A special but common type of scenario is one in which a company has a promotion that is designed to make the customer purchase more of their product than they otherwise might. Although this can be aimed specifically at children, it really applies to all persons. The basic premise is that the company issues a "set" of different items or coupons and…

Mathematical fiction has probably existed since ideas have been written down and certainly as early as 414 BC (Kasman, 2000). Mathematical fiction is a recently rediscovered and growing literature, as sales of the novels: "The Curious Incident of the Dog in the Night-time" (Haddon, 2003) and "The Da Vinci Code" (Brown, 2004) attest. Science…

The activity "First One Home" in the Shell Centre's "Problems with Patterns and Numbers" Blue Box gives rise to a number of interesting patterns for those looking beyond the basic solution given in the book. The game is for two players, each taking turn and turn about to move a single counter on the grid down and/or to the left until one or the…

In set theory, one comes across the notion of "vacuous truth." A statement is vacuously true if it is true but does not quite say anything. The structure of a vacuously true statement is typically of the form: everything with property A also has property B, with the caveat being that there is nothing in property A. For instance one could say: all…

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…

Numeracy in the workplace is much more complex than the simple application of mathematical knowledge and skills learned in school or vocational education. Although the knowledge and skills developed in compulsory education or in formal adult and vocational education and training courses play a foundational role, they are inevitably transformed…

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…

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…

Pierre Bezier was born on September 1 in Paris, 1910. Choosing the career path of his father, he gained electrical and mechanical engineering degrees by the time he was 21 years old. He began working for the car company Renault and stayed there for the next 42 years. In 1977 he received a doctorate in mathematics. Bezier, at the age of 50 began…

Multiplication and division have in general been much more difficult to perform than addition and subtraction. Perhaps, if we could find some device for reducing multiplication and division to addition and subtraction, computational loads could be lightened. One such device is that of logarithms of course. This note outlines another such device…

In this paper I illustrate how kinaesthetic experiences associated with dance might be used in teaching to promote engagement and learning in spatial, rhythmic, structural and symbolic aspects of mathematics.

In a previous article in this series, it was suggested that it is part of our responsibility as teachers to attempt to induce "perturbations" in our students' mathematical thinking. Especially when teaching seniors and capable students at any level, it is important that we unsettle them, shake their perceptions and attempt, wherever possible, to…

Prime numbers play an extremely important role in modern mathematics. Apart from still being the object of intense research activity, their applications in banking and security underline a key phenomenon: in the modern world, useful applications of mathematics often come from very "pure" abstract theories. Curiously, despite their undeniable…

Mathematics should not be studied simply because it is useful; mathematics should be also studied because it nurtures both the mind and soul with its beauty. By completing the four activities described in this paper, students will appreciate mathematical ideas both rationally and emotionally. Since students' appreciation of mathematical ideas…

One of the most remarkable devices embedded in a Microsoft Excel spreadsheet is known as the spinner. Its staggering simplicity is undoubtedly its strength. As an incrementing device that allows graphs to dance across the screen, it gives the concept of variability a whole new meaning. Spinners and their close cousins scroll bars can be grabbed…