A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. We contribute to these efforts by expanding the constructs in Cobb and Yackel's (Educational Psychologist 31:175-190, 1996) interpretive framework that allow for coordinating social and individual…

Within mathematics education research, the responses to the Programme for International Student Assessment's (PISA's) international testing regime tend to accept its framework and results as necessary points of reference, even when offering a critical reinterpretation or challenging national policy discourses based on PISA. In this…

What is the place of social theory in mathematics education research, and what is it for? This special issue of "Educational Studies in Mathematics" offers insights on what could be the role of some sociological theories in a field that has historically privileged learning theories coming from psychology and mathematics as the main…

In this article, the authors provide an overview of mathematics education as a research domain, identifying and briefly discussing four shifts or historical moments. They illustrate how researchers working in various moments conceptualize not only the interactions among teachers, students, and mathematics differently but also teachers, students,…

Empirical work has shown how mathematics education exhibits certain tensions between its value as being practically useful to production and consumption on the one hand and in offering access to scarce resources on the other hand. These tensions can be ultimately traced to the contradictions in the way mathematical knowledge enhances the use value…

We discuss contemporary theories in mathematics education in order to do research on research. Our strategy consists of analysing discursively and ideologically recent key publications addressing the role of theory in mathematics education research. We examine how the field fabricates its object of research by deploying Foucault's notion of…

Inversion is a fundamental relational building block both within mathematics as the study of structures and within people's physical and social experience, linked to many other key elements such as equilibrium, invariance, reversal, compensation, symmetry, and balance. Within purely formal arithmetic, the inverse relationships between addition and…

The article discusses the understanding of infinity in children, teachers and primary teacher students. It focuses on a number of difficulties that people cope with when dealing with problems related to infinity such as its abstract nature, understanding of infinity as an ongoing process which never ends, understanding of infinity as a set of an…

In this paper, we argue that history might have a profound role to play for learning mathematics by providing a self-evident (if not indispensable) strategy for revealing meta-discursive rules in mathematics and turning them into explicit objects of reflection for students. Our argument is based on Sfard's theory of "Thinking as Communicating",…

In this volume, Wolff-Michael Roth provides a critical but partial reading of Tony Brown's book "Mathematics Education and Subjectivity". The reading contrasts Brown's approach with Roth's own conception of subjectivity as derived from the work of Vygotsky, in which Roth aims to "reunite" psychology and sociology. Brown's book, however, focuses on…

It is our presupposition that there is still a need for more research about how classroom practices can exploit the use and power of visualization in mathematics education. The aim of this article is to contribute in this direction, investigating how visual representations can structure geometry activity in the classroom and discussing teaching…

In the multilingual mathematics classroom, the assignment for teachers to scaffold students by means of instruction and guidance in order to facilitate language progress and learning for all is often emphasized. In Sweden, where mathematics education is characterized by a low level of teacher responsibility for students' performance, this…

In this study we analyze students' understanding of two-variable function; in particular we consider their understanding of domain, possible arbitrary nature of function assignment, uniqueness of function image, and range. We use APOS theory and semiotic representation theory as a theoretical framework to analyze data obtained from interviews with…

In this article, I deconstruct the concept of understanding in mathematics education, examining how it is spoken into being and what work it does for primary school student teachers. I use poststructural analysis to unpack interviews with a student teacher, Jane, drawn from a larger longitudinal study. I show how she negotiates tensions between…

Representation is viewed as central to mathematical problem solving. Yet, it is becoming obvious that students are having difficulty negotiating the various forms and functions of representations. This article examines the functions that representation has in students' mathematical problem solving and how that compares to its function in the…