The economic fallout from the COVID-19 pandemic is exposing more and more Australians to financial loss, hardship and poverty. Even primary-aged students may be privy to conversations about unemployment, business closures, household budgeting, and difficulties making ends meet. Mathematics is a powerful tool that can raise awareness of inequity…

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

We investigated human performance on the Euclidean Traveling Salesperson Problem (TSP) and Euclidean Minimum Spanning Tree Problem (MST-P) in regards to a factor that has previously received little attention within the literature: the spatial distributions of TSP and MST-P stimuli. First, we describe a method for quantifying the relative degree of…

Rhetoric about the importance of students being equipped to apply mathematics to relevant problems arising in their lives, individually, as citizens, and in the workplace has never been matched by serious policy or curricular support. This paper identifies and elaborates authenticity implications for addressing this issue, and describes aspects of…

An experiment is reported comparing human performance on two kinds of visually presented traveling salesperson problems (TSPs), those reliant on Euclidean geometry and those reliant on city block geometry. Across multiple array sizes, human performance was near-optimal in both geometries, but was slightly better in the Euclidean format. Even so,…

This article presents a mathematical solution to a motorway problem. The motorway problem is an excellent application in optimisation. As it integrates the concepts of trigonometric functions and differentiation, the motorway problem can be used quite effectively as the basis for an assessment tool in senior secondary mathematics subjects.…

Pattern generalising problems offer a very rich context for exploring relationships among quantities, expressing generality and representing the same relationship in different ways. Selecting appropriate tasks for students to work on in class is by no means a straightforward process, but there are ways to handle it. This article aims to explore…

Mathematical skills and reasoning and their applications are considered as forming one of the basic and essential areas of knowledge and experience that should be available to all Australian children. This collection of essays explaining problem solving in mathematics as an organizing theme for current and future curriculum development is a means…

Attempts to raise some of the issues involved in incorporating mathematical modelling with classroom teaching, as well as providing some background for those unfamiliar with the area. (PK)

This Australian document is a guide to teaching mathematics as it relates to specific work situations. After a brief introduction, chapter 1 looks at problem solving, advises teachers to lower the reading level and thus raise the understandability of written math problems, and describes a four-step problem-solving process. Chapter 2 outlines a…

Predictors of retrieval times produced by students having difficulty developing a reliance on retrieval for simple addition were discovered. The findings support the notion that separate limitations operate in working memory when retrieval occurs and call into question the use of the term "retrieval deficit" to explain difficulties…

A cognitive/metacognitive framework is presented for analysing applications tasks and responses to these. Conditions facilitating or impeding access to such tasks at the upper secondary level were identified using qualitative data analysis techniques within this framework. Strategies employed in exploiting, or overcoming these conditions were…