ࡱ> vxstu5@ Cbjbj22 /HXX>""""#TCj########CCCCCCC$CERG6C]:##::6C##CAAA:##CA:CA AAA## 7"2>"ACC0CAwHTAjwHAwHA#+rA1\^5:###6C6C"A"ONLY CONNECT: TROUBLING OPPOSITIONS IN GENDER AND MATHEMATICS Heather Mendick London Metropolitan University, UK This paper focuses on the ways in which many researchers working in the area of gender and mathematics make sense of their data. In particular, it is argued that their use of the oppositional framing, separation versus connection (and others, such as cognition versus affect and objective versus subjective), operates to fix difference, and so to fix gender and mathematics within a structure of binary thinking that ultimately serves to re/produce gender inequalities. The aim is to suggest a more productive approach to understanding the continued gendering of participation in mathematics. This approach is based in deconstructing these oppositional patterns. This theoretical approach is illustrated using readings of interviews with two young mathematics students, Analia and Phil, talking about their relationships with the subject. The paper ends by looking at what this unfixing of difference means for mathematics pedagogy. Introduction It is well documented that mathematics, in its interrelated roles as an academic discipline, a school subject and a collection of everyday practices, is one of the ways in which gender inequalities are re/produced. Discussions about the relationship between the powerful role of mathematics and its male dominance have been part of feminist research and praxis in education in a range of countries since the start of the second wave of the feminist movement (Burton, 1990; Leder, 1992; Hanna, 1996). In this paper, I do not intend to survey the range of explanations that have been offered for this problem; instead, I want to focus on an opposition that is frequently used by researchers to make sense of their data: the dichotomy between separate ways of relating to mathematics and connected ones. This binary troubles me and, through this paper, I hope it will come to trouble you. My argument, which has implications for how to theorize gender equity beyond mathematics education, is that it fixes difference within an oppositional structure and so fixes gender and fixes mathematics. These fixings, of the masculine in opposition to the feminine and of mathematics aligned with the former, ironically serve to reinforce the gendered inequalities that feminist researchers set out to challenge. I begin by examining and problematizing the categories of separation and connection as they appear in the literature. I then explore what I maintain is a more productive approach to making sense of gender difference within mathematics. Instead of reinscribing the binary of masculine/feminine and the location of mathematics within this, I disrupt and refuse its demands by deconstructing the separation/connection binary. Deconstructing this binary involves making visible the logic from which it derives its meaning, in particular the mutual dependence of both sides of the binary and the power relationships implicated in it. Throughout, I use the verb trouble interchangeably with the verb deconstruct for reasons that Davies (2000, p. 14, original emphasis) expresses well: Too many readers of deconstructive texts take deconstruction to mean a dismantling that obliterates the binaries and the boundaries between them. Binaries are not so easily dismantled, and deconstructive work often can do no more than draw attention to the binaries and the their constitutive force. For some people, in some readings, deconstructive work may facilitate a different take-up of meaning, beyond the binaries. But this does not undo the continuing force of relations of power that operate to hold the binaries in place. I choose the word troubling to represent more closely what it is that deconstructive work can do. I carry out this troubling/deconstruction by telling stories based on interviews with two young people, Analia and Phil. They are in their first year of post-16 optional mathematics courses in England and both enjoy the subject. However, while Analia and Phil both talk about enjoying the separate pure, objective and cognitive pleasures of mathematics, I construct alternative stories, grounded in the data, in which what they enjoy in doing mathematics is the identity work they do through it. I use these stories to dispel the myths that the cognitive is not always already affective and that separate mathematics is all the things that it claims to be: rational, abstract, objective. Further, these stories raise questions about the gendered impact of the processes through which mathematics must be made to look separate by producing stories of it that exclude its Others: emotions, relations, subjectivities. In concluding, I explore the refiguring of difference within my arguments and their possibilities for a pedagogy that unfixes gender and mathematics. Separation versus connection The terms separation and connection derive from the influential feminist work of Gilligan (1993). Noting the absence of women from the research done by Kohlberg (1964, cited in Gilligan, 1993) to establish his scale of moral development, Gilligan (1993) decided to explore the ways that women make moral judgements. She found that males often reasoned from abstract points of justice, in a way seen by Kohlberg (1993, p. 26) as the highest ethical state, treating a moral dilemma as sort of like a math problem with humans (Gilligan, 1993, p. 26). She labelled this an approach to moral reasoning based in separation, and contrasted it with the approach favoured by women based in connection; connected reasoning starts from the relationships between people. So, for example, Amy is given the dilemma of whether Hans, whose wife is dying, should steal the drug he needs to save her, but which he cannot afford. Instead of reasoning abstractly, as traditional moral philosophy demands, Amy searches for a solution based in relationships. She refuses to accept the problem as it is presented, asking whether Hans cannot persuade the druggist to give him the drug more cheaply on humanitarian grounds, and considering the possibility that, should Hans steal the drug, he may be found out, end up in prison, and leave his sick wife alone. Belenky et al. (1986) described Womens Ways of Knowing developing Gilligans distinction between separation and connection beyond knowing about morality to knowing more generally. Their ideas of separate and connected knowing have then been taken up within the mathematics education literature (e.g. Becker, 1995; Boaler, 1998; Brew, 2001). The idea that girls and women seek connection in mathematics and so respond better to collaborative and open-ended forms of learning and assessment is supported by work on alternate methods of teaching and assessing mathematics (e.g. Barnes & Coupland, 1990; Forbes, 1996) and by recent research in English secondary schools. Boaler (1998) and Bartholomew (2001) found that girls were more alienated than boys by competitive, fast-paced, individualized, top set environments where they worked through a series of exercises and felt unable to pursue what Boaler terms their quest for understanding. To sum up: these approaches are based on the argument that there are separate (individual, abstract, rational and objective) ways and connected (relational, grounded, emotional and subjective) ways of doing mathematics and it would be better for us all, and for girls and women in particular, if we moved towards the connected ones. While these have undoubtedly been valuable interventions, they are limited. By aligning separate-ness with masculinity and connected-ness with femininity, these approaches feed the oppositional binary patterning of our thinking and, in the final analysis, reiterate it. In what follows I discuss two ways in which they do this: by underestimating the impact of existing power relations, and essentializing differences between the genders. Within education, providing access to girl-centred curriculum content, and methods of teaching and assessment, different from the dominant knowledges and modes of teaching and assessment found in schools, is not easy. This, as Paechter (2000) pointed out, is due to the power structures that pre-exist these interventions and so define the conditions in which they operate. For example, while having separate boys and girls versions of knowledge has been successful within marginal subjects, like physical education and technology, this has not proved a success in high-status parts of the curriculum; domestic science never offered any challenge to the power of real science and never showed any signs of becoming the female alternative to this that its originators envisaged (Paechter, 2000). This response to the devaluation of the feminine by reclaiming those traits, values and understandings for the purposes of a separate feminist education, does not challenge the oppositional division of the world into masculine and feminine. For: The affirmation of the value and importance of the feminine cannot of itself be expected to shake the underlying normative structure, for, ironically, it will occur in a space already prepared for it by the intellectual tradition it seeks to repudiate. (Lloyd, 1993, p. 105) Relatedly, gender opposition easily becomes gender essence. Although all of those researchers, whose work I have discussed above, pay more-or-less convincing lipservice to the idea that separate and connected ways of reasoning are not tied to men and women in any necessary way, it is difficult to rescue these approaches from essentialism (for arguments on Gilligans work, see Faludi, 1992). Essentialism is often used to label those positions that are based in an understanding of difference as biological. However, I follow Bohan (1997) in using gender essentialist to label those positions that locate gender within the individual, regardless of whether the essence is seen as biological, social or anything else. I do this because of the slippage between these positions. Differences slide from the social to the biological through a complex process, discussed in Henriques et al. (1984, p. 15), in which the individual reduces inevitably to the biological in essence once its opposite number, the social, has been posed to explain the rest. This slide can be seen not only in MarsVenus style selfhelp books, but also in Greers (1999) feminist best-seller, The Whole Woman. Greer argues that we must recognize womens difference from men. In so doing, she distinguishes femininity from femaleness and constructs the latter as the essence of woman, that which remains after menopause burns off the impurities (Greer, 1999, p. 294). Such approaches ignore both differences between women and between men, and how differences of class, race/ethnicity, sexuality and dis/ability intersect with each other and with gender in complex ways and, in many social and educational contexts, are more pertinent than gender differences. These cross-cuttings of dimensions of inequality are drawn out in both Analia and Phils stories. As well as fixing gender, separation/connection fixes mathematics. Separate and connected ways of doing mathematics slide into separate and connected versions of mathematics itself with the former preserved as a space free from the taint of connection. So, the introduction of the idea of connection, by positing the existence of separate mathematics, legitimates what it seeks to challenge. A similar process happens through the cognition/affect opposition. Work on affect in mathematics education takes a different domain from that of research on cognition; work on affect does not focus on the direct interaction of student or teacher with the mathematical object that characterizes cognition studies (Cabral & Baldino, 2002, p. 170; for a survey of the research on affect in mathematics education, see McLeod, 1994). So affective variables, such as anxiety, confidence and self-esteem, feature as the extra stuff that surrounds and affects the act of cognition, stuff that would ideally be removed in order to facilitate learning, rather than as the means through which learning happens. For example, McLeod (1992, p. 588) speaks about integrating work on the cognitive and the affective or linking these, and assumes that there are topics that can be classed as purely cognitive and strictly affective. This maintains the cognitive as different from, opposed to and prior to the affective (by processes parallel to those through which the masculine/feminine opposition functions to maintain the biological as prior to the social). Further, it legitimates the collective refusal to view emotions and relations as central to the learning of mathematics and maintains the power relations that, as I have argued, undermine feminist interventions into pedagogy and assessment. Cabral and Baldino (Baldino & Cabral, 1998, 1999; Cabral & Baldino, 2002) use psychoanalysis to attack the kind of processes which normally remain the domain of the cognitive and this is also central to my own methodological approach, which I explore in the next section. Methodology The interviews analysed in this paper are part of a qualitative study of the experiences of 43 young Londoners who chose to continue studying mathematics beyond the end of compulsory schooling (at 16). This study involved me in interviewing participants once, sometimes individually and other times with one or two friends, and in observing them in their mathematics classes. Participants were spread across seven classes in three research sites, which I have called Grafton School, Westerburg College and Sunnydale College. In the interviews, I asked students to describe a typical mathematics lesson, about what they had enjoyed most and least about their classes, to compare mathematics with other subjects, about what other people, not doing mathematics, think of the subject, and for their views on gender. Whilst this paper uses this empirical work it is not an empirical paper, instead I am using my readings of Analia and Phils interview talk to do particular theoretical work, based in a specific way of reading their choice of mathematics. Thus, it is the process by which I did this theoretical work which I elaborate in this section (for an account of the empirical methodology, see Mendick, 2003a). I see subject choice as being centrally about identity; it is a key site in which young people produce themselves/are produced as part of an on-going lifelong project of self. This identity work involves being positioned/positioning oneself within a range of discourses (Foucault, 1972) on mathematics, masculinity, femininity, education and much more. This approach, instead of fixing gender, keeps it in motion for gender is always a doing, though not a doing by a subject who might be said to preexist the deed for there is no gender identity behind the expressions of gender; that identity is performatively constituted by the very expressions that are said to be its results (Butler, 1999, p. 33). Female-ness and male-ness are produced through reiterative performances, in such a way that they appear to precede these performances, and so are experienced as authentic by the performer/possessor. This links to my main argument: that our use of academic concepts is part of these reiterative performances and so we need to be attentive to the ways in which we inscribe gender through our conceptual categorizing. These processes of identity work also involve psychic investments, desires, anxieties, defences, and fantasies. There are real tensions when combining Foucauldian with psychoanalytic approaches. Notably, the former retain a central discourse of a universal human subject which is in opposition to discursive and narrative approaches refusal of interiority (Walkerdine, 2003, p. 248). However, psychoanalysis is a plural approach: Psychoanalysis does not intend to uncover objective causes in reality so much as it seeks to change our very attitudes to that reality. This it achieves by effectively deconstructing that positivist dichotomy in which fantasy is simply opposed to reality, as an epiphenomenon. Psychoanalysis dismantles such a logic of the supplement to reveal the supposedly marginal operations of fantasy at the centre of all our perceptions, beliefs and actions. (Burgin et al., 1986, p. 2, original emphasis) In this paper, I use psychoanalysis to construct stories that move us beyond commonsense, drawing on recent work on the psychosocial subject (e.g. Walkerdine et al., 2001) and based in the commitment that social and cultural analysis needs an understanding of emotional processes presented in a way which does not reduce the psychic to the social and cultural and vice versa, but recognises their interweavement (Lucey et al., 2003, p. 286). I analysed my data through listening to the tapes and working with the transcripts to construct narratives based on each interview. These narratives read the interview talk as performative in the ways discussed above. It is difficult to explain exactly how I went about this process but in order to orient my work I finish this section with one such thought experiment from the work of Pimm (1994). Pimm looks at unconscious elements in learning mathematics by studying the metonymic/metaphoric associations and slips that are ever present in mathematical discourse. These, often denied links, add to meaning in mathematics. The looseness and gap between symbol and referent, regularly exploited for mathematical ends, also permits such slippage to a far greater extent than in other disciplines. Circumscribed is very close to circumcized and the connection is not arbitrary. Teenage girls working on the period of a function can and do make overt connections with menstrual periods. Adolescents can become preoccupied with freedom and constraints upon themselves, and geometry can offer them the possibility of working with the same material as well as the same terms (Pimm, 1994, p. 46). Pimm focuses on an example where a girl misremembers the word infinity as fidelity. He reads this as having both a sexual association in the discourse and one relating to romantic dreams of never-ending love. This approach provides another route to coming to understand doing mathematics as working on the self. It adds a further psychic twist to the central theoretical engine of this paper that the choice to do mathematics and the ways in which one engages with the subject can be read as ways in which people do identity work. The stories that follow are attempts to understand mathematical pleasure as the pleasure of engaging in the different kinds of gendered work on their psychosocial-self-in-relation that happens through mathematics. It is worth noting that there is, of course, nothing special about Analia and Phil that makes such readings possible, and I have done similar readings of other participants accounts. What is important is the theoretical approach to the data rather than the data themselves. Analias story Analia Kasersoze chooses her pseudonym to be a post-modern mixture of the exotic and popular culture (the surname belongs to the mythical underworld presence in the film The Usual Suspects; McQuarrie, 1995). She is a Turkish Cypriot and a Muslim but only up to a certain point, coz I dont wear a headscarf and all that. Her mum is a housewife and her dad a civil engineer and architect. At Westerburg she is studying biology, chemistry, history and mathematics. In her interview talk and in my observations of her, Analia appears determined and highly motivated. Her motto is: if you fail to prepare then prepare to fail. At the start of her history examination course at age 14, her teacher wrote this on the board, adding I can only give you the resources, I can only give you the knowledge, whether you choose to take it or at what point you choose to use it to, it depends on you. Analia has a second motto for when its coming up to exams: now or never. I pin it up right in front of my desk: now or never. So you gonna do it now, or you gonna fail? You know, if somethings gotta be done, youve gotta do it. Analia works hard and, aware that it makes her different, she speaks about it ironically: I enjoy my work. It gives me something to do at home. She laughs, takes your mind off things. Homeworks good. Lots of it! She also enjoys answering questions in class: I like it. It gives me a chance to show off that I know something. Yeah, I know that! You prove yourself, dont you? Thats good. I enjoy that. Given the status of mathematics as a proof of self (Mendick 2003b, 2005b) it is not surprising that the subject is central to Analias intellectual identity project. Mathematics represents a wanted and needed challenge to Analia. It will always keep my mind on tiptop condition. There are times when its difficult, but whats even more rewarding than being difficult is to find out where the difficulty lies. Thats the biggest reward. If you give up, then yeah youve lost a challenge you know, youre gonna look back and [say] I didnt do that in my lifetime. Mathematics is self taught you can find out your errors and even work out your own method, and you get satisfaction if you find out the methods. Once you can do it, you can always do it. And thats, like, the biggest reward. These comments suggest that her pleasure derives from a sense of her power to create mathematics, from the ownership that she feels once she has mastered something, and from the certainty that things, once mastered, stay mastered forever. Analia connects her pleasure in mathematical certainty to the nature of mathematics and the ways that it differs from humanities subjects: What I enjoy about maths is the fact that you can sit down and open up a page of exercises and you wouldnt have to write a long essay, youd have symbols, it would be, like, quick into it, find out the solution, work out the method, use it over and over again, if you get it wrong the first time, if you practise youll improve, and its all about how your mind works. You start focusing onto a question. You see in history or English there are several answers to one question, but in maths theres only one answer. Analias attachment to certainty and her individualistic and competitive approach to academic work are traits that are normally identified as separate and so masculine within the literature. However, in the rest of this section, I generate an alternative, connected story about what attracts Analia to mathematics. To do this I set what Analia says about her academic self alongside what she says about her gendered self in order to make sense of her earliest memories of doing mathematics: I remember how I learnt to do my multiplications. My dad told me to bring my marble box and do multiplication, and he had some marbles and he showed me it; and I remember I used to go to the shop with him and he used to find these little subtraction and, um, adding books, you know, they would be like thick and theyd have like five questions on every paper, 2 + 4, or something. You know, you used to get, you used to do them and take them up to him, and hed go oh, well done! And those others, well done! and youd think, wow! Analia tells me that gender has made a big difference to my life. She laughs when I ask her about this and then explains: Right, Im gonna be a bit honest here. Like being a girl in my family. Im the only girl in the whole family. I have no girl cousins, I have no girl aunts or whatever. Well I do have aunts that are married to uncles, but you know no family type, you know the same blood. Of course, Im gonna study, Im gonna go to university here and of course Im gonna get a job. But I know that when I come through that, Im gonna get married as well and that, and I will most probably give up my job and I will be at home and I will look after the kids. So thats why I think a girl loses out, whereas a boy, he, hell go to work. And I know its a bit traditional and all that, but Im OK with that, I dont think its, um, a big problem, Ill accept that yeah. So Im, Im perfectly happy sitting at home all day, so [she laughs] not doing any work. Analias imagined future here stands in stark contrast to the Analia who is concerned earlier in the interview that if I didnt do maths for a month, I think I might become really lazy. Analia goes on to discuss the gendered policing of sexualities: Boys can do certain things and like it wont give them a reputation but for girls it will give you a reputation. For example, me, I dont go out with any boys. Um, er, I am very flirtatious, but I think thats because I dont go out with any. Like Im trying to keep my purity to me because I know that the man I wanna marry isnt going to be someone who would like a wife thats been about. Here Analia acknowledges the tension that this double standard creates for her (one disturbingly similar to that described over 20 years earlier by the girls in Lees, 1986). These tensions around her sexuality are found in her reasons for not doing physics. She first gives me a reason when we are discussing her subject choices, explaining this in terms of her need for academic variety, if I chose to take physics as well, then that would just be three sciences and maths, and that might tear me down too much, yeah. Coz consistently [working] in the same sort of methods, and stuff. Later in the interview, when we are talking about gendered subject choices Analia gives me a different, less rational reason: I was thinking of taking up physics, but I thought a class full of boys might distract me a bit too much. She laughs. [Thats the reason?] Yeah, I thought physics, too many guys and so I thought no! My hormones might start playing up or something, I thought best to leave it. In another example Analia recalls: Ive had a guy that Ive liked for a year and then after about a year he noticed me as well, and he started to like me as well, and then he came to ask me out and I looked him in the face and said to him I cant, Im sorry, I know I really like you, but I cant go out with you coz I wont feel like going home at night and looking at my dad, whos got like, starting to have grey hairs and you know, seeing his face you know, all crinkled, beginning to get crinkled, because my dads not ninety. [she laughs] I cant sit at the table and eat with him you know it just wont feel right to me, because like I carry a name, I represent something, I represent my family, and I feel that, um, if I did do anything bad, which sometimes Im very tempted to do as well, [she laughs] I know that it will not only damage me, but it will damage them far more. And thats why. So, but I think its right, although its difficult, but its right, so I have to be stronger. And I accept that. I aint got a problem with that. Ill just carry on being really saucy and flirtatious and then reject everyone. [she laughs] Its fine with me and I think it gives me character as well, it makes up who I am I enjoy being who I am. Analia draws here on traditional discourses in which the woman is seen as custodian of her familys, in other words her male relatives, status. Her honour is their honour. Yuval-Davis (1997, p. 45) explains that many ethnic identity projects depend on a notion of authenticity which: Assumes fixed, essential and unitary constructs of cultures, identities and groupings. Authentic voices are perceived as their true representatives Women especially are often required to carry this burden of representation, as they are constructed as the symbolic bearers of the collectivitys identity and honour, both personally and collectively. A figure of a woman, often a mother, symbolizes in many cultures the spirit of the collectivity, whether it is Mother Russia, Mother Ireland or Mother India. This position seems to be more critical for Analia because she is the only girl in her family, and perhaps also because of the rigidity and freezing of cultures which takes place in diasporic communities (Yuval-Davis, 1997, p. 46). The understanding here, of Analias educational and employment choices as collective acts, contrasts with their inscription as individual within her mottos discussed above. However, Analia connects her emotional and sexual restraint not just to her public role as a representative of her family but also to her private feelings for her father. Her earliest memories of doing mathematics (quoted above) are also associated with her father, particularly with gaining his approval. As a child, Analia remembers that she was rewarded with love and respect from her father for success at mathematics. This leads me to conjecture an alternative reading of her attachment to mathematics. In this reading what she works on through doing mathematics is her imagined relationship with her father; within this work, she wants certainty from mathematics and finds pleasure in this because it gives her certainty/ safety in this relationship. In this reading even the most separate of pleasures the individual pursuit of definite answers is connected. Clearly such a reading is speculative and my connections are not ones made by Analia, although this could be said of many possible readings, and she did nothing to object to it after I e-mailed it to her. I use it to demonstrate how working against the separation/ connection framework opens up possibilities for looking differently at what students are enjoying when they do mathematics. This is a project that I continue in Phils story. Phils story Phil, a working-class Chinese Grafton student, is studying English literature, physics and information technology alongside mathematics. When asked what he has enjoyed most about mathematics, he is among a few participants who select a specific topic and speak about a fascination with the subjects power rather than about the ease with which they can do mathematics: Its quite interesting as well and stuff, stuff that you never thought of, you use mathematical methods I liked integration the fact that you can work out the area under a curvy graph its just stuff that Id never thought of before. His rejection of ease as a source of enjoyment is explicit in his comparison of GCSE with A-level mathematics (GCSE and A-level are English public examinations taken at ages 16+ and 18+, respectively): Well probably [I prefer] the GCSE coz its easier, but A-level, actually I prefer the A-level coz its more thinking. He later reiterates his intrinsic interest in the subject; I find maths quite interesting the way numbers and things just link up with each other. Phil prefers mathematics to English whose GCSE examinations he disliked because they involved too much writing and there was no set answer. This position is not one that many people occupy relative to mathematics. My study and others of A-level mathematics students (e.g. Burton, 2001) suggest that most people identify with the subject via extrinsic properties, factors that relate to how it is valued, for example, as difficult and hence a challenge, as a source of future earning power, or as a necessary stepping stone to a future career. Even for those who take pleasure in mathematics itself, there is normally an elision of ease and enjoyment. As in the previous story, I want to read Phils pleasure in mathematics as pleasure in the identity work that he does through it. In the passages quoted so far Phil frames his attachment to mathematics and its certainty as cognitive and rational. However, in what follows I deconstruct this reading of his mathematical pleasure by looking at the affective and the emotional and, in particular, how, through Phils claim to enjoy pure mathematics, he also claims an intellectual maturity and a cultural identity. Thus I am again writing deliberately against the separation/connection dichotomy. Moving into the sixth form seems to have been an important transition for Phil. He explicitly links this to the way the more immature laddish elements have left: Its a nice comfy atmosphere. Theres no immature people mucking around like you get in GCSE, you just get your lesson. Phil attaches importance to being able to joke around, as distinct from muck about, in class. What he enjoys least about mathematics is when its getting a bit too serious. We have the odd joke, now and then, which lightens the atmosphere. Phils construction of himself as intellectually mature is gendered. It is reminiscent of Redman & Mac an Ghaills (1997) account of his own experiences of schooling, where at 16 he became aware of the possibility of a masculinity based, not on aggression or sporting prowess, but on a muscular intellectualness or pushing people around with your mind. Redman & Mac an Ghaills acquire muscular intellectualness via history, Phil via mathematics. Mathematics with its intellectual status is an important part of Phils construction of himself as mature within the interview. He positions himself as self-disciplined in mathematics lessons, I tend to concentrate a lot when its maths compared to other lessons anyway and I always pay attention in my maths lessons. When asked about what other people not doing mathematics think of the subject, Phil says: They see it as its pointless, because youre not gonna use maths in the world, but I dont think they know what maths is about, its about, if youve got a good grade in maths it shows that youve got a good analytical mind and employers look for people who can do that. As well as being a claim to intellectual maturity, this statement sees Phil leaping to the defence of mathematics, against people ignorant of what it is really about. He positions himself as knowing the truth about mathematics. Phils sense of himself as mature also links to his expressing feelings of being out of place in Grafton: I find sixth form [16+ education] quite depressing the fact that I havent met anyone new its just the same old people. Its a sixth form but its in a secondary school [for students aged 1118] and when you walk round the school you feel out of place, everybody else is doing GCSE. His identification with mathematics enables him to establish an imagined community (Anderson, 1983) of like-minded individuals beyond the schools boundaries. I look at this community next. Phil has acquired notoriety in Graftons sixth form for having written a detailed account of the fundamental and mystical role of fish within our culture. One of the things he cites as evidence for his position is the way that the mathematical symbol for proportion bears a striking resemblance to a fish. He suggests founding a new religion based on this fundamental, fishy insight. With his friend Salvador he has written a series of humorous texts about the organization JFC. The first, quoted from below, is framed as an e-mail manifesto sent to potential customers: Being divinely funded by God, JFC is able to establish itself on very firm territory with extremely stable foundations. Once more, our headquarters is very flexible and is constantly on the move in the form of Jesus Fucking Christ himself. Our very stable capital (funded by God) is able to provide several different commodities. Firstly, as our very analytical sales department (located in the main area [the head] of Jesus Fucking Christ, in the upper right area of the holy brain), has spotted a gap in the fast food industry in that we believe we can do better than other companies currently on the market. After careful consideration, we have decided to imitate a well-recognized name in the fast food industry, and turn it into a very original and somewhat witty title. There will be two fast food chains, with each specializing in different meat products. The first would be titled: Jesus Fucking Chicken (or JFC for short). This would be backed up with a TV advertising campaign starring Jesus Fucking Christ himself advertising Jesus Fucking Chicken with cheesy music being played in the background, advertising our main product, which we believe would launch our name as a heavy weight in Fried Chicken fast food chains. The product to be advertised is our special St. Peters Feast with a free bottle of Holy water, together with 8 pieces of Fucking Chicken and 4 fries, complete with side dishes of Bread and Wine for only 9.99, with 5% of intakes donated to the Catholic Church. Alternatively, customers could go fuck and order the St. Peters Fucking Feast for an extra 2 and receive a special JFC big bottle of Red Fucking Wine complete with a practical tub to vomit in, with 10% of intakes donated to the Catholic Church of YOUR CHOICE. The next fast food restaurant would be titled Jesus Fucking Cows (or JFC for short) with a slogan of Now theres an image. The commodity will of course be beef cooked in various different ways from our highly trained secondary school students . I have quoted from this extensively to demonstrate that there is a very particular form of satire operating here. The content and style of the text are reminiscent of Douglas Adamss The Hitchhikers Guide to the Galaxy, a cult UK radio series/trilogy of five novels/UK television series that, although enjoyed by many, is a marker of identity for many mathematicians and computer scientists. In fact, Phil wants to study computer science at university and mathematics is his favourite school subject. For Phil his identifications with mathematics and computing can be read as being not with these subjects abstracted activities, but with concrete social practices and their associated cultural objects, such as books, films, games, modes of dress and talk, and with the imagined community of people who share these practices. Such gendered identity work can provide safe spaces for many young people, particularly boys. Through the responses of others, it can supply them with intellectual validation as well as allowing them to opt out of specific social expectations. The nomadic asexual life of the mathematician Paul Erdos (described in Hoffman, 1999) provides an interesting, if extreme, example of these processes at work, as does the reaction to Jon Tickle, ex-resident of the 2003 UK Big Brother house. The latter escaped four eviction votes and was swept back into the house on a wave of public enthusiasm in week 8, through his use of this pattern of identity work and the way that the general public read this as signifying authenticity, originality, intelligence, and lack of emotionality (e.g. the fan website at http://www.rabid.oneuk.com/jonreunited.html). The Westerburg further mathematics group (studying for two A-levels in mathematics) contained a group of four boys who fitted this pattern, labelled the techies by one of their teachers. In one lesson I saw two members of this group pass the note, as seen in figure 1, round the classroom. This is striking in its difference from the notes that are normally passed around classrooms (Hey, 1997) and substantiates my argument that to understand nerd stereotypes we need to look at elements of both ascription and self-identification, that is at the work that these stereotypes do for those who construct their boundaries from without and from within (Bucholtz, 1999). Figure 1. Note passed around a Further Mathematics classroom  Thus, I finish Phils story by suggesting two further things this identity work does for him. First, his identification with mathematics enables him to appropriate a particular form of cultural capital. He does this in order to mark his distance from those he classifies as younger and less mature, as discussed above, and also from his ethnic and working-class self. Asked about his ethnicity Phil says he was born in this country, but his parents are from somewhere in Asia, China probably. He agrees that it would be OK to identify him as Chinese. I ask what his parents do for a living. He slurs the word takeaway, the place where his father works, and, when I ask him to repeat it, adds shop as a descriptor. Perhaps Phil, like many of the participants in Parkers (1995, p. 103) study of British Chinese identities, is using academic success in order to break away: The generation that arrived and grew up here in the last twenty-five years is increasingly viewing the [takeaway] counter as a hurdle to be leapt over as they work on it to secure their escape. Second, Phil has clear beliefs in the naturalness of differences between people. This is evident twice in the interview regarding differences in ability and in gender. He shows a very clear sense of his own and others abilities when he discusses collaborative work: if you have the same ability then its good to work with other people, but if you have people who are of a higher ability than you or lower, theyll either get frustrated or youll get frustrated. When I ask him about gender differences in subject choices, Phil says, I think girls and boys have different abilities naturally because the way we develop our brains is different with girls, in general being more verbal and boys more numerical. This is something that Phil shares with the other five participants in this study who strongly identified with mathematics in their interviews. This was evident in the way they too constructed the differences between maths people and non-maths people and between men and women as natural. This suggests that the epistemological certainty of mathematics may have consequences for how young people who strongly identify with it think about knowledge in other areas and that this may provide them with security. One question that I consider in the next and final section of this paper, on un-fixing gender and mathematics, is: what would happen to students that seem happy with the status quo if school mathematical practices were to change? Unfixing difference In this paper, I have been interested in the ways in which the categories of separation and connection operate within the gender and mathematics literature and how many researchers use these to make sense of their data. One focus has been to trouble the ways that this binary construction of relationships to mathematics, slipping into a binary construction of the subject itself, parallels the masculine/feminine opposition. I argued that this functions to fix gender difference as opposition and essence. Within this, it fixes separate mathematics as a space of pure reasoning which is aligned as masculine and which creates problems for girls and women engaging with the subject. Instead of fixing difference I want to unfix it. In this paper one question has been central to my strategy to unfix difference: For those who enjoy mathematics, what is invested in their identification with the subject? The two stories that I have used read young peoples pleasure in working with mathematics as a pleasure in working on their psychosocial-self-in-relation: % Analia works on her relationship with her father and takes pleasure in the certainty in this that she gets from mathematics. % Phil finds a security in mathematics that enables him to construct himself as intellectually mature and as distant from his working-class, minority-ethnic self. Thus, I have argued that what these young people get from mathematics are opportunities to develop relations with others and to re-make themselves. This strategy blurs the distinctions between separation and connection, and cognition and affect. So that, while the terms in each pair are not synonymous, they are also never separable. Theoretical work such as mine is often constructed as having little or even nothing to say to educational practitioners. I think this is wrong: But in order to recognise the effectivity that such investigations may have, it is necessary to discard the last vestiges of those nineteenth-century philosophical disputes between materialism and idealism. They have done much to constrain our ways of understanding of the materiality of ideas, and to recognise the embeddedness of thought in the most prosaic aspects of social and economic life. But if human being is always being thought and if human practices are inescapably made up in thought, then thought itself can and does play a role in contesting them. To diagnose the historicity of our contemporary ways for thinking and acting is to enhance their contestability, to point to the need for new experiments in thought which can imagine new ways in which we can be and act. (Rose, 1999, pp. 5859) That is, I hope this paper makes visible some of the unquestioned commonsense assumptions within the ways in which we think, learn, teach and live, and so enables new experiments in thought and new ways of acting. In this final section I illustrate the shape some such experiments could take through a focus on how the unfixing of difference re-enacts gender and mathematics. Gender difference within feminism is usually defined as being in opposition to equality. When thought in this way difference figures as womens specialness and as the foundation of feminist political struggle. It is this kind of difference that operates within the discourses on separate and connected ways of knowing in mathematics which I discussed above. As I argued there, this idea of difference has some usefulness for challenging assumptions about how mathematics must be done but it has a double face (Snitow, 1990, p. 14); explanations based in gender difference easily become self-perpetuating as they feed the binary regime they are attempting to overcome. How can my analyses offer a resource to re/think gender difference? First, they do not suggest abandoning gender difference as an analytic tool; this is a central feature of both stories. In Rose s terms these stories  diagnose the historicity of our contemporary ways for thinking and acting gender: % Analia s story demonstrates the tensions between doing mathematics, something discursively inscribed as masculine, and being female, and so invested in producing oneself as recognizably female (see the discussion in Mendick 2005b). % Phil s story demonstrates the way that some young people use discourses about mathematicians as heroes and geniuses, set apart from the rest of humanity in their masculine identity projects (see the discussion in Mendick 2005a). Stopping feminist research on gender differences is not going to eliminate cultural stories about them it is just going to restrict further the range of stories through which gender difference is understood. If progressive social theories ignore difference, there is the danger that peoples awareness of differences lends plausibility to those theories which do base themselves on difference, but explain it in ways which have more pernicious, because determinist, implications (Henriques, 1984, p. 89). So my argument has been that we need to examine how difference operates with/ in binaries in order to move to something else. My aim in telling the stories in this paper has not been to tell the truth about this studys participants. Although these stories are firmly grounded in my data, there are many alternative possible tellings; in particular there are tellings which foreground the ways that mathematical pleasures are classed and raced. My purpose has instead been to open up possibilities for multiple ways of being in the mathematics classroom. So in understanding what is happening when people are learning mathematics, we need to be sensitive to the variety of different things that different students may or may not be doing when they do mathematics and make space for the play of identities outside and beyond the traditional binary frameworks. I am not advocating a pedagogy of diversity. We need the notion of a pedagogy which is based on unequal, uneven, multiple and potentially antagonistic identities which do actually articulate in challenging ways, either positively or negatively, either in progressive or regressive ways, often conflictually, sometimes even incommensurably not some flowering of individual talents and capacities (Bhabha, 1990, p. 208, original emphasis). It is a pedagogy that refuses ideas of difference as fixed, essential and oppositional. Snitows (1990, p. 38) insightful discussion of how we occupy the category woman is useful here: From moment to moment we perform subtle psychological and social negotiations about just how gendered we choose to be. One can be recalled to woman anytime by things as terrible as rape, as trivial as a rude shout in the street but one can never stay inside woman because it keeps moving. We constantly find ourselves beyond its familiar cover. Our explanations and actions must keep the categories of boy and girl, man and woman moving within the play of difference within the classroom. Such a pedagogy has implications for how we conceptualize mathematical reason and so I end by saying something about that. I have argued that choosing, doing and enjoying mathematics can be usefully read psychoanalytically as work on the self. Of course, it is understood that identity work is not all people do when they do mathematics. They can also, for example: prove things about abstract algebraic structures, total the shopping bill, program computers, or pass examinations. My aim in relegating to the margins these normally centralized outcomes is to stress that these aims are never separate from other less logical ones and so to trouble a range of interlinked oppositions that give mathematics meaning. These include: Cognition/Affect. Rational/Emotional. Objective/Subjective. Abstract/Relational. Separate/Connected. Masculine/Feminine When we locate mathematics as rational, objective and abstract we are not impartially describing it. We are constructing historically and culturally specific versions of mathematics. These are hegemonic versions and ones that have inequitable effects. These are oppositions that maintain a distinction between separate and connected ways of doing mathematics and between the cognitive and the affective realms in mathematics learning and which fix difference within this binary framing. It is apparent from the stories in this paper that while the language students use to describe mathematical pleasures is understandably drawn from these dominant discursive repertoires, very different readings of that pleasure can be constructed when their interviews are taken as a whole and read psychoanalytically. By focusing on finding the emotional, the subjective and the relational in the actions of students who talk explicitly about being drawn to the objective, the rational and the abstract, in mathematics, I do not hope to switch halves in the above binaries but to move beyond them. This contributes to a re-figuring of mathematical reason expressed well by Povey (1995, p. 202): It is a reason which permits, for example, metaphoric thinking, that acknowledges that knowledge is contextual and not universal ; a reason that is interwoven with emotive thought rather than distanced from it; and, crucially, a reason that attempts to integrate personal knowledge with the knowledge of others. It recognises and embraces the need for negotiating shared meaning and for constructing argument in a multiplicity of ways, attempting to interrupt the objectification, the formality and combativity of Reason and helping one remain paradoxically aware of ones complicity in that which one critiques. This raises questions about what becomes of students, like Analia and Phil, who like the certainty and black and white-ness of mathematics, those who find safety in numbers. I am optimistic about how young people would respond to such changes. Although certainty is a facet of mathematics that appealed to many of the 43 participants in this study, most young people also told me that they appreciated the opportunities for discussion and group work in other subjects but felt these to be inappropriate in mathematics lessons. Even, Phil, one of a group of six boys who most strongly identified with the subject, told me that he liked the way in English you can sort of have some room to find your own opinion. He felt that this was not possible in mathematics you need to discuss stuff in English, but you cant really do a lot of discussion in maths. While initially he found the uncertainty of English, the way theres never a wrong or right answer, difficult, by the time I interviewed him at the end of the second term of the course he told me, Im more comfortable with it now because I can deal with it better, before I couldnt. 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