this case that mathematics can make a strong appeal to and hold the interest of developing boys and girls. The outcome is most encouraging to those of us who believe that the study of mathematics is a necessary part of one's education, and who are striving, and not without success, to make it contribute largely to a stable and intelligent citizenship. The variability of pupils' interests for both studies and vocations is shown by an investigation of Mr. G. W. Willett, of Hibbing, Minnesota. A questionnaire was given for three successive years to the same pupils of a six year high school. The results have been brought up to date in a report in School and Society for March 22, 1919. Some of the questions asked were: 1- What subject that you have had in high school or seventh or eighth grades do you most prefer? 2- What is your second choice? 3- What subject did you most dislike? 4- What do you expect to make your life work? Judging from the 488 pupils questioned Mr. Willett concludes that permanence of interest in both studies and vocations is decidedly lacking. It seems, therefore, to be unwise to allow free election of studies, or to decide on a vocation, during the seventh, eighth, or ninth grades. During the period of adolescence interests are likely to be transient, and guidance is imperative. Preparation for life should be broad so that later when the individual has discovered himself he may select his vocation wisely. Studies of fundamental importance should be required of all, with possible rare exceptions, even though the subjects may not at first appeal to the pupil. Mathematics should be one of these required studies. 'ography of the Teaching of Mathematics-1911-1921 BY D. L. SMITH, Teachers College, AND J. A. FOBERG, State Department of Public Instruction, Pennsylvania TABLE OF CONTENTS' I. General Topics relating to the Teaching of Mathematics. 540 550 III. Arithmetic. 558 VIII. Graphs.. ........... XI. The Junior High School...... IV. Algebra .... V. Geometry.. VI. Trigonometry........... VII. Logarithms and Slide Rule.......... IX. The Metric System........ X. Advanced Mathematics in Secondary Schools...... XII. Needs of Special Groups.... XIII. College Entrance Examinations and Requirements.. XIV. Mathematics in Foreign Countries........................ 571 578 589 590 591 592 592 594 .. 595 598 600 1 This bibliography intends to include mention of all articles bearing on the teaching of mathematics which have appeared during the years 1911-1921 in the following Journals: The Mathematics Teacher School Science and Mathematics The Mathematical Gazette (England) The Educational Review Education The Journal of Education The Journal of Education (England) Educational Administration and Supervision The School Review The Journal of Educational Psychology I. General Topics Relating to the Teaching of Mathematics 1. Abbott, P. The Position of Mathematics in Educational Reconstruction. The Mathematical Gazette, vol. 9 (March, 1917), pp. 33-38. The effect of the war on conditions in England is discussed. Four specific reforms are suggested: (1) Compulsory attendance at day continuation classes until the age of 18; (2) Readjustment of curricula; (3) Reforms in examinations; (4) Developments in the training of teachers. Recommends that the minimum course in mathematics include algebra through easy equations, the trigonometry of the right triangle, the use of logarithms, and intuitive geometry. 2. Aitken, Robert. The language of mathematics. Journal of Education (Brit.), vol. 33 (1911), pp. 307-309. Discusses the bearing on modern mathematical education of the idea that the development of mathematical language accompanies closely, and at times even conditions, the development of the science itself. 3. Babb, Maurice. Are particular abilities necessary for the pupil to gain an understanding of the elementary and secondary mathematics as usually given at the present time? Mathematics Teacher, vol. 6 (June, 1914), pp. 209-216. A real leader rides not too far ahead. A tendency exists to neglect pedagogy in teaching mathematics. Accuracy, mental work and the comprehension of underlying principles are vital. Too much memorizing is a common fault. 4. Brookman, Thirmuthis. High school mathematics. Review, vol. 18, (Jan., 1910), pp. 20-28. School Suggestions concerning high school mathematics, the outcome of a year's study of various types of schools. 5. Carmichael, R. D. Mathematics and life-The vitalizing of secondary mathematics. School Science and Mathematics, vol. 15 (1915), pp. 105-115. 6. Discusses the part mathematics plays and should play in the development of the practical, esthetic, and moral phases of life. Carson, G. St. L. Some principles of mathematical education. Mathematical Gazette, vol. 7 (January, 1913), No. 103, p. 30. The three functions of mathematics: (1) starting from the postulates (truth of which is no concern at present) sets of deductions are evolved by use of the axioms; agreement with experience strengthens the evidence in favor of these postulates; (2) the investigation of the consistence of a set of postulates; (3) redundance of a set of postulates:-redundant if some of its members are logical consequences of others. 7. Chilcott, C. M. An experiment in coöperation. Journal of Education, vol. 75 (Feb. 1, 1912), pp. 125-127. Tells how new pedagogical ideas were worked out by the group method in first year high school mathematics classes. Individual, group and class progress the pupils represent by graphs. They took a marked stand against dishonesty; there was a strong spirit of coöperation, and the making of daily reports cultivated accuracy and helped pupils appreciate relative values. 8. Curtis, A. M. Recent criticisms of mathematics teaching and their results. Mathematics Teacher, vol. 9 (Dec., 1916), 9. 10. 11. pp. 94-102. Results of a questionnaire investigation involving the following questions: 1. Who are the leading critics of mathematics teaching? 2. What are their points of view? 3. What changes have you noted in the time allotted to mathematics in the high school course and in college courses? 4. Have there been appreciable changes in the arrangement of the courses? 5. What changes in length of courses do you suggest? 6. Is the preparation of your entering class improving or declining? 7. To what do you ascribe this change? Davis, Alfred. The status of mathematics in secondary schools. School Science and Mathematics, vol. 18 (Jan., 1918), pp. 25-35. A report of the answers to a questionnaire sent out to prominent doctors, lawyers, merchants, bankers, etc. in Chicago. It shows many interesting facts concerning the feeling entertained by the man of affairs toward high school mathematics. Valid aims and purposes for the study of mathematics in secondary schools. School Science and Mathematics, vol. 18 (1918), pp. 112-123; 208-220; 313-324. A report of a study by a committee of the Chicago Mathematics Club. Dobbs, W. J. Mathematics in secondary schools. Mathematical Gazette, vol. 9 (Mar., 1917), pp. 40-42. A scheme of study intended to reform the British curriculum. It is based upon the same general line of thought that has characterized the work of the National Committee on Mathematical Requirements. Recommends including mechanics in the secondary school, and an easy introduction to the Calculus. 12. Durell, Fletcher. Mathematics and efficiency. School Science and Mathematics, vol. 16 (1916), pp. 25-30. While this address is not concerned directly with the teaching of mathematics, it carries with it a suggestion in that it points out that mathematics may be an important aid in the "development to its full fruition of the leading thought of the age (efficiency)". 13. Dyson, F. W. A plea for astronomy. Mathematical Gazette, vol. 7 (Oct., 1914), No. 113, p. 394. 14. Astronomy and mathematics have grown up together and astronomical illustrations can be found which will enforce and perhaps enliven lessons in geometry and trigonometry. Goodwill, G. Some suggestions for a presentment of mathematics in closer touch with reality. Mathematical Gazette, vol. 9 (Mar., 1918), pp. 225-228. A plea for the elimination of certain details of secondary mathematics for the purpose of relating the subject more closely to mechanics and other branches in which it is easily applied. Mathe 15. Greenhill, Sir G. Mathematics in artillery science. matical Gazette, vol. 8 (March, 1915), No. 116, p. 25. Six months ago there was no such thing. But this is a mathematical war. Many real examples. 16. The use of mathematics. Mathematical Gazette, vol. 7, (Mar., 1914), No. 110, p. 253. Use not in sense of utilitarian applications but in the cultivation of intellect and correct thinking, in arriving at the right conclusion from data which are certain, and the enlargement generally of interest in life. 17. Hancock, Harris. Remarks on certain attacks that have been made upon the teaching of mathematics with counter criticisms. School and Society, vol. 6 (Sept. 22, 1917), pp. 339344. 18. Causes of defective Discusses adverse criticisms and deductions. education in our public schools are given as: 1. of teachers colleges--too much irrelevant and time-wasteful pedagogy; not enough actual and definite training. 2. Little emphasis on efficient scholarship of teachers. 3. Profession over feminized. study should be taken by What course of a boy who is entering high school? 1 (June 19, 1915), pp. 893-900. School and Society, vol. An account of an investigation which Mr. Hancock carried out in Cincinnati and other places in the United States. |