Although an understanding of time is crucial in our society, curriculum documents have an undue emphasis on reading time and little emphasis on core underlying ideas. Given this context, a one-to-one assessment interview, based on a new framework, was developed and administered to investigate students' understanding of core ideas undergirding the…

Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic…

Data from a pilot study concerned with pre-service teachers' perceptions of the numeracy demands on Australian teachers are reported. The sample comprised 211 students enrolled in pre-service teacher education courses at a large Australian university. While most recognised the importance of mathematics and its applications in everyday life, less…

Research that has explored students' interpretations of graphical representations has not extended to include how students apply understanding of particular statistical concepts related to one graphical representation to interpret different representations. This paper reports on the way in which students' understanding of covariation, evidenced…

This article presents a snapshot of the mathematical competencies of children aged four to five years in Australian early childhood education settings, as perceived by their educators. Data are presented from a nationally-representative sample of 6511 children participating in the Longitudinal Study of Australian Children (LSAC). The results…

Numeracy Skills testing was brought to the forefront following the Action Now: Classroom Ready Teachers report in 2015. The announcement was met with much concern by many pre-service teachers (PSTs). Given the body of research associated with mathematics anxiety and assessment, which suggests that students' self-efficacy and confidence in their…

Large-scale numeracy assessments are intended to facilitate the improvement of educational outcomes; however, it is not clear exactly how this is to be achieved. To move towards the goal of numeracy for all, it is necessary to systematically address issues that are known to be difficult, pervasive and persistent. This paper includes an analysis of…

As teaching is a cultural activity embedded in a unique context, professional development opportunities for teachers may be best placed amid the relevance of everyday classroom practice, and supported by an innovative curriculum. This progress paper reports on data collected as part of doctoral research studying the changes in mathematical…

This study explores the implications for mathematical knowledge and pedagogical practices of primary teachers in Papua New Guinea making a shift from a transmission approach to a connectionist approach to teaching mathematics. The research participants were engaged in a professional development program designed to support the teaching and learning…

Mathematical knowledge of pre-service teachers is currently "under the microscope" and the subject of research. This paper proposes a different approach to teacher content knowledge based on the "big ideas" of mathematics and the connections that exist within and between them. It is suggested that these "big ideas"…

In Australia we face a serious problem in that over the last twenty years the quality of students' mathematical knowledge and abilities has "deteriorated to a dangerous level" (Brown, 2009, p. 3). Too few students want to study further mathematics and are "unlikely to continue its study voluntarily" (Commonwealth of Australia,…

Pat was a 19-year-old attending a Special School for the Intellectually Disabled in Indonesia. She was interviewed by the first author regarding her mental calculation strategies when solving 1- and 2-digit addition and subtraction problems. Results indicate that she was able to see ten as a unit composed of ten ones and was facile in using…

This paper considers the responses of 26 teachers to items exploring their pedagogical content knowledge (PCK) about the concept of average. The items explored teachers' knowledge of average, their planning of a unit on average, and their understanding of students as learners in devising remediation for two student responses to a problem. Results…

This paper reports on one phase of a long-term project investigating mathematical content knowledge of pre-service teachers. A cohort of second year PSTs conducted a diagnostic assessment and a series of associated tutoring sessions with a primary aged child. The focus here is on the PSTs' ability to make appropriate task choices following the…

Information and communication technologies (ICT) are positioned in policy/syllabus documents as an essential resource in the teaching of mathematics. Given their youth and lifelong experience with technology, early career teachers (ECTs) are expected to excel in their use of ICT; however, we are not clear on the viability of these expectations and…