In this paper seventh-grade pupils' ways of handling aspects of probability have been investigated. The aspects in question were embedded in a dice game, based on the total of two dice. Four different set-ups of dice were included in the situation in which they were up to explore optimal strategies for winning the game. How children understand…

In extra-curriculum activities, the nature of the instructor-learner relationship differs from that in class. This constellation, if accompanied by a smaller gap between the mathematical skills of tutor and learner, has an impact on motivational aspects and on the choice of contents in these activities: The use of problem questions of competition…

Recent publications continue to show that significant numbers of students in junior grades, while competent in basic ruler skills, seem not to have acquired important concepts about how rulers work and units of length. This paper reports on the results of a set of tasks completed by students from Grades 5 and 6. The results show that many students…

Mathematical norms are important cultural knowledge of mathematical activities. This paper reports an analysis of mathematical norms in ten consecutive lessons taught by an eighth-grade Japanese teacher. The lessons were located in the unit of simultaneous linear equations. The videotapes of the lessons, their transcripts, and the interview data…

This research offers empirical evidence of the importance of supplying diverse symbolic representations in order to support concept development in mathematics. Graphical representation can be a helpful symbolic tool for concept development in the conceptual field of additive structures. Nevertheless, this symbolic tool has specific difficulties…

We present results from a study which investigated the influence of dynamic geometry-based activities in the development of proving skills (in geometry) in high-school students (15-16 years of age). After a 12-week course on Cabri and the writing of conjectures and proofs, students were asked to write and prove conjectures based on their…

A collaborative action research project with preservice teachers built on Wood's (2003) paper on strategy reporting, inquiry and argumentation and the NSW Department of Education and Training documents called substantive communication. There is little research on argumentation about space mathematics in primary schools so this is the focus of the…

In this paper we report an analysis of a teaching sequence in which Grade 11 students were asked to produce some graphs corresponding to the relationship between time and distance of a cylinder moving up and down an inclined plane. The students were also asked to carry out the experience using a TI 83+ graphic calculator equipped with a sensor,…

The paper describes the rationale and 10-day implementation in a 5th-grade classroom (n=19) of an experimental ratio-and-proportion instructional design. In this constructivist-phenomenological design, coming from our theoretical perspective, design research, and domain analysis, students: (1) link "real-world" and "mathematical" objects…