This book contains in revised form and with some additions the material of the author's textbook, Advanced Algebra and Trigonometry. The illustrations are instructive, and a large amount of graphic work is given in the exercises throughout the book. While all the topics and methods of trigonometry as a mere tool for the practical man are included, there is also some excellent work in vectors, harmonic analysis, trigonometric equations, complex numbers, and hyperbolic functions that the technical student really needs. The plan of giving answers to odd-numbered exercises only is good. A cardboard protractor, in degrees and radians, is provided in a pocket inside the book cover. In addition to tables of logarithms are natural functions, conversion tables, degrees to radians and, conversely, mathematical constants, log x to base e, e2 and e ̃, and squares, cubes, square and cube roots. H. E. C. Junior High School Mathematics, Second Course, by William L. Vosburg, Head of Department of Mathematics, The Boston Normal School, and Frederick W. Gentleman, Junior Master, Department of Mathematics, The Mechanic Arts High School, Boston. Pages x+212. 13×19 cm. 1918. 90 cents. The Macmillan Company, New York. This Second Course aims to bring the pupil who leaves school at the end of his eighth school year in contact with adult activities that require some knowledge of mathematics, and to aid the pupil who continues in school in deciding whether or not he is capable of continuing his work in mathematics with profit. It includes arithmetic of the home, farm, and city, mensuration, and linear equations. Those who are interested in the newer phases of junior high school mathematics will find it worth while to examine the two books in this series. H. E. C. The Course in Science, Vol. V, Francis W. Parker School Year Book. 168 pages. 64 illustrations. Francis W. Parker School, Chicago. The Year Book presents the science work as taught in this school, throughout both the elementary and high school grades. It represents a distinct step towards a new and improved school curriculum, and is the result of a number of years of independent, experimental, and developmental work on the part of many members of the faculty. It has not been written by a few in authority, with the expectation that other teachers will slavishly follow it, but as an attempt to improve the choice of materials, to suggest better methods of presentation, and to unify the science instruction of the school. Following a presentation of the general principles underlying the organization of the course, the detailed outlines are given grade by grade and course by course, showing how all the work in science may be based upon the interests, activities, and problems of the pupil. Not only is the course given in outline, but the outcome is indicated by many examples of the pupil's work, as shown by their own papers, or as given in morning exercises. The experimental work is fully presented, together with many references for class reading or as aids to the teacher. The book is well illustrated, and should be of interest to all teachers in the elementary school, to high school teachers of science, and to principals and superintendents interested in the making of a vital school curriculum based upon the interests and activities of the children. R. W. O. Infinitesimal Calculus, Section II, by F. S. Carey, Professor in the University of Liverpool. Pages x+352. 14.5X22.5 cm. 1918. $3.00. Longman, Green and Co., New York. K COMBINATION PHYSICS AND CHEMISTRY TABLE Substantial, Looks Well and is EXACTLY SUITED to the Purpose These are three very important qualifications of Kewaunee Laboratory Furniture. Kewaunee LABORATORY FURNITURE It Looks Well.-In inherent beauty of material and perfection of finish, Kewaunee easily We have a book that will interest schocl executives planning new equipment. It is free, with Kewaunee Mfg. Co. LABORATORY Please mention School Science and Mathematics when answering Advertisements. K K The topics covered in this section include exponential and hyperbolic functions, motion of a particle along an axis, definite integrals, arc formulas, partial differentiation, double integration, expansion in power series, curve tracing, envelopes, evolutes, roulettes, differential equations, graphics, and nomography. While much space is given to the development and discussion of principles and formulas there are many applications in geometry, physics, and mechanics. Students in calculus will find these two sections of Infinitesimal Calculus of value as books of ref erence. H. E. C. Predetermination of Prices, by Frederic A. Parkhurst, M. E., Organizing Engineer. Pages viii+96. 15x23 cm. 1916. $1.25. John Wiley & Sons, Inc., New York. In this book the author presents an argument on the possibilities of predetermining true costs, basing it on his own experience and the results of his methods during several years. The first chapters emphasize the fact that true costs cannot be obtained at any time unless all methods incidental to processing are under absolute control. The last chapter discusses the possible ideal, which can be attained through the science of management. The methods used are made plain by a large number of diagrams and illustrations of order forms, work order forms, time cards, and cost sheets. H. E. C. Scientific Method in the Reconstruction of Ninth-Grade Mathematics, by Harold O. Rugg, Associate Professor of Education in the School of Education, University of Chicago, and John R. Clark, Chairman, Department of Mathematics, Parker High School, Chicago. Pages vi+190. 17×24 cm. Paper. 1918. $1.00. The University of Chicago Press. During the ten or fifteen years that secondary mathematics has been under fire of friend and foe, various methods of investigation have been used and various correctives have been proposed. On the one hand we have the manner of procedure of a few authoritative specialists who arrive at conclusions through reflective assurance; and of superintendents and supervisors of schools who assign instruction in mathematics to teachers on the basis of convenience and saving of expense with little regard to their qualifications and abilities. In either case, possible questionnaires are sent out, hurried investigations are made, and then comes the grand pronunciamento, the teaching of mathematics in our high schools is a failure, let it be abolished. In marked contrast to this procedure we have in this monograph a report of a long-continued and well-planned study of the fundamental causes of the inefficiency of mathematics teaching, and a well-founded program for reconstructing ninth-grade mathematics. Above all it is an earnest call to teachers and supervisors of mathematical instruction throughout the country to coöperate in making such a program effective. What has been done by the authors and what can be done by teachers to aid in this work is clearly set forth in the following topics: an inventory of the material of the present course in algebra, how algebra became the ninth-grade course, the design and construction of standardized tests and what they reveal, development of abilities through drill, training in "logical thinking," curriculum-making in secondary mathematics, experimental teaching, and a program for the reconstruction of ninthgrade mathematics. H. E. C. In their report entitled "Training of Teachers of Elementary and Secondary Mathematics" a subcommittee of the International Commission on the Teaching of Mathematics named the following nine subjects as those which may later be expected to be involved in the preparation in pure mathematics of the prospective mathematics teacher: Calculus, differential equations, solid analytic geometry, projective geometry, theory of equations, theory of functions, theory of curves and surfaces, theory of numbers, and some group theory. The natural significance of the adjective some in connection with the last of these nine subjects would seem to be that the knowledge of the prospective teacher along the line of group theory need not be as thorough as that along the other lines named, but that he should know something about this subject. It is evident that strictly speaking, the adjective some should have modified each of the other subjects named above, since no one can know all about any one of the broad fields covered by them, but the common usage of these terms seems to justify the conclusion that what is meant is that the prospective teacher should have a good course, or its equivalent, in each of these broad fields of pure mathematics, except possibly the last one. In regard to this field it might be sufficient if he had listened to a course of lectures devoted to it or had looked over some of the literature relating thereto. Two questions naturally present themselves in this connection. The first of these is, Why should the teachers of elementary and secondary mathematics be expected to know anything about group theory? If good reasons exist for demanding such a knowledge, it is natural to ask, Why is a superficial knowledge in this field less objectionable than in the other fields noted above? The former of these questions could scarcely embarrass anyone who possesses at least a slight knowledge of the modern literature on elementary and secondary mathematics. When one reads that such fundamental notions of geometry as point, line, and plane can be based upon group notions, and "that the idea of displacement, and consequently the idea of group, has played a preponderant part in the genesis of geometry" one can easily see why teachers of elementary geometry should know some group theory. The teachers of elementary arithmetic and elementary algebra may have less conscious need of a knowledge of group theory than those of elementary geometry, but the former are likely to read about the groups and subgroups formed by certain sets of real or complex numbers with respect to multiplication, and the groups and subgroups formed by other sets of such numbers with respect to addition. Moreover, the group properties of the n roots of unity may easily present themselves to such teachers as soon as they think just a little beyond what they are actually expected to teach. Having established the fact that the teachers of elementary and secondary mathematics must know something about group theory in order to understand some of the best modern literature relating to the subjects which they are expected to teach, it remains to answer the second of the two questions raised above. Since there is an algebraic group theory, an analysis group theory and a geometry group theory, one might perhaps infer that the use of the adjective some in the list of subjects mentioned in the first paragraph of this article might have been due to a feeling that the subject of group theory was too broad to come within the mathematical purview of the prospective teacher, and that such a student should therefore confine his attention either to a special part of this subject or to a somewhat superficial survey of the whole field. It is, however, less interesting to consider the possible reasons for the use of the adjective some in the given connection than to inquire what elements of group theory are of most importance to the prospective mathematics teacher. It might be supposed that these elements should include only one definition of the word group as a technical mathematical term. Since various writers use this term with different meanings, the reader who has only a single definition in mind is likely to be embarrassed there 'H. Poincare, The Monist, vol. 9 (1899), p. 32. |