Abstract
Much of the literature on maths and gender takes either maths or gender, or both, as given. I use the work of R W Connell to argue that frameworks for describing and accounting for gender relations - particularly sex-role theory and categoricalism - have weaknesses as well as strengths. I adapt a framework developed by Connell for analysing gender relations within a theory of practice, and suggest that it can also be a useful tool for understanding mathematics as practice. I conclude by indicating how, after employing the feminist methodology of memory-work to collect data, I used the framework to analyse the mathematical practices of a group of women.

 
Much of the literature on maths and gender takes either maths or gender, or both, as given, unquestionable, categories. I want to consider here a framework for describing and accounting for both gender and mathematics that does not make this assumption, seeing them instead as historically constructed, changing and changeable, practices.

 
GENDER: given or made?

There has been a vast array of social analyses of gender in the literature of the last two or three decades, and a number of ways of categorising them. It is my intention here, not to explore these analyses and their logics very deeply, but to indicate my position in relation to this array, using Connell's approach as my basic framework. Two distinctions that I would like to follow up are:

Sex role theory is very prevalent in the literature on maths and gender and clearly has contributed insights into the relationship between the two. Most of the many different versions of sex-role theory have in common: a distinction between the person and her position; a set of actions belonging to the position - in keeping with the metaphor, an actor and a script; and accompanying expectations and sanctions from others. Role theory is an important shift away from biological to social explanation, and sees individuals in relation to social structures - although in the end these structures depend in fact on a biological dichotomy. Because sex role theory focuses on norms and gives explanatory priority to will, choice and attitudes, avoiding questions of power and social interest, it has no way of understanding the historicity of gender and is limited in what it can offer.

Categorical theory enables more attention to be given to power, to social institutions and social structures. In such theories, the social order is seen in terms of a few major categories - often only two - that are related by power and interests; the focus of the argument is on the whole category, rather than its particular members or how it is made up; and there is a close identification of opposed interests with specific groups of people.

Gender as social practice

Valuing both categoricalism's recognition of power, and the 'practical politics' of daily life, Connell calls for a theory of practice that would help us get a 'grip on the interweaving of personal life and social structure' (Connell 1987: 61). Work by Juliet Mitchell, Adrienne Rich, Jill Matthews and David Fernbach are cited as examples of studies that use such a framework for analysis. Practice, says Connell, is 'what people do by way of constituting the social relations they live in' (Connell 1987: 62), and he sees human action as involving 'free invention (if "invention within limits", to use Bourdieu's phrase)' (Connell 1987: 95). Such a position presupposes both the person as agent, and the existence of structure. Practice is specific, historical and constrained by structure. Connell argues that to describe the constraints of the particular situation to which the active individual responds is to describe structure:

Such a theory of practice would seek to avoid categoricalism, and so would be interested in differences within categories as well as between. It would try to locate these differences historically. It would ask how differently gendered practices of moral judgement, of knowing and thinking, had grown out of differently gendered experience, and how they had been structured by power and labour relations, by emotional signification and symbolization. From such a position, the 'givenness' of gender would melt into thin air and 'practical politics' would become possible (Connell 1987: 62). From such a position, we would be able to generate 'partial perspectives' of the complexity of gender construction, gender movement and gender relations (Haraway 1991).

Feminist writers have suggested other frameworks for the analysis of gendered practice. Sandra Harding, for instance, conceptualizes gender as 'individual, structural and symbolic - and always asymmetric' (Harding 1986: 52). Donna Haraway in supporting this view of gender, suggests that science as well as gender could be usefully analysed using Harding's three dimensions - as 'gender symbolism, the social-sexual division of labour and the processes of constructing individual gendered identity' (Haraway 1991: 250). Haraway however adds two extra dimensions of her own - material culture, and the 'dialectic of construction and discovery'. Joan Scott (1988: 42) conceives of gender as both a 'constitutive element of social relationships' and a 'primary way of signifying relationships of power'. The former is based on perceived differences between the sexes and involves four main elements: cultural symbols, subjective identity, normative concepts, and social organisations and politics.

These proposals overlap to a greater or lesser extent with each other and with Connell's elaborated framework (1996b), which allows a systematic view of questions that could be asked about the interplay between different levels of practice and different structures. Gender studies suggest that four structures currently play an important part in influencing practice: power relations, production and consumption, symbolization and emotional commitment or cathexis (Connell 1996a: 10). Connell suggests that practice can be explored at different levels: the level of personality, social relations or institution. He proposes a simple grid which cross-classifies structure by level as a way of systematically assessing the dynamics of change in gender relations; a parallel grid might also be useful in setting up an overview of other questions about gender - for example, its relationship to science - or mathematics.

 
MATHS: given or made?

Doing mathematics, learning mathematics, teaching mathematics, teaching teachers how to teach mathematics - pervading all these situations has been for many of us the image of mathematics as given, fixed, to be passively received and unquestioningly transmitted. How have such 'truths' come to be accepted? What effects do they have? These would be fascinating threads to unravel, but for the moment I want to explore an alternative possibility: that mathematical practice is constructed, by active people, that it is structurally connected with other practices and involved in the constitution of social interests.

This is not an idea that has come easily - in relation to maths. In relation to almost any other field it became increasingly clear to me over years of learning and teaching that knowledge was contextual, made by people and implicated in relations of power. The realisation of how this is true also of mathematics is a relatively recent achievement.

I have mentioned above Haraway's suggestion that Harding's framework ('individual, structural and symbolic') would be useful for exploring science as well as gender. A parallel proposal is that of adapting Connell's framework to explore mathematics. To do this is to ask how mathematical practice - its discourses, its institutions, its ideologies, its social relations and its practitioners - is 'organised as a going concern' (Connell 1987: 62). It is to work from the assumption that social structures, in maths as elsewhere, are not given but historically constituted, with the concomitant possibility that there might be more than one mathematics, more than one mathematical practice. To explore practice properly would involve looking at not just what maths is done, and what Connell calls its 'historicity', but the institutions within which it is practised, the ideology that informs it, the discourses it produces and is produced by, the way it shapes its practitioners and how they relate to one another.
 

Maths as a social practice: towards a systematic analysis

Using the methodology of memory work (Haug 1987), I have begun to explore the idea that mathematical practice is actively constructed and to examine how the mathematisation of the everyday world constructs us and how we construct or resist it.

I was one of a group of women involved in this exploration. We found that much of our mathematical experience had been of a dominating practice that alienated us from our own knowledge and the everyday world, separating mind, body and emotion, and prioritising abstraction and generalisation over meaning. Understanding both maths and gender as practice, however, allows us to see them as produced by humans, in specific historical circumstances, and therefore as able to be different from the constellation of arrangements at any particular moment. These hegemonic practices are therefore not the only ones possible; the work that is required to maintain them, in fact, demonstrates the degree to which they can be seen as denials of alternative experiences.

In order to demonstrate how Connell’s suggested grid (1996: 7) can be used to systematically document practice, I will indicate how I used it to analyse one dimension - the structure of power - of the dominating practice that we experienced. The other dimensions can be similarly analysed.

It is important to remember in using the grid that the categories are not discrete, that overlap occurs between structures - for instance between symbolization and power - and that, for instance, most social relations take place within institutions. The grid is simply a tool that allows us to obtain an overview of important issues in a particular field of practice, recognizing the different structures that affect that practice, and the different levels of social reality at which it is manifested. It also allows us to identify which areas have been well served and which ignored by research.

 

LEVEL OF PRACTICE
		personality	interaction	institutions
	power	capacities for power	practices of dominance	distribution of rights, office and influence
structure	labour	capacities for labour	work relations	distribution of income, systems of ownership
	symboliz- ation	capacities for meaning	social relations generating meaning	public & organizational representations
	cathexis	capacities for emotion	social relations enacting emotion	maths as truth

 

For example, power

Alison, Colleen, Kath, Louise, Maggie, Marie, Sophie, and Viv, mentioned below, were eight of the fourteen women involved in the memory-work study.

Capacities for power concern here the ability to participate in the decision-making processes of a democratic society as numerate citizens. Kath and Colleen illustrated different sides of our inadequate preparation: Kath in a mathematically refined but socially naive understanding of the process of cost benefit analysis, Colleen in a mathematically inept, but socially critical response to the teacher-student ratio ‘formula’.

Practices of dominance abounded, in control through measurement - the pressure of time in exams, in school, at home, at work; through language - a chain of meaning linking wrong with error with sin; through physical class arrangements - Maggie was shifted from the back of the room with the ‘good’ ones, to the middle with the ones who were not clever; through inclusion and exclusion - Viv was not one of the chosen few; and through humiliation and a veiled threat of force in Marie’s encounter with a teaching nun, Sister Peter. Teachers and fathers were prominent actors in these dramas; in particular, the measurers in our stories were men.

The distribution of what Viv called educational ’goodies’ often uses mathematics itself as a filter, and almost always uses some form of quantification. The power of number, in both these senses, was clear in Louise’s struggles as a teacher, around the entrance exam for the selective High School where she taught. Measurement - of time, of ability, of worth - was an organising and often violent strategy permeating our lives. We had been categorised, compared and measured from such an early age that measurement had become our normality: cost benefit analyses, student-staff ratios, merit, accountability, selection, productivity, disability were just a few of the contexts in which it emerged.

It could be argued, as Sophie and others did, that to be a success in maths as we knew it you had to be satisfied with a 'thin' maths, a maths that was stripped of context, of layers of meaning - of critique, of history, of everyday use; a maths that separated mind from body, proof from intuition, ourselves from our own knowledge, symbol from sense.
 

Other stories, other practices

To stop at that point, however, would be to deny the very theory of practice that I want to use. It would be to suggest that the only active parts we played, our only inventions, were those of complicit partners in a hegemonic drama, reading scripts we had been given. But Kath, agreeing with Sophie about what was missing in maths, continued:

And of course there are other stories, less visible at first and not so easily told, of practices that contest the dominant tales. They are often stories we had to invent words for, or stories that we apologised for as being irrelevant or embarrassing. Within the constraints of specific situations we and others did do things differently, we acted to weave different relations with others, we invented different lives.

In relation to structures of power, for example, Alison told how her experiences with ‘arbitrary’ teachers and their ‘incompetent labelling’ had helped her distance herself, making the relation with the teacher less powerful. Louise was able to use the memory-work group itself as a platform not only for exploring issues about gender equity at her school, but also for intervening actively in the struggle to change the system.
 

Conclusion

The theory of practice outlined here offers an alternative both to an ahistorical role theory, with its explanatory preference for norms, choice and attitude, and to a categorical theory, which acknowledges power but leaves out ‘practical politics’ and the concern with difference within categories. A theory of practice is eager to explore those very differences, to understand how people ‘invent’ their lives - gendered or mathematical - within the constraints of specific, historical, social structures. It is keen to tease out the implication that different constraints and interests could result in different organisations of practice. Like the method of memory-work that I used in my study of practice, it fosters possibilities for action and change.

 
References