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January 1999, Volume 92, Issue 1

FEATURES

Random Variables: Simulations and Surprising Connections
Robert Quinn, Stephen Tomlinson
Integrating probability and statistics within the curriculum provides a number of interesting and elegant connections that help students develop an appreciation for the inherent beauty of mathematics. This lesson on random variables incorporates class discussion and experimental activities in the practical and theoretical exploration of one such connection.

Cooperative Learning in Mathematics Teacher Education
Robert Quinn, Stephen Tomlinson
How a cooperative-learning activity was used in a college mathematics-teacher-education course to enable preservice and in-service middle and high school mathematics teachers to experience, learn about, and reflect on the intricacies, complexities, and values of effective cooperative-learning strategies.

The Postage-Stamp Problem, Number Theory, and the Programmable Calculator
Harris Shultz
The "postage-stamp problem" is a classic question in the area of Diophantine equations. Students can explore this rich and accessible problem to deepen their understanding of linear equations.

The Euler Line and Nine-Point-Circle Theorems
Frank Eccles
A train of ideas leading to the application of a particular transformation, a dilation, to the proofs of both the Euler line and nine-point-circle theorems, to help introduce students to the important role that functions can play in the field of geometry.

In Search of Perfect Triangles
Martin Bonsangue, Gerald Gannon, Ed Buchman, Nathan Gross
Working on the perfect-triangle problem was a real mountaintop experience in mathematics. Our problem-solving path started with basic geometry, followed by a little algebra, then more geometry and more algebra. Our tour was enhanced by using a computer not to solve the problem but to explore its solution.