Heinz Duthel: Theses on Karl Marx, Pierre Bourdieu and Michel Foucault E-Book

Heinz Duthel

• Herausgeber: neobooks
• Kategorie: Poesie und Drama
• Sprache: Deutsch
• Veröffentlichungsjahr: 2018

Seitenzahl: 652

Beschreibung

But to go to School on a summer mourn O, it drives all joys away. Under a cruel eye outworn The little ones spend the day In sighing and dismay. William Blake Karl's Voice Die Philosophen haben die Welt nur verschieden interpretiert, es kommt drauf an sie zu verändern. (The Philosophers have only interpreted the world in various ways; the point, however, is to change it.) (Karl Marx, 1845, Theses on Feuerbach) The real political task in a society such as ours is to criticize the working of institutions which appear to be both neutral and independent; violence which had always exercised itself obscurely through them will be unmasked, so that we can fight fear. [Foucault, 1969: Tr 1972 #16, p 171] Ser ideólogo camarada, Fazer-nos acredita en nós Quando ainda cremos em deus. Ensinar-nos o amanhã Quando os pés ainda se arrastam em ontem. Sergio Viera, 1970 (Poesia de Combate, Vol 2, Frelimo, Maputo) Neither the life of an individual, nor the history of a society can be understood without understanding both. [Mills, 1970 #562, p 3]

Leseprobe

Heinz Duthel: Theses on Karl Marx, Pierre Bourdieu and Michel Foucault

“Be an ideologue comrade, make us believe in ourselves, when we still believe in God. Teach us about tomorrow, when our feet are still stuck in yesterday.”

The real political task in a society such as ours is to criticise the working of institutions which appear to be both neutral and independent; violence which had always exercised itself obscurely through them will be unmasked, so that we can fight fear.

Heinz Duthel

‘Nothing exist that can proof that we exist’

© Heinz Duthel 2010 – second edition 2018

Heinz Duthel: Theses on Marx, Pierre Bourdieu and Michel Foucault

This book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, resold, hired out or otherwise circulated without the publisher’s prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser.

For my children

Karl’s Voice

Die Philosophen haben die Welt nur verschieden interpretiert, es kommt drauf an sie zu verändern.

(The Philosophers have only interpreted the world in various ways; the point, however, is to change it.)

(Karl Marx, 1845, Theses on Feuerbach)

The Poets’ Voice

But to go to School on a summer mourn

O, it drives all joys away.

Under a cruel eye outworn

The little ones spend the day

In sighing and dismay.

William Blake

Good sense which once ruled far and wide,

Now in our schools to rest is laid.

Science, its once beloved child,

Killed it to see how it was made.

Guiseppe Giuste (1808 – 1850) Epigrammi – 1849

(Gramsci’s translation)

We don’t need no education

We don’t need no thought control

No dark sarcasm in the classroom

Hey, Teacher, leave those kids alone

All in all we’re just another brick in the wall

The Wall, Pink Floyd, 1979

Abstract

. What I have tried to map out here is the basis of the theory of knowledge and social action on which I shall be basing my research; that fundamentally, human activity is social in character, that social structures are dynamic and relational, but exhibit a level of stability which results in dispositions gelling into objective structures. I develop a theoretical base and iteratively explore this in a setting, evolving a description of how we might understand (or model) the orientation of mathematics teachers. In other words, I am offering a detailed study of a context from which I present a description of an approach to conceptualising two teachers’ orientation. Although the particularities of the ‘cases’ are specific, the methodology is sufficiently transparent, and the theoretical development sufficiently well established to offer others an insight into diverse contexts.

The fundamental problem in which I am interested in this Study is how capitalist society is reproduced. Drawing significantly from critical social theory, the work of Karl Marx, Pierre Bourdieu and Michel Foucault, I approach this problem by looking specifically at the contribution made by mathematics teaching to the maintenance of structured relations of domination. I construct theoretical, conceptual and methodological frameworks to enable me to study some of the underlying relationships between mathematics teacher predispositions and social structure. I discuss the weaknesses in Michel Foucault’s description of how discourses are sustained, and attempt to resolve these theoretical difficulties by drawing on Pierre Bourdieu’s dialectical approach to the habitus. I begin by socially and politically locating myself before moving on to looking at how we can understand the way modern capitalist society operates. I move onto examining theories for understanding the interplay between human agency and social structure. Thereafter, I look at the social roots of mathematics education identifying those areas where our current ideas about teaching and learning are inadequately conceptualised. Methodologically, I draw heavily on in-depth sequential interviewing, and classroom observation. I construct a model for what I term the discursive positioning of two contrasting teachers of mathematics, and explore how these differences might relate to wider social structures. This discursive positioning relates the externalising discourses (through which mathematics teaching and learning encounter the wider social context), and the deep-rooted evaluative dispositions of teachers, which operate through mediating relations which balance the interplay between human agency and social structure. In addition, I illustrate how teachers’ beliefs and conceptions about their role, rest upon ideological foundations located in their inclination toward particular social relations.

Acknowledgements

For my son Teddy

Preface

The real political task in a society such as ours is to criticise the working of institutions which appear to be both neutral and independent; violence which had always exercised itself obscurely through them will be unmasked, so that we can fight fear.

[Foucault, 1969: Tr 1972 #16, p 171]

Ser ideólogo camarada,

Fazer-nos acredita en nós

Quando ainda cremos em deus.

Ensinar-nos o amanhã

Quando os pés ainda se arrastam em ontem.

Sergio Viera, 1970

(Poesia de Combate, Vol 2, Frelimo, Maputo)

In the everyday scheme of things, schools and the teaching of mathematics can seem to be both ‘neutral’ and ‘independent’ to quote Michel Foucault. Yet, there are too many stories of school and social failure for this to be particularly convincing. Seen in a different light schools are sites of contestation, resistance and violence - albeit mainly symbolic rather than physical. For many pupils, school days are happy days, a launch pad into successful careers and relative prosperity. For others, it is a daily experience of continued failure. It is this disparity which captures my imagination in this Study. If according to the poet Sergio Viera, it incumbent on us to liberate children from the limitations of today, to help them believe in themselves and to show them tomorrow, then we fail many children; children at the margins, children from ethnic minorities, children whose cultural backgrounds and outlook might be different from the norms of the majority of teachers.

This Study is one part of a project to try to change the way some people are constrained, oppressed and restricted in their development and aspirations. It is about clarifying the mechanisms by which systems of power are maintained and sustained at the level of human agency in the mathematics classroom. Surely, this is a worthy aim, and one that we might expect all reasonable people to subscribe to and work toward?

If Marx’s project be regarded as the furthering, through the conjunction of social analysis and political analysis, of forms of human society in which the mass of human beings can attain freedoms and modes of self-realization in excess of any they may have enjoyed before, who can dissent from it.

[Giddens, 1981 #233, p 24]

Well no doubt there are many - especially those who stand to lose by such change. In addition, it seems to be at least interesting if not socially incumbent on us to ask, if no one could dissent from freedom and self-realisation, how did it all come to be this way? In this Study, I attempt a clarification of this issue. How comes it to be this way? I hope in this Study what I say will be taken as conjectural, and propositional, an invitation to engage rather than ‘dogmatic assertions’. I am not a neutral observer, trying to construct some external or objective reality. As is inevitable in such a work as this, there is much of me in here. Whilst I am writing as an academic researcher, I am also writing (among other things) as a partner, as a socialist and as a father. As a partner, I am aware that one needs to understand others, and to give in order to feel fulfilled oneself. As a socialist, I have certain values, duties and responsibilities to others. As a father to two tiny females, I face the future with aspirations for their welfare as well as some trepidation. The work in this Study brings together these three fundamental drives.

Referencing and citations

I have used Endnote Plus 2.3® to manage references and form the bibliography in this Study. I have chosen to give original publication dates in citations, whilst publication dates for actual sources used are given in references. For example:

Durkheim, Émile (1938: 1977) L'evolution pedagogique en France, (also published in 1977 as The Evolution of Educational Thought. Lectures on the Formation and Development of Secondary Education in France, translated by Peter Collins, London, Routledge and Kegan Paul.

In most cases involving major translations – most notably the works of Pierre Bourdieu and Michel Foucault – I used the official English translations. In citations, I have used the original publication date, followed by the date of the English translation actually used. In this case, page numbers refer to the English translation. For example, [Bourdieu, 1979: 1984 #45, p 387] refers to page 387 of the English translation of:

Bourdieu, Pierre (1979: 1984) La Distinction. Critique sociale du jugement, (also published in 1984 as Distinction. A Social Critique of the Judgement of Taste, Translated by Richard Nice, published by Routledge and Kegan Paul, London)

In the case of the works of Karl Marx and Valdimir Lenin, I have where possible used the Collected Works published by Lawrence and Wishart, giving again in citations the dates of publication of the original manuscript rather than the (somewhat historically arbitrary) date of publication of the volume. For example:

Marx, Karl (1844) ‘Economic and Political Manuscripts of 1844’, Collected Works Volume 3, pps 229 – 346, published in 1977, London, Lawrence and Wishart.

I do this not to suggest that I have actually read the original in whatever language the author wrote, but rather to be truer to a sense of history. It may seem a little perverse to some, but surely not as perverse as citing (Foucault 1990), (Durkheim 1977) or (Marx 1975). If only I could! There will of course be deviations from this specifically in the works of Lev Vygotsky, where original dates seem hard to come by.

The issue of citations is not a trivial matter in a work such as this. I cite other authors to show some affinity or disagreement with their work, and in addition to locate myself into the community of scholars by identifying whose work I have sought to develop. In carrying out work of this type, one inevitably comes across work cited by other authors. Where the work seemed important in substance, I have gone back to the original source and cited the original author. For example in Graham Hitchcock and David Hughes’ book Research and the Teacher. A Qualitative Introduction to School-based Research, [Hitchcock, 1989 #598] I came across reference to Claus Moser and Graham Kalton’s book, Survey Methods in Social Investigation [Moser, 1983 #590] in which they referred to three aspects necessary for successful interviewing. However, on referring to Moser and Kalton, I found that they in turn had drawn on Charles Cannell and Robert Kahn’s chapter, ‘Interviewing’, in Gardner Lindzey and Elliot Aronson’s edited book Handbook of Social Psychology. Volume 2 – Research Methods, [Cannell, 1954, 1968 #603]. In this case, I went back to Cannell and Kahn’s book, which seemed to be the substantive work, and which had only been drawn on rather than developed in the subsequent texts.

On the other hand, a chapter by Stephen Lerman, ‘Culturally Situated Knowledge and the Problem of Transfer in the Learning of Mathematics’, in Leone Burton’s Learning Mathematics: From Hierarchies to Networks, referred to a book by Leslie Smith, Necessary Knowledge. Piagetian Perspectives on Constructivism in which a claim was made that Piaget had recognised the importance of the social dimension in learning. In referring to Smith, I found he referred in turn to citations from Jean Piaget. In this case I did not read the original Piaget – and made this clear in the text. My main reason was that in this particular case it did not seem important whether or not Piaget has actually said something or not, what was significant was how I interpreted the claim being made – that the social dimension was restricted to social interaction.

Throughout this Study, I refer to other authors by the use of both first name and surname. I do this deliberately out of respect, and a desire to feel that I am working within a community. I recognise that it runs counter to academic tradition, and apologise to those readers who may find it tedious.

The context of this Study

I am submitting this Study under the regulations appertaining to FLAEPA Academy Barcelona and hence, this Study is part of the central core of my work as an a scholar. There are no word limits – as indeed there would not be had I decided to apply for Master in Philosophy by published works, a route open to all Students. I outline my rationale for the length of this Study in more detail in the text – particularly in Chapter 1 by referring to my inclusion of a justificatory framework embedded within this Study. I have striven for clarity in expression and identification in key themes and concepts. In addition I have ‘shown my workings out’ in several places in this Study by giving some account of my journey to make sense of the theory and the data.

Chapter 1 - Setting the Scene

Synopsis of Chapter 1

In this chapter, I set the scene for the rest of the Study. Opening with a quote from Antonio Gramsci, I give you an opportunity to read some indication of how I see myself. You will of course make your own mind up, but the least I can do is to try, as honestly as I can, to give you some biographical background. I hope you will let me hold your hand as I take you on the journey I am making and let me be your guide. First, I want to encourage you to trust me by trying to indicate what drives me to undertake the journey. Second, I give you some sense of why I feel the journey needs making at all. Lastly, I give you a map of the journey we are about to make. I had just written an early draft of this chapter when I watched a BBC TV programme called “Grammar School boys” where several ‘celebrities’ recounted their experiences on passing the 11+ and going to the Grammar School. I was quite astonished at the similarities between my own experiences and some of the stories that were told in that programme. Surprise, joy, disappointment, segregation were all emotions that figured highly.

I have chosen to focus here on my formative early years for two main reasons. First because a central feature of the (social) theoretical approach I take underlines the importance of the influence one’s parents and early socialisation has on subsequent development and trajectory. Second, it helps to give an alternative view to the official view of educators and teachers. It was in my easily years that the basis for my research questions began their process of sedimentation.

Because narrative and personal stories are easy to read, this might be the chapter you enjoy reading most - if only out of prurient inclinations. Do bear in mind, it holds the seed of the start of a journey, and for that reason is intellectually demanding.

1.1. Introduction to Me

The first important task in studying the intellectual contribution of a writer is the reconstruction of the author’s biography, not only as regards his practical activity, but also and above all as regards his intellectual activity

[Gramsci, 1971 #282, p 382 – 383]

1.2. Background to the Study

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

[Walker, 1970 #476, p 143]

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 #477, p 42]

Neither the life of an individual, nor the history of a society can be understood without understanding both.

[Mills, 1970 #562, p 3]

1.2.1 The mathematics education context

“Mathematics is often about nothing at all” was how one correspondent to the Cockcroft Report, Mathematics Counts, published in 1982, summarised what must be many children’s experience of the subject. Mathematics is about collecting like terms, removing brackets and all manner of things that seem quite divorced from our everyday lives, interests or needs. Yet, it is a naïve description because it merely takes some of the surface features and ignores the complexity and underlying structure. Paradoxically, it is exactly because someone can say this that makes the situation more worrying - showing how alternative descriptions can be lost and how complete the hegemonic control can be over the nature of educational experiences.

One response to the criticism that mathematics is ‘about nothing at all’, is to tinker with the curriculum, to trying to make mathematics ‘more relevant’ using ‘real life’ or ‘real world’ examples. Yet, as I will go on to argue, and as Paul Dowling has demonstrated [Dowling, 1998 #391], this does little to change the situation since many of the contexts are unreal and mythological.

The three epigraphs that open this section are intended to give a feel for my position in this Study. It is my desire to liberate and empower; to liberate by exploring the ordinary, the everyday common normal practices. By problematising these everyday practices, such interactions and relations as may appear normal, insignificant or even essential in mathematics classrooms are raised as problematic.

Recently there have been attempts to describe, understand and theorise the contribution (or constraints) made to learning through the social and cultural context in which teaching and learning takes place and there is a fast growing literature base. While this development does signify a move away from an embeddedness in psychology, it does not necessarily represent a significant change in orientation. Rather what appears to be underway is the development of a cultural psychology, concerned with changes within psychology to incorporate social influences and contexts [Lerman, 1998 #726, pps 333 – 334]. As Stephen Lerman points out “fully sociological approaches to mathematics education have not been prevalent” [Lerman, 1998 #726, p 333]. It is just such a sociological approach that I am attempting to develop and so my theoretical and conceptual underpinnings come from social theory rather than psychology. Consequently, I draw on such scholars as Michel Foucault, Pierre Bourdieu, Karl Marx and other social theorists, rather than Piaget, von Glasersfeld, Vygotsky etc. (although their contribution to our understanding of social processes is important, acknowledged and in places incorporated). My main task is a sociological one. Put simply, this Study is an attempt to better understand the ways in which the teaching and learning of mathematics contributes to uneven social and educational outcomes and opportunity.

My approach to this is to look into the ways in which teachers conceive of their work as teachers of mathematics, and more specifically how this is organised by and related to their social imagery. By ‘social imagery’, I refer here to conceptions about social relationships, the patterns of relationships between different groups they envisage, the relational values that teachers hold and which allow them to operate as agents in the social field of mathematics teaching. This might seem an ambitious task, so in this section I will try to justify my decision to undertake it.

1.2.2 The social context

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 #612; Anyon, 1983 #613; Anyon, 1981 #221; Anyon, 1981 #168; Anyon, 1980 #514; Bernstein, 1975 #201; Bernstein, 1975 #262; Craft, 1970 #631; Dubberley, 1988 #601; Jackson, 1962 #404; Robinson, 1976 #629; Tyler, 1977 #630; Willis, 1977 #22]. 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 has now been found that pupils from working class backgrounds do less well at school than those with middle class backgrounds [Croll, 1981 #575, 110]. Whilst this may partly be attributable to a paucity of material conditions in the home, it cannot totally be attributed to this because the trend is that even children from more affluent semi-skilled working class homes do less well than middle class children [Croll, 1981 #575, p 111]. At least in part then, the cause must lie elsewhere and may include attitudinal factors, differential resources available for educating children from different social backgrounds, and in addition teachers’ behaviours and the very nature of education favouring the thinking and disposition of some children rather than others. I will look further into this issue in later chapters, but it is a concern in this Study to look at the contribution to this inequity that might be played out in mathematics pedagogy. It is my contention that Mathematics plays a significant role in organising the segregation of our society.

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

[Willis, 1989 #768, p 35]

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. Either 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, 1998 #767, p 63].

For all of my working life – now 25 years – I have been in mathematics education and have worked in largely working class areas of East London, Beira in Mo*ambique and Milton Keynes. I have therefore seen and been part of the very battles between pupils and a curriculum in which they could see little relevance. I have experienced the tensions and contradictions in being cast in the role of the enforcer and having to find my way through that and round that.

1.2.3 The research context

It was a natural progression for me to use the opportunity of doing a Master in Philosophy. to try to explore some of the roots of social discrimination. There is considerable research evidence, publications and doctoral theses demonstrating that mathematics education is unfair, unjust and that certain sectors of society are inequitably treated. Here I want to develop this work, but to do something further. I want to stand on the shoulders of those that have gone before me and to study the mechanisms and present a framework for explaining how and why some of the precursors to this injustice occur. Hence, in this Study there is a considerable section where I undertake a development of a theoretical framework. I found I could not separate easily the theoretical framework from the literature review. What I have tried to accomplish is to present three cognate areas – theories of social structure and organisation (Chapter 2) theories of the conceptualisation of human agency (Chapter 3) and theories of the social foundations of mathematics education (Chapter 4).

The importance of this triad lies 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 #700, 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 #687, 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 teachers’ work. I thus wanted to explore and analyse individual teachers working in their natural setting, within a set of objective relationships. Pierre Bourdieu, the French social theorist, offered me an approach, which seemed fruitful through his notions of ‘field’ and ‘habitus’.

For Pierre Bourdieu, social action is localised and contextualised in both space and time. The driving force of human action and interaction are the conscious and unconscious dispositions that make us act and interact in the ways we do. This is what Pierre Bourdieu call the habitus – which I will explore in more detail in Chapter 3. However, human society does not consist of a loose coupling of individuals, but rather human social practice takes place in social fields, which Pierre Bourdieu defines as:

a network, or a configuration, of objective relations between positions objectively defined.

[Bourdieu, 1992 #342, pps 72 – 73]

Fields are therefore relational structures representing a collection of differing social positions often competing for power and are embedded with fields at different levels representing different levels of activity as “hierarchically intersecting sets” [Bourdieu, 1989 #41, p 44]. A classroom may be seen and analysed as a field, as also might be a subject department, school or the entire educational system. The particular field that a researcher might want to focus on will therefore be related to the level or focus of analysis.

The notion of a social field is an attempt by Pierre Bourdieu to free up social analysis from a rigid and over-deterministic class analysis in which social classes are seen to exist by and for themselves. Pierre Bourdieu's approach is to see social class indeed as social division, but as a dynamic set of relationships representing the state of play, in both time and space, of competing positions of power [Bourdieu, 1979: 1984 #45]. I find this a particularly useful conceptualisation for understanding the mathematics classroom because it offers a flexible approach to how we can conceptualise the way in which classroom practice emanates from teachers with differing social perspectives and intentions.

A further notion used by Pierre Bourdieu to explain the process whereby social classes are differentially favored by the education system is symbolic violence. The idea is that the education system takes norms, ideas, beliefs etc of the dominant groups, which are otherwise arbitrary, and enforces these through systems of power relations so that the cultural arbitrary is misrecognised not as arbitrary, but as legitimate thereby reproducing and legitimising relations of domination [Thompson, 1984 #331, p 57]. A central question here is how it is that symbolic violence becomes legitimised and operationalised through the characteristics and practices of individual teachers. Exploring this question requires us to operate at the deepest level of human agency.

In applying his epistemological framework to research, Pierre Bourdieu suggests a three level approach:

1.Analyse the objective position of the field with respect to the field of power

2.Map out the objective structure of relations of the positions held within the field

3.Analyse the habitus of individual agents

[Bourdieu, 1992 #679, pps 104 - 107]

Applying a Bourdieuian framework to my research, I needed to explore the political foundation of the discipline. In other words, I needed to explore the nature of mathematics education as a social field connecting this to notions of social power, and this forms Chapter 4. This draws on a wider theoretical understanding of the nature of society (Chapter 2) and on nature of culturally situated individuals (Chapter 3). Certain questions then needed to be considered. How can we understand everyday practices as a social phenomenon? How might we understand the common sense, taken-for-granted assumptions underpinning classroom practice? What alternative interpretations might be possible if we adopt alternative conceptual frameworks? My intention then is to construct some descriptive model for teachers’ differential engagement in the process of education.

1.2.4 The political context

It was important that I located this work within a political and theoretical framework. I justify my decision to include a considerable section on the theoretical background through its importance for me in detailing the direction of my analysis. Sections on the work of Bourdieu, Foucault, Marx etc. are necessary because they are central to the story I wish to tell and in addition are underutilised in philosophy education. Hence, readers from that domain may be unfamiliar with the frameworks and concepts I wish to use. The areas I draw on are controversial, where we regularly see multiple interpretations and positionings. It is therefore important that I try to show as clearly as possible the positions I take and the assumptions and interpretations I am making. The knowledge I wish to construct and develop here is theory laden and theory led. Usually the role of a literature review is to explore the area and identify gaps in the literature that can be explored. What I am trying to do, is to explore the main themes and directions in mathematics education research and then to look to apply some fresh perspectives from social theory in my attempt to map out certain features of the domain. What I have tried to map out here is the basis of the theory of knowledge and social action on which I shall be basing my research; that fundamentally, human activity is social in character, that social structures are dynamic and relational, but exhibit a level of stability which results in dispositions gelling into objective structures.

I am adopting a materialist approach to social theory and social action. This has a number of implications, one of which is to assert “the primacy of the real over thought about the real” [Althusser, 1970 #784, 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. There are certain assumptions I make at the outset, which influence, shape and structure what I do:

1)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

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

3)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, 1970 #784, pps 187 – 198];

4)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;

5)That I am committed to social change;

6)That educational research should be critical and emancipatory, 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. The word ‘Study’ possibly comes from Thesseus, the Greek hero who slayed the Minotaur and conquered the Amazons. Unlike Thesseus, I make no claim that this Study is heroic! But I can dream.

You can say I am a dreamer. But how can you be an educator without dreaming

(Ubiratan d’Ambrosio, Paolo Freire Memorial Lecture, MEAS1)

You may say I’m a dreamer but I’m not the only one. I hope some day you’ll join me, and the world will live as one.

(John Lennon, Imagine)

So this Study is part of my dream – I freely admit to being a dreamer. How can I be a socialist without being a dreamer? As a socialist, it behoves me to take sides. Yet as a researcher too, I have to take sides, since as Howard Becker tell 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 #622, 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. David Silverman offers three possibilities to Howard Becker’s question by offering three ethical positions [Silverman, 1985 #623]

a)Scholar – where one assumes no set of ethical values can be applied to research

b)State Counselor – where research is intended for policy makers

c)Partisan – where one adopts a political position committed to political practice.

[Silverman, 1985 #623, pps 179- 197]

Clearly, I locate myself in the final position, which does not suffer from an illusion that the world may be held at arm’s length. It is one in which I am not an agent of the state and where I want “to provide the theoretical and factual resources for political struggle” [Silverman, 1985 #623, p 184]. Karl Marx himself had used traditional research techniques to ask questions, the answering of which generated further critical questions in the minds of workers he surveyed showing methods can become “a didactic and political instrument” [Marx cited by \Silverman, 1985 #623, p 195] for social change. Taking sides then does not imply bias or distortion, but a commitment to ‘tell it how I see it’, identify our intentions and stand up for what we believe.

We take sides as our personal and political commitments dictate, use our theoretical and technical resources to avoid the distortions they might introduce into our work, limit our conclusions carefully, recognise the hierarchy of credibility for what it is and field as best we can the accusations and doubts that will surely be our fate.

[Becker, 1967 #622, p 247]

One reason for studying social practices is that of seeking emancipation - to help participants see the meaning and form of their own oppression and domination - and illuminate potential ways of overcoming them. Pierre Bourdieu’s approach is one that seeks to establish ways in which the social world is constructed, and how social structure is formulated and maintained. However, there is no point outside the system where a researcher can stand to be objective, neutral or disinterested. My reasons for pursuing this research is not disinterest, but of passionate interest and a desire for change. My work therefore will not attempt to be neutral, descriptive, illuminative. Rather I wish to offer a critical perspective. I therefore subscribe to the same point of view as that stated by Henry Giroux:

Are schools to uncritically serve and reproduce the existing society or challenge the social order to develop and advance its democratic imperatives. Obviously I opt for the second.

[Giroux, 1992 #178, p 18]

I too opt for the second, and in so doing try to reject a position of ‘uncriticallity’ and too little ‘challenge’.

1.2.5 The paradigmatic context

So, where do I locate this research? Well the detail will emerge in the unfolding of the Study, but I need to locate my basic, fundamental position, the paradigm in which I am working. Here I am taking ‘paradigm’ to refer to the basic set of beliefs and assumptions which guide my decisions, my actions and my interpretations. A paradigm has three elements of foci: ontology, epistemology and methodology [Denzin, 1998 #697, p 185 - 186] which are each defined by basic beliefs [Guba, 1998 #713, pps 200 – 201].

•Ontology is about the nature of reality and what can we know about it. Here I take a historical realist position by which I see reality being shaped over time by social, political, cultural and other factors, which crystalise or become reified into social structures. I discuss this in more detail in Chapter 2.

•Epistemology is about how we come to know the world, the relationship between the knower and the known. My position here is that this is 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 I am closely and interactively linked to the people I research. To some extent this position challenges the distinction between ontology and epistemology, in that what can be known derives from the interaction between me and the particular teachers and school I research. I discuss his more fully in Chapter 3 and it is influential in Chapters 4 and 5.

•Methodology is about how we gain knowledge of the world. My position here is both dialogic and dialectical. Because I see knowledge as created transactionally, my methodology needs to be based upon a setting up a dialogue with the teachers. 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. I discuss this in more detail in Chapters 5 and 6.

This profile locates my work in a Critical Theory paradigm [Guba, 1998 #713, pps 205 – 205].

The work in this Study has been nurtured for years, but it took off with a concerted period of theoretical searching. I needed to go deeper into social theory and sociology. This was followed by decisions about the data that I would need to collect, how and where I would collect it and how it was to be analysed. This pushed me into clarifying my stance on ontology, epistemology and methodology. My choice of setting is fully detailed in Chapter 6, but I decided I wanted to choose a school that was not on the margins. It is difficult to describe such a school – ‘typical’, ‘ordinary’, ‘average’ all seen oversimplified; in my case, typicality comes through a lack of extremes.

My interest had developed into the link between human agency and social structure and in order to explore this I wanted to get to know the teachers well, to become familiar with their work, professional desires as well as their diversity. My work as a teacher educator takes me into many schools, working alongside teachers in training. It made sense therefore to identify a school where I was familiar with the people and the set up. It was at this point something fortuitous happened. A colleague, who had been a Head of Mathematics, resigned to take up a promoted post. In addition the Headteacher, who had been in post for some 25 years, also resigned. Furthermore, the school was about to be subjected to a full inspection by the Government’s Office for Standards in Education (OfSTED). I decided to approach the school to undertake my data collection and field study there. Both the (old) Head of Mathematics and the (new) Head of Mathematics agreed.

One of the advantages of educational change is the possibility of consequent tensions that would bring to the surface some of the more unconscious elements of our practice. The new Head of Department was appointed early in the first stage of my literature study and I was informed by various people that he was considerably different in outlook from the incumbent. It seemed too good an opportunity to miss.

Given that I wanted to get to know much about how teachers organised their intellectual engagement with their work, it seemed important that the data I collected focused largely on teachers, their views and their practices. This firmly suggested that interviews and classroom observation would be the main research tools. Analysing the data took me back to the theoretical perspectives to try to characterise the ways in which local contributions are connected to social life. Hence the data collection and analysis, and the empirical and theoretical modeling, were carried out iteratively and inferentially. While Chapters 2, 3 and 4 lay the groundwork for the theoretical ideas I used in designing the study, the particular structural model was informed by the study being an inductive empirical struggle to construct a descriptive model underpinning two teachers’ professional discourse. The empirical construction of this model is described in Chapters 7, 8 and 9 and evaluated in Chapter 10.

I have already described the theoretical assumptions on which this Study is based. I wanted furthermore to develop a language to describe and analyse the complexity of the social world of the classroom and teachers’ predilections toward classroom practice, classroom organisation and the structure of tasks and curriculum choice. Pierre Bourdieu offered me a way through the subjectivity/objectivity issue in educational research as well as a tool for analysis in the habitus. Michel Foucault offered me a challenging perspective on the formation of discourse and a fresh perspective on power – but one with which I felt a little uncomfortable. By exploring this unease, I was able to identify certain distinctive features of the approach to discourse and power I needed. Antonio Gramsci helped me to understand the way in which I could apply Bourdieu and Foucault to a study of capitalism through hegemony and ‘common sense’. I attended a Symposium on Bourdieu and Educational Research at the BERA Conference in 1996, and joined both the Bourdieu and Foucault email discussion lists all of which helped me to grapple with theoretical and methodological issues.

I see this Study as located within the shift away from the purely psychological paradigm in which much mathematics education research is located, towards a social or cultural paradigm. This is not merely a change in focus, or a shift of academic fashion, but reflects both a change in the way we understand the working of the self, and in changes in the social fabric itself. As society incorporates faster and more all encompassing forms of communication – or ‘social saturation’ we do become more ‘social’ in our thinking. Thus the current resurgence in interests and activity in Vygotskian perspectives is no accident [Gulerce, 1995 #576, p 152].

1.2.6 The personal context

I have to admit that some of the driving force behind this work comes from my own anger and frustrations, and my own passions. I am not apologising for feeling about my research; I will go further and claim that passion is centrally important to my research. An ethnographer “must not suppress a sense of outrage whilst in the field” (Erikson, quoted in [Adelman, 1985 #507, p 45]. Rather this sense of outrage should be used to advantage as an illustration of how some aspects of a social practice or culture are unacceptable or undesirable and thereby illustrate social and cultural difference. In rejecting ‘objectivity’, Clem Adelman calls this approach “disciplined subjectivity” [Adelman, 1985 #507, p 45] and this is something with which I feel considerable empathy.

There is a question of for whom – and what - this Study is written. It well argued that teachers find much educational research irrelevant and consequently they play little part in it [Woods, 1986 #607, p 1]. The reasons include: the research questions not being defined by teachers; the language not being the language of teachers; the link between research and practice being weak. There is undoubtedly some truth here, but none of these would seem to me to be insurmountable by a research community committed to educational change.

There is an alternative rationale for why research and practice seem to be disconnected. Schools are conservative institutions. They are both slow to change, and unwilling to change. They are however part of a wider set of social institutions and have limited autonomy. The considerable research on pupil subcultures and labeling would seem to offer very real challenges to schools, yet ability grouping and pupil segregation not only still go on – but are being more positively encouraged. I was recently asked by a student teacher why it was that all the maths educators and educational research he had come across seemed to be from within at a liberal tradition – and this I think is a serous question. I like to think that research is fundamentally an enquiry about how to understand the world in order to improve matters. Hence, it is fundamentally emancipatory. This is not the message that schools want to hear since it challenges the dominant hegemony of the educational system – which is constructed not by educational researchers, but by politicians, media tycoons, and so on. Hence, research findings would seem to challenge sacred cows and the hegemonic control of education. I am not suggesting the process simple, for it is not, I merely want to suggest that one reason why research and practice are often in conflict is political. Yet, just wherein lies the political?

The ubiquitous quote from Karl Marx about the importance of change over interpretation identifies a need for a socialist to look for ways to bring about change rather than merely interpret the world. I unashamedly claim that in this Study I am trying to understand better the micro-mechanisms of relations of domination and their legitimisation. This Study itself is not a manifesto for change – although I close with some implications for the future. In order to bring about change, we need to understand better the mechanisms that keep us moving in the ways we go. This Study is therefore not a description of a journey, it is rather an attempt to describe and understand the way “mathematics education plays its part in keeping the powerless in their place and the strong in positions of power” [Gates, 1997 #509, p 3].

One of the difficulties of trying to pin down complex sociological concepts is the interconnectedness that arises out of this complexity. It is not easy to organise a Study such that it expresses a neat progression from one idea to the next as might be implied in a piece of writing where one chapter follows another. So this isn’t a linear Study, neither is it one that can chart my own progression through a research biography. However, in writing a Ph.D. Study – as with any such writing – there has to be a linear structure for the reader to follow. Unfortunately, this linearity may give a false impression of the process behind the research. Far from linear, this Study, and the work reported in it was more of an iterative process, where new reading and reflection on empirical data introduced new ideas and organisation. This is particularly true of my process of struggle to construct and refine an empirical model.

Are there different voices in this Study? Naturally, I want my voice to come through, but what of the voice of the participants in the research? Whilst I have a strong desire to work for the greater emancipation of the powerless, I also see the need to engage with different discourses. Often the discourse of emancipation and voice foregrounds the involvement of the participants. Patti Lather gives a good example of this approach [Lather, 1991 #78, see especially pages 41 – 49]. Yet it is her adherence to certain postmodernist approaches that seems to limit her view of what role a researcher might play in working toward greater emancipation. For her, the post-modern “raises questions about vanguard politics and the limits of consciousness raising … and the efforts of intellectuals to inspire the aspects of liberatory politics most problematised by postmodernism” [Lather, 1991 #78, p 4]. While I agree with her use of ‘empowerment’ as “analysing ideas about the causes of powerlessness, recognising systematic oppressive forces, and acting both individually and collectively to change the conditions of our lives” [Lather, 1991 #78, p 4], and made use of her suggestions for organising reciprocity in research [Lather, 1991 #78, p 60 – 61], I do not accept her conclusion that this implies that “empowerment is a process one undertakes for oneself” (p 4). I am in no way antagonistic to this claim – and see it as an essential element in fighting an oppressive system. I would not want however to discount ‘vanguardism’ as an essential part of that process. The existence of a ‘vanguard’ or “transformative intellectual” [Aronowitz, 1985 #636] is at times a necessary element in transforming society. It is over-simplistic, and if I may be so bold as to say somewhat liberal, to suggest that “who speaks is more important than what is said” [Lather, 1991 #78, p 47]. It is also dangerous and potentially sterile to separate the two. What radicals need to do is to bring the two together within a theoretical orientation that can deconstruct the underlying intentions and power relations – something that Vladimir Lenin recognised some 90 years ago. It is not enough to give voice to the oppressed, nor is it enough to be a critical transformative intellectual. We must do both by being “cultural workers taking away barriers that prevent people from speaking for themselves” [Apple, 1991 #658, p ix]. One of the dangers of undertaking research to liberate the powerless, is that it might be theoretically blind, impotent, lacking in both an understanding of root causes for oppression and strategies for change. In so doing, we must move on from such liberal notions that see the individual as made potentially powerful by being engaged by researchers in their work. Patti Lather gives an example here where “researchers with emancipatory aspirations, doing empirical work offers a powerful opportunity for praxis to the extent that it enables people to change by encouraging self-reflection and a deeper understanding of their particular situation” [Lather, 1991 #78, p 56]. Though I deeply wish it were otherwise, I do not see self-reflection or a deeper understanding of the situation as anywhere near sufficient to bring about real social change. This position explains the place that the teachers have in my Study.

1.3 Study Structure

To establish a clear and wide-ranging theoretical foundation for the work I wish to produce, it seems important to deal with issues in some depth and rather than risking a superficial presentation in a few paragraphs. I have chosen to open up the conceptual and theoretical space to consider such ideas as ideology and habitus in much more detail. A cursory reference to some concepts would mask the very analysis I wanted to describe. Indeed, it is this very simplistic treatment in other places that holds us back from understanding more fully such processes as the educational task of social reproduction. Hence the first part of this Study might be seen as “building bridges” between disciplines [Murphy, 1996 #646]. I try to achieve this bridge building by incorporating the concept of a Justificatory Framework, which is overlaid on top of the Theoretical, Conceptual and Methodological Frameworks – as in the diagram on the next page. Chapters 2 – 6 develop explicit, inter-related and consistent frameworks for:

•Theorising the context of the study

•Developing the concepts and constructs used in analysis

•Developing a methodological approach to the study

However in order to more firmly establish the foundations of the study, I feel I need to occasionally reach outside of the immediate area of the study for ideas, connections, implications and justifications. This can be seen for example in those sections in which I discuss Models of social reproduction (Section 2.2) and The political nature of educational research (Section 5.2.3). It might be helpful to see these as the hidden piles that support the bridge and allow it to gain its strength

My concern is to locate mathematics education into a social field and it is therefore essential that I spend some time looking into the development not only of mathematics education, but also of the education system in general. My Study is a sociological analysis of an aspect of mathematics education and I need to introduce the sociological tools I will use to examine the classroom. Chapter 2 - Understanding Society is be an examination of approaches to the understanding of society that will be important in my study and in particular the issue of social reproduction. One of my overriding concerns in this Study is the manner in which mathematics education plays its part in the reproduction of dominant social relations through the way teachers conceptualise and organise their work, so clearly I will need to consider the critical issues and themes here.

Chapter 3 – Conceptualising Human Agency is about the nature of human agency and consists of examinations of Pierre Bourdieu’s habitus, approaches to ideology, and conceptualisations of discourse. These form a significant contribution to my analysis of data and some space is needed to expand upon the nature and form of the concepts I use and on how they inter-relate.

Chapter 4 – Exploring the Social Roots of Mathematics Education is an exploration of the issues, themes and approaches that seem to be at the heart of a sociology of mathematics education and which therefore have a bearing on the significance and orientation of my work.

Chapters 5 – Theoretical Orientation and Chapter 6 – Design of the Study are the methodological and empirical chapters in which I examine my own methodological background, discuss the methods I use, and the analyses I undertake. One of the difficulties in presenting such a structured piece is the integration of epistemology and methodology. For me the two are quite interconnected and merge into one another. Hence, I did not want clearly definable ‘methodology’ and ‘methods’ chapters. Consequently, I see Chapter 5 as an articulation of my theoretical orientation, and Chapter 6 the design of the research study at Highview School. In Chapter 5, I develop the approach that characterises my work as critical ethnography, and explore the issues arising from that. In Chapter 6, I apply these frameworks to the empirical work undertaken. I give in this chapter my reasons focusing on two teachers as ‘paradigmatic’ examples.

Chapter 7 – Introducing Alan Brown, Chapter 8 – Positioning Fran Gregory and Chapter 9 – Positioning Alan Brown, between them form the detailed empirical analysis, and contain the analysis of the two mathematics teachers I focus on, culminating in an empirical model for describing their discursive positioning and ideological foundations. Chapter 10 – Theorising the Model is the discussion of the model I have developed, and finally Chapter 11 – A Manifesto for Change is a consideration of the implications for the future.

The Appendices contain examples of my analysis through an annotated interview transcript (Appendix 1), two examples of lesson observation field notes (Appendix 2) and some analytical materials created by the computer-aided analysis I carried out using NUD*IST (Appendix 3). Finally, Appendix 4 contains extracts from the OFSTED report of the school. For reasons of maintaining anonymity and confidentiality, this is omitted from the public version of the Study.

Chapter 2 - Understanding Society

Synopsis of Chapter 2

The over-riding aim of this chapter is to draw together elements of a theory of description for an understanding of society, which could help us make sense of the practices we see in mathematics classrooms. I lay out the theoretical framework I am adopting in this study and make the case for an acceptance of a structuralist analysis, incorporating a conflict theory approach to social activity. I also lay out my argument for why we need to look closely into the nature of education in the UK and how this argument implies certain theoretical, conceptual and methodological approaches, all of which are developed in subsequent chapters. In addition to justifying my theoretical perspective, I make a case for rejecting arguments that we are in an era of postmodernity. In writing this chapter, I have chosen to draw together and synStudye a set of ideas from various theorists which best describe the essence and coherence of the approach I am adopting. Hence this is both a theoretical framework and a justificatory framework.

There are four key ideas I draw on in the first section of this chapter: a dialectical approach to the understanding of history, a recognition of the importance of social class in the functioning of the education system, Marx’s theory of alienation as an explanation for the popular perception of mathematics and the role of hegemony in the mathematics curriculum. In the second section of this chapter, I discuss various models of social reproduction theory.

This chapter is important because I need to lay the foundations for a study of human agency at the individual level of the teacher of mathematics from a social perspective rather than an individualising psychological perspective. Furthermore, the framework of ideas I present here is needed to justify my claim that this social perspective needs to be – and can be – derived from a position that goes beyond social interactionism and becomes embedded in mechanisms and structures of social organisation.

2.1 The Place of Human Agency in Social Theory

Marx has thus proved, not for the first time, to be a difficult customer to silence.

[Callinicos, 1999 #722, p 318]

The problem with Marxist ideology was that, in the end, it suppressed the individual by starting with society.

[Blair, 1996 #781, p 59]

There is no such thing as society, only individuals.

Margaret Thatcher

In this section, I discuss the stance I take in this Study. Fundamentally I am arguing that a social theory purporting to have some relevance to improving our understanding of critical sites, has to incorporate the position that social organisation is not a static structure, but is a dynamic operational system. We have to be able to conceptualise the interrelationship between the social structures and the operation of members and groups in that system. Hence my discussion of alienation - a central tenet in social theory. Alienation is not some abstract concept, but is a process of differential relationships effected in a variety of locations, in my case, the mathematics classroom. Similarly, hegemony is a central plank of an understanding of the mechanism of social organisation – yet it too needs people to operationalise it. This section then develops the underpinnings of social theory that focusses attention on human agency in the symbiotic interrelationship between agency and structure. This is important because I go on to look at the nature, structure and organisation of some teachers’ understandings of their work and in doing so focus closely on the individual level, but with the intention of locating this within a sociological approach.

2.1.1 Why study the sociology of mathematics education?

In this section, I want to explore the political framework to this study. I hope that I have already given some indications of my own background and values. Now I will look at examining the basis for a theoretical understanding of the Study. I will endeavour to do three things in this section. First, to present a brief synopsis of the essence of the theoretical framework I will be adopting for understanding the society in which mathematics teachers work (Section 2.1.1). Second, I will briefly discuss two important issues related to this – alienation (Section 2.1.2) and hegemony (Section 2.1.3). Lastly, I will offer a refutation to the claims that since we now live in an age of post-modernity, Marxism no longer offers a valid form of analysis (Section 2.1.4). My reason for introducing this into this Study at this stage is to demonstrate my rationale for drawing on Marxist philosophy and analysis at a time when it is coming under sustained attack, not only from the usual political opponents, but also from proponents of postmodernism. I will argues why I believe it is still relevant.

Authors - Marx, Durkheim, Weber and so on - represent landmarks which structure our theoretical space and our perception of that space.

[Bourdieu, 1990 #38, p 30]

I am, however, not intending to label this Study as a ‘Marxist analysis of mathematics education’. I take my perspective again from Bourdieu:

You get what you can where you can.

[Bourdieu, 1990 #38, p 29]

It is this position that justifies my incorporation of habitus, hegemony and ideology - ideas that are traditionally ‘structuralist’ from Marx, Gramsci and Bourdieu, with discourse - which is traditionally viewed as ‘post-structuralist’ from Foucault. In the relevant sections, I discuss how I adapt discourse into a more structuralist framework and how I develop ideology into a system of classifications rather than socially structured and determined positions. I described earlier what aspects were central to my conceptual and analytical framework, but they bear repeating here:

•A view of society as being in conflict between differing interests – usually class interests based upon economic distinctions.

•A view therefore which sees the economic structure as fundamental.

•An approach that considers the interconnectedness of the whole social system.

•That life is essentially social. That cognition is essentially a social act. Therefore that material conditions exert a significant effect on us. This approach looks for connections between objective structures and human action.

•That I am committed to social change.

•That educational research should be emancipatory, through analysing power relations.

Adopting such a conflict perspective is not unnecessarily negative or pessimistic, but is based upon the recognition by George Hegel, subsequently developed by Karl Marx, of the importance and power of contradiction, considered not as some temporary abnormality or paroxysm to be avoided, but as the driving force of history.

Contradiction is at the root of all movement and life, and it is only in so far as it contains a contradiction than anything moves and has impulse and activity.

[Hegel, 1812 - 1816 #747, Vol II, p 67]

This ‘dialectical process’ is seen by George Hegel as teleological – moving inexorably towards some goal. Karl Marx took this idea forward, removed George Hegel’s idealism, rooting it instead in a materialist conception of history and used the method of dialectics as a way of understanding issues, as stages in a process, looking at inner stresses and opposing forces to explain the intrinsic possibilities for change [Reiss, 1997 #748, p 84].