Ann Downton

Mathematics interventions play a critical role in supporting primary school students who experience difficulties with learning mathematics but do not have a diagnosed disability. However, the intervention approaches used in schools vary considerably in their theoretical orientations, content focus, and instructional approaches, and research in this field is similarly diverse. This systematic review investigated the characteristics and instructional approaches of mathematics interventions for primary students. A comprehensive search of eight databases identified 1,321 studies published between 2000 and 2024, of which 38 met the inclusion criteria. Interventions were included if they involved small-group formats (fewer than seven students), were conducted outside the classroom, and targeted students identified as experiencing difficulties in learning mathematics. Data were extracted concerning intervention characteristics, mathematics content focus, delivery, and instructional strategies. Findings identified that most studies were conducted in the United States and were delivered by researchers or research assistants, with fewer interventions implemented by classroom teachers. The majority of interventions in the early years addressed the topics of number and operations. Fractions and word problems were prevalent topics in later primary years. Nine instructional strategies were examined for each intervention, with representations, computational fluency, and explicit instruction most frequently employed, and problem-solving employed least frequently. The findings indicate that existing mathematics interventions typically focus on a narrow curriculum. Valuable directions for future research include investigating the potential of interventions using broader and more connected mathematics topics, diversifying international research contexts, and prioritising teacher-led interventions in authentic school settings.

In a large study, the Multiplication and Division Investigations project sought to understand the intuitive knowledge young children develop about multiplication and division before they are introd...

This study examines teachers’ perspectives on implementing challenging mathematics tasks in the early years of schooling (Foundation– Year 2), focusing on beliefs regarding frequency, timing, and enabling conditions, as well as affective outcomes for teachers and students. Findings are drawn from 82 teachers across 16 schools who completed a research-informed professional learning program, which focused on teaching with challenging tasks in the early primary years. Mathematical Sequences of Learning (MSoL) provided sequenced task resources and pedagogical support for structured inquiry. Following participation in MSoL, a substantial majority of teachers advocated introducing challenging tasks from Foundation, with three-quarters recommending their use multiple times per week. Collaborative planning and leadership support were identified as critical enablers. Quantitative analysis revealed statistically significant increases in teacher confidence and enjoyment when teaching mathematics, alongside a significant decrease in teacher anxiety. Teachers also reported perceived improvements in student enjoyment and confidence. Teachers’ qualitative reflections, used narratively to contextualise the quantitative findings, pointed to how specific lesson characteristics and task features supported both engagement and emotional safety. In particular, collaborative classroom norms and variation across sequences of tasks helped to sustain motivation while reducing apprehension. The findings suggest that structured professional learning, when combined with high-quality resources and school-based supports, can shape affective outcomes in mathematics education and promote broader pedagogical change. These results underscore the potential of a challenging tasks approach to enhance teaching and learning in the early years, while questioning assumptions that such pedagogies are only suitable for older or higher-achieving students, or that it is necessary to start all lessons with teachers telling.

This study was designed to report on the questioning strategies and pedagogical moves a Year 1 teacher used during a lesson, specifically focusing on using student work samples to support mathematical reasoning. The single-case research approach considered questions selected by the teacher, their distribution throughout the lesson, and the implementation of anticipated questions. The results show how the teacher leveraged student work samples as they responded to an open-ended problem (a challenging task) and how she employed pedagogical moves to support students’ mathematical reasoning. A qualitative analysis of classroom discussions provided insights and recommendations for pedagogical moves for facilitating, eliciting, responding to and extending student reasoning. We also offer a practical Questioning Move model teachers can refer to when helping students interpret tasks; supporting those who may struggle; clarifying misconceptions or partial conceptions and supporting understanding; exploring multiple strategies, identifying all possible solutions and extending responses, ensuring all learners have opportunities to develop their reasoning skills.

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 year of school (mean age 5 years 6 months) who participated in a teaching experiment of five lessons taught by their classroom teacher. The tasks introduced children to the “equal groups” aspect of multiplication. A theoretical framework of constructivist learning, together with research literature underpinning early multiplicative thinking, tasks, and children’s thinking, was used to design the research. Our findings indicate that young children could imagine equal group structures and, in doing so, recognise and enumerate composite units. As the children came to these tasks without any prior formal instruction, it seemed that they had intuitive understandings of equal group structures based on their life experiences. We argue that the implications for teaching include creating learning provocations that elicit children’s early ideas of multiplication, visualisation, and abstraction. The research has also shown the importance of observing children, listening to their explanations of their thinking, and using insights provided by their drawings.

The shift from additive to multiplicative thinking is challenging for students. A professional learning program was developed that focused on an identified area of need by teachers, namely multiplicative thinking. Program content focused on concepts underpinning multiplicative thinking, pedagogical approaches, challenging tasks, and application to classroom practice. It was delivered via six 90-min modules in 13 participating schools across terms 2–4, as part of regular after school professional learning. Whilst all staff participated, the research focus was year 3–4 teachers. Students’ historical data were collected across four years (2016–2019) to determine mean growth over time, in participating and non-participating schools. National Assessment Program Literacy and Numeracy (NAPLAN) and Mathematics Assessment Interview (MAI) data were used to determine the impact of the learning, as both assessments are administered annually. Analysis of year 4 students’ longitudinal data showed greater mean growth in student learning over a 2-year period in schools involved in the learning and additional in-class coaching support, than students in non-participating schools. Our findings showed that targeted school-based professional learning, with in-class support from a knowledgeable other, leads to teachers’ improved understanding of multiplicative thinking and subsequent pedagogical content knowledge to support student learning.