Formal inference, which makes theoretical assumptions about distributions and applies hypothesis testing procedures with null and alternative hypotheses, is notoriously difficult for tertiary students to master. The debate about whether this content should appear in Years 11 and 12 of the "Australian Curriculum: Mathematics" has gone on for…

The notion of periodicity stands for regular recurrence of phenomena in a particular order in nature or in the actions of man, machine, etc. Many examples can be given from daily life featuring periodicity. Mathematically the meaning of periodicity is that some value recurs with a constant frequency. Students learn about the periodicity of the…

The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

Trigonometry is a well known branch of Mathematics. The study of trigonometry is of great importance in surveying, astronomy, navigation, engineering, and in different branches of science. This paper reports on the discovery of flaws in the traditional definitions of trigonometric ratios of an angle, which (in most cases) make use of the most…

Educators look for "teaching opportunities" within the curriculum to "bring the practice of knowing mathematics in school closer to what it means to know within the discipline". The need to emphasise disciplinarity--and the concomitant canons of logic, consistency, and connections--in the teaching of mathematics is in line with the proficiency…

When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…

This paper is presented in two parts. Through an example the first part takes up the issue of applying mathematics to situations that form part of the life context of students--the priority expressed in three curriculum statements presented. Then, noting the particular point in time--development of a National Curriculum for Mathematics--the second…

This article describes a laboratory module on Fourier series and Gibbs phenomenon which was undertaken by 32 Year 12 students. It shows how the use of CAS played the role of an "amplifier" by making higher level mathematical concepts accessible to students of year 12. Using Mathematica students were able to visualise Fourier series of functions…

One of the author's undergraduate students recently asked him whether it was possible to generate a random positive integer. After some thought, the author realised that there were plenty of interesting mathematical ideas inherent in her question. So much so in fact, that the author decided to organise a workshop, open both to undergraduates and…

In this article, the authors present a lesson whose goal is to utilise a scientific environment to immerse a trigonometry student in the process of mathematical modelling. The scientific environment utilised during this activity is a physics simulation called "Wave on a String" created by the PhET Interactive Simulations Project at Colorado…

Trigonometry is an integral part of the draft for the Senior Secondary Australian National Curriculum for Mathematics, as it is a topic in Unit 2 of both Specialist Mathematics and Mathematics Methods, and a reviewing topic in Unit 1, Topic 3: Measurement and Geometry of General Mathematics. However, learning trigonometric ideas is difficult for…

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution…

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…

The quest to find the equation of a catenary makes an ideal investigation for upper secondary students. In the modelling exercise that follows, no knowledge of calculus is required to gain a fairly good understanding of the nature of the curve. This investigation is best described as a scientific investigation--a "hands on" experience that…

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…