The Birthday Paradox problem can be investigated either with a carefully constructed spreadsheet (for greatest precision) or a calculator process (for reasonable precision). A number of ways of approaching this problem as a class activity are provided.

Mathematics problems that are unfamiliar to students and contain multiple sets of information can overwhelm many struggling learners (Swanson & Beebe-Frankenberger, 2004). Academic interventions utilising visual representations can support students who are struggling to remember information and think through challenging multi-step problems…

Should proof by induction be reserved for higher levels of mathematical instruction? How can teachers show students the nature of mathematics without first requiring that they master algebra and calculus? Proof by induction is one of the more difficult types of proof to teach, to learn, and to understand. Thus, this article delves deeper into…

Manfred Hauben proposes an approach to teaching non-transitive relationships between 'paradoxical' dice using simple statistical graphics. This method usefully supplements traditional approaches of conditional probability calculations and trees, and students are thereby better able to see what is going on and the mechanism of these relationships.

The simple and compound interest formulas in isolation have limited usefulness for financial planning--until the concept of a regular payment is introduced. This article presents and discusses a simple investigation given to an advanced Year 10 mathematics class, with most students looking to study Mathematical Methods in Years 11 and 12. This…

The Three-Square Puzzle shows a remarkable relationship between three angles. What happens when the number of squares increases? This article explores that question and brings in Fibonacci and Lucas sequences.

Inspiration from 'Confessions of a Shopaholic' led this team to explore how comics can be used for mathematics instruction about percentages. In this article, the authors describe how they conceptualised and developed a teaching package that uses comics to teach percentage concepts to Grade 7 students (age 13 to 14) in Singapore. It goes on to…

Increasing and decreasing functions can be combined into a quadratic to explore the competing demands of number of sales, price points and profit (or loss). An interesting application of taxation rates is also explored.

In mathematics, there are countless connections between apparently unrelated topics. Students often find these relationships interesting, and they contribute to expanding their mathematical repertoires. This article describes one of these unusual connections, between the sum of periodic functions and the commensurable and incommensurable numbers.…

The mathematics standards for many countries include teaching and learning ratios, typically with efficient algorithms and strategies (Australian Curriculum: Mathematics, Assessment and Reporting Authority, 2017; National Council of Teachers of Mathematics, 2014). In the 1990s, Cramer and Post (1993) claimed that school mathematics mostly involves…

Integrating the disciplines of mathematics and science is one way to place the calculations of volume and surface area into a real life context. The authors present an activity for middle-school students that aims to promote their learning of these key concepts in a personally meaningful way, whilst also developing inquiry and problem solving…

In this article, the authors present the use of digital tape diagrams--implemented using GeoGebra (2001) dynamic mathematics software--as a support to static diagrams to pose and solve proportional reasoning tasks. They show how dynamic sketches can allow students to explore standard tasks in proportional reasoning in ways that emphasise…

A perspective developed and implemented forty years ago, the teaching of mathematics for social justice has grown as an area of importance in Australia. The authors present an example of algebraic activities focusing on social justice.

Explaining the complexity of mathematics teaching to others can be challenging. The Knowledge Quartet, a pedagogical content knowledge (PCK) framework from the UK, provides a fresh lens to reflect on mathematics classroom practice. Developed from videotaped mathematics lessons taught by final year pre-service teachers, the Knowledge Quartet…

Estimation skills are critical for students in the 21st century. The ability to estimate or approximate is widely accepted as fundamental to problem solving, and important for checking the reasonableness of results. (Dowker, 2003; Reys & Reys, 1989). Therefore, estimation should be an important aspect of problem solving in all year levels but…