Artificial satellites are easily observed most nights when the weather is fine. The website called "Heavens Above" at www.heavens-above.com will help locate these satellites flying over one's location. It also includes how bright they will appear. The direction of travel of each satellite in the night sky also indicates the type of satellite. For…

In this article, the authors present an approach to developing open-ended problems through capturing contextualised mathematics in photographs. They draw upon their research with the Problem Posing Research Project, a collaborative venture between an Australian and a Canadian university to broaden pre-service teachers pedagogical practices in the…

This case study describes an "out of field" teacher's use of the Internet to teach a range of mathematical topics in a modified Year 8 mathematics class. It highlights the importance of three factors for implementing a discernible web-based teaching strategy: appropriate choice of web objects, effective "virtual" pedagogy, and technical support…

Archimedes, the famous Greek mathematician, lived from 287 BCE until approximately 212 BCE. He thought that the figure of two semi-circles on a straight line enclosed by a larger semi-circle resembled a shoemaker's knife. Archimedes called this figure an "arbelos" since arbelos is the Greek word for a shoemaker's knife. The author describes the…

Circle Geometry, a senior mathematics topic, is often regarded as time-consuming and associated relational concepts difficult for students to grasp. Units of work that introduce students to circle geometry theorems are frequently described as a string of tedious constructions. This article explores teacher-designed dynamic geometry software…

There is much to be learned and pondered by reading "Proofs and Refutations" by Imre Lakatos (Lakatos, 1976). It highlights the importance of mathematical definitions, and how definitions evolve to capture the essence of the object they are defining. It also provides an exhilarating encounter with the ups and downs of the mathematical reasoning…

The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the formula b2 +…

Statistics is often presented to students as a series of algorithms to be learnt by heart and applied at the appropriate time to get "the correct answer". This approach, while it may in fact produce the right answer, has been shown to be minimally effective at helping students understand the underlying statistical concepts. As Holmes noted,…

In this article, the authors show how students can form familiar geometric figures on the calculator keypad and generate numbers that are all divisible by a common number. Students are intrigued by the results and want to know "why it works". The activities can be presented and students given an extended amount of time to think about them. As…

Dice are considered one of the oldest gambling devices and thus many mathematicians have been interested in various dice gambling games in the past. Dice have been used to teach probability, and dice rolls can be effectively simulated using technology. The National Council of Teachers of Mathematics (NCTM) recommends that teachers use simulations…

Almost every adult in Australia has played Noughts and Crosses at some time in their life--it is that sort of game, a universal classic. Very few Australian adults play Noughts and Crosses, adult against adult, unless they are bored, witless and cannot think of anything better to do. Adults stop playing this game. Many will say it is boring, while…

This paper reports on the experiences of a group of teachers engaged in an action research project to develop critical numeracy classrooms. The teachers initially explored how contexts in the media could be used as bases for activities to encourage student discernment and critical thinking about the appropriate use of the underlying mathematical…

The way quadratic factorisation was usually taught to students in Bukit View Secondary was through the familiar "cross-method." However, some teachers felt that a significant number of students could not use the method effectively even after careful demonstration through repeated examples. In addition, many secondary mathematics teachers find it a…

The spread of swine flu has been a cause of great concern globally. With no vaccine developed as yet, (at time of writing in July 2009) and given the fact that modern-day humans can travel speedily across the world, there are fears that this disease may spread out of control. The worst-case scenario would be one of unfettered exponential growth.…

All common fractions can be written in decimal form. In this Discovery article, the author suggests that teachers ask their students to calculate the decimals by actually doing the divisions themselves, and later on they can use a calculator to check their answers. This article presents a lesson based on the research of Bolt (1982).