Visualising positive and negative numbers on a number line is helpful for exploring problems involving operations with positive and negative numbers. This is because number lines lend themselves to exploring problems involving continuous linear contexts such as travelling distances and temperature. Teachers in a professional development program…

This article is the first in a series about teaching statistics. The authors discuss the role of statistics and the difference between mathematics and statistics.

In this article, Mark Colyvan argues that formal mathematical notation is more than just the language of mathematics. He gives examples of where notation plays a role in extending mathematical theory and in delivering explanations. He concludes that good mathematical notation, in both mathematics and empirical domains, helps us to think,…

In this paper, Richard Ollerton presents two alternative approaches to proving the six standard trigonometric angle sum and difference identities. They are suitable for students who have an understanding of rotation matrices.

The authors describe strategies a pre-service teacher used to orchestrate classroom discussions that encourage thinking. They show how small shifts in the questions posed can lead to substantial changes in student participation in classroom discourse.

Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…

In order to interpret students' attitudes about mathematics, Vesife Hatisaru asks: What do students find necessary or useful in learning mathematics? And what are the connections between their perceived needs for mathematics and their attitudes, views and feelings about mathematics? In this article, she provides evidence on these critical issues…

In this article, the authors present an inquiry activity presented to Year 7 students in a mathematics excellence class at a P-12 school in regional Queensland. Different students solved the activity (comparing the sugar content of fruit) using decimals, percentages, ratio and rates. By asking the students to solve a problem they were much more…

This article is the first in a series of activities that discusses some interesting relationships with triangles. Brian Sherman shows how to find five centres for a triangle--the circumcentre, the incentre, the orthocentre, the centroid and the nine-point centre, with four of the five to be found on the Euler line. With these centres, he shows…

In this edition's Discovery, the problem of interpreting the term "mean" is discussed with examples of the different kinds of mean. Mathematics teachers should therefore use the term "arithmetic mean" when introducing measures of central tendency in statistics. Some various definitions of the term "average" and sports…

This article argues the importance of teaching students about the philosophical and mathematical underpinnings of Australia's superannuation system as an example of a real-world problem context. It also provides a rationale for teaching financial modelling and decision-making in ways that respect the diverse financial realities represented in…

This article is the second in a series of activities that discusses some interesting relationships with triangles. Brian Sherman shows how to determine the altitudes of a triangle, its area, and the lengths of its circumradius and inradius. [For the first activity in the series, see EJ1259412.]

Peter Dunn and Margaret Marshman present the second of their data files articles in which they discuss the statistical investigation cycle which describes the whole process of conducting a statistical research study. [For "The Data Files: A Series of Articles to Support Mathematics Teachers to Teach Statistics," see EJ1259108.]

Like terms are usually defined for variables with numerical coefficients. While the definition is sufficient to combine polynomial terms, it does not help the students to combine radical, logarithmic, or trigonometric terms. The purpose of this paper is to propose a lesson that introduces a broader definition of like terms and trialed with a group…

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker…