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Just as students experience productive struggle or spend time in the 'zone of confusion' when engaging with challenging tasks, teachers also experience similar difficulties and periods of confusion when engaging with new pedagogical approaches. Prior to a 19-week lockdown due to Coronavirus (COVID-19) during 2020, two Foundation teachers implemented a student-centred pedagogical approach when teaching with challenging tasks. While they had some initial success implementing the pedagogical approach and a three-phase lesson structure, they struggled to do so online during the lockdown. It is the experiences of these teachers, in particular their experience of confusion relating to aspects of the pedagogical approach, and how this confusion was overcome, that is reported in this paper. Central to our findings is the importance of teachers reflecting on their own experiences of struggle and the impact this had on their professional learning, as well as the notion that adversity can be a catalyst for change.

In this article, educational and psychological perspectives are used to examine how anxiety and uncertainty in the mathematics classroom can be reframed to benefit mathematical teaching and learning. Links between anxiety and uncertainty are discussed and from this discussion, two methods are proposed for reducing the negative impact of mathematics anxiety on learning. Firstly, it is argued that initiatives designed to teach students to use emotion regulation skills can help to reframe anxiety and improve students' ability to regulate negative emotion. In particular, the skill of reappraisal is discussed. Secondly, it is proposed that pedagogical approaches that encourage students to embrace challenge will help to normalise uncertainty in classrooms and promote more positive affect and engagement with mathematics. These approaches include choosing suitable tasks, differentiating those tasks, orchestrating classroom discussions that include all students and consolidating the learning with further tasks suitably varied. Rather than teachers seeking to remove anxiety, students can be encouraged to manage their anxiety in order to promote more positive mathematical learning and to develop mathematical resilience.

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).

This paper reports on a New Zealand iteration of the Encouraging Persistence, Maintaining Challenge (EPMC) project, which proposes that students learn mathematics best when they build connections between mathematical ideas for themselves. This iteration explores the actions, perceptions and learning of 12 primary teachers and their 281 students during the implementation of a set of challenging tasks related to geometric reasoning. The teachers launched the suggested tasks, ensuring that the challenge was maintained. The students explored these tasks with minimal input from the teacher, and learning was summarised and extended. The teachers were positive about the intervention. The challenging task approach enabled students' thinking became visible and, at times, the teachers' prior perceptions of their students' ability were challenged. A highly significant difference between the students' pre- and post-assessment scores was found. The students were supported to have autonomy in their learning and make mathematical connections themselves. The students became less reliant on their teachers' help and were positive about their involvement in the project.

Australian schools, like schools elsewhere, have been through a period of closure. The closure creates both threats and opportunities for teachers and students. In the context of a project exploring approaches to teaching in early years, we outline some considerations and offer advice to teachers and educators on strategies for welcoming students back to school.

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.'

While the general planning advice offered to mathematics teachers seems to be to start with simple examples and build complexity progressively, the research reported in this article is a contribution to the body of literature that argues the reverse. That is, posing of appropriately complex tasks may actually prompt the use of more sophisticated strategies. Results are presented from a detailed study of young children working on tasks that prompt multiplicative thinking. It was found that the tasks involving more complex number triples prompted the use of more sophisticated multiplicative thinking.

This is the report of an investigation in partnership with a team of junior secondary classroom teachers of the potential of posing more challenging tasks to their students. A range of data sources are used to represent the experience of teachers and students in a unit of work that incorporated a range of challenging tasks. Students learned the intended mathematics and they reacted positively to the challenges. The teachers identified both opportunities and constraints in such teaching, especially those related to changes to their pedagogies and assessment of student work.

The Encouraging Persistence Maintaining Challenge (EMPC) Project has been working with secondary teachers in Melbourne as they seek to build persistence in students, during work on challenging mathematics tasks. The authors have developed sequences of tasks in various topic areas for Years 7 and 8, which require students to connect different aspects of mathematics, to devise solution strategies for themselves and to explore more than one pathway to solutions. There is an expectation that students record the steps in their solutions, and justify their thinking to the teacher and other students. The authors have surveyed teachers on their strategies for encouraging student persistence, before and after the experience of teaching some challenging tasks which have been provided to them. This article provides examples of the kinds of challenging tasks teachers are using with students, and share teacher insights on helpful strategies.

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.)

The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. An underlying assumption is that lessons can seek to build a sense in the students that their experience has elements in common with the rest of the class and that this can be done through attention to particular aspects of the mathematical and socio-mathematical goals. We examine three teacher actions that address the mathematical goals: using open-ended tasks, preparing prompts to support students experiencing difficulty, and posing extension tasks to students who finish the set tasks quickly; as well as actions that address the socio-mathematical goals by making classroom processes explicit. To illustrate and elaborate these actions, we describe a particular lesson taught to a heterogeneous upper primary (age 11-12) class.

Many students are unsuccessful in the study of school mathematics, not because of some innate ability, but because of pedagogical practices. Bernstein (1996) has argued that pedagogy serves as a mechanism for cultural reproduction, so that for those students whose cultures are different from that represented in and through pedagogy, the task of constructing school mathematics is made more difficult. The paper explores the ways in which a teacher changes the pedagogic relay in order to be more inclusive of her students. Her practice is informed by understanding the ways in which pedagogy is a subtle tool for marginalization in mathematics.

Discusses the advantages of teaching with open-ended tasks and compares students' responses to open-ended, closed-area, and perimeter tasks. (ASK)

Reports results from one component of a larger project that explored the classroom potential of content-specific, open-ended tasks. Examines responses from 1200 students to comparable closed and open-ended tasks and explores the effect of using specific contexts for such tasks. Concludes that both open-ended and closed tasks can contribute to effective classroom programs. (Contains 14 references.) (Author/ASK)

Examined the quality of responses of six classes of grade six students to four questions requiring multiple and generalized solutions posed under varying conditions. Results indicated that this type of question can be useful in classrooms because students can respond at a variety of levels. (13 references) (MDH)

Presents three features of "Good" questions: requires students to do more than simply remember a strategy to answer; promotes student learning while answering the question; and have several acceptable answers. Considers how questions can be used to cater to the range of student abilities. (MDH)

Discussed is the case for problem solving in mathematics classrooms. The characteristics of "good" questions are identified. The assessment of questions and questioning techniques is considered. (CW)

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.

Describes attempts to move physics discussions out of the classroom and onto the Internet where students can participate any time through the use of an electronic message board. (WRM)