junior high school. Books I and II together furnish material for a modernized course in mathematics for grades seven and eight, or for the first of three definite biennial cycles of the modern six-year secondary school. The following principles, consistent with those which guided in the preparation of Book I, have been observed in the preparation of Book II. I. The course must be practical. In grade eight, this means that: 1. There must be continued drill upon the fundamental operations. In Book II, the first eleven pages provide the preliminary drill necessary at the beginning of the school year. It takes the form of exercises which are motivated for the pupils by the idea of learning short cuts. Only such short cuts have been introduced, however, as can readily be mastered by the learners at this time. Chapter II affords further drill upon the fundamentals in a form which is motivated for the pupils by instruction in the use of the formula and the equation. In the miscellaneous review exercises (See pages 52, 72, 90, etc.). drill upon the fundamental operations is not neglected. Finally, at the back of the text, there are abstract drill exercises for timed tests and for individual drill for pupils who are deficient in computation. 2. The instruction on new topics must be limited to processes and applications which are encountered by the average person. For this reason, many topics are listed as supplementary topics (See pages 29, 53, 106, etc.). II. The course must be enriched. The necessity of new incentives for the pupils of this grade is greater even than for those of the grade preceding. Moreover, there has long been a demand for enrichment of the material and the procedure of this grade. Fortunately, the two aims may be attained by the same means. First, there is the obvious expedient, not new, of correlation with business (See pages 42, 92, 115) and civic interests (See pages 62, 74, etc.) and the use of modern problem material. Second, and more potent with the learners, is the enlarged use of the formula, started in Book I, and of the equation, and the gradual introduction of algebra proper. 1 In this text, true unification of arithmetic, algebra, and parts of geometry has been attained through the consistent use of the formula and the equation as working tools in the solution of problems. Introduced first in Chapter II, they are used thereafter whenever possible (See especially Chapters III, IX, and X). This reform talked about for over a generation, is made the dominating feature of this text. It is general mathematics in the best sense, for nowhere are there any forced or fictitious correlations. As used, it elevates the whole procedure of the text to a plane which is at once desirable educationally and satisfying to the learners' demand for something new. In Chapters XI-XIII, more formal algebra is taught in accordance with the best secondary school ideals. Boys and girls of this grade like algebra. In this text, they will study it at a time when their thoughts are being directed toward grade nine. III. The course must be thorough. In this text, as in Book I, the subject matter is separated for instructional purposes into small teaching units (See §§ 5, 6, 8, 9, etc.); where possible, instruction is based upon a brief review of related material in Book I (See §§ 3, 10, 19, etc.); a large number of graded examples and problems are provided; review lists of examples and problems appear periodically (See pages 52, 72, 90. etc.). |