The Teaching of Mathematics in Secondary Schools

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Macmillan, 1912 - Mathematics - 370 pages
 

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Page 197 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 33 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 360 - A. sin (A + B) - sin A cos B + cos A sin B. sin (A - B) - sin A cos B - cos A sin B. cos (A + B) - cos A cos B - sin A sin B. cos (A - B) = cos A cos B + sin A sin B.
Page 266 - The study of solid geometry strengthens the student's space imagination and his power to image space configurations, and it gives him an understanding for drawings that represent spatial objects. Altogether it seems that the utilitarian advantages are somewhat greater, but the purely cultural advantages somewhat smaller, than in plane geometry. With such restrictions the study of solid geometry will not offer great difficulty to the student. It may require a little more time and a little more study,...
Page vi - This book is modern in the sense that it attempts to make mathematical instruction less informational and tries to show how to train students in attacking mathematical problems instead of merely making them learn mathematical facts. But it is not modern in the sense that it advocates certain recent fashions which aim to replace the true study of mathematics by applications of doubtful value. While admitting...
Page 192 - A line parallel to one side of a triangle divides the other two sides proportionally.
Page 174 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page v - Cloth, 12mo, 370 pages, $1.25 The author's long and successful experience as a teacher of mathematics in secondary schools and his careful study of the subject from the pedagogical point of view, enable him to speak with unusual authority. " The chief object of the book,' he says in the preface, "is to contribute towards making mathematical teaching less informational and more disciplinary. Most teachers admit that mathematical instruction derives its importance from the mental training that it affords,...
Page 337 - S = vat + \gf, where g = 32.16. 21. In what time will a body fall 1000 feet if thrown downward with a velocity of 20 feet per second ? 22. With what velocity must a body be thrown downward in order that it shall fall 360 feet in 3 seconds ? 23. A stone is dropped into a well, and the sound of its striking the bottom is heard in 3 seconds. How deep is the well if sound travels 1080 feet per second ? A body thrown upward with a certain velocity will rise as far as it would have to fall to acquire this...
Page vi - This book covers a much more restricted field, but does it in greater detail. All references to elementary school work, to history, to the description of movements in other countries, to the material equipment, to mathematical clubs, etc., are excluded, and the discussion of general methods is restricted to their fundamental and most useful phases.

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