Student transition from arithmetical understandings to algebraic reasoning is recognised as an important but complex process. An essential element of the transition is the development of a rich understanding of variables. Drawing on findings from a classroom-based study, this paper outlines the instructional tasks and pedagogical actions a teacher…

In this paper, we explore how students' algebraic noticing's and explanations changed across a two-year period with the introduction of designed instructional material. The data in this report is drawn from n=53 Year 7-8 students' responses to a free-response assessment task across two different years. Analysis focused on how students noticed and…

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 this paper, we explore student solutions to a free response mathematical assessment task which had opportunities for students to notice structural properties in the context of number systems. In total, 308 students aged between 10 years to 13 years participated in the study. Their responses were analysed to determine whether they noticed…

In many Western countries, there has been an emphasis on ways in which to support teachers to shift practice from traditional mathematics instruction to inquiry-based classrooms. As a form of professional learning and development, lesson study offers the potential for teachers to develop their ability to respond to students' thinking through…

In this position paper, we review the practice of differentiation -- a universal concept aimed to support diverse students in our classrooms. In exposing the wide-ranging practices of differentiated instruction, and critiques of current implementation, we argue that differentiation in the mathematics classroom needs to be reframed in terms of a…

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,…

Pasifika cultures have a rich background of mathematics including a strong emphasis on patterns used within craft design (Finau & Stillman, 1995). However, there have been limited studies which have investigated the use of contextual Pasifika patterns in mathematics classrooms. The aim of this study was to explore how contextual Pasifika…

Grouping children by achievement levels is a thriving practice in New Zealand primary school mathematics classrooms. In this paper we look at the impact of a formative intervention project--"Developing Communities of Mathematics Inquiry"--that required a whole-school shift to mixed achievement grouping. Engeström's Cultural Historical…

While there is widespread agreement that "all" learners of the 21st century need to be numerate and literate, reforming pedagogical practices to achieve such an outcome is challenging for many teachers. This is a report of one aspect of a project which aims to integrate a culturally responsive pedagogical mathematics practice within…

In the current reform of mathematics classrooms teachers are charged with the role of facilitating collaborative groups during problem-solving activity. The challenge is for teachers to engage students in making mathematical meaning during collaborative group discussions. In this paper we draw on the concept of adaptive expertise to report on…

In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…

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…

In recent years there has been an increased emphasis on algebraic reasoning in primary school classrooms. This includes introducing students to the mathematical practices of making conjectures, justifying and generalising. Drawing on findings from a classroom-based study, this paper explores one teacher's journey in shifting her task design and…

This paper reports on the use of lesson study as a professional development tool. In particular the paper focuses on the way in which the teachers increased their understanding of how tasks, classroom activity and teacher actions scaffolded student learning of early algebraic reasoning of equivalence and the commutative principle. Teacher voice is…