Exploring Word Problems across the Ages

A little bucket, one-third full, is 8 inches deep, and its upper and lower diameters are 7 inches and 6 inches, respectively. How large is the frog which, jumping into the bucket, causes the water to rise 3 inches? Word problems not unlike this example are a staple on math tests and of abiding interest to students, teachers, and professional mathematicians alike. Frank Swetz, a highly regarded mathematics educator, gathers hundreds of these problems in this fun and fascinating introduction to mathematics from around the world.

*Mathematical Expeditions* is a collection of over 500 culturally and historically diverse mathematical problems carefully chosen to enrich mathematics teaching from middle school through the college level. What better way to teach students the multicultural aspects of math than by assigning them problems first composed on clay tablets by Babylonian scribes, included in the Rhind papyrus, or Vedic problems scratched on tree bark? From Egypt to Greece to China to India, Swetz’s problems—both practical and abstract—span centuries and cultures.

Swetz has organized the problems by culture and historical period, showing, through the various constructs and contexts of the problems, the history and development of mathematics throughout the world. Along the way, he tells us what various cultures knew about math and how they came to learn it, providing instructors with a wonderful way to incorporate multicultural mathematics into the middle school, high school, and college classroom.

**Frank J. Swetz** is a professor emeritus of mathematics and education at The Pennsylvania State University. Among his numerous books are *Learning Activities from the History of Mathematics; Five Fingers to Infinity: A Journey through the History of Mathematics; *and *Capitalism and Arithmetic: The New Math of the 15th Century.*

"Swetz has collected word problems, or story problems, used to teach mathematics around the world and throughout history, so mathematics teachers in middle and secondary schools can use them today. University students of mathematics and its history might also find them useful as well as entertaining."

— Reference and Research Book News

"Swetz’s choice of problems is diverse and insightful. They provide a lively and engaging way to incorporate history into a mathematics course."

— Amy Shell-Gellasch, Beloit College

" *Mathematical Expeditions* is a wonderful resource for any teacher who would like to use old problems in a course to help students understand the context of mathematical ideas."

— Victor J. Katz - Mathematical Reviews

"The book is well thought-out and is recommended to readers interested in the history of mathematics."

— E. Keith Lloyd - London Mathematical Society Newsletter

"One of my graduate students, who is majoring in mathematics, was excited when I showed her a sample of problems in the book. A month later, she asked whether I had finished my review—she wanted to borrow the book!"

— Winifred A. Mallam - Mathematics Teacher