A major problem for teachers is that students are different, they learn mathematics differently, and at different rates. Regardless of this, schools organise students into large groups or classes of 20 to 30 students all about the same age. Then there is the "Australian Curriculum: Mathematics" that states the student learning outcomes…

The importance of ratio and proportional reasoning is regularly emphasised, however, the teaching and learning of these concepts continues to present challenges. In this article the authors explore a hands-on task, designed to encourage student visualisation of the concept of ratio. Teacher perceptions of this task were positive, indicating the…

The role of manipulative materials in mathematics can be a contentious one. It seems that in the mind of some teachers, manipulatives are fine in the early years but have no place in a rigorous maths classroom as the students get older. It is a topic worth our consideration.

This article describes part of a study in which researchers designed lesson sequences based around using a string number line to help teachers support children's development of relative thinking and understanding of linear scale. In the first year of the study, eight teachers of Years 3-5 participated in four one-day professional development…

Productive struggle leads to productive classrooms where students work on complex problems, are encouraged to take risks, can struggle and fail yet still feel good about working on hard problems (Boaler, 2016). Teachers can foster a classroom culture that values and promotes productive struggle by providing students with challenging tasks. These…

One of the challenges facing teacher educators is providing our pre-service teachers (PSTs) with authentic experiences that cross the boundaries between Initial Teacher Education (ITE) and the classroom. An additional challenge facing the mathematics teacher educator, is addressing and deepening PSTs' mathematical content knowledge (MCK), which…

Providing students with an opportunity to explore mathematical content through games allows teachers to include tasks that: (1) present alternative representations of the content; (2) welcome various expressions of mathematical reasoning; and (3) incorporate variations that empower all students to engage in the problem solving process. Games not…

Very recently, in the "Australian Association of Mathematics Teachers (AAMT)/Australian Industry Group quantitative report" (2014), concerns were raised that school mathematics is lacking real world application. This report highlighted the gaps between school mathematics and the requirements of the workplace. After interviewing industry…

Introducing challenging tasks in such a way that makes them accessible, rather than daunting, to students is a challenge for teachers. Solving challenging tasks involves students having to grapple with the problem. The role of the teacher is to motivate and clarify the problem rather than showing students how to solve the problem.

The use of enabling and extending prompts allows tasks to be both accessible and challenging within a classroom. This article provides an example of how to use enabling and extending prompts effectively when employing a challenging task in Year 2.

This paper reports on a large national project that explored successful numeracy practices in remote and very remote schools. While there have been a number of significant findings, the middle leader has been identified as a key role in the development of successful numeracy/mathematics practices in schools. The middle leader plays a critical role…

Rich learning tasks embedded within a familiar context allow students to work like mathematicians while making sense of the mathematics. This article demonstrates how 11-12 year-old students were able to employ all of the proficiency strands while demonstrating a deep understanding of some of the "big ideas" of probabilistic thinking.

This article describes activities in which students deepen their relational understanding of the equals sign through exploring inequalities in a competitive dice game, built around the familiar fairy-tale "The Three Little Pigs" and "The Big Bad Wolf." The activity can be adapted to different abilities by choosing more or less…

Using Garden Based Learning (GBL) as an integrated mathematics and science unit, this article describes the mathematical journey of students as they work through the process of designing their own garden beds.

The Smarties-Box Challenge encourages students to apply several different mathematical capabilities and concepts--such as, estimation, multiplication, and the notion of being systematic--to solve a complex, multistep problem. To effectively engage in the Smarties-Box Challenge, students are required to demonstrate aspects of all four proficiency…