Many primary school students have difficulties understanding mathematical equivalence with considerably poorer performance in some countries than in others. However, students' formal understanding of equivalence has significant and long-lasting effects, as it predicts arithmetic and algebra achievement throughout school years. Currently, little is…

A key aspect of young children's development of algebraic reasoning is the process of visualising and identifying structures to both abstract and generalise. There has been a growing body of research focused on how students form generalisations, this article adds to the existing body of research by examining how young culturally diverse students…

Teaching in ways responsive to the cultures of our students is vital towards enhancing equity of access to mathematics achievement and putting educational policy into practice. New Zealand has the largest group of Pasifika people in the Western world, a multi-ethnic group of indigenous people from Pacific Island nations who have differing cultural…

Participation structures are important in relation to who gets equitable access to mathematics within classrooms premised on co-construction of mathematical reasoning. This paper takes a strength-based focus to explore how two teachers extended their Pasifika students' known repertoires of practice to encompass others, which supported them to…

In New Zealand and internationally, diverse groups of people are under-represented in mathematics. Disrupting deficit discourses requires educators to recognise the funds of knowledge of learners. This article focuses on stories of mathematics at home and in the community of Pacific learners to highlight what we can learn from the voices of…

We administered specially-designed, free-response mathematics tasks to primary students (N = 583, ages five to 12 years old). Our focus was on whether (i) the children's responses could be reliably assessed, and (ii) the responses could provide insights into children's mathematical thinking. We used a contemporary comparative judgement technique,…

This article reports the findings of a study using tasks where a family orders and considers sharing the cost of a "Fish n Chips" meal. Purchasing take-away food is an example of an everyday situation where literacy and numeracy must be applied to make sense of tabulated price information. Originally developed for use in Australia, the…

Teachers' perceptions of students' capabilities are particularly important in efforts to support ambitious instructional reforms. In this paper, we explore one teacher's efforts to resolve conflicts and tensions as she engages with new practices associated with ambitious mathematics teaching. While many conflicts arose in the first year of the…

Interaction and dialogue are seen as essential components of mathematics classrooms of the 21st century. In this paper we explore the pedagogical actions a teacher takes to reposition his diverse learners as active and engaged participants in the classroom. The findings illustrate the need for explicit teacher modelling of ways for students to…