In this paper, we analyze and compare two didactical designs for introducing primary school pupils to proportional reasoning in the context of plane polygons. One of them is well-documented in the literature; the other one is based on our own data and is accordingly presented and discussed in more detail in this paper. The two designs come from…

In this article we consider how elementary education students' views of mathematics changed during their mathematics methods course. We focus on four female students: two started the course with mainly positive views of mathematics and a task orientation, two with negative views of the subject and an ego-defensive orientation. The biggest change…

This article presents a Vygotsky-inspired analysis of how a teacher mediated a "thinking aloud" whole-group discussion in a 6th grade mathematics classroom. This discussion centered on finding patterns in a triangular array of consecutive numbers as a phase towards building recursive and direct algebraic formulas. By a "thinking aloud" discussion…

This paper draws on data from the development of annual national mathematics assessment materials for 7-year-old pupils in Wales for use during the period 2000-2002. The materials were developed in both English and Welsh and were designed to be matched. The paper reports on item analyses which sought items that exhibited differential performance…

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 examines 6th grade children's local conceptual development and mathematization processes as they worked a comprehensive mathematical modeling problem (creating a consumer guide for deciding the best snack chip) over several class periods. The children and their teachers were participating in a 3-year longitudinal teaching experiment in…

Elementary education students enrolled in an experimental mathematics course participated in this study. The course is taught using a social constructivist approach and is designed to improve students' mathematical problem-solving ability and deepen their understanding of mathematics. The research question for the present study is as follows: In…

Presents a preliminary analysis from a study designed to investigate the participation of students learning English as an additional language in primary school mathematics. Concerns how students make sense of mathematics classroom interaction. Describes and uses the findings of three patterns of attention in the process of two students'…

Explores the teaching of four elementary teachers as they incorporated a model of culturally relevant teaching into their mathematics instruction. Examines how teachers sought to: (1) foster critical mathematical thinking and critical consciousness; (2) build on informal mathematical and cultural knowledge; and (3) utilize empowerment orientations…

Examines changes in the problem posing strategies of a group of elementary preservice teachers as they posed problems to pupils. Indicates that the teachers' problem posing practices were changed from posing traditional single steps and computational problems to multiple approaches and solutions with open-ended and exploratory problems.…

Explores commonalities across and differences between learners in mathematics classrooms. Explores commonalities between learners across mathematics and between communities of practice. Discusses how to address teachers' roles and responsibilities. Investigates differences between syllabus and practice, school mathematics, mathematics in the…

Investigates the conditions and constraints of the integration of the dynamic geometry software Cabri into the teaching of geometry in primary school classes (10-year-old pupils). Focuses on the way the dialectic between old and new is working during this integration, looking at the types of tasks and techniques proposed in class by teachers.…

Reanalyzes data obtained in 1987 on mental calculation strategies used by 11-year-olds in England, Wales, and Northern Ireland. Classifies mental strategies developed in the past decade in international research. Compares frequency and effectiveness of the strategies used by pupils of different levels of attainment. Discusses basic arithmetic…

Describes formative and self-regulating evaluation, developed by Citogroep and used for primary schools in the Netherlands to signal the progress of 6-12-year-old students and monitor their learning. Presents the structure, principles, and tools of the management of the improvement of differential pedagogy and key ideas for teacher education.…

Reports on a study in which three 3rd grade students were presented with the volume of cuboids. Examines the problem solving actions students demonstrate and analyzes students' strategies and solutions. Explores the connection between spatial structuring and the use of numerical operation. Considers perseverance and control emerging when solving…