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This paper outlines the rationale for, and some elements of, a particular approach to teaching and learning mathematics in the early years. The researchers worked with two school systems to offer both centrally delivered and school-based teacher professional learning, which included the application of illustrative teaching resources. The project gathered a range of data from teachers and leaders on their dispositions and knowledge, as well as the opportunities and constraints they experienced, and the influence these variables had on planning, teaching and student learning outcomes.

The current study explores how teachers report using enabling and extending prompts when teaching with sequences of challenging mathematical tasks. Twenty-nine early years primary school teachers completed a questionnaire following their participation in a professional learning project. Findings suggest that teachers': view prompts as important when teaching with challenging tasks; generally prepare prompts in advance of the lesson; consistently allow students to engage with the core task before making prompts available; and consider prompts equally valuable for augmenting learning across all content areas.

This paper reports results from an investigation of the impact of an intervention program which was designed to help underperforming students reengage in mathematics learning. The paper outlines teacher and tutor perceptions of the program's impact on students who participated in the intervention which intends to "get students ready" for their subsequent mathematics lesson. Over the course of the iteration, the students' cognitive and behavioural engagement improved. Perhaps even more encouraging was the improvement in the students' dispositions, leading towards greater valuing of mathematics learning.

As part of a project exploring the use of challenging mathematical tasks, data from New Zealand teachers and their students were analysed to explore teachers' actions that encouraged students to persist. Rather than rescuing the students when they needed help, the teachers' actions included arranging for and encouraging students to work independently and cooperatively, asking questions, providing materials, and getting students to reflect on the process. When the teachers performed these actions, they reported students persisted and were better able to navigate through the zone of confusion.

The following outlines the rationale and structure of a professional learning initiative that seeks to explore teachers' ways of engaging students more actively in building mathematical connections for themselves. An example of one of the suggested experiences is presented.

Highly capable mathematics students are not usually considered strugglers. This paper reports on a case study of a Year 6 student, Debbie, her response to a lesson, and her learning involving a challenging mathematical task. Debbie, usually a highly capable student, struggled to complete a challenging mathematical task by herself, but as the lesson unfolded she was able to solve the problem. Rather than relying on teacher explanations during the lesson introduction, Debbie benefitted from the support of her teacher during the lesson and sharing of other students' thinking when applying her knowledge to an unfamiliar task. [NOTE: Debbie is a pseudonym.]

This paper examines the learning by students who were participating in a project designed to promote persistence while working on mathematical tasks. We examined their learning of mathematics concepts and learning about the processes of engaging in mathematical tasks. There were substantial increases in students' knowledge of angles and also evidence that the students built on their prior knowledge, made connections between concepts, found the tasks rewarding, valued concrete materials and engaged in mathematical communication.

As part of a project exploring various aspects of teachers' choice and use of challenging mathematics tasks, we sought some responses from students on their preferences for the difficulty of tasks on which they might work and also on the ways of working. Despite the common finding that teachers are reluctant to pose challenges to their students for fear of adverse reactions, many students reported that they prefer tasks to be somewhat challenging and many prefer to work on the tasks before having the process explained by the teacher. An important finding was the diversity of student preferences. There are implications for the information that educators offer to teachers on structuring their lessons.

The following is a report of an exploration of what mathematical reasoning might look like in classrooms. Focusing on just one lesson in one classroom, data are presented that indicate that upper primary students are willing and able to reason for themselves, especially in classrooms in which the culture for such reasoning has been established. It seems that the opportunities to reason are a product of the tasks that are posed, the structuring of the classroom, and the willingness of the teachers to allow students to engage with the tasks for themselves.

While there are many considerations for effective mathematics teachers, one key factor is the development of a classroom culture that supports the desired form of learning. In examining the opportunities and constraints associated with posing challenging tasks, we are exploring ways that teachers might influence classroom culture positively. The data presented below suggest that it is possible to foster a classroom culture in which teachers pose tasks that challenge students and encourage them to persist when working on those tasks. The key elements seem to be the ways the tasks are posed, the interactive support for students when engaged in the tasks, collaborative reviews of class explorations and assessment against criteria.

At some stage when planning, teachers make decisions about the mathematics tasks they will pose and how they will structure lessons. It seems, though, that these decisions are complex, and that this complexity has been underestimated by curriculum developers and teacher educators. The following is a report of data collection that simulated some of these planning decisions. The results suggest that teachers may need support in matching tasks to curriculum content statements, in articulating the purposes of tasks, and in considering how tasks might be used to address differences in student readiness. [Additional funding was provided by New South Wales (NSW) Department of Education and Training, Victorian Curriculum and Assessment Authority, Catholic Education Office Melbourne and the Australian Curriculum Assessment and Reporting Authority. The project is collaboration between Monash University, Australian Catholic University, University of Sydney, University of Technology Sydney, University of Newcastle, and the University of Melbourne.]

The research reported here was motivated by curiosity about ways of suggesting tasks and activities to teachers that assist them in their planning and which allow them to see the purpose of the suggested tasks. A group of junior secondary teachers involved in a larger project worked through a set of tasks that sought to address the content they were about to teach, and then completed a survey about those tasks. A comparison group also completed the survey. There was consensus across the groups of teachers about the potential of the tasks, they felt they could implement them and that such tasks were preferable to comparable textbook exercises. There are implications for both teacher educators, and for resource developers.

Insights into aspects of teachers' planning reported here were gathered as part of a broader project examining aspects of the implementation of the Australian curriculum in mathematics. In particular, responses of teachers to a survey of various aspects of decisions that inform their planning are discussed. While there is diversity in processes teachers use for planning, a consistent theme was that teachers make active decisions at all stages in the planning process. There were slight differences in the ways that primary and secondary teachers plan. There are important implications from our findings for those who support teachers in the transition to the Australian Curriculum: Mathematics.