This paper reports results of a design experiment regarding young children's concepts of mass measurement. The research built on an earlier study in which a framework of "growth points" in early mathematics learning and a related, task-based, one-to-one interview to assess children's understanding of the measurement of mass…

This is the report of an investigation in partnership with a team of junior secondary classroom teachers of the potential of posing more challenging tasks to their students. A range of data sources are used to represent the experience of teachers and students in a unit of work that incorporated a range of challenging tasks. Students learned the…

The importance of mathematics or its alter ego "numeracy" is being cemented in the public's mind with the instigation of national, high-stakes testing in Australia. Discussions about national testing in press releases, online news articles and online public comments tacitly attribute importance to mathematics. In these discussions,…

The use of formal observation in primary mathematics classrooms is supported in the literature as a viable method of determining effective teaching strategies and appropriate tasks for inclusion in the early years of mathematics learning. The twofold aim of this study was to (a) investigate predictive relationships between primary mathematics…

This study explores, from both constructivist and cognitive perspectives, teacher guidance in student-centered classrooms when addressing a common learning difficulty with equivalent fractions--lines or pieces--based on number line models. Findings from three contrasting cases reveal differences in teachers' facilitating and direct guidance…

Students living in disadvantaged contexts and whose second language is English (ESL) are at risk of not succeeding in school mathematics. It has been internationally recognised that students' socioeconomic background and their achievements in mathematics is more pronounced for Australian students (Thomson et al. 2011). This gap is even more…

Drawing on evidence from the Longitudinal Investigation of the Effect of Curriculum on Algebra Learning (LieCal) Project, issues related to mathematics curriculum reform and student learning are discussed. The LieCal Project was designed to longitudinally investigate the impact of a reform mathematics curriculum called the Connected Mathematics…

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…

This paper explores the outcomes of the first year of the implementation of a mathematics program ("Representations, oral language and engagement in Mathematics": RoleM) which is framed upon research relating to effectively supporting young Indigenous students' learning. The sample comprised 230 Indigenous students (average age 5.76 years) from 15…

In classrooms tests, students are regularly required to demonstrate their understanding of mathematical concepts. When children encounter problems in demonstrating such understanding, it is often not clear whether this is because of the language of the teachers' questions and instructions or a genuine non-understanding of the concept itself.…

This study concerns pupils' experience of unit and non-unit fractions of a discrete quantity during specially designed lessons. The aim was to explore pupils' understanding of operations such as "b/c of a" in lessons where the teachers were aware of some pupils' difficulties beforehand and what needed special attention.…

Factors that contribute to strong teacher-student relationships are vital to understand because of the influence these relationships have on achievement and motivation, particularly for minority group students. This article draws from a substantial quantity of empirical data, grounded in a wide theoretical and cultural base, regarding aspects of…

Asian children, including Chinese children, perform better than their English-speaking peers in cross-national mathematics studies. This superior Asian performance is attributed to several factors including cultural beliefs, educational systems and practices, and the Chinese number naming system. Given the limited empirical evidence on pre-school…

The structure of two-tier testing is such that the first tier consists of a multiple-choice question and the second tier requires justifications for choices of answers made in the first tier. This study aims to evaluate two-tier tasks in "proportion" in terms of students' capacity to write and select justifications and to examine the effect of…

"Streaming" for mathematics remains a contentious issue and particular forms of the practice have been considered inequitable. In the study reported here, the focus was on the extent to which streaming is used for mathematics at years 7-10 in Victorian secondary schools. Also of interest were the forms of streaming adopted and the criteria for…