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…

In this paper, we discuss the process of identifying and validating students' abilities to think proportionally. More specifically, we describe the methodology we used to identify these proportional reasoning attributes, beginning with the selection and review of relevant literature on proportional reasoning. We then continue with the…

This paper presents a comparative analysis of prospective elementary teachers' mathematical problem solving-related beliefs in Cyprus and England. Twenty-four participants, twelve from a well-regarded university in each country, were interviewed qualitatively at the exit point of their undergraduate teacher education studies. Analyses…

This study is focused on identifying and describing the reasoning patterns of middle grade students when examining potentially similar figures. Described here is a framework that includes 11 strategies that students used during clinical interview to differentiate similar and non-similar figures. Two factors were found to influence the strategies…

Today's students increasingly engage in online environments, with ready access to digital resources and mobile technologies. While much of this activity is socially motivated, the internet is also a source of knowledge for students and frequently accessed for school assignments, projects and assessment purposes. As mathematics continues to be…

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…

Unlike a child's observable, physical interactions with mathematical tools (e.g., physically touching blocks in order to count them), the subtle manifestations of imagery construction can be considerably more challenging to identify and act upon. Although there have been substantive examinations of mental imagery in a variety of mathematical…

This article is a report on a longitudinal case study that investigated the problem of lowered engagement with mathematics and students' perspectives of the factors that influenced their engagement during the middle years of schooling. The article provides a synthesis of the entire study and a summary of its findings. In order to address the…

The project "Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice" aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian…

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students' conceptions of rate, focussing on the influence…

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…

Information and Communication Technology (ICT) offers the potential for changing mathematics education for both teachers and students. However, how ICT is used, and by whom, is critical to realizing this potential. This paper reports on an investigation of the use of ICT in the learning and teaching of mathematics in rural and urban primary…

The levels of engagement in mathematics experienced by students during the middle years of schooling (Years 5 to 8 in New South Wales) has been of concern in Australia for some years. Lowered engagement in school has been attributed to factors such as inappropriate teaching strategies, curricula that is unchallenging and irrelevant, and cultural…

In Australia, concerns about the quality of mathematics education that students experience are particularly salient in rural schools. These schools typically report great difficulty in attracting and retaining qualified teachers of mathematics. Teachers in non-metropolitan locations may also experience professional isolation if they have limited…

The following paper describes the development of an instrument designed to assess middle school students' interest in statistical literacy. The paper commences with a review of the literature as it relates to interest in this context and then proposes a theoretical model upon which the proposed instrument is based. The Rasch Rating Scale model is…