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Mathematical Expeditions: Exploring Word Problems across the Ages

Frank J. Swetz
Johns Hopkins University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Charles Ashbacher
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Although cultural differences change the contextual surroundings of mathematical word problems in terms of the words and situations, the problems themselves are largely similar across cultures. For example, the problem

A farmer buys ducks, chickens and geese with each chicken worth one {currency}, a duck two {currency} and a goose three {currency}. If the farmer spends 60 {currency} how many of each animal did he buy?

is found in all cultures. Building problems are also universal, since a right-angle construction was the same in ancient China and Egypt as it is now. There is a lot of truth to the argument that any initial communication that humans may have with space aliens will be via mathematics. I cannot read a single word of ancient Chinese, Japanese or Egyptian, yet it is generally possible to discern what the message is in the images of problems from those cultures.

This book is a history of the mathematical word problem, with the timeframe being from the beginning of recorded history up through the nineteenth century. The book is split into chapters based on the combination of location and historical era. For example, some of the chapter headings are:

  • Ancient Babylonia 2002–1000 BCE
  • Ancient Egypt
  • Ancient China
  • India
  • Islam
  • Japanese Temple Problems

A large number of word problems are given in each chapter, each a translation of a problem that appeared in that era and location. Solutions are given in an appendix. There is a lot of repetition in terms of types of problems.

This book is an excellent supplement to a course in mathematical history as well as a resource for problems in a high school or college algebra class. It will provide a way for mathematics teachers to demonstrate how universal and timeless mathematics is.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

The table of contents is not available.