Geometry for the Classroom by C.Herbert Clemens (PDF)

Description

Intended for use in college courses for prospective or in-service secondary school teachers of geometry. Designed to give teachers broad preparation in the content of elementary geometry as well as closely related topics of a slightly more advanced nature. The presentation and the modular format are designed to incorporate a flexible methodology for the teaching of geometry, one that can be adapted to different classroom settings. The basic strategy is to develop the few fundamental concepts of elementary geometry, first in intuitive form, and then more rigorously. The rest of the material is then built up out of these concepts through a combination of exposition and “guided discovery” in the problem sections. A separate volume including the solutions to the exercises is also available.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book makes me appreciate the technology we have now. The father and son team who wrote the book used old computer technology we would struggle with now. I appreciate their proofs and opportunities to try things out. Great for teachers and students. If I were a parent I would buy this for my junior high student.

⭐this looks like quite possibly the book i need for my college course for geometry teachers. Other books either assume the students still remember all their high school geometry, and are only interested in the most esoteric parts of the subject that eluded mathematicians for centuries, or are actually written for high school students, with too many superfluous pictures of catchy things, and pages of irrelevant and trivial material.Dr Clemens has written a very spare, absolutely elementary, and yet substantive treatment of the most important fundamental and useful parts of euclidean geometry. He has also sketched the other main geometries “sphereworld” and “hyperbolicland” in his eminently understandable yet authoritative style.Just glancing through it I already learned that the sum of the interior angles of a polygon apparently does not depend on the polygon being convex which I had assumed to be needed.He even teaches the cavalieri principle that two figures with the same size cross sections actually have the same size. he makes everything look so easy, because he understands it so deeply, that he can include topics others might think too advanced, without departing from the elementary tone of the book.Early on you find simple tasks like “copy this segment on that line with your compass.” and you think boy this is easy, anyone can do this. A short time later you are learning to construct a pentagon! something not evryone knows how to do at all. He even includes a wonderful attempt by an eighth grader to construct a heptagon, something which is theoretically impossible, but it is not easy to see whay the very good approximation given is not quite perfect. Indeed in the real world of approximations, it would do very nicely!The price is also reasonable in a market where many mediocre books cost over twice as much.If you need a book that starts from scratch, quickly reviews the basic intuition of elementary geometry, then passes to constructions, and only then to the idea of proofs, take a look at this little work by a world expert geometer who is deeply commited to teaching and improving teaching throughout the world.For students who are more advanced, I recommend hartshorne’s new book, Geometry: Euclid and Beyond.

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