This study examined how opportunities to incorporate numeracy across different primary curriculum areas and grade levels are highlighted in the Australian Curriculum v9.0. A document analysis approach was used to track the numeracy opportunities in the document across different curriculum areas and grade levels. The results showed that Science has…

Fractions are among the most problematic concepts that children encounter in their primary school years because of the many different conceptions of fractions. Textbook analyses have tried to provide insights into how fractions are introduced, focusing on the different concepts and representations of fractions. In this paper, we contribute to…

Conceptual body movement in education is an external representation mode that research suggests can support children's learning about mathematical phenomena. Children's learning and understanding of mathematical concepts and processes, such as number structure and relationships, number sequencing, position, or geometric properties, may be…

Teaching towards big ideas provide opportunities for teachers to think deeply about content and pedagogy in order to support their students to see connections in mathematics. However, teachers may not always activate or mobilise their knowledge in classroom situations. This paper looks into how a teacher, Peter, think about the tasks in his…

Ambiguity of language can form a barrier to understanding mathematical concepts. The word 'capacity' is problematic as it holds a variety of meanings and might not be understood in school mathematics, to be an aspect of volume. We investigated pre-service primary school teachers' interpretations of 'capacity' when given the definitions of 'volume'…

Mathematical thinking is a complex, multi-faceted process that has been described as messy and difficult but can also show growth and insights into conceptual understanding and knowing. This paper explores the application of Edward de Bono's practical thinking, in particular, the occurrence of porridge words to examine the mathematical thinking of…

This qualitative study aims to investigate novice undergraduate mathematics students' first encounter with the First Isomorphism Theorem, which is, more often than not, the pinnacle of a typical introductory course in Group Theory. Several studies have reported on the challenges that this mathematical result poses to inexperienced mathematicians,…

Big Ideas can be seen as overarching concepts that occur in various mathematical topics and strands within a syllabus. Within our project on Big Ideas in School Mathematics, we developed instruments to measure two Big Ideas: Equivalence and Proportionality. The instruments we developed seek to assess students' ability to see these Big Ideas as…

This conceptual paper discusses two frameworks, developed independently by the lead author, that will provide the conceptual foundation for the identification and evaluation of mental computation strategies students demonstrate during an upcoming research project entitled Mental Computation in Year 5. These frameworks will be used by the lead…

Research has shown that many primary students experience transition barriers between additive and multiplicative thinking. This paper analysed responses from 253 Years 3 to 6 students to a diagnostic assessment which consists of whole number multiplication and division problems involving equal groups, arrays, multiplicative comparison and…

In Ireland, Initial Teacher Education [ITE] standards require all teachers to possess an adequate level of numeracy themselves in order to teach for numeracy learning across the school curriculum. This paper reports on a study that investigated 204 pre-service post-primary teachers' numeracy capabilities. Analysis of questionnaire data from…

Diminishing duplication and finding connections between the "Australian Curriculum: Mathematics" and "Digital Technologies" were a focus of the revision to version 9. This emphasis has provided enhanced opportunities for integration of these learning areas. In this exploratory multiple case study, interviews with teachers…

An understanding of the equal sign is a fundamental concept for early algebra. While literature claimed that Chinese students commonly master the relational understanding of the equal sign in the elementary school, these claims are under-researched. This study used the Mathematics Equivalence Assessment with 237 Chinese Grade 5 students. The…

Fostering students' bidirectional conception of the equal sign (viewing the equal sign as indicating an equivalence of two sides rather than a 'show result' symbol) is challenging, and students' misconception of the equal sign is persistent. Some studies mention that in China, the pedagogical approach to introducing the equal sign supports…

Decimals and the related areas of ratio and proportion are recognised as one of the most challenging and complex areas of mathematics for young children to learn. In this study, four dynamic digital representations were used by Year 4 (9-10 years old) students in a set of video-recorded, individual task-based interviews to explore key concepts of…