Efectos del crecimiento urbano

There are times in life when the question of knowing if one can think differently than one thinks, and perceive differently than one sees, is absolutely necessary if one is to go on looking and reflecting at all. (Foucault, 1984c, p8-9)

Introduction

Research in mathematics education which is primarily concerned with questions about school mathematics as a social institution needs theory which can address forms of social organisation. It requires a theory which is able to address the positions that are occupied within its realm and account for the social meanings and normative systems which support or contest the forms and functions of these positions. Research that is able to engage with the realities of girls in mathematics education must register a set of overt commitments to theory which will ultimately provide analytic tools for describing mathematics educational practice.

In this work the question of theory is centred around the question of the theoretical positions offered by Foucault as advancing gender work in the field. I begin by setting out those ideas and constructs, discussed in the previous chapter, which I see as useful to the field, and turn to a consideration of how those ideas have been utilised in educational analyses. The problem which then confronts is the extent to which Foucault's ideas about domination and the constitution of human subjects as docile bodies conflicts with, or even undermines, an emancipatory politics in mathematics education. I then pose a rejoinder to this difficulty in Foucault's work by looking at his final work in which he elaborates a notion of the self. I suggest how this concept of the self overcomes the limitations of his earlier theorising and how it might be useful for mathematics educational research in general and specifically for work on girls in school mathematics. What I want to explore is what an engagement with Foucault's final work, which critiques the foundations and the status of the individual, might do for, and demand of, this work. Implicated in this discussion are the questions that his formulations of discourse, subjectivity and power pose for an understanding of how girls become gendered learners in the mathematics classroom. My goal is to establish a potentially productive point of convergence between his radical thinking, and work on gender in mathematics educational research.

Paradox, Partiality and Promise Refining Theory

The fundamental question of mathematics educational research

Theory that is useful to mathematics education should be able to respond to the fundamental question of inquiry: How does research understand the subject and her relationship with her world? Research cannot begin to make sense of social forms and functions until the notion of the subject is unpacked, that is, until assumptions of subjectivity are made. Humanist assumptions that underpin commonsense liberal feminist views of subjectivity presuppose an essence at the heart of the individual which is unique, fixed and coherent and which makes her what she is. Such views of subjectivity tend to reiterate that individuals are born with a human potential which, given the right environment, can be realised through education and personal development.

In the previous chapter it was argued that in mathematics education literature the basic assumptions and beliefs which have up until now been fundamental to a progressive politics for girls in schooling are drawn from liberal humanist thinking. Like the labouring Marxist subject, the Kantian transcendental subject, the psychological ego, and the sociolinguistic language user, the liberal humanist subject of mathematics education effectively closes off any discussion of always-already existing social structures and relations of power. Even as categories of boy/girl and their derivative terms masculinity and femininity, might instil contradictory meanings in society, nevertheless we are, it is claimed, assumed to be whole and coherent subjects with a unified sense of identity, with a fixed core or essence. The explanation implicit is that making sense of notions such as masculinity and femininity is a knowledge that is learned through experience and this experience is expressed in language. The motivation for this explanatory tactic lies in an assumed unproblematic relationship between the individual, experience and language which allows little scope for theorising contradictions either in our sense of ourselves or in the meaning of our experience. It could also be said to practise a complex form of marginalisation which ultimately serves to inhibit its analyses.

Increasingly other fields have been drawn to Foucault's philosophical critique of the rational subject as a means to circumvent the limitations of essentialist theorising. It would be useful at this point to recall that 'subjectivity' represents a theoretical development from the notion of the 'subject' in structuralism:

The 'subject' is the generic term used in philosophy for what in lay terms would be 'the person' , 'the individual' or 'the human being' , and what in psychology is referred to as 'the individual'. The term 'theories of the subject' has tended to refer to approaches which are critical of psychology's assumptions about individuality, theoretical approaches which emphasize the way in which the social domain constitutes the individual, rather than the other way round. (Henriques et. aI ., 1 984, p93)

Paradox, Partiality and Promise Refining Theory

We use 'subjectivity' to refer to ... the condition of being a subject - but understand in this usage that subjects are dynamic and multiple, always positioned in relation to discourse and practices and produced by these. (Henriques et. al., 1 984, p3)

The subject, as Usher and Edwards ( 1 994) note, is always in caught up in a movement, inextricably involved in an on-going changing relationship between herself and that which she knows. In the French language Derrida ( 1 978a) has named this movement as

differance. The word sets itself up as a disruption to the ever-familiar notions of the

individual which are described by the logic of identity's trajectory. It does this not by posing as a new oppositional logic but as a challenge to the wholeness, the totality and closure of the spectrum divided by binary pairs. According to Derrida, fixed oppositions conceal the extent to which they are in fact interdependent and hierarchical. In other words binary pairs derive their meaning from a particularly established contrast where one term is prior to or dominant over the other. In Chapter 1 , I discussed how this binary oppositions plays out in the construct of 'female nature' . Scott ( 1 988) and Lloyd ( 1 984), among others, have taken this point further to argue that the western philosophical tradition itself is founded on binary oppositions such as unity/diversity ; identity/difference; masculine/feminine; and presence/absence.

This notion of difference, whereby meaning is made through implicit or explicit contrast, has appealed to a number of social analysts. Feminist scholars have noted how oppositions rest on metaphors and cross-references which serve to encode or establish meanings that are literally unrelated to gender or the body. In analyses of meaning which seek to unearth negations and oppositions the meaning of gender is seen to become tied to many kinds of cultural representations and these in turn establish terms by which relations between women and men are organised and understood. These analyses draw on Derrida's notion of differance to provide an insight into the way meaning is constructed. The question of difference for Derrida I is a question of suspending temporal-space in which the 'whole spectrum' can never be complete. Differance marks all totalities as merely localities dependent on relationships. To capture this understanding Spivak ( 1989) proposes the English translation deferring as more in keeping than the word differing

with Derrida's intentions for differance. It is a difference which is no longer reducible to an opposition between identity and difference. Rather, it defers the identity of either term against a play of identification and differentiation which never fixes either identity or difference. It shifts the focus of the act of valorising the subject from the realm of essential and unchanging ontological conditions to the realm of provisional and partial claims.

Derrida writes of this difference which he claims can no longer be reduced to a binary opposition between identity and difference: "Here there is a kind of question, let us call it historical, whose conception, formation, gestation and labour we are only catching a glimpse of today" ( 1 978a, p293).

Paradox, Partiality and Promise Refining Theory

Socialist feminists in particular have been drawn to these poststructural arguments of the subject and have taken them together with Foucault' s notion of power in order to criticise their more radical sisters' acceptance of essentialist ideas of the individual. For Foucault there is no originary moment establishing pure identity which can be rationally unpacked, but only a flux of experiences, ever being shaped into new wholes, reproduced through new vocabularies and new stories. These ideas have been taken up to a much lesser extent in the educational arena. Social analyses which do engage with Foucault' s work draw on his decentring of the subject and the way that it problematises unitary and universal categories such as boy/girl, traditionally regarded in research as natural, and historicised concepts such as equality/justice that are commonly taken as absolute. His notion of

subjectivity appeals in that is presents an open-ended, contradictory and culturally specific cluster of different subject positions, constructed by discourse. This is seen to be a useful strategic device for contemporary feminist analyses because Foucault' s deessentialising manoeuvres resonate strongly with the feminist critique of rationality2 as merely a masculine construct, and clears yet another space for denial of the claim that women/girls are essentially different from menlboys. Taken together these two theoretical convergences in poststructuralist and feminist notions of subjectivity can be made use of in my work as a way of overcoming some of the limitations of gender work in mathematics education.

To see gender as neither fixed nor finite is to occupy a very different position in authorising what can count as legitimate knowledge and experience. This might be seen as a radical or subversive move in the politics of the knowing subject and one which is detrimental to the feminist cause. However the opposite is more the truth of it. In its denial of essentialism Foucault's theorising is able to relate the individual woman/girl to the social and thus view her social constitution as subjected to different social relations and processes from menlboys. In other words it recognises the importance of the subjective in the constitution of the meaning of girls' lived reality and is able to relate this to an understanding of power. Who the girl 'is' and who she 'becomes' is determined by what is said (and unsaid) to her, and what is said about her. As Confrey ( 1 990) has written in the mathematics education literature, modes of understanding become available through social structures and processes and hereby provide a perspective to the individual: "we construct our understanding through our experiences and the character of our experience is influenced profoundly by our cognitive lenses" (p l08). The decentred subject is offered an explanation of where her experience comes from, and why this

2 Later, in chapter 6, I elaborate more fully on the feminist critique of rationality. It is mentioned merely in passing here to signify that body of work being carried out by feminists which, aligns itself with the poststructural position in subverting the notion of essentialism.

Paradox, Partiality and Promise Refining Theory

experience might be contradictory or incoherent, and why it might be different from the experience of others (Weedon, 1 987). This is done by claiming that all knowledge is linked to power and as such is contested, and is merely temporal and emergent.

Foucault's poststructuralist deessentialising of 'the subject' allows an understanding of the subject as a position within a particular discourse. It follows from this that the subject is no longer isomorphic to the individual. Rather the powerlknowledge relations which produce a subject-position imply that there need not be any coherence to the multiple sites in which sUbject-positions are produced, and that these individual sites might themselves be contradictory. For the girl in schooling, the social institution of her classroom, her family, the world of leisure, fashion and so on, are all prior to her being. She learns about their operational regimes of truth and the values which they maintain as true. Hence her subjective experience, that is, the way in which she make sense of her school life leads into an understanding of how power relations structure society. Meanings become enmeshed in discursive battles that influence, dominate, parody, translate and subvert one another. And the girl becomes dynamic, expansive and intrinsically shaped by power.

This form of power applies itself to immediate everyday life which categories the individual, marks him by his own individuality, attaches him to his own identity, imposes a law of truth on him which he must recognise and which others have to recognise in him. It is a form of power which makes individuals subjects. There are two meanings of the word subject: subject to someone else by control and dependence, and tied to his own identity by a conscience or self-knowledge. Both meanings suggest a form of power which subjugates and makes subject to. (Foucault, in Dreyfus and Rabinow, 1 982, p2 1 2)

The methodological significance of abandoning belief in essential subjectivity lies in its capacity to generate new methods of analysing constructions of meaning and relationships of power. Questions of difference and the body factor into the analysis more in terms of how the body is invested with certain properties and the ways in which it is placed into regimes of truth, rather than with the questions concerning the body's essential core. The consideration centres around the relationship of the body to the discursivity and the historical presence of the everyday school life of girls. In these analyses the starting point is with the body and the task is to analyse the effect of power in its most specific and concrete forms. The interest is in examining the way in which the body is constructed in order to legitimise different regimes of domination; to show how power relations are embodied without depending on the mediation of the subject's own representations. The focus is not on the meanings which the girls attach to their activities or ways of thinking, since the interest goes beyond the role of language and textuality . Its explicit consideration is of the nature and role of power and the mechanisms whereby domination and power consolidate their hold on girls in schooling.

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Paradox, Partiality and Promise Refining Theory

Foucauldian approaches to educational research span the domains of philosophy of education, teacher education, curriculum, minorities' and girls' interests, and research itself. Britzman ' s ( 1 99 1 ) and McWilliam's ( 1 992) interest has been with teacher education. B oth have examined teacher education as an arena where dominant sociocultural discourses compete to construct and position teachers and students. Extensive work has been carried out in the curriculum field to scrutinise the construction of particular areas of school knowledge and curriculum in texts and in classroom interactions. An important and widely read work in the curriculum field of mathematics is that of Walkerdine ( 1 988). In other subject areas the work of Baker and Freebody ( 1 989), Gore ( 1 995), Jones ( 1 997), Luke ( 1 988), Middleton ( 1 995), and Singh ( 1 993) figure as significant. McElroy-Johnson ( 1993) and Nieto ( 1 992) work specifically for the advancement of minority students. Ellsworth ( 1 992) draws on Foucauldian ideas in a consideration of her own teaching practice. And for both Lather ( 1 99 1 ; 1 992) and Cherryholmes ( 1 993) the interest is in theoretical reframing of educational research. Their work looks at the possibility of moving data collection, analysis and experiment to an understanding as discourse practice.

In the sparse Foucauldian research in education which works on behalf of girls' interests, understanding who the girl 'is' involves unearthing the physical, social and discursive mechanisms by which she is produced. It moves from a concern with behaviour, skill and mind towards the notion of discourse as a constitutive pedagogical category. Its purpose is in revealing how pedagogic discourse is implicated in systems of government, surveillance and moral regulation. The recent work of Cherland ( 1 994); Christian-Smith

( 1 993); Davies ( 1 989, 1 994, 1 997, 1 998); Fine ( 1 992); Gilbert & Taylor ( 1 99 1 ) and Rhedding-Jones ( 1 997) all draw on the Foucauldian concepts of discourse and subjectivity in their analyses to seek an understanding of how 'the girl ' has been constituted out of particular systems of subjugation. This they do by tracing the circuitous paths by which the girl's constitution takes place. The particular interest is centred on the mechanisms through which a form of personal existence is created for the student within the classroom by the labelling of the category 'female learner' to her, her actions and her classroom relations, given that the discursive activity of learning positions the student as 'learner' amongst other learners, as well as amongst ' others' within the educational apparatus.

Each of these analyses shares a common concern to move beyond a-historical and depoliticised notions of educational research. The intent for each is to discover how the discourse of the classroom, or 'regimes of truth' , operate in relation to the dominant power structures of a given society. To do this these analyses explore how a multiplicity of what Foucault calls· 'micropolitics' prohibit or sanction certain effects on learning in

Paradox, Partiality and Promise Refining Theory

everyday practices in general and, in particular, on the dispositions of the girls and others they subjugate. The way in which this is undertaken varies immensely. There is no one conceptual strategy, approach or language that defines their practice but each takes account of the inherent perspectivity of knowledge production and the unavoidable open­ endedness that this entails. In its own way each piece of research critiques what seems

'natural' , recasts 'experience' , unsettles received definitions, multiplies subject positions, and connects the 'voice' to the structural and the collective.

The question of power and possibilities for agency

Foucault' s ideas have provided a useful analytical framework to explain how girls' experience is controlled within certain cultural determinations. In those analyses in which the main concern is with the effective history of girls in schooling Foucault ' s understanding of the body as the main target of the transmission of powerlknowledge relations is able to sidestep the question of difference and the colonisation of the body' s 'natural' resources. The difficulty is that i n taking on board Foucault's undifferentiated theory of power and its effects on the body for educational analysis is to make a case for