It is well established that children need to learn to solve addition and subtraction problems using fast, efficient and accurate strategies. However, it is unclear if derived-fact strategies represent such strategies for solving basic problems. In this study we individually interviewed 132 students in Years 3 and 4 (9 and 10 years of age) to investigate the strategies they used to solve addition and subtraction problems within 20. The problems the students solved were carefully planned to represent different problem sets within 20 and an elaborate coding scheme was used to distinguish different types of derived-fact strategies, along with the known fact that was applied. Our findings challenge commonly held assumptions relating to expectations of retrieval and highlight the prevalence of derived-fact strategies. Suggested implications are discussed in terms of, (i) how the teaching of subtraction might be improved, (ii) the number facts children should know, and (iii) the importance of defining terms like proficiency and fluency with basic additive problems to represent the reality of children’s solution strategies. Possible directions for future research are shared.
Despite global prioritisation of STEM (Science, Technology, Engineering and Mathematics) for developing student thinking and problem-solving skills, tensions may arise from unequal disciplinary emphases and the differing natures of disciplines. Given the unique nature of mathematics learning, this article provides insight into the perceived affordances and challenges of a STEM approach for mathematics learning and teaching to gauge whether a STEM approach enhances learning outcomes. Interviews with five key international researchers in mathematics and STEM education were analysed using reflexive thematic analysis, with four major themes evident: Interdisciplinarity emphasising mathematics’ nature, mathematics learning as a focus in a STEM approach, affective impacts of a STEM approach, and using mathematics in applications in the context of a STEM approach. Overall, an interdisciplinary approach provides learning contexts and may highlight the nature of mathematics (e.g., sequential characteristics) in contrast to other disciplines. A perceived challenge of a STEM approach includes reduced focus on mathematics learning due to multiple foci in a STEM approach. Perceived affordances include increased student interest and engagement in learning mathematics. The study proposes a novel STEM Approach for Mathematics (SAM) model, placing mathematics learning and application at the centre of implementation of a STEM approach.
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.
We explore the shift in doing mathematics classroom research from a “traditional” (i.e. white-centered or Eurocentric) perspective to one that decenters whiteness and interrupts Eurocentrism, so that students can experience their cultural and community assets being perceived as strengths rather than requiring intervention. We use our experience as part of a diverse research team committed to this shift to investigate the question: What does it actually look like to decenter whiteness and interrupt Eurocentrism in mathematics education research to build more humanizing, liberating mathematics classrooms and learning experiences, especially for students who have experienced repeated harm? We describe Critique—Reimagine—Redesign—Repeat (CR3), a framework that organically emerged from our intentional efforts to decenter whiteness and interrupt Eurocentrism in our work, unpack its key components, and provide examples of what it looks like it in action. We illustrate how CR3 can expand research and researchers through a cyclical process that leverages diverse perspectives and new learning and questions in ways that support both incremental and exponential growth.
Our study examines the evolution of the Instructional Coaching for Tech Enhanced Approaches to Mathematics (iCoachTEAM), focusing on how mathematics instructional coaches overcame initial resistance to implementing Asset-Centered Mathematics Instruction (ACMI). ACMI emphasizes leveraging students’ mathematical strengths and prior knowledge to foster conceptual understanding, identity, and agency. Initially, coaches exhibited resistance due to insufficient knowledge, fear of neglecting other students, and perceived lack of teacher buy-in. Through continuous improvement research, resistance was identified as a professional learning problem, not a rejection of ACMI’s value. Programmatic adjustments in the second-year equipped coaches with concrete tools and guidance for implementing ACMI. Findings from the second year reveal a significant shift: all coaches moved to actively promoting ACMI. This study highlights that effective instructional change requires addressing systemic, organizational, and individual learning needs through targeted support and adaptable program design.
