Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

The notion of emergence has considerable currency in mathematics education. However, the notion tends to be used in a descriptive way rather than being theorized and developed as a phenomenon sui generis. The purpose of this article is to contribute to building a theory of "emergence." After providing an exemplifying description and…

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…

Drill-and-practice mathematics software offers teachers a relatively simple way to use technology in the classroom. One of the reasons to use the software may be that it motivates children, working on the computer being more "fun" than doing regular school work. However, students' own perceptions of such software are seldom studied.…

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 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…

Proportional reasoning as the capacity to compare situations in relative (multiplicative) rather than absolute (additive) terms is an important outcome of primary school mathematics. Research suggests that students tend to see comparative situations in additive rather than multiplicative terms and this thinking can influence their capacity for…

We analyze a classroom design experiment, conducted in a fourth grade classroom, that served to explore an instructional path in which the introduction of unit fractions and supporting proportional reasoning coincide. Central to this path is the use of means of support in which the objects that unit fractions quantify are not characterized as…

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…

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…

Current reforms in mathematics education advocate the development of mathematical learning communities in which students have opportunities to engage in mathematical discourse and classroom practices which underlie algebraic reasoning. This article specifically addresses the pedagogical actions teachers take which structure student engagement in…

The content and purpose of written unit plans in mathematics is an under-researched area. In this article, we provide a brief overview of research on teachers' planning processes and the place of mental and written plans. We report on data from a questionnaire completed by 357 teachers from Victorian Catholic primary schools, where we focused…

As part of a teacher professional learning project in mathematics education, university mathematics educators taught demonstration lessons in project primary schools. These lessons were part of a "pre-brief, teaching, and debrief" process, in which up to eight teachers observed each lesson. Using brief questionnaires completed in advance of the…

This article reports on a study that was conducted with 378 primary teachers from Catholic schools in Victoria who participated in the first year of a 2-year research and professional learning program in mathematics. One aim of the program was to enhance teacher knowledge in mathematics in its many forms. As part of the larger study, the teachers…

The first goal of this Project is the development of elementary school mathematics curricula sensitive to indigenous mathematical thought and experience. A necessary prerequisite for the achievement of this goal is to recapture and honor the mathematics developed and practiced in the Micronesian communities. This is the Project's second goal. The…