Children's multiplicative thinking as the recognition of equal group structures and the enumeration of the composite units was the subject of this research. In this paper, we provide an overview of the Multiplication and Division Investigations project. The results were obtained from a small sample of Australian children (n = 21) in their first…

This paper describes the role of data and task context in young children's interpretation of and reasoning about data tables. A design-based descriptive study was conducted with fourteen 5-year-old children in their first year of formal schooling. A picture storybook provided the data context for a data modelling activity that focused on…

Technology can play a pivotal role in mathematics education. Qualitative methods were used to report on how a Year 1-2 teacher incorporated "Conveyance technology" (iPads), to support the teaching and learning of mathematics through student reasoning and problem-solving. The study was conducted in Australia. A single case was chosen,…

Promoting reasoning is the goal of mathematics education. While reasoning behaviours can be observed, how to characterise them and nurture their growth remains ambiguous. In this article, we report our effort in drafting a learning progression and geometric thinking model and using them to investigate Australian students' geometric reasoning…

In this article the authors overview how the recently revised (version 9) Australian Curriculum (Australian Curriculum Assessment and Reporting Authority, 2022) and student difficulties with fractions relate to five developmental Fraction Schemes developed from multiple research projects in the literature. The article shares research findings from…

The proposed revisions to the "Australian Curriculum: Mathematics" highlight the importance of learning to mathematise, problem-solve and reason in real world contexts, including financial contexts. Through the Economics + Maths = Financial Capability research project, the authors have been imagining fresh ideas for connecting the…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

Research findings: No research to date has compared mental state language (MSL) in conversations between children and different adult talk partners, such as mothers and educators. The aim of this study was to investigate the use of MSL (verbalization of mental states such as remembering, knowing and thinking) by children, educators, and mothers…

Teachers play a critical role in promoting dialogic interaction in their students. The purpose of this case study was to investigate how one very effective teacher taught two, cooperative, inquiry-based science units to her Year 6 class. In particular, the case study focused on how she used different discourses to capture students' curiosity in…

The concept of variability is central to statistics. In this research report, we review mathematics education research on variability and, based on that review and on feedback from an expert panel, propose a learning progression (LP) for variability. The structure of the proposed LP consists of 5 levels of sophistication in understanding…

That the quality of teachers' knowledge has direct impact on students' engagement and learning outcomes in mathematics is now well established. But questions about the nature of this knowledge and how to characterise that knowledge are important for mathematics educators. In the present study, we examine a strand of "Specialised Content…

After passage of the Every Student Succeeds Act (ESSA) in 2015, states assumed greater responsibility for designing their own accountability and assessment systems. ESSA requires states to measure "higher order thinking skills and understanding" and encourages the use of open-ended performance assessments, which are essential for…

The Every Student Succeeds Act (ESSA) opened up new possibilities for how student and school success are defined and supported in American public education. States have greater responsibility for designing and building their assessment and accountability systems. These new opportunities to develop performance assessments are critically important…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…