Most educational research on argumentation comes from science, with argumentation in mathematics tending to focus on proof. We contend that argumentation can be used productively in learning mathematics even at the primary level. A research study was designed to explore children's development of argumentation in an Australian primary mathematics classroom. The classroom of 23 children (aged 9-10) had regularly used an inquiry-based approach to address extended, complex, ill-structured problems. The children's discussions and use of evidence is reported as they considered contentious media claims. The results of the design-based research study suggest that the children became proficient with Toulmin's argument framework (simplified). They were able to use this framework to plan, implement and defend the outcomes of a mathematical investigation they designed to provide evidence for or against the media claims. The paper highlights benefits and challenges with which student grappled while making and substantiating their final claims.

Describing and analyzing teaching practice has been a focus of researchers interested in the interaction and connections between teachers’ content knowledge and their pedagogical knowledge. This study described the role of a teacher’s mathematical content and pedagogical content knowledge in involving students in learning and solving Science, Technology, Engineering, and Mathematics (STEM) problems in an Australian primary school context. The Knowledge Quartet (KQ) is a widely recognised framework originally developed to observe classroom mathematics teaching and analyze mathematics teaching practices. We use the KQ as a theoretical/organizational framework against which to thematically analyze one teacher’s classroom pedagogy to investigate 1) the utility of the KQ framework for describing and analyzing a teacher’s mathematical lesson within an integrated STEM inquiry context and 2) how a teacher’s pedagogical mathematical knowledge supports a focus on inquiry-based STEM integrated teaching. The study involved a teacher and 26 Year 5 students in an Australian classroom. Data included classroom video recordings, researcher observation notes, and students’ artefacts. The video recordings were transcribed and analyzed using the KQ framework. The observation notes and artefacts were used to validate and support this analysis. The paper identifies and provides examples of different aspects of the KQ in the teaching sequence and provides examples of how integrated STEM content can be effectively incorporated into the primary school classroom. The relevance and significance of the KQ framework and the teaching of integrated STEM content in primary school are reviewed and discussed within the paper.

Engaging with Maths through Picture Books can be used as a form of professional learning and a springboard for developing educators' own exciting literature-based mathematics lessons by using the ideas as they are, adapting them for the needs of learners and/or taking the ideas and applying them to different books. It is designed to stimulate children's thinking and mathematical experiences by building strong foundations for their future enjoyment and success with mathematics.

Currently we find ourselves in turbulent waters within the context of mathematics education research and in debates about current policy, curriculum, and practice reform. The debate that pits ‘traditional’ approaches to teaching mathematics against ‘reformoriented’ approaches has recently been making waves, yet these debates are certainly not new. We seek to advance our understanding of effective pedagogies to help researchers, policy-makers, and practitioners navigate these waters.

Previous research into the knowledge required for teaching has focused primarily on pre-service and in-service teachers' knowledge. What is less researched, however, is the role of the teacher educator in helping pre-service teachers (PSTs) develop the knowledge needed in order to teach mathematics to students. The focus thus shifts from examining school teachers' knowledge for teaching mathematics to school students, to studying teacher educators’ knowledge for teaching teachers. This raises the question of what is the nature of this knowledge as required by teacher educators, and how evident is it in their practice? This paper documents the interactions among two teacher educators and two cohorts of PSTs enrolled in a unit designed to teach mathematics pedagogy to early childhood and primary PSTs. Over one semester, two teacher educators observed each other’s classes, engaged in reflective professional conversations, and surveyed PSTs about lesson material and delivery. The results indicated there were a number of issues faced by the teacher educators that could be interpreted through the use of a teacher knowledge framework, with examples for this study focussing on a representative lesson. The findings add to the field of research into teacher educator knowledge and have implications for mathematics teacher educators and the pre-service teachers they teach.