Stephen Lerman

Cultural, Discursive Psychology: A Sociocultural Approach to Studying the Teaching and Learning of Mathematics

From a sociocultural perspective an object of research on mathematics teaching and learning can be seen as a particular moment in the zoom of a lens. Researchers focus on a specific part of a complex process whilst taking account of the other views that would be obtained by pulling back or zooming in. Researching teaching and learning mathematics must be seen in the same way. Thus in zooming out researchers address the practices and meanings within which students become school-mathematical actors, whilst zooming in enables a study of mediation and of individual trajectories within the classroom. In each choice of object of research the range of other settings have to be incorporated into the analysis. Such analyses aim to embrace the complexity of the teaching-learning process. This article will present a cultural, discursive psychology for mathematics education that takes language and discursive practices as central in that meanings precede us and we are constituted within language and the associated practices, in the multiple settings within which we grow up and participate.

A Review of Research Perspectives on Mathematics Teacher Education

Research on mathematics teachers and mathematics teacher education has grown substantially over the last 10 to 20 years with the recognition of the enormous influence of the teacher on children’s learning of mathematics. This chapter argues that theoretical frameworks for such studies are not always coherent, nor are they well examined in the literature, remaining largely implicit. The chapter attempts an overview of research and an investigation of the implicit assumptions about the process of teacher learning. I propose that social theories of teacher learning that draw on notions of developing identities are more relevant and fruitful for these domains of educational research.

Theories of mathematics education: Is plurality a problem?

In this developed contribution to the Research Forum, held at the recent meeting of the International Group for the Psychology of Mathematics Education, the theme being “Theories of Mathematics Education”, I focus on the call by the organisers: ‘the time seems ripe for our community to take stock of the multiple and widely diverging mathematical theories’. I examine empirically the diversity of theories and I draw on the sociological theories of Basil Bernstein to relate the developments to the nature of intellectual communities and their productions. In particular, I suggest that the multiplicity and divergence are not surprising nor are they necessarily damaging to the field. I end by discussing concerns about accountability in relation to research in education.

Analysing Concepts of Community of Practice

This chapter is based on the notion that Lave and Wenger (1991) and Wenger (1998) work with similar, although characteristically different concepts of ‘community of practice’ and our goal is to compare and contrast these. We point out the relative strengths and weaknesses of each, illustrating our arguments with research examples drawn from the literature. We conclude by indicating ways in which each perspective informs research in the mathematics education community and to directions in which they might be developed to support our understanding of teaching and learning across a range of contexts.

Mathematics and ICT: a framework for conceptualising secondary school mathematics teachers’ classroom practices

Using a case study research strategy of data collection, the empirical component of the study presented in this paper is aimed at exploring the interplay between content knowledge and pedagogy when information and communication technologies (ICT) are used by a number of secondary school mathematics teachers. An orienting framework advanced as a result of critically reviewing research on teachers’ professional knowledge base for teaching structured what was noticed, paid attention to and taken as important in teachers’ accounts of their practices with ICT. Cross‐case analysis of the data collected by means of interviews and lesson observations followed the writing of each teacher’s profile, enabling comparison of the seven teachers’ practices with ICT. The analysis of the data yielded a number of salient factors, of both contextual and personal nature, which were identified as key to the integration of ICT into mathematics teaching. The findings of this study add new dimensions to understanding teachers’ use of ICT by treating the teaching of mathematics and ICT use as interwoven aspects of a teacher’s practice. A framework which conceptualises teachers’ learning about ICT and teachers’ incorporation of ICT in their teaching of mathematics is advanced with the aim of contributing to a better understanding of the pedagogy of teaching mathematics with ICT.

Challenges for teacher education: the mismatch between beliefs and practice in remote Indigenous contexts

The poor performance of Australian Indigenous students in mathematics is a complex and enduring issue that needs a range of strategies to enable success in schooling for these students. Importantly, large numbers of teachers in remote Indigenous contexts are new graduates who, although full of enthusiasm, lack experience. Similarly, many of them are unfamiliar with the demands and nuances of teaching in remote and/or Indigenous contexts. This paper explores the nexus between the beliefs and practices of teachers working in a remote, Indigenous region of Australia. In particular, it proposes that the discrepancy between beliefs and practices found in the reconnaissance phase of a design study is due to the teachers realising that they need to implement changed practices to enable students to learn but having little knowledge of what such practices may look like. This finding has implications for pre-service and in-service teacher education.

Research on Socio-Cultural Perspectives of Mathematics Teaching and Learning

A feature of the changing trends in research in mathematics education during recent years has been the growing interest in and focus on the social context of the mathematics classroom (Bishop 1988; Keitel 1989; Lerman 1994; Nickson 1992; Nickson & Lerman 1992). The role played by the social context in the development of the individual or of groups has been theorized, implicitly or explicitly, in many ways. What demarcates current interests is a move away from the identification of social factors as the realm of the affective to a concern with the part that the social and cultural environment plays as a whole in the development of the child. This chapter commences with a discussion of the models offered by different theoretical frameworks in their interpretations of the role of the social context, in order to identify and distinguish what are increasingly being called socio-cultural theories (Cobb 1994a) from more individualistic approaches.

Getting the Description Right and Making It Count: Ethical Practice in Mathematics Education Research

Building on the work on ethics in educational research in recent publications, we present a framework for ethical practice in mathematics education research. In particular, we discuss what are the implications of claiming or denying a particular piece of research as acceptable within the community. We argue that researchers must be aware for whom they advocate, thus making it count. We present a map with which researchers should engage the ethics of their practice, and we suggest that they must consider whether they are getting the description right.

Learning Theory in Mathematics Education: Using the Wide Angle Lens and Not Just the Microscope.

The current desire of mathematics educators to devise variations of constructivist models of learning, combined with growing interest in the Soviet school of social constructionist theory, has perhaps clouded a bigger picture regarding the place and role of learning theory, especially as it relates to mathematics classroom practitioners. This paper attempts to step back from a detailed examination of theoretical orientations and adopts a more holistic perspective of contemporary learning theory as it impacts upon mathematics pedagogy, along with providing a framework for psychological and philosophical implications of a theoretical model.

Changing Focus in the Mathematics Classroom

The dominant paradigm within which research, testing, and theorising on the meaning of understanding are framed is a psychological one, which is generally interpreted as the study of the mind Inevitably, therefore, it focuses on the individual. Recent ideas in mathematics education, drawn from discourse analysis (e.g. Pimm, 1990, this volume; Walkerdine, 1988, 1989) and social practice theory (e.g. Evans and Harris, 1991; Dowling, 1991), indicate that a consideration of social interactions does more than merely shed light on the understanding of the individual. Their critique suggests that understanding cannot be approached except through a focus on the social. The chapters in this book all pick up on a socio-cultural focus for the mathematics classroom and elaborate it from their own particular interests. In this chapter I will offer an interpretation of this shift in focus towards the socio-cultural, and suggest some activities for the mathematics classroom that may be seen to be fruitful in this context.