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We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.
Tractatus Logico Philosophicus, New York, 1922.
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Tools of American Mathematics Teaching, 1800-2000
Tools of American Mathematics Teaching 1800-2000, Peggy Aldrich Kidwell, Amy Ackerberg-Hastings and David Lindsay Roberts, 2008 , 418 pp. hardback $56.00, ISBN 13:978-0-8018-8814-4, Johns Hopkins University Press, Baltimore, www.press.jhu.edu
If you are used to reading books with fast action, car chases and multiple layers of intrigue, this book might be for you (except for the car chases). It covers over 200 years of math education evolution in its pages, and lets you in on the behind-the-scene development of much of what young math teachers now consider omnipresent and indispensable tools of the trade. How did textbooks begin and evolve? What are the origins of the blackboard? Who is responsible for the concept of the standardized test? What did the Cold War have to do with overhead projectors?
I am a child of the 60s, and remember SMSG, as well as programmed texts and the metric push, and it was interesting to read about the origins and struggles and fates of all. I remember Dolciani’s texts with the built-in transparencies, computers with multiple teletype terminals (I think I still have my punched-cards copy of my first program). Do you remember LOGO and Turtle Geometry? This book gives the story of the development and demise of all of these.
Some of my favorite sections dealt with the creation of various manipulatives, and the development of reliable graph paper. Each was slower to be embraced than I had imagined. Also, I have always been intrigued by the abacus/slide rule/calculator evolution, and I was able to grasp the panoramic scene of that movement with this book.
In short, I think three types of people will enjoy this book. Old math educators, who have lived through many of these developments, will find the reminiscing to be enjoyable. New math educators, who are clueless about the days of academic yore, will be interested to learn about their heritage. The third set of people is the complement of the union of the first two sets, those who are occasionally curious about such things and want to have the information available without having to resort to a Google search (about the only tool of math instruction that was not discussed). It is not a book to be read in one sitting, but each chapter is an enjoyable short story, and worh having on an educator's shelf.
Don Crossfield, Mathematics Teacher, Roseburg High School, Roseburg,OR
Crossfield, Don, "Tools of American Mathematics Teaching, 1800-2000," Loci (August 2008), DOI: 10.4169/loci002860