Combining Strands of Many Colors: Episodes from Medieval Islam for the Mathematics Classroom

In my first- and second-year college classes, I infuse the standard curriculum with a small number of historical and cross-cultural activities closely linked to traditional topics. The activities, which I developed and have used since 2001, take the form of written, self-paced lessons or modules. Each activity focuses on a mathematical technique used in the medieval Arab or Islamic world. My students look at the cultural and historical context of the technique and its links to other methods, most often from the mathematics of medieval India and China. They explore the theory behind the technique, and they see how it is used to solve “real-world” problems, including the type of problem that prompted its discovery.

On the pages that follow, I will describe:

• how the presence and interests of my culturally diverse students prompted me to find ways to learn and to teach about the mathematical contributions of Muslim, Indian, Chinese, and other peoples (page 2);
• the goals I had in mind as I created my classroom activities (page 3);
• how these goals are met by the activity, “Combinations and Their Sums,” based on counting tassels of colored silk (pages 4 and 5);
• reactions from my students (page 6);
• creating a calculus activity, “Using the Derivative to Solve an Optimization Problem,” for which the challenge of modernization was greater than for the activity on combinations (page 7); and
• more ideas for activities and projects based on Islamic mathematics (page 8).  

The five modules may be downloaded from this page and also at other convenient points throughout the article:

• Combinations and Their Sums (Elementary Statistics, Finite Mathematics)
• Binomial Coefficients and Subsets (Finite Mathematics)
• Using the Derivative to Solve an Optimization Problem (Calculus for Business and Social Sciences)
• The Rule of Double False Position (Calculus for Business and Social Sciences)
• The Rule of Double False Position (Linear Algebra)