Harry completed his first year of primary school (Kindergarten) during 2004 in New South Wales, Australia. He enjoyed school; made great friends; played lots of sport; continued to read quite successfully; was well-liked by his teachers; participated in many activities; and, on reportedly rare occasions, did some mathematics. In this paper,…

Increasing numbers of mathematics educators, policy makers, and researchers believe that algebra should become part of the elementary education curriculum. Such endorsements require careful research. This paper presents the general results of a longitudinal classroom investigation of children's thinking and representations over two and a half…

There have been many efforts to change mathematics education and teachers. However this has proved to be very difficult. The starting point for this study was the question: Should we change people? There might be good reasons why things remain stable for longer periods. My aim is to approach the difficult question of teacher change from the…

There is a growing interest in the mathematics education community in the notion of abstraction and its significance in the learning of mathematics. "Reducing abstraction" is a theoretical framework that examines learners' behavior in terms of coping with abstraction level. This article extends the scope of applicability of this…

The teaching and learning in algebra has been much debated. Traditionally early algebra has relied heavily on arithmetic. Recently our focus has changed to teaching algebraic thinking with arithmetic thinking. This paper explores the models that assist young students generalise the patterns of arithmetic compensation. A teaching experiment was…

This paper describes a theoretical model for examining teaching and learning in primary mathematics classrooms. The model in intended to be both analytical--to provide insights into classroom incidents--and heuristic--to inform planning and practice. This paper reports on the elements of the model, which are based on Vygotskian theory and…

If we consider the gap between mathematics at elementary and secondary levels, and the logical nature of the higher level, it is important that aspects of children's logical development in the latter grades in elementary school be clarified. We focused on 5th graders' learning "division with decimals" as it is known to be difficult to…

This study investigated the development of an additive schema from the perspective of the schema's flexibility in coping with new context and unfamiliar semantic structure. It followed 27 first graders who learned addition and subtraction using an experimental curriculum. The instruction involved a didactical model combining the context of two…

This is a study of how urban elementary grades students develop and express functions. Data were analyzed according to the forms of representations students used, the progression in students' mathematical language and the operations they employed, and how they attended to one or more varying quantities. Findings indicate that students are capable…

This paper addresses the first year of a three-year, longitudinal study which introduces mathematical modeling to young children and provides professional development for their teachers. Four classes of third-graders (8 years of age) and their teachers participated in the first year of the program, which involved several preliminary modeling…

Recent curricular reforms are following the lead of the Standards 2000 and, in diverse ways, integrating some algebraic work into primary school mathematics. Our research aims at producing a tool that will allow researchers to track the development of algebraic thinking in children as they progress through various primary programs. In this paper…

Because cognition is the core substance of understanding and sense making, cognition-based assessment is essential for understanding and monitoring students' development of powerful mathematical thinking. The Cognition-Based Assessment System (CBAS) project is applying the results, theories, and methods of modern research in mathematics education…

Assessment practices influence and are influenced by a number of educational as well as social factors. The present study looks at these practices of five primary teachers displayed in the mathematics classroom and in a relevant pedagogical discourse developed in the context of an interview. The results show that, on the whole, their practices…

This paper reports on a study carried out in the Netherlands which is aimed at finding an explanation for the curious evidence that the reformed approach to mathematics education appears to have a less positive influence on girls' results. Over and over it turns out that girls' achievement scores in primary mathematics are lower than those of…

The case study presented in this report was part of assessing a teaching proposal on ratio and proportion. A group of sixth-grade students of elementary education in Mexico participated in the implementation of the proposal. The girl of the case study was representative of those students in the group who had a lot of recourse to handling…