We investigate the use and knowledge of graphs in the context of a large industrial factory. We are particularly interested in the question of "transparency", a question that has been extensively considered in the general literature on tool use and, more recently, by Michael Roth and his colleagues in the context of scientific work. Roth uses the…

The study focused on the interaction between two secondary school students while they were working on computerized mathematical investigation tasks related to probability theory. The aim was to establish how such interaction helped the students to learn from one another, and how it may have hindered their learning process. The assumption was that…

Teaching and learning fractions has traditionally been one of the most problematic areas in primary school mathematics. Several studies have suggested that one of the main factors contributing to this complexity is that fractions comprise a multifaceted notion encompassing five interrelated subconstructs (i.e., part-whole, ratio, operator,…

This paper summarizes our analysis of the complexity of ratio problems at Grades 6 and 7, and reports a two-year experiment related to the teaching and learning of rational numbers and proportionality in these grades. Two classes were followed and observed. Part of the teaching material was common to both classes, mainly the objectives and the…

In the context of a three-year professional development program in mathematics, practicing elementary teachers persistently engaged in collaborative inquiry and reflection to build connected meanings for slope. One teacher invented a compelling representation for slope as a process of repeated addition, using Cuisenaire rods, based on teachers'…

We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson;…

This paper reports the findings of a study that sought to identify particular centrally held beliefs of secondary mathematics teachers that underpinned the establishment of classroom environments that were consistent with the principles of constructivism. The nine crucial beliefs identified were held by one or other of two teachers and emerged…

This report focuses on prospective secondary mathematics teachers' understanding of irrational numbers. Various dimensions of participants' knowledge regarding the relation between the two sets, rational and irrational, are examined. Three issues are addressed: richness and density of numbers, the fitting of rational and irrational numbers on the…

Despite increased appreciation of the role of "proof" in students' mathematical experiences across "all" grades, little research has focused on the issue of understanding and characterizing the notion of proof at the elementary school level. This paper takes a step toward addressing this limitation, by examining the characteristics of four major…

This study described mathematics teachers' views on the significance of reasonable answers and how they address this concept in their classrooms. Data were gathered from thirteen eighth-grade Kuwaiti mathematics teachers in two middle schools. All teachers in Kuwait use the national textbook and follow the accompanying instructional plans provided…

Two strands of research motivate this study. One is the interest in school students' development of understanding of the concept of average, historically part of the mathematics curriculum and prominent in the statistics curriculum introduced in the early 1990s. The other is the belief of some educators that students learn meaningfully when…

We ground Cultural-Historical Activity Theory (CHAT) in studies of workplace practices from a mathematical point of view. We draw on multiple case study visits by college students and teacher-researchers to workplaces. By asking questions that "open boxes", we "outsiders and boundary-crossers" sought to expose contradictions between College and…

The CAME project was inaugurated in 1993 as an intervention delivered in the context of mathematics with the intention of accelerating the cognitive development of students in the first two years of secondary education. This paper reports substantial post-test and long-term National examination effects of the intervention, yet, by discussing the…

Trainee teachers, new and non-specialist teachers of elementary mathematics have a tendency to avoid thought about reasons in mathematics. Instead, they tend to favour the development of computational skill through the rote application of procedures, routines and algorithms. Could elementary mathematics textbooks serve as models of practice and…

This paper provides a microanalysis of one Algebra I teacher's instruction to explore the advantages that are afforded us by coordinating two perspectives to document and account for the teacher's mathematical understandings. We use constructs associated with Stein, Grover and Henningsen's domain of mathematical didactics and Realistic Mathematics…