Pattern recognition is a critical component of success in mathematics. Students at all levels should be provided with opportunities to investigate and uncover patterns throughout their mathematical careers. Further, they should be allowed to explore situations in which pattern recognition plays a vital role in the construction of important…

The Internet, an exciting and radically different medium infiltrating pop culture, business, and education, is also a powerful educational tool with teaching and learning potential for mathematics. Web-based instructional tools allow students and teachers to actively and interactively participate in the learning process (Lynch, Moyer, Frye & Suh,…

For many years I have been advocating the use of hands-on materials to assist students in the understanding and application of mathematical concepts. Some of the methods have been introduced as small parts of earlier Discovery articles, (de Mestre, 1994, 1996, 1998, 1999a, 1999b, 1999c, 2000a, 2000b, 2001), but here I propose to devote the whole…

This document shows a different way of adding lists of numbers to find a way of getting general formulae for figurate numbers and use Gauss?s method to check it.

This article describes sound waves, their basis in the sine curve, Fourier's theorem of infinite series, the fractal equation and its application to the composition of music, together with algorithms (such as those employed by meteorologist Edward Lorenz in his discovery of chaos theory) that are now being used to compose fractal music on…

This article discusses prime numbers, defined as integers greater than 1 that are divisible only by only themselves and the number 1. A positive integer greater than 1 that is not a prime is called composite. The number 1 itself is considered neither prime nor composite. As the name suggests, prime numbers are one of the most basic but important…

Ever since the first mariners sailed off the east coast of Scotland the Bell Rock has claimed many vessels and countless lives. Also known as the Inch Cape Rocks they lie 18 km off the coast at Arbroath. Located near the mouth of the Firth of Forth and its important shipping ports these dangerous rocks cover an area some 440 m long and 90 m wide.…

The focus of this article is on Australian teachers' and pre-service teachers' gendered beliefs about their students and about computer use for mathematics learning. To illustrate what is happening in these areas, I will draw on results from two studies in which I have been engaged in recent years. I will also present the findings from other…

Trinity College is a low-fee independent school in Gawler, South Australia. The college has an enrolment of 3500 students of varied socioeconomic mix, drawn from the northern suburbs of Adelaide. Trinity has recently been restructured into four R-10 schools and one senior school for Years 11-13. The schools share a common mathematics curriculum.…

Tennis is a sport in which the mathematics involves an unusual scoring system together with other applications pertinent to the draw for different types of tournaments and the relative ratios of points won and lost. The name of the sport is thought to have originated from the French word "tenez", which translates roughly as "to receive (the…

This article is the sequel to the use of "Flatland" with beginning algebra students reported in Sriraman (2003). The use of "Flatland" with beginning algebra students resulted in the positive outcomes of cultivating critical thinking in the students as well as providing the teacher with the context necessary to introduce sophisticated mathematical…

The Golden Ratio is sometimes called the "Golden Section" or the "Divine Proportion", in which three points: A, B, and C, divide a line in this proportion if AC/AB = AB/BC. "Donald in Mathmagicland" includes a section about the Golden Ratio and the ratios within a five-pointed star or pentagram. This article presents two computing exercises that…

In early 2004, Cabrilog released version "II plus" of their interactive geometry package. According to the author, "Cabri Geometry II plus" is clearly a much more useful package than the earlier version. However, unlike other sophisticated applications packages, the designers have avoided creating so many options that secondary students lose their…

Technology is evolving and now some secondary classrooms see students using computer algebra systems (CAS), however, Zbiek (2003) points out that "graphical representations seem to abound in CAS-using classrooms" and "many [research] studies of the use of CAS depend highly on the graphing component of the tool". Kissane (2001) suggests that with…

This article presents a brief biography of Paul Erdos, who focused on problem-solving, particularly in the areas of number theory, combinatorics and graph theory. During his life he had no property, no family and no fixed address. He buttered his first piece of bread at age 21. He never cooked, nor ever drove a car. Another mathematician, Ron…