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.

Spatial visualisation is an essential component of geometric thinking and measurement sense. It is a particular type of spatial skill that involves manipulation of spatial images and may not be naturally occurring for students. However, research shows that it is malleable and can be developed through instruction. This article presents an…

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.…

Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content…

It is frequently surprising to new teachers (and even those with experience) when they find that not only do some children need to recount the group they have just counted to be assured of the total but also that this need seems to be resistant to intervention. Although moving from "counting-all" to "count-on" is sometimes…

The importance of ratio and proportional reasoning is regularly emphasised, however, the teaching and learning of these concepts continues to present challenges. In this article the authors explore a hands-on task, designed to encourage student visualisation of the concept of ratio. Teacher perceptions of this task were positive, indicating the…

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 article provides a range of activities designed to engage students in using an early form of graphing. While the "Australian Curriculum: Mathematics" (2014) highlights understanding, fluency, problem-solving, and reasoning, the National Research Council (2001) describes five strands of mathematical proficiency, with the additional…

In Australia, early childhood education takes a play-based approach to supporting children's engagement with mathematical ideas and numeracy development. To assist preschool teachers' implementation of the outcomes in the national Early Years Learning Framework for Australia, the Northern Territory (NT, Australia) has introduced the NT Preschool…

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.

This article describes part of a study in which researchers designed lesson sequences based around using a string number line to help teachers support children's development of relative thinking and understanding of linear scale. In the first year of the study, eight teachers of Years 3-5 participated in four one-day professional development…

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.

In this article, the authors present two activities in which students explore angles and related geometric properties in the context of dance, namely ballet. The activities have been successfully implemented in pre-service numeracy classes at Monash University's two-year, post-degree teacher education program (MTeach). Specifically, the activities…

Snowflakes falling in Brisbane, Australia would likely make news headlines during any season of a given year, even during winter. Year 8 students at Ormiston College which is located in Brisbane, have made their own snowflakes--of a kind. Using the programming language Scratch, all Year 8 Mathematics students wrote code to construct Swedish…