Anne Roche

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.

The Getting Ready in Numeracy (GRIN) program is a targeted intervention designed to support students struggling with mathematics by preparing them for upcoming lessons through small-group tutoring. This study examined changes in students’ attitudes towards mathematics (enjoyment, coping, valuing), students’ views on mathematics as a problem-solving discipline (mathematics as solving open problems flexibly), and descriptive norm-referenced achievement data to contextualise students’ learning trajectories, following participation in the GRIN program. Using a mixed-methods approach, data were collected from 102 primary and secondary students across 14 schools in Victoria, Australia. Quantitative measures, including pre- and post-program surveys, were analysed alongside qualitative data from open-ended student responses. Quantitative findings indicated significant improvements in students’ coping ability and their valuing of mathematics, and an increased tendency to view mathematics as flexible problem-solving; however, improvements in enjoyment did not reach statistical significance. Descriptive norm-referenced data indicated movement toward year-level expectations. Moreover, qualitative analysis revealed that the aspects students viewed as most helpful for their learning (e.g., social context) aligned with the program’s underlying design principles. These results highlight the potential of well-structured preparatory interventions like GRIN to support more positive student attitudes towards mathematics and greater engagement with the subject. Viewed through an equity lens, the findings suggest that strengthening students’ affective readiness and participation in mathematics may support more equitable classroom experiences.

Mathematical games are widely used in primary mathematics classrooms internationally, yet there remains limited conceptual clarity about what features define a mathematical game, and whether teachers' understandings align with definitions articulated in the research literature. This study examined how primary teachers across Australia (n=193), Indonesia (n=225), and Italy (n=107) prioritised eight characteristics commonly used in the literature to define mathematical games. Using an anonymous online questionnaire, descriptive analysis revealed strong overall alignment between teachers' judgements and the research-articulated definition. At least 90% of teachers in each country rated enjoyment, clear rules, explicit mathematical objectives, player choice, and interactivity as at least somewhat important. However, teachers weighted characteristics unevenly: enjoyment was consistently the most strongly prioritised feature, functioning less as one criterion among many and more as a threshold condition for whether an activity counts as a game at all. In contrast, features tied to mathematical integrity, particularly the expectation that mathematical knowledge should meaningfully shape gameplay outcomes, were endorsed less consistently, especially among Italian teachers—24% of whom rated this as very important compared with 62% and 61% of Australian and Indonesian teachers respectively. These findings highlight productive tensions between affective engagement and mathematical rigour in how teachers conceptualise games.

1. Mathematics is often described as a gatekeeper to future academic and career opportunities (Douglas & Attewell, 2017), yet many students struggle to engage meaningfully with the subject (Lein et...

When teaching fractions, teachers make instructional decisions about if, when, and how to use the many different types of fraction models and manipulatives. In this study, we sought insights into their pedagogical reasoning with fraction representations via their preferences, both for solving tasks themselves and for teaching (in general and for specific fraction concepts and operations). Nearly 200 practising Australian primary teachers participated in an online survey and we drew on a Fraction Schemes theorisation to analyse quantitative and qualitative data. A majority of teachers indicated a personal preference for the set model for four out of five schemes; for one scheme most teachers preferred the circle model. Their reasons suggested that the nature of each task in a scheme and the specific fractions involved, played a role in influencing their preferences. With respect to teaching fractions, the teachers also indicated a high level of preference for teaching with the set model in general, and secondly for the rectangle model. Their preferences, except for number lines, were not found to be associated with the teachers’ nominated year level. We found that a high personal preference for a set model was associated with a preference for teaching with the same model in general, but not for teaching with the matching manipulative (counters or chips). The teachers indicated a high level of preference for teaching with the fraction bars manipulative for several fraction concepts, but this was not associated with a personal preference for linear models. Implications for further research are discussed.

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.