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Hands on History, A Resource for Teaching Math

Don Crossfield, reviewer

Hands on History: A Resource for Teaching Math, Amy Shell-Gellasch Editor, 2007,  177pp, $53.95 list price, $42.95 member price, paperbound , ISBN 978-0-88385-182-1 , Catalog Code NTE72.

This resource fills a noticeable void in the supplemental material available to the mathematics instructor.  The editor points out that although the huge resources of the Internet provide a vast virtual world for exploration, that touching and holding and measuring should still be a significant part of every student’s education.

The articles include puzzles like the Tower of Hanoi, tiling to discover Pythagoras’ theorem, string models of conic sections, tools to construct mechanical curves, instruments for surveying both land and space, clocks of both the sundial and pendulum variety, completing actual squares and cubes to illustrate the parallel algebraic operations, and a blueprint/article for building and using a brachistochrone (a curve of quickest descent), which intrigues this Calculus teacher.  A great picture of students and teachers exploring a working model of a brachistochrone may be found on the cover of the Fall 2002 issue of The Mathematical Intelligencer, and the March/April 1999 issue of Quantum has an excellent supplemental article to the curve’s history, including its relationship to the pendulum clock.

If even a few of these apparati were available to be played with, or simply displayed in cases for the curious, the mathematics educations of our charges would be enhanced.  Nice work putting together this resource.

Other relevant and related materials, for the reader whose curiosity has been piqued by this book, are

  • H. M. Cundy, A. P. Rollett. Mathematical Models. Second Edition. Oxford University Press, London, 1961.   This describes methods for building a wide variety of models and instruments.
  • P. A. Kidwell. ``American Mathematics Viewed Objectively: The Case of Geometric Models'' in Vita Mathematica, R. Calinger, ed. Mathematical Association of America, 1996.
  • The University of Arizona math site shows some photos of ruled surfaces, which are the string models mentioned above, at
  • One of many sites on the Tower of Hanoi is  This one suggests that the tower’s ancient history is fraudulent, and that the French mathematician Edouard Lucas invented both the game and the history in 1883. 
  • A most excellent historical reference on the brachistochrone, with much interesting detail including the wording of Johann Bernoulli’s challenge problem, may be found at  This site should be visited.

Don Crossfield, Mathematics Teacher, Roseburg H.S. , Roseburg, OR

See also the MAA Review by Álvaro Lozano-Robledo.


Don Crossfield, reviewer, "Hands on History, A Resource for Teaching Math," Convergence (March 2008)