Equity In Mathematics Education

Influences Of Feminism And Culture

Gabriele Kaiser, Pat Rogers

• Publisher: Routledge
• Year: 2005
• Print ISBN: 9781138180482
• eBook ISBN: 9781135718916
• Topic: Education
• Subtopic: Education General

This text provides a critical overview of current thinking about equity issues in the teaching and learning of mathematics. Grounded in feminist theories of curriculum change and a broad range of cultural perspectives, the new approaches described here go beyond "special programmes" and "experimental treatments" designed to correct perceived problems and deficits. Instead they establish how improved instructional practices and a fuller understanding of the nature of the mathematical enterprise can overcome the systemic obstacles that have thwarted women's participation in this important field.; This book will appeal to all those who are interested in the mathematical education of women, including teachers, parents, administrators and researchers.

Chapter 1

Introduction: Equity in Mathematics Education

Gabriele Kaiser and Pat Rogers

Research and intervention over the past three decades have greatly increased our understanding of the relationship between gender and participation in mathematics education. Research, most of it quantitative, has taught us that gender differences in mathematics achievement and participation are not due to biology, but to complex interactions among social and cultural factors, societal expectations, personal belief systems and confidence levels. Intervention to alter the impact of these interactions has proved successful, at least in the short term. Typically, interventions sought to remedy perceived ‘deficits’ in women’s attitudes and/or aptitudes in mathematics by means of ‘special programmes’ and ‘experimental treatments’. But recent advances in scholarship regarding the teaching and learning of mathematics have brought new insights. Current research, profoundly influenced by feminist thought and methods of enquiry, has established how a fuller understanding of the nature of mathematics as a discipline, and different, more inclusive instructional practices can remove traditional obstacles that have thwarted the success of women in this important field. Some argue that practices arising out of contemporary analysis will improve the study of mathematics for all students, male and female alike.

This book provides teachers, educators and other interested readers with an overview of the most recent developments and changes in the field of gender and mathematics education. Many of the chapters in this volume arose out of sessions on ‘Gender and Mathematics Education’ organized by the editors for IOWME (International Organization for Women and Mathematics Education) as part of ICME-7 (the Seventh International Congress on Mathematical Education) held in Quebec City, Canada in August 1992. We are fortunate to have in one volume the perspectives of internationally renowned researchers and practitioners from all over the world, and from a variety of ethnic and cultural backgrounds.

However, the book does more than provide a review of current thinking in the area for we have grounded our overview in a model for understanding how change occurs. This model, developed by Peggy McIntosh (1983), arose out of an examination of the evolution of efforts in North America to loosen curriculum from a male-dominated, Eurocentric world view and to evolve a more inclusive curriculum to which all may have access. We acknowledge the danger and the difficulties inherent in attempting to classify anything into what might be narrow or restrictive categories. Nonetheless, we believe that applying this model to mathematics education provides new insight and guidance for future endeavours. Using the model as a lens for examining attempts to change the relationship between gender and mathematics education, we are able to discern and question underlying assumptions, to appreciate where we have been and to understand how certain feminist theories and cultural influences have affected and transformed our practical efforts to implement changes suggested by the research. We are then able to ask the important questions: where are we heading and to what end?

In this introductory chapter, we describe the McIntosh model and locate work in the area of gender reform of mathematics education in phases of her model (for an earlier application of the McIntosh model to mathematics education, see Countryman, 1992). In terms of the McIntosh model, we are in a transitional stage, between Phase Three (seeing women as victims or as problems in mathematics) and Phase Four (seeing women as central to the development of mathematics). This book is organized to lead the reader through this transition; as well it presents some critical perspectives and insight from researchers in developing countries which broaden and enrich the discussion.

Understanding Curriculum Reform

According to Peggy McIntosh, her typology of interactive phases of personal and curricular revision derive from her work in helping ‘traditionally trained white faculty members to bring into the liberal arts curriculum new materials and perspectives from women’s studies’ (McIntosh, 1989). The model comprises five stages of awareness which, according to McIntosh, are patterns of realization or frames of mind which occur in succession as individual scholars re-examine the assumptions and grounding of their discipline and enlarge their understanding of the field. For example, in the field of history,

[t]raditionally trained white…[historians]…were likely to move from thinking and teaching in Phase One: Womanless History, to Phase Two: Women in History. Then followed an expansion into Women as a Problem, Anomaly, Absence or Victim in History. All of these are, or can be, conceptually male-centred. I identify as Phase Four the far more daring Women’s Lives As History and looked toward Phase Five: History Redefined and Reconstructed to Include Us All. (McIntosh, 1989)

The issue for the authors of the chapters in this book is how to reform mathematics education to ‘include us all’, or more specifically, to include a greater proportion of women. Efforts in the west to achieve gender balance in mathematics education have derived from the essentially monocultural view that a certain measure of familiarity and competence with mathematics is important to every individual’s future growth and economical survival. According to McIntosh (1989), those who ‘think monoculturally about others, often imagine…that others’ lives must be constituted of “issues” or “problems”…’. Thus, in attempting to change a perceived gender imbalance in mathematics participation, we have tended to see women who do not embrace mathematics as deprived, as having ‘a problem’ which we need to fix. When we enlarge the scope of our reform efforts, another danger of monocultural thinking is evident when we blindly apply methods that have been successful in one culture or one ethnic group to another without any, or at best with only minimal, adaptation to local needs and circumstances (see in particular, Chapter 14 by Saleha Naghmi Habibullah, for a spirited attack of this view).

Applying McIntosh’s model to mathematics, we discern five phases, which we name (adapted from Countryman, 1992, p. 84):

• Phase One: Womanless mathematics;
• Phase Two: Women in mathematics;
• Phase Three: Women as a problem in mathematics;
• Phase Four: Women as central to mathematics; and
• Phase Five: Mathematics reconstructed.

This book is organized according to these phases. In this introductory chapter we draw extensively on McIntosh (1989) to describe the first three (essentially monocultural) phases of the model in the context of reform in mathematics education. However, we should warn the reader, as does McIntosh herself, that these phases do not always occur in the succession given here. Individuals may weave back and forth between and among the phases. Part 1 provides an overview of approaches to gender reform of mathematics education which challenge the monocultural assumptions and deficit philosophy of Phase Three and by virtue of their debt to feminist influences exhibit qualities which place them somewhere in the transition between Phase Three and Four. It is also important to remember that the McIntosh model has grown out of a North American perspective. The situation may be very different in other countries and in particular in the developing world, an issue which is raised in Part 2 of the book. Furthermore, not all western countries are currently at the same stage of awareness of the issues. For example, scholars in Germany and Sweden began to work in this area only in the late 1980s (see, for example, Kaiser-Messmer, 1994 and Grevholm, this volume, Chapter 6), while work in England, Australia and North America has been in progress for over two decades. The chapters in Part 3 describe recent advances in developing a Phase Four approach to mathematics education, one in which women’s experience is central to the discipline and to its pedagogy. The chapter we have used as our epilogue allows us to imagine where we will be when our work is done.

The Early Phases of Gender Reform in Mathematics Education

Phase One: Womenless Mathematics

When the editors of this book were in secondary school, it was unusual for women to specialize in mathematics beyond the compulsory years of schooling, even rarer for them to go on to university to study mathematics. None of the theorems listed in our mathematics textbooks were named after women, or if they were, this fact was not made apparent to us. The language of instruction was unselfconsciously male, examples dealt with male experience. One of us, Rogers, developed a habit of personifying mathematical objects and was not even aware that she did so until years later when one of her students pointed out that she referred to mathematical terms and objects exclusively as ‘him’ or ‘he’. Before leaving school to enrol in a prestigious university to study mathematics, she did not think it incongruous that the book prize she received for excellence in mathematics was entitled Men of Mathematics (Bell, 1937). Mathematics was what men did. We learned that women had not been necessary to the development of mathematics, and were unlikely to be essential to its future development. In this phase, many women who nevertheless pursue mathematics experience silence and exclusion, a feeling that ‘this is not about me’, a feeling not unlike the first stage of knowing described by Belenky et al. (1986) and discussed by Becker in Chapter 20.

Phase Two: Women in Mathematics

This phase in mathematics education reform began in North America in the 1970s when scholars began to investigate the lives and works of the few exceptional women throughout history who had been successful in mathematics, for example, Hypatia, Sonya Kovalevskya, and Emmy Noether. Although this phase challenges the allmale face of success in mathematics, it presents no challenge to the terms of success. Despite its roots in early North African civilizations, ‘Mathematics remains what white men do, along with a few token women’ (Countryman, 1992, p. 77). The history of exceptional women in mathematics was injected into our experience (see, for example, Lynn Osen’s 1974 reply to E.T.Bell, Women of Mathematics). The problem with the Phase Two— ‘famous few’ approach (McIntosh, 1989) is that it teaches about women mathematicians as exceptions and can convey the impression that most women do nothing of any value in mathematics, and that they can only be worthy of notice if they become more like men. It ascribes to women in the field a ‘loner’ status that makes them vulnerable to every setback. It leaves women mathematicians believing that they can make it on their own by virtue of sheer hard work, and that if they don’t, their failure has something to do with personal merit rather than with the way mathematics culture is organized. In contrast, those who are successful may begin to fear they will not be seen as female anymore. For example, Rogers, who went to an all-girls secondary school, learned to be proud of being good at something in which women didn’t excel—she was one of only three girls who continued to study mathematics to the end of secondary school and the only one who ultimately pursued a career in pure mathematics. But privately, she also began to experience a nagging feeling that perhaps she wasn’t a real women. Her self-image during this period of her life was that of a long bean-pole with a large pulsating sphere on the top. Her internal struggle between the life of a woman and the life of the mind made it difficult for her to embrace the intellectual life she enjoyed and retain an integrated sense of herself at the same time.

A further problem with this ‘woman mathematician as exception’ phase is that it focuses on individual success, on ‘winners and losers’, and thus devalues those who prefer collaborative approaches. Group work is thus not encouraged in the classroom and mathematics is seen as the property of experts. Again referring to Belenky et al, this is a phase that encourages and promotes a received view of knowledge (see Becker, Chapter 20).

Phase Three: Women as a Problem in Mathematics

An illustration of a shift in approach to Phase Three is provided by the residential mathematics camps for 15 year-old girls, entitled ‘Real Women Don’t Do Math!’ (Rogers, 1985), which Rogers organized in the summers of 1985 and 1986. The title of this camp was inspired by the phrase ‘real men don’t eat quiche’, popularly used at that time to challenge conventional notions of what it meant to be a man. In the playful title of Rogers’ camp, we can discern the shift from seeing the woman mathematician as a ‘loner’ to viewing mathematics as for all women. We can also sense the frustration with the prevalent assumption that mathematics is a field in which women have difficulty (this is perhaps more evident in the title of the video that grew out of the camp: ‘Real Women Don’t Do Math!—Or Do They?’).

In North America since the early 1980s, and in other English-speaking western countries such as Britain and Australia, gender reform of mathematics has been dominated by intervention projects. The largest and most influential of these projects is the North American EQUALS project which has developed a variety of teaching materials, workshops and one-day careers conferences (with titles like ‘Expanding Your Horizons’) with the explicit purpose of increasing women’s interest in mathematics. The aim was to make female students more aware of the need for mathematics in an increasingly technologically driven world and of the importance of keeping their career options open in order to compete successfully in it, and to make their teachers and parents aware of the problem of women’s poor participation in mathematics (see, for example, Kaseberg et al, 1980).

Undoubtedly programmes such as these have had a crucial influence on the evolution of our thinking on the issue and they have met with much success in achieving their goals. However, as mentioned earlier, a difficulty with these approaches is that they derive from a monocultural perspective that does not notice that women may have made conscious choices to avoid a subject that was in itself alienating. Rather, it is assumed that women avoid mathematics because of ignorance concerning the importance of mathematics to their futures and the dire consequences should they avoid mathematics. A different, still popular means of intervening, is to focus on math anxiety, a term invented by Sheila Tobias (1978, 1994) to describe a psychological fear or anxiety associated with engaging in mathematical activity. This approach uses essentially clinical means to help women overcome their anxiety towards, and hence their avoidance of, mathematics. It too, although for different reasons, places the blame for lack of participation in mathematics firmly on the shoulders of women themselves. In all of these approaches, the mathematics itself is not questioned, only the learners. It is assumed that women have to come to terms with their problems (their ignorance of consequences, their faulty beliefs, their ‘mathophobia’), and that when they do all will be well.

The views of proponents of such intervention programmes are typical of liberal feminism (see Leder, Chapter 13), or feminism of equality (see Mura, Chapter 19), in that they ‘“work within the system,” attempting only to improve the lot of women within a society which is otherwise left unchanged’ (Damarin, 1994). It is evident in this phase, that while the focus is on important issues, such as sexism and oppression, in attempting to make mathematics a more open discipline the emphasis is on disempowerment (why women can’t do mathematics, why they avoid it) rather than on empowerment (how women can learn the skills to challenge the discipline and change the mathematics). Programmes of remediation, self-help and career information...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Acknowledgments
• Chapter 1
• Part 1 Effecting Change
• Part 2 The Cultural Context
• Part 3 Feminist Pedagogy in Mathematics Education