Spatial reasoning is seen as increasingly important in STEM fields. Within mathematics, geometry is a potential site to study and support young children's spatial reasoning. In this paper we revisit Piaget and his colleagues' theoretical perspective on children's development of geometry concepts and take note of projective geometry in that theory.…

The paper explores one episode from a larger study, where a multilingual student (10-year-old) described her understanding of what makes a shape 2D or 3D. Bakhtin's dialogic theory and Garfinkel's ethnomethodology inform the theoretical framework. Transcribed data of the episode is presented, which is analysed at micro-level and macro-level. The…

As part of a much larger study where spatial reasoning is the focus, this paper draws on the language aspects of this strand of the curriculum. The quarantined part of the project discussed in this presentation is based in remote Indigenous schools. We draw on the challenges of the concept of symmetry and where the language of instruction (and…

South Australia's PISA performance has been in constant decline since 2003 with the proportion of PISA participants meeting the Australian national proficient standard dropping from 73% (in 2003) to 50% (in 2018). In contrast, Singapore is a consistently strong performer. To better understand student readiness in answering PISA questions, this…

As a multifaceted concept, the learning of angle concepts takes years to achieve and is beset with challenges. This paper explores how the processes of constructing and validating a learning progression in geometric reasoning can be used to generate targeted teaching advice to support the learning of angle concept. Data from 1090 Year 4 to Year 10…

The interactional role of language use in the mathematics classroom is explored in the last few decades. This paper adds to the knowledge base by exploring different ways of talking that children and their teacher use in a New Zealand primary geometry English-medium classroom. Bakhtin's concept of speech genres is used for an analysing transcript…

Guided Mathematical Inquiry (GMI) supports the development of deep understandings about mathematics concepts as students learn to address inquiry questions with evidence-based claims. Developing an evidence-based focus has been shown to be problematic with children. This paper presents how a framework for evidence was developed through the expert…

The capacity to recognise, represent, and reason about relationships between different quantities, that is, to think multiplicatively, has long been recognised as critical to success in school mathematics in the middle years and beyond. Building on recent research that found a strong link between multiplicative thinking and algebraic, geometrical,…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

This paper explores three multilingual students' (9 to 11-years-old) conceptual understanding of three-dimensional (3D) shapes as displayed through peer and classroom interactions in two New Zealand primary classes. Bakhtin's dialogic theory and Garfinkel's ethnomethodology inform the theoretical framework. The paper presents two excerpts from…

The paper presents a systematic review synthesising and evaluating literature that focuses on developing a conceptual understanding of shapes and their representations. It maps out literature from 2010-2018 targeting students (5-13 years) based on a set of inclusion and exclusion criteria. The analysis revealed that studies fail to take account of…

Research in both the New Zealand and international contexts identifies the need for New Zealand classrooms to foster culturally responsive and mathematical practices that align with Påsifika students' cultural values, backgrounds, interests and experiences. The aim of this study was to investigate how the use of culturally responsive tasks along…

How can basic research on mathematics instruction contribute to instructional improvement? In our research on the practical rationality of geometry teaching we describe existing instruction and examine how existing instruction responds to perturbations. In this talk I consider the proposal that geometry instruction could be improved by infusing it…

Developing students' geometric reasoning skills is dependent on the quality of task designs and the role of the teacher. The purpose of this study was to apply Sfard's (2008) interpretive framework to analyse changes in students' mathematical discourse. This paper reports on the results of an investigation into the ways one class of Year 7…

The Ghanaian mathematics curriculum expects teachers to adopt technologies as an instructional tool to assist students to learn mathematics relationally. Teachers' dispositions (knowledge, beliefs, and attitudes) towards technology are critical in translating the curriculum intention into practice. This paper presents teachers' initial…