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This article is based upon Peter Sullivan's (2021) structured inquiry approach to teaching mathematics, in which the authors take a deep dive into the technique of "Spotlighting" in the "Explore" phase of this model to assist in optimal learning experiences for students. Working from the premise that students are best placed to connect with instruction after a powerful and sometimes confusing learning experience, Sullivan et al.'s (2021) model provides three distinct phases to structure a mathematics lesson. They are: (1) The Launch phase--poses the task to students without any further instruction about the strategies required to solve the task; (2) The Explore phase--where collaboration and peer learning is encouraged as a support for students to consider multiple solutions and solution pathways; and (3) The Summarise/Review phase--provides an opportunity for the teacher to orchestrate class discussions by presenting various student solutions that reflect the mathematical focus of the lesson. The authors conclude they have been pleasantly surprised at how particular student explanations, derived from real time spotlight moments, were critical in shaping successful learning opportunities for the rest of the class.

Peter Sullivan and colleagues present a report on an initiative at a Victorian primary school which embraced opportunities offered by purposeful collaborative professional learning communities. They utilised a form of Japanese Lesson Study as part of their approach. There are three parts to the story of this initiative: (1) a description of the approach to professional learning; (2) an explanation of the model of instruction being explored; and (3) a summary of the 'polished' lesson on middle primary mathematics (fractions).

In this article, the authors from Monash University and the University of Sydney have collaborated to present a research-informed model to support the planning and teaching of mathematics, using a student centred structured inquiry approach.

The fear of making mistakes and avoidance of risks can create disabling anxiety and limit learning opportunities. However, it is possible to teach mathematics in ways that not only reduce student agency but also have the effect of excluding some students. This article proposes approaches that are intended to both foster student decision making and a sense of inclusion in classroom learning. It describes some characteristics of classrooms that may go some way to minimising student anxiety without reducing the opportunities for cognitive activation. There are three parts that are discussed: features of tasks posed, pedagogical approaches, and classroom culture.

In this article, the authors emphasise the importance of purposeful mathematical discussion and using sequences of connected, cumulative, and challenging tasks in advancing students' spatial reasoning in the early years of schooling.

This article reports on a project which involved introducing challenging tasks in the early years' classrooms of twenty Victorian primary schools. The obstacles teachers encountered and how they overcame those obstacles are discussed.

The authors describe a mathematics lesson designed to allow students to use their own thinking to solve elapsed time problems. Their approach emphasises student-centered structured inquiry, and follows a 'Launch, Explore and Summarise' format.

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 tasks are designed in such a way that they are accessible to all students and the expectation is that everyone will persist when solving challenging mathematical tasks. This article looks at examples of challenging mathematical tasks designed to enable students of all abilities to experience productive struggle, and examines the lesson structure and teacher's role when implementing a challenging task, along with students' responses to being challenged through the tasks. It adds to existing research on challenging tasks, including in previous editions of "Australian Primary Mathematics Classroom" (APMC) (e.g., Cheeseman, Clarke, Roche, & Walker, 2016; Roche & Clarke, 2014; Russo, 2016) through challenging tasks being used to evoke productive struggle, and illustrative examples of what productive struggle 'looks like.'

This article from Carly Sawatzki and Peter Sullivan encourages schools and teachers to consider ways to embed financial literacy tasks in mathematics lessons more often, and includes an authentic task to try with your students.

This article promotes the use of mathematically appropriate, engaging and challenging tasks to support learning that is worthwhile. The authors share insights from a three-lesson design experiment and the three tasks along with the results from their implementation are explored.

The Australian Curriculum: Mathematics encourages teachers to consider seriously the four proficiencies: Understanding, Fluency, Problem Solving and Reasoning. In responding to the reasoning proficiency, many teachers may find that the language of the classroom may well change. In this article, we discuss the meaning given to the term reasoning within the AC:M and elsewhere, share an example of a classroom task with the potential to develop mathematical reasoning, consider the language involved in describing reasoning, and present some survey responses on teachers' current understanding and use of the relevant terms. (Contains 3 tables, 2 figures and 1 footnote.)

At some stage in the planning process, teachers develop or select tasks which prompt the type of activity that can offer students experiences that can help them learn the intended content. This article presents results from an item on a survey that invited teachers to match particular content descriptions with selected tasks. While many teachers matched the tasks with the content descriptions that we anticipated they would, there were also many teachers who chose descriptions that we consider do not match the tasks. It is suggested that teachers should discuss within their planning teams the purpose and potential of particular tasks, and that such discussions also form part of teacher professional learning. It is recommended that the notion of matching tasks to the curriculum is incorporated into teacher learning sessions. (Contains 1 table.)

We are interested in exploring the processes teachers use when planning. We sought responses from teachers on aspects of their planning from a survey of various aspects of their decisions. We found that, while there is diversity in processes teachers use for planning, a consistent theme was that teachers make deliberative decisions at all stages in the planning process. Likewise teachers make active use of assessment information, especially to address the needs of their students. There are important implications from our findings for those who support teachers in the transition to the Australian Curriculum: Mathematics. (Contains 2 tables.)

In recent years, there has been greater attention in research and professional development work to discussion of the kinds of knowledge teachers need to teach effectively in the mathematics classroom. It seems reasonable that in planning at the school level, teaching team level and then specifically for a given lesson, teachers might have a sense of the most important mathematical ideas on which they wish to focus. In this article, we discuss written statements by teachers in surveys regarding the most important ideas on which they intended to focus in their next teaching topic. There was considerable variation in teachers' capacity to articulate these important ideas. We discuss the implications of this for teacher professional learning and planning. (Contains 1 footnote.)

The Australian Curriculum: Mathematics (AC:M) prompts consideration of planning processes teachers typically use (as a whole school, in grade levels, and at the classroom level). In order to gain insights into the nature of the planning decisions teachers make, Australian teachers drawn from every state and territory were invited to respond to a survey on planning processes, during professional learning programs or voluntarily online through the Australian Association of Mathematics Teachers' website. In this article, we provide background to the overall project in which this survey was situated, and describe the process through which the survey was developed. Subsequent articles in this journal detail some important findings from the survey data. (Contains 1 table and 1 footnote.)

Essential to teachers' planning are decisions regarding what should be taught. Curriculum documents are the most obvious authority. But what is a "curriculum document" for a mathematics teacher in Australia? Are there other credible sources of information that Australian teachers draw on when deciding what to teach? This article examines the responses of a national sample of Australian teachers to a survey examining their planning practices. (Contains 2 figures.)

The Task Types and Mathematics Learning project is investigating the opportunities and constraints that teachers experience when using particular types of mathematics tasks. Some assumptions underlying this aspect of the project are: (1) that teachers seeking a balanced curriculum choose to use a mix of types of tasks; (2) open-ended questions offer students and teachers opportunities for both creativity and different ways of thinking about mathematics; and (3) trialling exemplars of particular types of tasks, reflecting on the experience by writing a report, and reporting back to colleagues involves substantial teacher learning, and can form the basis of sustainable professional development. This article explains what is meant by content specific open-ended tasks, illustrates the ways that teachers wrote up trials of such tasks in their classrooms, and uses excerpts from teachers' reporting on their trials at meetings of project teachers from a cluster of nearby schools, to illustrate the type of teacher learning that resulted from this process. (Contains 1 figure.)

This article illustrates a teaching exploration at an Indigenous Community School in the Kimberley region of Western Australia that sought to use a specific way of thinking about particular content domain, subtraction, to develop focused, mathematically-rich learning experiences. First, the authors explain the importance of having clear mathematical goals (knowing where you are going), and then they describe some illustrative activities (how to get there) that were used over the four 90-minute lessons. They also present data that indicate that there was positive student achievement as a result of the experience. (Contains 2 figures.)

It is frequently surprising to new teachers (and even those with experience) when they find that not only do some children need to recount the group they have just counted to be assured of the total but also that this need seems to be resistant to intervention. Although moving from "counting-all" to "count-on" is sometimes assumed to be constrained by developmental factors, it is the teacher's responsibility to continually explore methods and pedagogies for accelerating such transitions. Similarly, it is surprising how difficult some students seem to find answering questions like 32 + 10, 95 - 10, 326 + 100, etc. Although many students in Year 1 may begin to grasp place value in an elementary sense, applying this knowledge dynamically (i.e., as a number changes), rather than statistically (i.e., to an individual number), is often a far slower process. Moreover, it is difficult to find the right experiences to help students develop fluency in flexibly applying their knowledge of place value to solve such problems. In this short article, the authors present the principle of Dynamic Counting, and a set of activities related to this principle, as a teaching tool that might be useful in addressing both of these issues.