Mendick Only Connect: Troubling Oppositions in Gender and Mathematics

ONLY CONNECT: TROUBLING OPPOSITIONS IN GENDER AND MATHEMATICS

Heather Mendick

London Metropolitan University, UK

heathermendick(at)yahoo.co.uk>

This paper focuses on the ways in which many researchers working in the area of gender and mathematicsmake 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 versussubjective), operates to fix difference, and so to fix gender and mathematics within a structure ofbinary thinking that ultimately serves to re/produce gender inequalities. The aim is to suggest amore productive approach to understanding the continued gendering of participation in mathematics.This approach is based in deconstructing these oppositional patterns. This theoretical approachis 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 unfixingof 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 inwhich gender inequalities are re/produced. Discussions about the relationshipbetween the powerful role of mathematics and its male dominance have been part offeminist research and praxis in education in a range of countries since the start of thesecond 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 beenoffered for this ‘problem’; instead, I want to focus on an opposition that is frequentlyused by researchers to make sense of their data: the dichotomy between separate waysof relating to mathematics and connected ones. This binary troubles me and, throughthis paper, I hope it will come to trouble you. My argument, which has implicationsfor how to theorize gender equity beyond mathematics education, is that it fixesdifference within an oppositional structure and so fixes gender and fixes mathematics.These fixings, of the masculine in opposition to the feminine and of mathematicsaligned with the former, ironically serve to reinforce the gendered inequalities thatfeminist researchers set out to challenge.

I begin by examining and problematizing the categories of separation and connectionas they appear in the literature. I then explore what I maintain is a more productiveapproach to making sense of gender difference within mathematics. Instead of reinscribingthe binary of masculine/feminine and the location of mathematics withinthis, I disrupt and refuse its demands by deconstructing the separation/connectionbinary. Deconstructing this binary involves making visible the logic from which itderives its meaning, in particular the mutual dependence of both sides of the binaryand the power relationships implicated in it. Throughout, I use the verb trouble interchangeablywith the verb deconstruct for reasons that Davies (2000, p. 14, originalemphasis) expresses well:

Too many readers of deconstructive texts take deconstruction to mean a dismantling thatobliterates the binaries and the boundaries between them. Binaries are not so easilydismantled, and deconstructive work often can do no more than draw attention to thebinaries and the their constitutive force. For some people, in some readings, deconstructivework may facilitate a different take-up of meaning, beyond the binaries. But this doesnot undo the continuing force of relations of power that operate to hold the binaries inplace. I choose the word troubling to represent more closely what it is that deconstructivework can do.

I carry out this troubling/deconstruction by telling stories based on interviews withtwo young people, Analia and Phil. They are in their first year of post-16 optionalmathematics courses in England and both enjoy the subject. However, whileAnalia and Phil both talk about enjoying the separate — pure, objective andcognitive — pleasures of mathematics, I construct alternative stories, grounded inthe data, in which what they enjoy in doing mathematics is the identity work theydo through it. I use these stories to dispel the myths that the ‘cognitive’ is notalways already ‘affective’ and that ‘separate’ mathematics is all the things that itclaims to be: rational, abstract, objective. Further, these stories raise questionsabout the gendered impact of the processes through which mathematics must bemade to look separate by producing stories of it that exclude its Others: emotions,relations, subjectivities. In concluding, I explore the refiguring of difference withinmy 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 workof Gilligan (1993). Noting the absence of women from the research done byKohlberg (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 away seen by Kohlberg (1993, p. 26) as the highest ethical state, treating a moraldilemma as ‘sort of like a math problem with humans’ (Gilligan, 1993, p. 26). Shelabelled this an approach to moral reasoning based in ‘separation’, and contrastedit with the approach favoured by women based in ‘connection’; connected reasoningstarts from the relationships between people. So, for example, Amy is given thedilemma of whether Hans, whose wife is dying, should steal the drug he needs tosave her, but which he cannot afford. Instead of reasoning abstractly, as traditionalmoral philosophy demands, Amy searches for a solution based in relationships. Sherefuses to accept the problem as it is presented, asking whether Hans cannotpersuade 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 foundout, end up in prison, and leave his sick wife alone.

Belenky et al. (1986) described Women’s Ways of Knowing developing Gilligan’sdistinction between separation and connection beyond knowing about morality toknowing more generally. Their ideas of ‘separate’ and ‘connected’ knowing havethen been taken up within the mathematics education literature (e.g. Becker,1995; Boaler, 1998; Brew, 2001). The idea that girls and women seek connectionin mathematics and so respond better to collaborative and open-ended formsof learning and assessment is supported by work on alternate methods of teachingand 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 aseries of exercises and felt unable to pursue what Boaler terms their ‘quest forunderstanding’.

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 bebetter for us all, and for girls and women in particular, if we moved towards theconnected ones. While these have undoubtedly been valuable interventions, they arelimited. By aligning separate-ness with masculinity and connected-ness with femininity,these approaches feed the oppositional binary patterning of our thinking and, inthe 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 differencesbetween the genders.

Within education, providing access to girl-centred curriculum content, and methodsof teaching and assessment, different from the dominant knowledges and modesof 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 sodefine the conditions in which they operate. For example, while having separate boys’and girls’ versions of knowledge has been successful within marginal subjects, likephysical education and technology, this has not proved a success in high-status partsof 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 itsoriginators envisaged (Paechter, 2000). This response to the devaluation of the feminineby reclaiming those traits, values and understandings for the purposes of aseparate feminist education, does not challenge the oppositional division of the worldinto masculine and feminine. For:

The affirmation of the value and importance of ‘the feminine’ cannot of itself be expectedto shake the underlying normative structure, for, ironically, it will occur in a space alreadyprepared for it by the intellectual tradition it seeks to repudiate.(Lloyd, 1993, p. 105)

Relatedly, gender opposition easily becomes gender essence. Although all of thoseresearchers, whose work I have discussed above, pay more-or-less convincing lipserviceto the idea that separate and connected ways of reasoning are not tied to menand women in any necessary way, it is difficult to rescue these approaches from essentialism(for arguments on Gilligan’s work, see Faludi, 1992). Essentialism is oftenused to label those positions that are based in an understanding of difference asbiological. However, I follow Bohan (1997) in using gender essentialist to label thosepositions that locate gender within the individual, regardless of whether the essenceis seen as biological, social or anything else. I do this because of the slippage betweenthese positions. Differences slide from the social to the biological through a complexprocess, discussed in Henriques et al. (1984, p. 15), in which ‘the individual reducesinevitably to the biological in essence once its opposite number, the social, has beenposed to explain the rest’. This slide can be seen not only in Mars–Venus style selfhelpbooks, but also in Greer’s (1999) feminist best-seller, The Whole Woman. Greerargues that we must recognize women’s difference from men. In so doing, she distinguishesfemininity 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 howdifferences of class, race/ethnicity, sexuality and dis/ability intersect with each otherand with gender in complex ways and, in many social and educational contexts, aremore pertinent than gender differences. These cross-cuttings of dimensions ofinequality are drawn out in both Analia and Phil’s stories.

As well as fixing gender, separation/connection fixes mathematics. Separate andconnected ways of doing mathematics slide into separate and connected versions ofmathematics 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 separatemathematics, legitimates what it seeks to challenge. A similar process happens throughthe cognition/affect opposition. Work on affect in mathematics education takes a differentdomain from that of research on cognition; work on affect does not focus ‘on thedirect interaction of student or teacher with the mathematical object that characterizescognition studies’ (Cabral & Baldino, 2002, p. 170; for a survey of the research on affectin 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 actof cognition, stuff that would ideally be removed in order to facilitate learning, ratherthan 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 priorto the affective (by processes parallel to those through which the masculine/feminineopposition functions to maintain the biological as prior to the social). Further, it legitimatesthe collective refusal to view emotions and relations as central to the learningof mathematics and maintains the power relations that, as I have argued, underminefeminist interventions into pedagogy and assessment. Cabral and Baldino (Baldino &Cabral, 1998, 1999; Cabral & Baldino, 2002) use psychoanalysis to attack the kind ofprocesses which normally remain the domain of the cognitive and this is also centralto 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 experiencesof 43 young Londoners who chose to continue studying mathematics beyond the endof compulsory schooling (at 16). This study involved me in interviewing participantsonce, sometimes individually and other times with one or two friends, and in observingthem in their mathematics classes. Participants were spread across seven classesin three research sites, which I have called GraftonSchool, WesterburgCollege andSunnydaleCollege. In the interviews, I asked students to describe a typical mathematicslesson, about what they had enjoyed most and least about their classes, tocompare 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 thisempirical work it is not an empirical paper, instead I am using my readings of Analiaand Phil’s interview talk to do particular theoretical work, based in a specific way ofreading their choice of mathematics. Thus, it is the process by which I did thistheoretical work which I elaborate in this section (for an account of the empiricalmethodology, see Mendick, 2003a).

I see subject choice as being centrally about identity; it is a key site in which youngpeople produce themselves/are produced as part of an on-going lifelong project ofself. This identity work involves being positioned/positioning oneself within a rangeof discourses (Foucault, 1972) on mathematics, masculinity, femininity, educationand 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 preexistthe deed’ for ‘there is no gender identity behind the expressions of gender; thatidentity is performatively constituted by the very ‘expressions’ that are said to be itsresults’ (Butler, 1999, p. 33). Female-ness and male-ness are produced through reiterativeperformances, 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 mainargument: that our use of academic concepts is part of these reiterative performancesand so we need to be attentive to the ways in which we inscribe gender through ourconceptual categorizing.

These processes of identity work also involve psychic investments, desires, anxieties,defences, and fantasies. There are real tensions when combining Foucauldianwith psychoanalytic approaches. Notably, the former retain ‘a central discourse of auniversal human subject which is in opposition to discursive and narrativeapproaches’ refusal of interiority’ (Walkerdine, 2003, p. 248). However, psychoanalysisis a plural approach:

Psychoanalysis does not intend to uncover objective causes in reality so much as it seeksto change our very attitudes to that reality. This it achieves by effectively deconstructingthat positivist dichotomy in which fantasy is simply opposed to ‘reality’, as an epiphenomenon.Psychoanalysis dismantles such a ‘logic of the supplement’ to reveal the supposedlymarginal operations of fantasy at the centre of all our perceptions, beliefs andactions.(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. Walkerdineet al., 2001) and based in the commitment that ‘social and cultural analysis needs anunderstanding of emotional processes presented in a way which does not reduce thepsychic 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 transcriptsto construct narratives based on each interview. These narratives read the interviewtalk as performative in the ways discussed above. It is difficult to explain exactly howI went about this process but in order to orient my work I finish this section with onesuch thought experiment from the work of Pimm (1994). Pimm looks at unconsciouselements in learning mathematics by studying the metonymic/metaphoric associationsand slips that are ever present in mathematical discourse. These, often deniedlinks, add to ‘meaning’ in mathematics.

The looseness and gap between symbol and referent, regularly exploited for mathematicalends, 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 girlsworking on the period of a function can and do make overt connections with menstrualperiods. Adolescents can become preoccupied with freedom and constraints upon themselves,and geometry can offer them the possibility of working with the same material aswell 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 relatingto romantic dreams of never-ending love. This approach provides another route tocoming to understand doing mathematics as working on the self. It adds a furtherpsychic twist to the central theoretical engine of this paper that the choice to do mathematicsand the ways in which one engages with the subject can be read as ways inwhich people do identity work. The stories that follow are attempts to understandmathematical pleasure as the pleasure of engaging in the different kinds of genderedwork on their psychosocial-self-in-relation that happens through mathematics. It isworth noting that there is, of course, nothing special about Analia and Phil that makessuch readings possible, and I have done similar readings of other participants’accounts. What is important is the theoretical approach to the data rather than thedata themselves.

Analia’s story

Analia Kasersoze chooses her pseudonym to be a post-modern mixture of the exoticand popular culture (the surname belongs to the mythical underworld presence in thefilm The Usual Suspects; McQuarrie, 1995). She is a Turkish Cypriot and a Muslim‘but only up to a certain point, coz I don’t wear a headscarf and all that’. Her mumis a housewife and her dad a civil engineer and architect. At Westerburg she is studyingbiology, chemistry, history and mathematics.

In her interview talk and in my observations of her, Analia appears determined andhighly motivated. Her motto is: ‘if you fail to prepare then prepare to fail’. At the startof 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, whetheryou 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 it’s coming up to exams: “now or never”. I pinit up right in front of my desk: “now or never”. So you gonna do it now, or you gonnafail? … You know, if something’s gotta be done, you’ve gotta do it’. Analia works hardand, 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. …Homework’s 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!” … Youprove yourself, don’t you? That’s good. I enjoy that’. Given the status of mathematicsas a proof of self (Mendick 2003b, 2005b) it is not surprising that the subject iscentral to Analia’s intellectual identity project.