In high school geometry courses, students are often given a prepackaged statement that they are asked to prove. In these situations, the process of writing proofs is being abridged, if not misrepresented. To provide her students with a more authentic experience in writing a proof, the author provided them with a summative project for which they…

A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…

In Volume 23(2) of the "Australian Senior Mathematics Journal," Boncek and Harden present an exercise in fitting a Markov chain model to rainfall data for Darwin Airport (Boncek & Harden, 2009). Days are subdivided into those with precipitation and precipitation-free days. The author abbreviates these labels to wet days and dry days. It is…

The United States of America is a large and diverse country; nevertheless, high schools have a lot in common across the nation. In particular, mathematics teaching in American high schools, while not stereotyped, has some accepted norms which would be seen as unusual here in Australia. In order for the Australians to learn from the Americans, as…

Being a mathematician, the author started to wonder if there are any theorems in mathematics that seem very ordinary on the outside, but when applied, have surprisingly far reaching consequences. The author thought about this and came up with the following unlikely candidate which follows immediately from the definition of the area of a rectangle…

This article examines an innovative question taken from the 1988 Extension 1 (3 unit) Mathematics New South Wales Higher School Certificate examination. Similar questions have made regular subsequent appearances in trial examinations around NSW and many texts now devote whole chapters to the subtle and somewhat laborious process of establishing…

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…

Traces the history of vocationalism in education and differentiates between competency-based education and training and the Key Competencies. Highlights recent developments in mathematics for the vocational education and training sector. Addresses the concept of vocationalism in schools and some issues associated with the implementation of…

Presents an activity carried out by aboriginal students that addresses solving a real-life problem that could be linked to number sequence, graph theory, and combinations. Contains 14 references. (ASK)

Focuses on the issues of the course advice given to secondary students who were intending to study one of the more demanding mathematics subjects in year 12. Concludes that all students would benefit from studying as much mathematics as they are capable of in terms of the problem-solving skills they would acquire and future course and career…

Describes four 50-minute lessons in which complex numbers are introduced to year-12 calculus students using hand-held calculators and laptop computers. (ASK)

Considers the use of technology, particularly programmable or graphics calculators and computer software, in the transition years from secondary to higher education. Discusses use of software systems like Mathematica in the extended investigative, problem solving, and modeling Common Assessment Tasks of the Victorian Certificate of Education.…

Explores and illustrates the range of ways in which the design of mathematics examination tasks can be influenced by graphics calculators from the perspective of the people designing the exams. Also discusses principles for awarding partial credit to student responses. (Author/PVD)

Demonstrates the capabilities of graphics calculators in assisting with a simple mathematical investigation. Subjects covered include Direct Calculation, Tables, Graphing Particular Cases, Logarithms, Parametric Solutions, and Three-Dimensional Plots and Contours. The question posed for investigation with the calculator is, for what pairs of…

Discusses the implications for teaching of the decision to permit use of graphics calculators in some Victorian Certificate of Education examinations. Also explores the impact of this decision on assessment in mathematics, argues that some amendments should be made to the policy, and looks ahead to the near future when students will have ready…