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*Historical Modules for the Teaching and Learning of Mathematics*, Victor Katz and Karen Dee Michalowicz, editors, 2004, CD-ROM $41.95, ISBN 0-88385-741-3, The Mathematical Association of America, /.

This CD contains materials for eleven topics that are normally taught in the secondary curriculum; they can be used in classes from Pre-Algebra up through Calculus. Each topic contains a historical background, student pages, and teacher pages with teaching suggestions and solutions to the student problems. The activities vary in length, and the time frames vary from fifteen minutes to one or more weeks.

Several lessons from the Exponentials and Logarithms were successfully used in Algebra II classes. Students actually calculated logarithms of numbers and used them to make their own slide rules. They were able to see how the rules of logarithms were really used in these rudimentary calculations. Even though the slide rules were rather simple devices, our students were surprised at the accuracy of their answers. This was truly an outstanding teaching/learning activity.

The activities in the Trigonometry module were quite informative. As in the activities described above, students were able to calculate selected values of the trig functions in several lessons. Students were also able to derive a number of formulae, including Heron’s Formula and The Law of Cosines; it was nice to see the students doing the details instead of having the teacher derive the rules on the board. The use of trigonometry in astronomy was very informative; students were surprised to learn that ancient civilizations were able to achieve such a high degree of accuracy in determining measurements. The variety of both right and non-right triangle problems was a break from standard textbook problems.

Students learned a great deal by doing a variety of lessons in the Length, Area and Volume section. Students were called upon to develop early formulae and then compare them with the versions that are now in use. It is important for students to know that mathematical ideas are not always perfect from the start, and they sometimes take long periods of time until they are corrected and verified. Many of these problems can be used on a stand-alone basis, and they could be quite useful before a holiday or with a shortened class period.

The lessons we used in our classes were all extremely worthwhile, and we plan on using more during the coming years. The only drawback is going through the CD and looking at an individual activity to determine its usefulness in the classroom. Although each module has a Table of Contents, there is no description of what each lesson entails. It does take time to go through each topic, since most modules contain well over one hundred pages of notes and student pages. If this were to be corrected, it would be a wonderful tool for each teacher to use in the classroom. The amount of history and mathematics that the students could learn would be almost limitless!

Lynn Godshall, David Lutz, and Neil Via, Mathematics Department, Susquehanna Township High School, Harrisburg, PA

Lynn Godshall, David Lutz, Neil Via, reviewers, "Historical Modules," *Loci* (July 2007)