How can we engage all primary school students in rich mathematical learning, support them to make connections, and develop their mathematical language and reasoning? In this article, we draw on one school's experience in considering an approach to mathematics instruction that could support teachers in addressing this question, specifically…

The revised Australian curriculum presents a new emphasis in primary schools on the process of Mathematical Modelling. A modelling focus brings close attention to confidence and capability with a potentially new problem-solving process, associated language, and pedagogical processes. This paper presents a Year 4 classroom modelling experience that…

This is the third in a series of articles describing CODAP and where it might be used to address content in the "Australian Curriculum: Mathematics" v9.0 (ACARA, 2022). We've talked before about model-ling and about statistics; this time, we'll talk about exploring probability using CODAP. As before, we have also prepared online pages…

Mathematical thinking is a complex, multi-faceted process that has been described as messy and difficult but can also show growth and insights into conceptual understanding and knowing. This paper explores the application of Edward de Bono's practical thinking, in particular, the occurrence of porridge words to examine the mathematical thinking of…

Number fact knowledge spans far beyond conventional automatic mastery practices involving rote learning. Having the ability to automatically recall number facts fluently does not mean students will have strong conceptual understanding. This article provides suggestions for how number fact thinking and fluency might be developed in primary…

In this article, the authors explore a number of interesting games as contexts for students learning geometry and enhancing their development of problem solving and reasoning. The games selected were appealing, content-aligned games for approximately four players with simple rules and 10-30 minutes of play time. The games were integrated by…

Despite a focus on teaching mathematics through challenging, problem solving tasks, there has been limited research into student attitudes towards these learning experiences. To address this gap in the literature, we asked 52 Australian primary students who had recently experienced mathematics taught in this manner to convey their feelings about…

Co-written by a student and his teacher, this article illustrates how a carefully structured individual education program supported by appropriate software can provide suitable challenges for a gifted Year 3 student. While the focus is on one student's statistical investigation, the story has relevance to the wider primary school environment.

Estimation is such an important yet sometimes overlooked skill. Enhancing estimation skills through exposing students to enumeration ('how many') problems where they are required to estimate before calculating is a critical aspect of developing number sense (Reys et al., 2012). This article describes a 'how many' problem undertaken with a small…

This study reports on the capabilities of 53 Year 4 students as they completed the final stages of their first complete statistical investigation. In the context of becoming acquainted with students in a sister school in another city, students in both schools wrote and refined questions, which were answered by all students in an on-line survey.…

Teaching from an informal statistical inference perspective can address the challenge of teaching statistics in a coherent way. We argue that activities that promote model-based reasoning address two additional challenges: providing a coherent sequence of topics and promoting the application of knowledge to novel situations. We take a models and…

This paper outlines a seven-step process for developing problem-solving tasks informed by cognitive load theory. Through an example of a task developed for Year 2 students, we show how this approach can be used to produce challenging mathematical tasks that aim to optimise cognitive load for each student.

Working within the context of a contest to find the most beautiful tourist attraction in the world, Year 5 students investigate the most symmetric building from a short-list of three iconic buildings. This involves investigating both line and rotational symmetry in order to make an informed decision about the symmetrical nature of each building.

This article encourages approaches that develop children's understandings of data representations. In particular, when children develope flexibility in their approaches to data representation and understanding, the same data can be represented in different ways. Flexible and adaptive use of representations is part of mathematics competence which…

As an extension to an activity introducing Year 5 students to the practice of statistics, the software "TinkerPlots" made it possible to collect repeated random samples from a finite population to informally explore students' capacity to begin reasoning with a distribution of sample statistics. This article provides background for the…