Terence Mills introduces us to Keynsian probability and discusses its implications for teaching probability. The author considers it unlikely that Keynes's theory would replace how we teach probability, but argues that it may make us think more deeply about the use of terms such as chance and probability when used in our lessons.

There are both educational and cultural benefits to first language (L1) instruction, particularly in the early years of school, but in Australia, few Indigenous language-speaking students are taught in their own languages. Teaching mathematics in Indigenous languages requires both linguistically capable Indigenous educators and the identification…

Supporting students' problem-solving skills, solution planning and sequencing of different stages that are involved in successfully developing a meaningful solution to a problem has been a challenge for teachers. This case study was informed by reflective investigation methodology which explored how procedural flowcharts can support student…

Despite substantial research exploring multiplicative thinking and students' difficulty in the domain, the topic of multi-digit multiplication is under-researched. In this paper, I share a learning trajectory for multi-digit multiplication that combined social and cognitive perspectives of learning. Using Design Research methods and involving 45…

Mathematical games can be used to engage learners, promote fluency and deepen conceptual understanding. When considering the level of engagement of students, sometimes a small change can have a large impact. Something as simple as switching dice for cards in a game and, importantly, introducing a 'non-replacement' mechanism to the gameplay, can…

This paper employs Cultural Historical Activity Theory (CHAT) as an analytical heuristic in exploring the internationally prevalent situation of teaching out-of-field. Drawing on interview transcripts, we use CHAT to frame the activity of a young teacher teaching mathematics out-of-field in a small rural K-12 school in Australia. We identify and…

With the aim of engaging more students in meaningful thinking in mathematics, a cohort of Year 7 students were introduced to a 'Building Thinking Classrooms' framework for learning in mathematics. In this paper, the authors outline the key features of the implemented framework and share reflections on challenges and benefits.

The relationship Terry and I developed as colleagues and friends illustrates elements of the legacy she leaves. Our overlapping research interests stimulated conversations about synergies and differences between our theoretical perspectives. Depending on the situation and purpose, these interactions possessed different characteristics. Terry…

This paper reports on university students' responses to an inverse proportion question. The authors conclude that inverse proportion is a difficult concept that requires constant reinforcement, using approaches to teaching that facilitate deeper conceptual understanding.

Describing and analyzing teaching practice has been a focus of researchers interested in the interaction and connections between teachers' content knowledge and their pedagogical knowledge. This study described the role of a teacher's mathematical content and pedagogical content knowledge in involving students in learning and solving Science,…

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…

There is growing interest in mathematics learning progressions in early childhood education. Counting is a skill usually developed early in life. The application of the counting principles in early childhood typically entails counting objects. This poses challenges for learning about zero. Indeed, the word "zero" is seldom used in the…

Young children often explore partitioning as the idea of fair sharing in contexts where equal parts are created and distributed based on spatial constructs of the objects, rather than enumerating parts or collections. However, the presence of spatial reasoning in children's early fraction experiences is implicit within much of the literature and…

In his work leading professional development, Peter Klosterman found that teachers specifically asked for help teaching optimisation more effectively. To address challenges students often experience solving optimisation problems, he explains useful pedagogical strategies to support the teaching of optimisation and student learning in this topic.

At the school level statistics begins with exploratory data analysis, or EDA. Statistical learning goes on to include statistical inference, which will be discussed in the second part of this article. In this article, the author will talk about EDA and CODAP. EDA can be thought of as looking for patterns in data using graphs and simple statistics…