Paul Ernest

Mathematics education, especially the central activities of teaching and learning mathematics, is thoroughly entangled with issues of power, authority, necessity, compulsion and submission. Schooling is compulsory almost everywhere as is mathematics. What is the ethical basis of universal schooling and the imposition of mathematical study within it? General areas of authority in schooling and mathematics teaching can be identified at several levels from the macro-view down to the micro-view. Drawing on four ethical principles from medical ethics (beneficence, non-maleficence, autonomy and justice), an ethical audit of the teaching and learning of mathematics is conducted. Evaluating the mathematics curriculum means applying these principles to its aims, content, pedagogy and assessment system. Two outstanding problems are identified: first, the large number of ideological assumptions in most education systems and mathematics curricula, which cause distortions and harm; second, the central embedding of power and authority in mathematics itself, which, in the way it is manifested in schooling, is empowering for many, but harmful for some. The findings of the chapter are that school mathematics is beneficial for some students (and for society), is harmful to a minority and offers very restricted autonomy—less than is possible for children. However, the major ethical deficit of school mathematics is with regard to social justice. In most societies, school mathematics does not benefit all alike and does not fully develop everyone’s talents and potential.

The widespread ‘ethical turn’ in philosophy, the humanities and social sciences has left the research field of mathematics education behind. Mathematics education, especially its central activities of teaching and learning mathematics, is thoroughly entangled with issues of ethics and justice. While there are many books on social justice and mathematics education, no dedicated volume on the ethics of mathematics and education has yet been published. This book aims to fill this gap. Perhaps this lack is no accidental oversight, for mathematics holds itself aloof from ethics claiming that as it is objective it is beyond good and evil. Given mathematics education’s birth from, and continued identification with mathematics itself, it is no surprise that it is one of the last bastions to wake up to the relevance and importance of ethics. This book explores the philosophical foundations of ethics and mathematics, offers a re-envisioning of what we mean by ethics and then provides an ethical critique of mathematics education from multiple perspectives. The common ground shared by ethics and social justice in mathematics is explored, as is the ethics of teacher and learner perspectives. After looking at ethical content in the teaching and learning of mathematics, the book concludes with a critical self-examination of this whole inquiry, questioning the ‘ethics of ethics’ and what we might mean by the ‘good’.

This edited volume is an inquiry into the ethics of mathematics education, and to a lesser extent, the ethics of mathematics. The imposition of mathematics for all raises questions of ethics. What are the ethics of teaching school mathematics? What are the costs as well as the benefits? What are the ethical issues raised by the official aims of mathematics teaching, the planned curriculum, the pedagogies employed in school and college mathematics and the assessment systems? These questions are addressed in the book as well as what systems of ethics we might use. The volume ventures into a burgeoning new field. It offers a unique set of investigations, both theoretical and in terms of practices. It announces the ethics of mathematics education as a new subfield of research and includes valuable contributions from many of the best-known researchers in mathematics education; additionally, it is a valuable resource for students, teachers and researchers in the field. This is an enduring and classic source book in the field. From the wisdom of leading scholars to the little heard voices of students, this collection offers the reader many striking new insights into the ethics of mathematics and education.

In this chapter I challenge the idea that mathematics is an unqualified force for good. Instead I show the harm that learning mathematics can inadvertently cause unless it is taught and applied carefully. I acknowledge that mathematics is a widespread force for good but make the novel case that there is significant collateral damage caused by learning mathematics. I describe three ways in which mathematics causes collateral damage. First, the nature of pure of mathematics itself leads to styles of thinking that can be damaging when applied beyond mathematics to social and human issues. Second the applications of mathematics in society can be deleterious to our humanity unless very carefully monitored and checked. Third, the personal impact of learning mathematics on learners’ thinking and life chances can be negative for a minority of less successful students, as well as potentially harmful for successful students. I end with a recommendation for the inclusion of the philosophy and ethics of mathematics alongside its teaching all stages from school to university, to attempt to reduce or obviate the harm caused; the collateral damage of learning mathematics.

This chapter offers an overview of the philosophy of mathematics education. This sub-field is characterised in both narrow and broad terms, concerning the aims of mathematics education and all philosophical aspects of research in mathematics education, respectively. The sub-field is also explored in terms of its questions and practices, which can be called a bottom-up perspective, as well as in terms of the applications of branches of philosophy to mathematics education, which might be called a top-down perspective. From the bottom-up one can characterize the area in terms of questions, and I have asked: What are the aims and purposes of teaching and learning mathematics? What is mathematics? How does mathematics relate to society? What is learning mathematics? What is mathematics teaching? What is the status of mathematics education as knowledge field? In characterizing the sub-field from a ‘top down’ perspective I look briefly at the contributions of ontology and metaphysics, aesthetics, epistemology and learning theory, social philosophy, ethics, and the research methodology of mathematics education. This reveals both how rich and deep the contributions of philosophy are to the theoretical foundations of our field of study. But even these different approaches leave many questions unanswered. For example: what are the responsibilities of mathematics and what is the responsibility of our own subfield, the philosophy of mathematics education? I conclude that the role of the philosophy of mathematics education is to analyse, question, challenge, and critique the claims of mathematics education practice, policy and research.

This chapter examines the role and need for ethics in mathematical practice. Mathematics is one of the few areas of study in which ethics is widely perceived as irrelevant. Many mathematicians and others resist the idea that we need to consider the ethics of both pure and applied mathematics. The foundations of this resistance are analyzed and located in background philosophies and ideologies of purism and neutrality. The range of social practices is investigated, and different ethical problems and issues are brought to light. It is argued that virtuous mathematicians can legitimately pursue mathematics for its own sake, but as citizens they also have a responsibility to care about the social impacts of mathematics. A review of the literature on the social responsibility of science and mathematics reveals that, although long neglected, concerns about the ethics of mathematics are starting to emerge in publications and training practices. Some of the more ethically sensitive areas are explored and three problematic categories are distinguished and exemplified. These are (1) mathematics in public communications, (2) overt applications of mathematics with powerful social impacts, and (3) the hidden performativity of mathematics in restructuring society, institutions, and social practices.

The concept of infinity has a long and troubled history. Thus it is a promising concept with which to explore rejection, disagreement, controversy and acceptance in mathematical practice. This paper briefly considers four cases from the history of infinity, drawing on social constructionism as the background social theory. The unit of analysis of social constructionism is conversation. This is the social mechanism whereby new mathematical claims are proposed, scrutinised and critiqued. Minimally, conversation is based on the two roles of proponent and critic. The proponent puts forward a proposal, which is reacted to and evaluated by those in the role of critic. There is a continuum of contexts in which such conversations take place from inner conversations the mathematician has within themselves, and casual face-to face interactions between mathematicians at the chalkboard, all the way to the formal responses of referees and editors to submitted journal papers. Such responses vary from unconditional acceptance, partial acceptance through to outright rejection. There may be disagreements between proponents and critics, among those in the joint role of critic, and broader, community-wide disagreements and controversies, according to specific mathematical proposal and the critical judgements of it.

This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future.

A traditional problem of ethics in mathematics is the denial of social responsibility. Pure mathematics is viewed as neutral and value free, and therefore free of ethical responsibility. Applications of mathematics are seen as employing a neutral set of tools which, of themselves, are free from social responsibility. However, mathematicians are convinced they know what constitutes good mathematics. Furthermore many pure mathematicians are committed to purism, the ideology that values purity above applications in mathematics, and some historical reasons for this are discussed. MacIntyre’s virtue ethics accommodates both the good mathematician and the ethics of the social practice of mathematics. It demonstrates that purism is compatible with acknowledging the social responsibility of mathematics. Four aspects of this responsibility are mentioned, two concerning the impact of mathematics via education, and two concerning explicit and implicit applications of mathematics. The last of these opens up the performativity of mathematical and measurement applications in society, which change the very processes they are supposed to measure. Although these applications are not explored in detail, they illustrate the importance of considering the ethics and social responsibility of mathematics in society. MacIntyre’s virtue theory opens a broad approach to the controversial topic of the ethics of mathematics encompassing purism, and absolutist and social constructivist philosophies of mathematics, but still enabling ethical critiques of the impact of mathematics on society.