There is a battle 'for truth', or at least 'around truth' - it being understood ... that by truth I do not mean 'the ensemble of truths which are to be discovered and accepted' , but rather 'the ensemble of rules according to which the true and the false are separated and specific effects of power attached to the true' , it being understood also that it's not a matter of a battle 'on behalf of the truth, but of a battle about the status of truth and the economic and political role it plays. (Foucault, 1 980, p 1 32)
Introduction
The history of genderl and mathematics, like the broader educational research history, has been written as an instantiation of traditional research models. What follows in this chapter is yet another history. However its orientation is not couched within the traditional logic of the field. It writes against the waves of other more conventional historical trajectories, but this is not to suggest that there is some presumption on my part that it constitutes a better, more exact history. To suggest this would be to commit modernity' s mistake and interpret a different way of writing educational history as the latest in a progressive and refined 'state of the art' in a succession of disciplinary truths. To do so would fail to acknowledge the origins and purposes of such other histories, for, as I endeavour to show in the following chapter, no discourse can claim higher status or provide better truths than another, without regard to the issues of economy, of structure, of institutional politics and of temporality.
It is a different concern from traditional or revisionist literature reviews that motivates and is expressed in this account of gender and mathematics: a concern for an alternative method for an alternative purpose of inquiry, in general, and an explanatory evidence of how the girl in school mathematics has been constituted in the published academic discourse, in particular. My intent is to trace and analyse the development of ideas, the rules and relations of the discursive trajectories about the girl in school mathematics as these have been constructed and subsequently mapped in scholarly discourses over a five decade period. This necessitates locating the disciplinary sites and junctures at which the discourse on gender and mathematics has been formed and reformed. By considering the In the preceding chapter, I suggested that the practice of equating gender with sexual difference has become something of a liability. I proposed that gender is more usefully understood as an aspect of social organisation. However, the word 'gender' is used in the mathematics education literature interchangeably with the word 'sex ' . That being the case, in this chapter I use the words 'sex' and 'gender' , precisely as they are used in a particular piece of research.
Paradox, Partiality and Promise Constructing the Girl
conditions which produced the various strands of knowledge of the girl in school mathematics I hope to demonstrate the inseparability of 'truths' about girls in mathematics from the very conditions of their emergence and their development. I attempt to do this by outlining how epistemological, sociocultural, political and institutional rules converged historically to enable and constrain the production, authorisation, and legitimation of scientific knowledge about girls in school mathematics.
The text proceeds chronologically as far as possible in order that conceptual, theoretical and methodological transformations can be identified. The material was sourced utilising the following criteria and research procedure. I began with the 'ensemble of truths' manifest in books, overviews of the field, handbooks, and articles, rendered as official knowledge (Apple, 1 993) of girls in school mathematics. The final intent was not to produce an exhaustive history of all that has been said and written about the way in which girls have been constituted by mathematics education in its published academic discourse. This unfolded during the process as a daunting and inevitably impossible task. Sources, of neccessity, became selective with a particular aim paramount: to map those constitutions that are considered as authoritative in that they are regularly articulated and referenced2. My starting point was the recent research of the past decade and from these texts I traced references to the preceding three decades. A computer search of the literature was also conducted to complement the research generated through the citation network. Both these sources - the citation network and the computer database - together with my subsequent reconstruction of them both, must be considered as discourse-specific rule systems upon which I make my claims about girls in school mathematics. That is, these sources which I have selected to legitimate my knowledge claims, can only ever be seen as merely partial. My hope is that in laying bare the construction of knowledge about the girl in school mathematics as it is ritualised and manifested in academic knowledge exchange, we can be better placed to locate these girls as we proceed towards the twenty first century.
Within the gaze of the Politics of the Women's Movement
Intensive interest in research and scholarship in the field of gender and mathematics in Western cultures emerged at a particular historical moment of social and political unease. There are two aspects that contribute to this historical moment: the question of scientific leadership and economic security, and the question of women' s representation. The question of leadership and security manifests itself in the sense of emergency that
2 For comprehensive bibliographies of easily accessible and published work in the field of gender and mathematics, see, among others, the reviews provided by Fennema and Leder, 1 990; Forgasz, 1994;
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pervaded the American public and fIltered into New Zealand society, following the launch of Sputnik in 1 957. Faithful to Descartes' legacy, mathematics and science education came to be seen as a 'political panacea' , a major instrument of economic and social policy for achieving national objectives, regulating contemporary technoscience and commerce (Rotman, 1 993). Such investments in school mathematics were reflected in the status it assumed, both within the community and within schools themselves. In New Zealand, as in other Western industrialised societies, qualifications became highly valued and progression and access to further education, employment, and higher status jobs often became dependent upon mathematical success (Pitman, 1 989). Moreover, mathematics came to absorb a large proportion of the resources of every Western education system - resources of fmance, of teachers, and of time. As Apple ( 1995) has noted, the importance invested in school mathematics still perpetuates as Western societies confront crises in the nature of work and the structure of employment, economic recessions and technological change.
Concern for scientific leadership and economic security before too long came to be enmeshed in the much wider social and cultural crisis of the late 1 960s. This was an era of 'decentred' social experiences, of emergent political groups with increasingly divergent ideas and demands concerning justice, equality, social legislation, of decline in public confidence of the state, of changes in the structure of the economy, the family, and of the declining authority of previously powerful social institutions. It is in this era that renewed feminist politics were made possible and the representation of women became a key issue for feminist cultural politics. Constituted by and in the breakdown of widely shared categories of social meaning and explanation, feminist movements began by probing the gendered nature of housework (Friedan, 1 963) and extended the scope of their vigilance to encompass more and more aspects of social and economic life. One of these sites was the school.
Although the relationship of gender to learning had been explored historically and theorised extensively, secon� wave feminists, as they came to be called, sought to undermine prevailing ideas regarding the possibilities for the education of women. Within a few years feminist interest in gender and schooling, both in New Zealand and further abroad, had left permanent marks on the face of education. In short, education came to be
perceived as an object of demand, as a means of employment, as a source of ideas, and as a site of struggle for broader social change. It was in this social milieu that research interest on gender and mathematics developed. Subsequently, between and within existing discourses, a distinct, identifiable field of study, gender and mathematics, emerged, and girls in school mathematics were constituted for the first time as a distinct group for whom separate research questions were to be formulated. This field of inquiry
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was founded upon the conjunction of the dominant disciplinary knowledges current at the time, together with established scientific 'truths' about pedagogical subject positionings.
The Girl as Constructed within the Psycho-social Discourse
Setting out gender research in mathematics in this way, is to see its emergence as in part the product of intense social change in countries that previously had conceived of themselves, and of the teaching and learning of mathematics, in genderless terms. But its story unfolds not only through its entanglement with this unique set of social conditions but also with the theoretical movements of the era and the purposes which they presuppose. What is the distinguishing feature of most of the early gender work is its vision to develop in all students, girls and boys, the universal power of reason: a power which would empower them collectively to create a better form of social life.
Nye ( 1990) claims that for generations, philosophical and scholarly discussion on what is distinctive about the life of women pointed to the idea that what is true or reasonable for men might not be at all so for women and girls. Proceeding from the premises of biological determinism3, the position that women' s inferior biology was advanced to render her inferior mentally and spiritually (Agonito, 1 977). This position had received a very clear expression in New Zealand during the first half of the twentieth century through the publicised work of Sir Truby King, the founder of the Plunket Society for the care and protection of women and children. Further afield, researchers used various (and often spurious) means to locate the origin of differences within the human body. In this respect Leder ( 1 992) notes the work in 1 9 1 5 of both Morrison and Thomas, and also makes mention of a certain Harvard (USA) physiologist, Dr Edward H. Clarke, in the 1 870s who claimed that the learning of algebra was harmful to the development of the reproductive organs.
Much of early reported research in the 1 960s was founded on sexual relativism and reflected on the priorities of mathematical life for students and on the 'proper' relations between the status of the knower and his or her sex (Agonito, 1 977). An early study reported in the "Journal of Educational Psychology" in 1 958 was more concerned about establishing a reasonable mathematical character for girls than it was in entering into any philosophical debate about the criteria of truth. This study by Sommer ( 1 958) made a comparison between women' s and men's ability to recall quantitative information from 3 Biological determinists argue that inequities in the social order are the natural and accurate
reflections of inherent biological differences. For an interesting discussion of the evolution of biological determinism, see Stephen Jay Gould's historical analysis of the science of differences, 'The mismeasure of man" (198 1), New York: W.W. Norton.
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within a paragraph. The results argued on the one hand for women's lesser capacity for recall. On the other hand, these same women demonstrated comparable ability in recalling decontextualised numbers of six or seven digits. In his conclusion, contrary to what his results suggested, Sommer argued that this may be an indication that many women are unable to retain large numbers (thousands or millions) (p I 9 1). Sommer' s study is noted here for it directs attention towards an awareness of the political 'uninnocence' of the history of the discourse on mathematics and girls. His piece of gender research, like many others conducted in the 1950s and 1 960s (see for example, Northby, 1958; and Charles & Pritchard, 1 959) begins in the understanding of the schoolgirl as mathematically deficient, and constructs knowledge of her around that inferiority.
The production of 'facts' and 'truths' about girls' inferiority in school mathematics was duly established. In 1 974, these 'self-evident' truths were to be made problematic when Fennema steered theoretical and methodological practice away from a reliance on biological determinism towards an epistemological stance which viewed mathematical practice in terms of quantifiable, observable behaviours. This new direction was seen to ensure the kind of rigorous analysis required by the gender-mathematics problem and was made possible by a particular set of knowledges about the girl in mathematics. The 1960s and early 1 970s had seen the development of an extensive literature, devoted predominantly to examining girls' supposed lesser inherent ability in mathematics (for example, Poffenberger and Norton, 1 959; Riffenburgh, 1960; and Stinson and Morrison, 1 959). Within this discursive framework research had reported, as Leder, Forgasz and Solar ( 1 996) note, primarily on differences in the learning of mathematics. What Fennema was able to introduce into the field in the mid- 1 970s was a greater scepticism about prevailing beliefs regarding the nature, extent, foundations and implications of gender differences. However a preoccupation with conflating mathematical ability with the body did not cease abruptly, since, as Longino ( 1 990) has noted, the body continues to be a source of models and metaphors for current everyday thought.
In the 1 974 publication of her jnfluential paper Mathematics Learning and the Sexes: A Review in the "Journal for Research in Mathematics Education" Fennema not only clearly revealed that most studies conducted after 1 960 did not clearly establish the existence of differences between the sexes, but perhaps more importantly, were problematic in the way in which they arrived at their conclusions. These assertions could lay claims to referential status through the original journal in which they was published. Fennema herself became widely cited in the academic discourse following her publication. As such her work counts as part of the authoritative discourse on gender and mathematics, and the orientation which emerged from it is situated within what is commonly known as classic scientific research.
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In her reinvestigations Fennema and her research colleagues queried generally accepted answers regarding both the nature and direction of gender differences research. This body of work inspired Wise, Steel, and Macdonald in 1 979 to reexamine the conclusion derived from the data collected earlier in 1959 and 1 960 in the research known as Project TALENT, a large-scale testing effort designed, with scientific leadership and security in mind, to identify talented high school students. The researchers were able to show that all of the differences attributed to gender in the original analysis disappeared when the number of mathematics courses taken was controlled.
Later in 1 990, Hyde, Fennema, and Lamon resurveyed the research on achievement provided by 100 studies which had investigated quantitative ability through analysing computational skills, mathematical conceptual understanding, and problem solving. Their meta analysis attempts to unify a set of studies under one conceptual umbrella, aimed at discursive self-defmition for work in the field. Drawing upon the standard approaches of positivist research, Hyde, Fennema, and Lamon reported differences between male and female mean scores of standardised tests and their effects across varying contexts. Previously, test data available from the United States, viz., the SAT -ability test, the National Assessment of Educational Progress (NAEP), the Differential Aptitude Test (DAT) national norming groups, and the Preliminary Scholastic Aptitude test Mathematics (PSAT-M), had all revealed a decline in gender differences in quantitative tasks (Dossey, Mullis, Lindquist, & Chambers, 1988; Feingold, 1 988).
The conclusion of Hyde, Fennema, and Lamon ( 1990) argues that there is a performance difference between the sexes for computational procedures and conceptual understanding. Females up to the age of 1 5 perform better on computation, and perform equally well as males after that age. Differences in conceptual understanding are insignificant whilst males show a small advantage at problem solving. Males outperform females on applications of mathematics to measurement, sports and science, while females perform better than males on applications to aesthetics, interpersonal relationships, and traditionally female tasks, such as typing and sewing. However they note that where differences do exist they generally emerge within specialist selective groups of students. This makes any generalisation to the whole population highly suspect. They also note that the SAT -ability instrument, contains inherent gender factors, which leads to heterogenous gender differences across test questions (Burton & Lewis, 1988; Chipman, 1 988; McCarthy, 1 976; Meehan, 1 984). Leder, in 1 992, also added caution. She argued that differences are dependent on the content, format and cognitive level of the test administered, the student's age and achievement level, and whether the results are drawn
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Quantitative ability was not the only measure under investigation. In their 1 974 landmark analysis Maccoby and Jacklin had reported that gender differences existed for verbal ability and spatial ability, in addition to quantitative ability. Spatial ability thus became a valid research focus for the measurement of mathematics performance. The various research programmes of performances on quantitative or spatial tasks which have looked for differences in performance in mathematics rest on a unique set of assumptions which presuppose that sex-linked differences do indeed occur, and that a positive correlation equates to causation. They then look to spatial ability or computational skills or conceptual understanding to support the assumption. Many researchers have found this notion compelling, assuming that there are indeed differences in aptitudes between boys and girls that have innate causes. What this body of work attempts to do is isolate the nature of these differences, targeting spatial and quantitative ability as two distinct dimensions of these differences.
Spatial ability studies look at the process of assimilitating spatially presented material through a field of activities spanning such diverse tasks as locating a single figure within a complex figure to mentally rotating an object as rapidly as possible. The justification for measuring spatial visualisation is based on its apparent logical relationship with mathematics. The Fennema-Sherman studies investigated spatial ability over a three-year period in collaboration with Lindsay Tartre (Fennema & Tartre, 1985). Earlier Maccoby & Jacklin ( 1 974), among others, had noticed differences between females and males in spatial skills, particularly spatial visualisation or the ability to visualise movements of geometric figures in the mind. In their conclusions Fennema & Tarte reported a positive