There are substantial and ongoing concerns in the Australian and international secondary and tertiary education sectors about students' transition from secondary to tertiary mathematics. Of recent concern is the number of students choosing Advanced Mathematics (AM) in the last two years of secondary school. Declining enrolments in AM in secondary…

In contemporary Australia, an informed citizenry and a workforce with strong STEM-related skills are increasingly taken for granted. Yet it has also been well-established that females are underrepresented in STEM-related fields. In this article, Helen Forgasz and Gilah Leder focus on the M in STEM, that is, mathematics, and with a particular…

South Australian Secondary Mathematics teachers consider their testing parameters (duration and frequency) to be consistent with teachers elsewhere in the state, however, formal evidence is not available. A review of literature presented similar gaps in this evidence in other jurisdictions in Australia. The logic model that underpins the resource…

The proposed revisions to the "Australian Curriculum: Mathematics" highlight the importance of learning to mathematise, problem-solve and reason in real world contexts, including financial contexts. Through the Economics + Maths = Financial Capability research project, the authors have been imagining fresh ideas for connecting the…

The authors describe and discuss an activity in which primary school students were instructed how to use graph theory to solve a spatial puzzle. This activity was aligned with the design principles of vicarious failure. They discuss how this impacted the type of dialogue observed in the classroom and found that students were more likely to focus…

The integration of Science, Technology, Engineering and Mathematics is increasingly advocated by government and industry, in a world where complex global challenges require knowledge from multiple disciplines. The author explores approaches to integrating the breadth of learning described in the curriculum for each STEM discipline. She concludes…

Quadratic equations are a notorious topic for the challenge it provides to students in secondary mathematics. Despite this, there is limited research, particularly in the Australian context, that explains why such challenges persist. This article details the causes of Year 11 students' difficulties in solving quadratic equations. Observing…

Mathematical representations are 'visible productions' that embody mathematical ideas. The author guides teachers with suggestions for the use of representations in mathematical problem solving with students. Representations can be used to help make abstract mathematical ideas accessible, allowing teachers and students to interpret, communicate,…

In this article the authors describe how standard textbook questions can be turned into open questions to promote problem solving and reasoning. Six example solutions are given to one problem showing how an open problem can cater to the diversity of students in your class.

Derek Holton and Duncan Symons present the first in a series of three papers that address sequences and their patterns. Their explorations lead to classroom teaching suggestions that involve creative thinking.

This paper introduces tools for converting circular-featured-waste into polygonal construction parts and then 3D polyhedra. The tools, including diagrams, 3D printable joiners and mathematical formulae are designed for mathematics-related play, re-use, learning, design and improvisation. Activities for students include making assemblies, gathering…

In this article, the authors present variants to the classic problem the Prisoner's Dilemma. They discuss how senior secondary school students can use these variations to explore basic game theory concepts and develop mathematical proficiencies and practices. They also suggest how students can apply these concepts to decision-making processes in…

Barry Kissane describes a statistical modelling activity using a graphics calculator. Senior secondary students can explore Bureau of Meteorology data to determine whether the number of years with record breaking temperatures are more than expected--a sort of global warming null hypothesis.

The author, Sirin Budak, discusses how to model the problem of a frog climbing out of a well using piecewise functions and GeoGebra.

Two examples of mathematical modelling are explored. Firstly, optimising the distance travelled when jumping from a swing is discussed. The second concerns optimising the distance travelled by monkeys when swinging from branch to branch.