It is always interesting to challenge more capable students with things that they have tended to take for granted. One area in particular that students often tend to overlook in their senior years concerns the important understandings associated with domains and ranges of functions. In this article, the author shares a few favourite questions that…

Despite the assurances of store employees, whenever a deal is on offer it always pays to apply a little logic (and mathematics) to see just how to use it most effectively. In this article, the author displays how to employ this technique by using the example of a shoe store that advertised "second pair half price" (with the fine print…

Between the 17th and 19th centuries, the Japanese government closed its borders to the outside world in an attempt to become more powerful. Foreign books were banned, people could not travel, and foreigners were not allowed to enter the country. One result of this isolation was the flourishing of sangaku--wooden tablets inscribed with intricately…

Perhaps next time teachers head towards the fundamental theorem of calculus in their classroom, they may wish to consider Fermat's technique of finding expressions for areas under curves, beautifully outlined in Boyer's History of Mathematics. Pierre de Fermat (1601-1665) developed some important results in the journey toward the discovery of the…

As time has progressed, the role of applied mathematics has become increasingly important. Indeed there are now more students enrolled in applied mathematics courses in senior high schools and colleges than in pure mathematics. Such courses become more relevant both to the student and to future employers, if the same constants and equations that…

The author of this article, while recently working through some problem sets on determining volumes by triple integrals in cylindrical and spherical coordinate systems, realized that, although the textbook he was using included many interesting problems involving spheres, cylinders and cones and the increasingly complex solids that arose from the…

The motivation of students is of great import to mathematics teachers. Such an abstract powerful language needs to be valued or students will not wish to study it. This article argues that mathematics may be better appreciated through the beauty of the language in which problems are written, respect for the cultures of others and through relevance…

This article presents two classroom episodes in which students were exposed to the value of asking questions and to the different roles played by proof in mathematics. The conversation in the two episodes is outlined in the article. The setting was a classroom of fifteen good high-school students, who were studying calculus. These episodes…

The concept of function is central to the teaching and learning of mathematics. As a mathematical notion, the concept of function is fundamental, yet powerful, and is a unifying theme that is found running throughout most branches of mathematics. Until quite recently, when it came to the elementary transcendental functions it was commonly…