Teaching Classic Probability Problems with Modern Digital Tools

ABSTRACT

This article is written to share teaching ideas about using commonly available computer applications—a spreadsheet, The Geometer's Sketchpad, and Wolfram Alpha—to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors’ work with prospective economists, mathematicians, and teachers. The historical contexts include the problem of the division of stakes (14^th century), the problem of the Grand Duke of Tuscany (17^th century), and the problem of co-primality of two natural numbers chosen at random (19^th century). The suggested use of computers can be extended to other probability contexts to achieve at least two goals: to make complex mathematical ideas more accessible and to emphasize the importance of experimental evidence as a means of conceptual development in mathematics for all student populations.

KEYWORDS:

• Probability
• relative frequency
• historical perspectives
• mathematics education
• spreadsheets
• Wolfram Alpha
• computational experiments

Acknowledgements

This paper is written in the framework of the Agreement for Cooperation (08/2-04-P-016-033) between the State University of New York and Saint Petersburg State University. Research of the second author was supported by RFBR grant No. 16-01-00258 and SPbU – DFG grant 6.65.37.2017.