Stephen Lerman

London South Bank University | LSBU · Department of Education

In the spirit of the conference, this article is not to argue for a socio-cultural perspective. I have been working in this area for close on a decade now and although I sometimes engage in discussions about theoretical perspectives (see Lerman, 1996; 2000) the intention of this paper is somewhat different. Instead I will first summarise some of wh...

Research exploring undergraduates’ tool preferences in tertiary mathematics is currently limited. In this paper, we explore the tools mathematics and engineering students use when studying mathematics and the ways undergraduates combine these tools. Results from our survey (N = 628) showed that students in our sample use mostly their notes, the uni...

Updated Encyclopedia entry on Mathematics Teacher Identity

Review of Tony Brown's Springer book, A Contemporary Theory of Mathematics Education Research

One of the hardest tasks for new researchers, actually all researchers throughout their careers, is what theory to use to inform their work, and how to work with theory. In this chapter I try to set out what theory is for, in research, and what are the challenges for theory choices. I indicate that we are in a period of proliferation of theories, o...

Different histories of the development in Uk and French of reesarch in education mathematics and in France of didactic

This paper arises from a study of how concepts related to understanding functions develop for students across the years of secondary/high school, using small samples from two different curricula systems: England and Israel. We used a survey consisting of function tasks developed in collaboration with teachers from both curriculum systems. We report...

This article traces the development of theoretical perspectives in the English and French mathematics education research cultures from the 1960 and 70s to the present. The main parts of the article are the separate accounts of development in the two domains. The two areas are presented separately since they are very different both in terms of what...

From a Marxian/Vygotskian perspective, learning is social in origin and it happens in the presence of others that are more knowledgeable. Extending this view to the learning of mathematics, such learning also becomes inseparable from the presence of others (people and artefacts). Researchers over decades have studied different interactions to see h...

Currently, there is a dearth of studies exploring the kind of tools that undergraduates use when studying mathematics with previous approaches focusing mostly on digital or institutionally provided resources. In this article, we present and discuss the results from our investigations into the different types of tools that a cohort of second year en...

This paper presents results from a survey exploring the kind of resources that engineering undergraduates (N=201) use when studying for their mathematics modules. By using Factor analysis, we were able to produce a typology of these resources. The resulted typology was further analysed by combining Leontiev's version of Activity Theory and Wartofsk...

This book marks some of the huge contributions Jill has made and continues to make in mathematics education research and development in South Africa and internationally, and her service to the mathematics education research community in South Africa and internationally. The chapters are written by people who have known Jill and her work, and many h...

In this paper we present and discuss the results of a survey from our investigations into the kind of resources that engineering undergraduates use, their conceptions of mathematics and their goals when studying mathematics. By adopting an Activity Theory perspective, we performed correlational analysis between the components of the basic mediation...

The influences on governments for policy changes in schools range across many agencies, including the political party in power. When policies change, the sources of these influences are not always clear. The project whose work is presented in this special issue examines what these changes look like in terms of the differences in assessment tasks of...

This volume is dedicated to the career of Jill Adler and the role she has played in growing mathematics education research in South Africa, Africa and beyond. Her work epitomises what is referred to as the ‘engaged scholar’: i.e. doing rigorous and theoretically rich research at the cutting edge of international work in the field which at the same...

Background: Curriculum changes are a regular feature of nurse education, yet little is known about how such changes are managed. Research in this arena is yet to emerge. Objective: Evaluation of how a curriculum change in nurse education was managed through the application of a business change management model. Method: A qualitative case study...

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice teache...

Definition: Mathematics teacher identity (MTI) is commonly ‘defined’ or conceptualized in recent publications of the mathematics education research community as ways of being, becoming and belonging; as developing trajectories, and in narrative and discursive terms.

Whilst research on the teaching of mathematics and the preparation of teachers of mathematics has been of major concern in our field for some decades, one can see a proliferation of such studies and of theories in relation to that work in recent years. This article is a reaction to the other papers in this special issue but I attempt, at the same t...

Of late there has been growing interest in the potential of technology to support children with Autistic Spectrum Disorders (ASD) with social and life skills. There has also been a burgeoning interest in the potential use of mobile technology in the classroom and in the use of such technology to support children with ASD. Building on these developm...

Of late there has been growing interest in the potential of technology to support children with Autistic Spectrum Disorders (ASD) with social and life skills. There has also been a burgeoning interest in the potential use of mobile technology in the classroom and in the use of such technology to support children with ASD. Building on these developm...

Changes in school mathematics curricula, pedagogy and assessment, and as a consequence the pressure for changes in initial teacher preparation, are consequences both of government policy initiatives and pressure from unofficial agents such as the research community, teachers and others, though with great variation across the world. In the case of E...

Although the history of internationalization in mathematics education goes back more than a century, the last few decades have witnessed a notable acceleration in the establishment of bodies aiming at grouping together members of the community. The purpose of this chapter is to survey international or multinational organizations created to support...

Dealing with representations and changing between them plays a key role for both mathematics as a discipline and for building up mathematical knowledge in the classroom. Hence, professional knowledge and views of teachers related to using multiple representations can be considered as a prerequisite for creating conceptually rich learning opportunit...

This paper is drawn from a doctoral thesis (Rosa, 2008) that examines the relations established between the construction of online identities and the teaching and learning of the definite integral concept in an online learning course. The role-playing game (RPG) is played out through chat and calls for the creation of characters (online identities)...

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 th...

This article presents the results of an investigation carried out across 20+ country-regions under the auspices of ICMI Study 15 into the structures, approaches and general characteristics of the mathematics preparation and development of teachers. We use a global framework provided by the larger research literature on teacher education to contextu...

There has been developing interest in the potential for the use of mobile technology to achieve educational objectives, in particular for children with Autistic Spectrum Disorders (ASD). The HANDS project has developed a software application for mobile phones, which helps children with ASD to develop social and self management skills. The applicati...

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 ar...

Teachers’ learning about teaching mathematics from their practice is problematic to identify and analyze. Among many other things, teachers need to enact their knowledge of how students’ ideas might develop, what tasks might support that development and how to elicit the expression of students’ ideas. This enactment in practice potentially provides...

From a system as well as from an institutional perspective, the education of teachers is dependent on the occurrence of a number of interconnected events which are in turn closely related with the life cycle of teachers’ careers: entry to teacher education signals the beginning of teachers’ careers, and it comes accompanied by recruitment and selec...

Learning to teach mathematics is a complex undertaking, and in the last twenty years there has been a great deal of research looking at aspects of the process. There are many ways one might structure an analysis of research on learning to teach mathematics. It is clear, though, from all the research on learners in all kinds of situations that what...

The preparation of teachers of mathematics takes various forms across the world, but there is no doubting its importance in every country. There were many papers addressing aspects of initial teacher education in use across the world presented at the 15th ICMI Study. In this section we have provided an overview of research perspectives to represent...

In this chapter we examine the research on and by mathematics teachers working together on their practice. We examine both groups of teachers within a school, that we are calling face-to-face communities, as well as wider networks across schools, in regions or even national initiatives. We give examples of research and we raise a range of issues th...

Notions and concepts of theory play key roles in mathematics education research, as they do in any scholarly or scientific discipline. On closer inspection, the notion, concept, and nature of what is termed " theory " in such research are very varied indeed, as are the roles, uses and implications of theories employed in mathematics education resea...

In this chapter, we draw on Derrida's concept of writing in order to bring a closer reading of his work to mathematics education. We engage with the theme of the “math wars” by looking at the transcriptions of a panel debate held in Brazil between two mathematicians and two mathematics educators. We explore the conflict of mathematics versus mathem...

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 lit...

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 m...

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 res...

In this chapter I aim to give an account of the communication taking place in a particular classroom between the particular children chosen by the research team for the video camera’s focus, and also to account for that account. In that this chapter seeks to treat both ‘levels’ of accounts as social research, and in its attempt to be reflexive, it...

Various models of Mathematical Problem Solving (MPS) have been suggested since 1957; however most of them did not take place within a structure of a theory. In this paper we focus on the theory of Self-Regulated Learning (SRL) in order to develop a satisfactorily comprehensive model of MPS, especially adjusted to the principles of the aforementione...

This paper explores the use of ICTs in the middle years of schooling where the tools have been used to support mathematics learning towards more equitable outcomes. Drawing on the productive pedagogies framework to analyze over 40 classrooms lessons, it was found that there were some aspects of pedagogy that were more evident than others. The resul...

It is taken for granted today that research on teaching and learning mathematics must take into account the social, historical, and cultural milieu of schooling and pupils and of mathematics. There are quite different interpretations, however, of how ‘social’ and ‘individual’ interact, what role the social environment plays in the development of th...

This report is divided into two parts, the mechanics of the organization and presentation of the study group, and the content of the presented papers.

This is a record of the proceedings of International Round Table at ICME 9. Issues like technology, preparation of teachers, and others were discussed, and views given. The speakers identified some current issues of great concern. Furthermore, they offered their views on future trends.

In consideration of the very limited time for oral contributions, and of the strong demand of many participants to present their results at WGAs & TSGs, presentation by distribution(PbyD) at WGAs & TSGs which was accepted and carried out by many COs except WGA8, TSG4, TSG 11, TSG 17 and TSG 18.

Among organizations devoted to mathematics education, The International Commission on Mathematical Instruction (ICMI) is distinctive because of its close ties to the mathematics community. The great challenges now facing mathematics education around the world demand a deeper and more sensitive involvement of disciplinary mathematicians than we now...

Mathematics as a discipline has a long history, emerging from many cultures, with a truly universal character. Mathematicians throughout the world have a fundamentally common understanding of the nature of mathematics and of its central problems and methods. Research mathematicians in any part of the world are part of a cohesive intellectual commun...

The six chapters in this section focus on studying teachers’ beliefs with a particular concern for how those beliefs might change in order to improve the teaching of mathematics in our schools. Five of the chapters draw on empirical studies whilst the sixth gives an overview of recent research to investigate how researchers interpret teachers’ beli...

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 t...

Recent curriculum reforms have led to a wider variety of methods of assessment in formal 'high stakes' assessment regimes in many countries. Morgan's study of mathematics coursework assessment in UK schools identified a number of positions adopted by teachers as they assessed student texts. Using Bernstein's theoretical framework, we revisit Morgan...

In this paper we present ananalysis of the articles in EducationalStudies in Mathematics since 1990. It ispart of a larger project looking at theproduction and use of theories of teachingand learning mathematics. We outline thetheoretical framework of our tool ofanalysis and discuss briefly some of themethodological difficulties we face. Wethen pre...

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 liter...

In their response to my (1996) article, Steffe and Thompson argued that I have taken an early position of Vygotsky's and that his later work is subsumed in and developed by von Glasersfeld. I argue that the two theories, Vygotsky's and radical constructivism, are, on the contrary, quite distinct and that this distinction, when seen as a dichotomy,...

The Culture of the Mathematics Classroom is becoming an increasingly salient topic of discussion in mathematics education. Studying and changing what happens in the classroom allows researchers and educators to recognize the social character of mathematical pedagogy and the relationship between the classroom and culture at large. The volume is divi...

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...

Radical constructivism is currently a major, if not the dominant, theoretical orientation in the mathematics education community, in relation to children's learning. There are, however, aspects of children's learning that are challenges to this perspective, and what appears to be "at least temporary states of intersubjectivity" (Cobb, Wood, & Yacke...

Radical constructivism is currently a major, if not the dominant, theoretical orientation in the mathematics education community, in relation to children's learning. There are, however, aspects of children's learning that are challenges to this perspective, and what appears to be “at least temporary states of intersubjectivity” (Cobb, Wood, & Yacke...

Research into gender issues in mathematics education and, in particular, into the effectiveness of related intervention programs is summarised in this chapter. Where possible, international and cultural dimensions are emphasised, and duplication of research summarised in recent reviews has been avoided. The review embraces both traditional approach...

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...

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; Walke...

Mathematics teaching and learning have been dominated by a concern for the intellectual readiness of the child, debates over rote learning versus understanding and, recently, mathematical processes and thinking. The gaze into today's mathematics classroom is firmly focused on the individual learner. Recently, however, studies of mathematics in soci...

This article reports on a doctoral dissertation that examined the current state in the philosophy of mathematics, with a view to identifying possible connections with, and influences upon, mathematics education. Recent work in the sociology of knowledge, proposing a strong case for a fallibilist epistemology, can be seen as one perspective, counter...

Learning theories such as behaviourism, Piagetian theories and cognitive psychology, have been dominant influences in education this century. This article discusses and supports the recent claim that Constructivism is an alternative paradigm, that has rich and significant consequences for mathematics education. In the United States there is a growi...

In this article, which is in criticism of a previous paper by Eric Blaire in this journal, I suggest that one's perspective of mathematics teaching is a logical consequence of one's epistemological commitment in relation to mathematical knowledge, and not merely one of expediency in response to societal pressures, or of pedagogical convenience. I s...

The field of mathematics education research has seen a proliferation of theoretical frameworks and perspective being adopted by researchers. There are concerns that this phenomenon might be detrimental to progress in developing findings that can improve practice and therefore the learning experience of students in schools. In this paper I sketch a...

There is not only a consensus that modelling is a big idea for mathematics as a scien-tific discipline, but also that this big idea should have an impact on the mathematics classroom. Consequently, teachers should be aware of this big idea and know how modelling relates to a variety of curricular contents. However, empirical research into views of...

Professional knowledge of mathematics teachers related to big ideas in mathematics and mathematics instruction can enhance teachers' competencies of designing rich learning opportunities in the mathematics classroom. Responding to a need of empirical research on professional knowledge connected with big ideas in mathematics, this study presents res...