This paper describes a model of mathematics bianshi teaching using one problem with several solutions, changes, and applications in an inquiry-based classroom. Based on the model of mathematics bianshi teaching, the author discusses a class-room experience where one Chinese mathematics teacher takes a simple plane geometry problem to guide…

In this article, the authors present a task that promotes mathematical creativity. The task focuses on defining new geometric concepts, whilst providing students with creative thinking opportunities. They discuss prospective mathematics teachers' experiences while conducting a geometric definition task. Prospective mathematics teachers who…

Informal Australian discussion suggests that calculators are still widely regarded as devices for calculation, consistent with their naming, and are rarely recognised as potentially helpful to support students learning mathematics. In this paper, Barry Kissane explores some of the ways in which modern calculators might support students learning…

It is wildly held belief that one way to interest students in mathematics is to use real-world examples. Mathematics teachers are aware of the lack of interest in mathematics by many students and seek ways to improve their motivation. It seems reasonable to suggest that demonstrating to students the ubiquitous nature of mathematics may help…

In this article, the author reflects on the value of integrating concrete experiences into secondary mathematics classrooms. Her motivation in writing about this came from her experience as a secondary mathematics teacher, a specialist primary mathematics teacher, and a tertiary educator in both primary and secondary mathematics education. Through…

In this article, the author will demonstrate how gestures--often used in combination with offloading information on scratch paper--can be used to help students with difficulties in mathematics succeed with secondary level algebra. The authors will provide key examples from three studies of the algebra learning of students with mathematics…

This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…

Inductive reasoning is used when generalizing from particular cases to a general theory. The purpose of this paper is to present some highlights in the history of the problem of induction through notes on a selection of writers from ancient Greece to modern times. These notes contribute to the argument that there is a fundamental problem with…

This article is motivated by the importance of developing statistically literate students. The authors present a selection of problems that could be used to motivate student interest in probability as well as providing additional depth to the curriculum when used alongside traditional resources. The solutions presented utilise natural frequencies…

When teaching practice changes due to unwelcome forces, like COVID-19, there still could be pedagogical innovations worth keeping in post-pandemic toolboxes. This leads to the questions: What teaching practices from the pandemic do we want to keep or modify? What lessons learned from the pandemic should we consider keeping when moving forward?…

Whilst there has been significant focus on STEM in Australian education for several years, there has been very little focus on the integration of Digital Technologies (especially coding) with the other STEM disciplines. Similarly, high school mathematics education remains largely a standalone discipline. This paper describes a full year…

The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

Across nearly 20 years working as a secondary mathematics teacher, the author noticed two overarching goals that most teachers of mathematics consider to be important in their practice: (1) students knowing and understanding the content; and (2) students engaging with the learning and enjoying their time in class. However, in practice, attaining…

The mathematics curricula of Australia (ACARA, 2019), Scotland, England and America all require an understanding of proof by contradiction. Specifically, proof by contradiction is included as a Geometry topic in Specialist Mathematics (Version 8.4). In Specialist Mathematics, it is expected that students construct proofs in a variety of contexts…

The short activity presented in this article continues a discussion related to the value of golden ratio explorations in secondary mathematics, and acts as a companion to the earlier paper in this journal (Crawley, 2023). Exploring meaningful ways in which teachers can elicit students' interest and engagement in mathematics is vital, and…