The interactions young children have with adults are of vital importance in developing mathematical reasoning. This paper describes the behaviours of teachers who work with young children in school yet manage to have individual and natural mathematical conversations with children. These mathematical interactions young children have with their…

This is the third article in the "On the Shoulders of Giants" series that takes an outstanding mathematician, tells something of their life and work, and provides an item or two based on their achievements that can be used in a primary class. This article focuses on the work of Cheryl Praeger, with an activity based upon her work with…

Beginning a mathematics lesson involving a challenging task with a carefully chosen preliminary experience is an effective means of activating student cognition. In this article, the authors highlight a variety of preliminary experiences, each with a different structure and form, all designed to support students to more successfully engage with…

Nicolas Senior shows how EMC3 's Launch-Explore-Summarise/Review model for mathematics lesson structuring sets the conditions to get the most out of both dialogic and direct instruction. He argues that this model will help teachers walk the balance between order and chaos.

This article builds on the work of Professor Robyn Jorgensen and Associate Professor Peter Games and others on social justice and mathematics and links to the Ethical Understandings capability of the "Australian Curriculum." Presented in this paper is an argument for the importance of a social justice approach to teaching mathematics,…

Using mathematical modelling to solve problems appears in all year levels in the Australian Curriculum: Mathematics (v. 9), and is probably the most authentic way of teaching mathematics in context. However, the term mathematical modelling, even if familiar to teachers, may not be well understood or enacted confidently by teachers in their…

This paper focuses on the importance of identifying students' Prior Knowledge (PK) for the teaching and learning of mathematics. Specifically, we present a framework that exemplifies the core elements teachers need to consider in relation to the purpose, design and implementation of learning experiences that enable PK to be activated and assessed.…

Creative thinking in mathematics is an essential 21st Century skill that can be developed and encouraged through an exploration of mathematical concepts. In the context of the new "Australian Curriculum: Mathematics," this article explores the possibilities that are unlocked when students engage with tasks creatively in mathematics. By…

Professional learning that includes coaching is an effective method of supporting teachers to make changes to their teaching practice. This article provides an overview of the initial in-situ professional learning and coaching in a primary school in Western Sydney facilitated by a Mathematics Teaching Educator. In this article I present the…

For students to develop adequate conceptual understanding about fractions, they require experiences that afford them opportunities to think flexibly about multiple interpretations of fractions. This article presents a sequence of lessons designed to offer such experiences for students in Years 3 and Year 4. The lessons adopt a challenging tasks…

This article is based upon Peter Sullivan's (2021) structured inquiry approach to teaching mathematics, in which the authors take a deep dive into the technique of "Spotlighting" in the "Explore" phase of this model to assist in optimal learning experiences for students. Working from the premise that students are best placed to…

This article aims to outline the important role of the summary phase within a mathematics instructional model and provide six strategies to support teachers to move beyond "share time." By drawing upon good teaching strategies during the summary phase, teachers can enhance the learning experience for themselves and for their students.…

Encouraging students' ability to reason can be looked at through the lens of both oral and written representations. In 2022, the author participated in the first intake of the Teacher Excellence Program run by the Victorian Teaching Academy. Being part of an in-depth professional learning program challenged the author's teaching practices to focus…

In this article Dan Jazby also explores the issue of noticing, but this time from the teacher's perspective. Dan argues that teacher noticing is a purposeful activity that requires both the technical skills to recognise how students are thinking and the tactical skills to know when and where to look for particular cues.

In this article, the authors argue that teachers need to possess appropriate understanding and diverse pedagogies to successfully move learners from additive to multiplicative thinking. Herein, they offer five pedagogical strategies that teachers can use to help students make this transition. Some of the challenges of learning multiplicative…