Harris Shultz, Janice Shultz, Richard Brown
Questions from various branches of mathematics that have answers that many teachers and students will find to be rather unexpected.
Timothy Gutmann
Students struggle with the formulas for computing the sines and cosines of sums of angles. My experience suggests this in part caused by the disconnect between the common, algebraic derivations of these identities and more hands-on approaches to trigonometry in which the sine and cosines functions can be experienced by students as measurements of segments within the unit circle. Here I explain a measurement-based derivation of these identities that has been helpful to my precalculus students.
Jeremy Kahan, Terry Wyberg
A probabilistic situation that can be studied through simulation, tree diagrams, and generating functions. This example illustrates the more general theme of teaching through problem solving.
Alexander Karp
The objectives, methods and tasks of the high school final examinations in mathematics administered in St. Petersburg (Russia).
David Hansen
Some remarkable relationships between the radii of a right triangle's inscribed and escribed circles and its sides, leading to the solution of a fascinating problem in number theory.
Martin Bonsangue, Gerald Gannon
How a problem involving sums of integers gave students insight into the idea of necessary and sufficient conditions.