This paper explores the role of organising data in representing numerical data in an organised way--a skill which does not come naturally to most students. Grade 6 children were given a series of lessons on organising data and then representing the data graphically. It was found that after instruction, more students were able to reorganise the…

This paper provides an analysis of a teacher development experiment (cf. Simon, 2000) designed to support teachers' understandings of statistical data analysis. The experiment was conducted as part of collaborative efforts between the author and a cohort of middle-school mathematics teachers during the 2000-2001 academic year. Analysis of the…

The purpose of this paper is to discuss the activities of collective learning structures. Drawing from ecological-complexity theory it elaborates on a theoretical framework for observing and acting upon collective learning. To interpret the relation between individual action, social interaction and the collective cognitive domain we adopt the…

Based on a survey of 3067 Finnish 5th and 7th graders and a task-based interview of 20 7th graders we examine student's understanding of fraction. Two tasks frame a specific fraction (3/4) in different contexts: as part of an eight-piece bar (area context) and as a location on a number line. The results suggest that students' understanding of…

In this paper we will concentrate on pupils' self-confidence in mathematics, which belongs to pupils' mathematical beliefs in themselves, and beliefs on achievement in mathematics. Research described consists of a survey of more than 3000 fifth-graders and seventh-graders. Furthermore, 40 pupils participated in a qualitative follow-up study…

In a previous study, we posited a link between Chinese sixth grade students' problem solving and problem posing based on a pattern-formation strategy (Cai & Hwang, 2002). A similar parallel structure between problem solving and problem posing did not obtain for the U.S. sixth graders in the study. The present study attempts to locate this type of…

While the influence of individuals' participation in practices of economic subsistence on the development of mathematical knowledge has been widely reported in the literature, there are not as many studies about the relationship between cultural life and mathematical cognition in the context of recreational practices. This article reports a study…

This paper presents a rationale and a conceptual framework for a wider research project dealing with mathematical communication, and in particular with actions performed by interlocutors whenever they wish to clarify their use of a symbol, a word or an expression. The aim of such actions is often to repair a communicational breach resulting from…