Very young preverbal children (aged around 12 months) actively engage with their environment, whether at home, on outings, or in early learning centres. Their engagement with their environment can occur in many different ways involving physical and mental activities. In an early learning centre, there are many activities that very young preverbal…

Proportional reasoning is important to students' future success in mathematics and science endeavors. More specifically, students' fluent and flexible use of scalar and functional relationships to solve problems is critical to their ability to reason proportionally. The purpose of this study is to investigate the influence of systematically…

Digital natives are now of age and comprise the new generation of early career teachers (ECTs). This is an important change in teacher demographics given that new technologies have been introduced into classrooms with expectations that teachers embed them effectively into the teaching of mathematics. This paper draws on the data of three separate…

Mathematical reasoning is now featured in the mathematics curriculum documents of many nations, but this necessitates changes to teaching practice and hence a need for professional learning. The development of children's mathematical reasoning requires appropriate encouragement and feedback from their teacher who can only do this if they recognise…

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.…

Proportional reasoning involves the use of ratios in the comparison of quantities. While it is a key aspect of numeracy, particularly in the middle years of schooling, students do not always develop proportional reasoning naturally. Research suggests that many students do not apply proportional methods appropriately and that they often erroneously…

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…

Mathematics education researchers conducting instruction experiments using a design research methodology are challenged with the analysis of often complex and large amounts of qualitative data. In this paper, we present two case studies that show how multimedia analysis software can greatly support video data analysis and theory development in…

It has been recognised that many student perspectives on equations and their use of the equals sign have not mirrored those that mathematicians would like to see in tertiary students. This paper tracks transition of understanding of the equals sign by comparing secondary school students' thinking with that of first year university students. We…

The study describes levels of thinking in regard to the design of statistical studies. Clinical interviews were conducted with 15 students who were enrolled in high school or were recent high school graduates, and who represented a range of mathematical backgrounds. During the clinical interview sessions students were asked how they would go about…

Investigated the relationships among mathematics achievement, affect, and home background for Hong Kong students (n=1766) in grades 7-13. Achievement was most closely related to academic and nonacademic self-concepts and attitudes toward mathematics, and the latter was most influenced by self- and parental expectations. (LDR)