How do we research the social dimension in mathematics education - as sociologists and as socialists?

Peter Gates

University of Nottingham, United Kingdom

Abstract

Much of the history of research in mathematics education has been located in – or at least derived from – individualistic and individualising paradigms such as psychology. Given the growing awareness of the importance of the social dimension we need to look more closely at the implications this has, not only for our research questions, but also for the very constructs we adopt. In this paper I adopt a sociological – and, I consider, a socialist – perspective on where we might look for constructs in order to undertake research that had wider implications for our discipline.

Introduction

I begin this paper with a statement of my own position as a socialist involved in research in mathematics education.

Any description of classroom activity that cannot be related to the social structure and culture of the society is a conservative description.

(Walker 1970, p 143)

This for me has to be a starting point for those of us intent on researching ‘the social’ in mathematics education. However, it requires us to develop our conceptual apparatus

To explain any educational process we must have a conceptual apparatus that relates the economic and social structure of society to the teaching process.

(Lundgren 1979, p 42)

This paper is intended to offer a contribution to this.

In the introduction to their book – New Directions for Equity in Mathematics Education – Walter Secada, Elizabeth Fennema and Lisa Adajian call for:

the kinds of enquiry that will enable us to understand how opportunity is unequally distributed in this society, the role that mathematics and education plays in that stratification, and how we might reclaim the aegis of educational reform to include the creation of a fairer social order as a legitimate goal.

(Secada, Fennema and Adajian 1995, p 4 - 5).

That is quite an ambitious undertaking, but connects us to exploring what Henry Giroux calls “the imprints and texture of domination and resistance” (Giroux 1983, p 63). My hope is that such an understanding might help us to conceptualise how the influences that lead to an unequal distribution of power and success in society that we see all around us, work themselves into and work themselves out in the context of mathematics teaching. Furthermore, it might help us to develop a manifesto for where social change might be possible to contribute to a reclamation of educational reform for a fairer social order.

The social role of mathematics

It can hardly be contested that we live in an uneven and unjust society where access to education and to justice depend on the capital one can appropriate and accumulate. There is ample evidence in the literature to support this contention such that it is hardly now contentious (See as a selection for example Aggleton 1988; Anyon 1983, 1981b, a, 1980; Bernstein 1975b, a; Craft 1970; Dubberley 1988; Jackson and Marsdon 1962; Robinson 1976; Tyler 1977; Willis 1977). But unfairness, injustice and prejudice are not abstract concepts of macro-social analysis of an internecine class struggle. They are felt through the disappointment, hopelessness and frustrations of ordinary people as they get though their everyday lives. They exist in the knots in the pit of the stomach and the tears in the eyes. Injustice is a process that goes on all around us, even when - and arguably especially when - we do not look for it or recognise it.

It is my contention that mathematics plays a significant role in organising the segregation of our society, as Sue Willis cogently argues:

Mathematics is not used as a selection device simply because it is useful, but rather the reverse.

(Willis 1989, p 35)

In other words, mathematics education plays its part in keeping the powerless in their place and the strong in positions of power. It doesn’t only do this through the cultural capital a qualification in mathematics endows on an individual. It does this through the authoritarian and divisive character of mathematics teaching – it is often supposed that one can do maths or one can’t, but an accusation or admission that you can’t is more than just plain fact of capability; it is a positioning strategy – something that locates one in particular relations with others. It locates you as unsuccessful, and lacking in intellectual capability; it locates you on the edge of the employment and labour market, as virtually unemployable. Mathematics education thus serves as a “badge of eligibility for the privileges of society” (Atweh, Bleicher and Cooper 1998, p 63).

In order to look to useful research strategies, we need to have a conceptual apparatus that allows us access to the social structure of society and its influence on the process of teaching and learning mathematics. It seems to me that there are three cognate areas – theories of social structure and organisation, theories of the conceptualisation of human agency and theories of the social foundations of mathematics education. In this paper I will touch on the first, look more deeply into the second, and leave the third until another time.

Theories of social structure

The importance of this triad lays in the role mathematics plays in society. It is, in short, the foundation of the technological age. “Mathematics and mathematics education are carrying the scientific and technological superstructures of our time” (Skovsmose in preparation, p 1). Less triumphalist, Pierre Bourdieu compares the teaching of mathematics to the teaching of the classics and dead languages claiming it to be “no less derealising and gratuitous” (Bourdieu 1989, p 110 – 111). Mathematics education thus stratifies, demarcates, legitimises and enculturates. Yet, we know relatively little about the mechanics of these social processes, including the way in which social reproduction is achieved through acceptance or subservience. Consequently, I want to argue less that mathematics education can benefit from drawing on sociology, by arguing instead that sociology can benefit from studying mathematics education as an example of a mechanism for distributing power.

My own experience within mathematics education has led me to want to look for foundations, predilections and structuring frameworks that would support a social model for understanding the discipline. I am adopting a materialist approach to social theory and social action. For me the quintessential statement on a materialist conception of history was written by Karl Marx:

Men make their own history, but they do not make it just as they please; they do not make it under circumstances chosen by themselves, but under circumstances directly encountered, given and transmitted from the past.

(Marx 1852)

Here is the argument for a reorientation in the psychology of mathematics education - to see the frameworks and theories we use as politically located, and legitimising particular social norms. Arguments that place psychology outside or above social structure are no longer tenable since:

Structure is not '‘external'’ to individuals: as memory trace, and as instantiated in social practices, it is in a certain sense more '‘internal'’ than exterior to their activities in a Durkheimian sense. Structure is not to be equated with constraints but is always both enabling and constraining.

(Giddens 1984, p 25)

This is a helpful development, and for me brings together a Marxist - historical materialist - perspective of consciousness with Pierre Bourdieu’s notion of habitus. In order to see the role that mathematics education plays in the process of social reproduction, we need to adopt a perspective that explores the social structure of society and the roles played by teachers, learners and theories of learning. In addition, it requires us to recognise the existence and nature of oppression, and how it comes about both through social stratification and human practices. Hence, what is important is to look at:

how it comes about that structures are constituted through action and reciprocally, how action is constituted structurally.

(Giddens 1976 2nd Edition 1993, p 11)

This has a number of implications, one of which is to assert “the primacy of the real over thought about the real” (Althusser and Balibar 1970, p 87). This in turn influences how we see the effect and the influences of objective structured social relations upon the various components of those social relations. The approach one takes to research design needs to be informed by the approach one takes to the nature of social organisation and there are certain assumptions I make at the outset, which influence, shape and structure what I do:

· I hold a view of society as a conflict between differing interests – usually interests based upon economic distinctions and rooted in the underlying relations of production;

· I hold a view which sees the economic structure, the mode of production, as a fundamental determinant of social life;

· I hold a view that we need to consider the interconnectedness of the whole social system rather than explore in isolation locations of social activity e.g. the maths classroom - what Louis Althusser calls “structural causality” (Althusser and Balibar 1970, pps 187 – 198);

· I believe that life is essentially social. That cognition is essentially a social act and therefore that material conditions exert a significant effect on us all. This is an approach that looks for connections between objective structures and human action;

· I am committed to social change;

· I believe that educational research should be critical and emancipatory, achieved through analysing power relations.

The central question for me is what governs the practices that are at work in mathematics teaching and learning which can be located empirically and theoretically into a social reproduction process.

As a socialist, it behoves me to take sides. Yet as a researcher, too, I have to take sides, since as Howard Becker tells us neutrality is imaginary.

For it to exist, one would have to assume, as some apparently do, that it is indeed possible to do research that is uncontaminated by personal and political sympathies. I propose to argue that it is not possible and, therefore that the question is not whether we should take sides, since we inevitably will, but rather whose side are we on?

(Becker 1967, p 239)

I hope to be on the side of the weak and dispossessed, a considerable responsibility that calls on a radical approach to understanding the classroom, and a commitment to be penetrating while unpatronising.

A social research paradigm

A research paradigm has three elements of foci: ontology, epistemology and methodology (Denzin and Lincoln 1998, p 185 - 186) that are each defined by basic beliefs (Guba and Lincoln 1998, pps 200 – 201). In order to undertake research into the social dimension of mathematics, there are some implications for our theories of knowledge and consequent methodologies.

· Ontology is about the nature of reality and what can we know about it. Here we need to adopt a historical realist position by which reality is seen as being shaped over time by social, political, cultural and other factors, which crystalise or become reified into social structures.

· Epistemology is about how we come to know the world, the relationship between the knower and the known. Such knowledge needs to be transactional and subjectivist. The knowledge we hold or build of the world is based upon our interactions and our relationships to other individuals and to the dominant forces in society. This means that we need to be closely and interactively linked to the people we research. To some extent this position challenges the distinction between ontology and epistemology, in that what can be known derives from the interaction between the researcher and the researched.

· Methodology is about how we gain knowledge of the world. This needs to be dialogic and dialectical. Because I knowledge is created transactionally, methodology needs to be based upon setting up a dialogue with teachers and learners, to explore and exchange meanings, assumptions and positions. It is dialectical because this dialogue needs to uncover and potentially transform culturally and socially situated norms.

This profile locates such research in a Critical Theory Paradigm (Guba and Lincoln 1998, pps 205 – 205).

In adopting a critical theory paradigm, we are taking the position that human activity is fundamentally social in character. I want to take this a step further and argue that social structures are dynamic and relational, yet exhibit a level of stability that results in dispositions gelling into objective structures. In developing such a theoretical framework, I need to be able to conceptualise this dialectical relationship between the individual and the social. For me, Pierre Bourdieu offers a way through this in his appreciation of the interplay between objective social structure and subjective personal dispositions which forms the central methodological and conceptual organisation of his work and informs his empirical studies (Bourdieu 1972, 1990b). It is his assertion that objective structures are actualised and reproduced through subjective dispositions (Bourdieu 1972, p 3). This does not mean to me that subjective dispositions have a primacy over more objective social structures. Pierre Bourdieu’s position is that the development of individual dispositions is influenced and constrained by objective structures, the nature of hierarchy, the form of hegemonic positions and so on, which in their turn reinforce the objective structures. What distinguishes Pierre Bourdieu’s approach from that of, say, Ervin Goffman or Anthony Giddens is the way in which social structural properties and social and economic conditions are always embedded in everyday lives and events of individuals (Harker, Mahar and Wilkes 1990, p 8). Of course implicit in here is a readiness to accept the objective existence of social structure(s). I find myself in accordance with Pierre Bourdieu here when he claims that