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The Ethics of Mathematical Knowledge: Imagination and Empathy to Produce Social and Ecological Solidarity
Abstract
In this chapter, I focus on the ethics encapsulated in mathematical knowledge. I assume that there is more to our relationship with mathematics than just teaching and learning it. Ultimately, learning mathematics is not just about the knowledge we gain: crucially, it is also about what we do on the basis of that knowledge. This represents a significant ethical stance. Therefore, in this chapter, I do not focus on what counts as mathematical knowledge or on different ways of teaching and learning mathematics, but instead on the ethics of mathematical knowledge. In other words, how do we become ethically responsible with the knowledge we call mathematics?
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In this theoretical research report we propose a socio-ecological perspective, as relevant for research in mathematics education that takes account of our complex, precarious present and imagined future, while recognising its historical roots. We discuss briefly work that considers the social, political and ecological, and build from this scholarship. A ‘socio-ecological’ perspective considers the social and ecological as entangled, and mathematics (education) as both shaping and shaped by these entanglements. This is a mathematics (education) that gains meaning from questions that emerge in socio-ecological relations. We ground our theoretical argument using a project located in a community living in a polluted region of Mexico, where a river is central to the questions motivating community activism and our research.
What are the effects of teaching the dominant mathematics on the wholeness and integrity of the cultural, social and linguistic resources of diverse communities? In this text, I seek to capture the risks associated with utilising non-Western resources in the teaching of the dominant mathematics in order to elucidate possible types of harms that conventional mathematics education could cause to various non-Western communities. In particular, I challenge various dominant theoretical views that endorse the employment of the social, cultural and linguistic (re)sources of others to teach and learn mathematics, without paying similar or even deeper ethical attention to the mutual and reciprocal effects of the taught and learnt mathematics. I propose an epistemology of interrelationships; I call attention to possible harms caused by utilising the social, cultural and linguistic (re)sources of some non-Western communities as part of the teaching and learning of dominant school mathematics on the same (re)sources of those communities.
Climate change is one of the most urgent human concerns. Mathematics, in various degrees of complexity, is used to communicate climate change to scientists, politicians, policy makers, the general public and children. Drawing on ideas from critical citizenship and critical mathematics education, we ask how incorporating issues of climate change into the teaching and learning of mathematics can be understood as a moral and ethical act? We consider the possible ethical and moral role of mathematics education at large, as well as the role and challenges of individual teachers who consider addressing climate change in mathematics classrooms. We illustrate our discussion with analysis of Canadian and Norwegian mathematics teachers' explanations of their thinking about climate change in their teaching. We conclude that although including climate change in mathematics classrooms can be (and is) viewed as an ethical responsibility of mathematics teachers, in their day-today practice their decisions about this issue are complex.
Ethnomathematics school practices favor respect for, solidarity and cooperation with, the others. It is associated with the pursuit of peace. The main goal of ethnomathematics is building up a civilization free from truculence, arrogance, intolerance, discrimination, inequity, bigotry, and hatred of the others. These are basic questions that define philosophical and ideological postures, which are the roots of a holistic theory of knowledge, looking into the generation, the individual and social organization, and the institutionalization, transmission and diffusion of knowledge. This concept of ethnomathematics is primeval in recognizing the emergence of perceptions of space and time and the techniques of observing, comparing, classifying, ordering, measuring, quantifying and inferring that are different styles of abstract thinking in the school curricula. This is can be achieved by the application of the trivium curriculum, which is an innovative ethnomathematical approach that needs more investigations to address its pedagogical purposes.
On the grounds of our work as researchers, teacher educators and teachers engaging with a socio-political approach in mathematics education in Colombia, we propose to understand democracy in terms of the possibility of constructing a social subjectivity for the dignity of being. We address the dilemma of how the historical insertion of school mathematics in relation to the Colonial project of assimilation of Latin American indigenous peoples into the episteme of the Enlightenment and Modernity is in conflict with the possibility of the promotion of a social subjectivity in mathematics classrooms. We illustrate a pedagogical possibility to move towards a mathematics education for social subjectivity with our work in reassembling the notion of geometrical space in the Colombian secondary school mathematics curriculum with notions of space from critical geography and the problem of territorialisation, and Latin American epistemology with the notion of intimate space as an important element of social subjectivity.
This article reports on a 2-year study about teaching and learning mathematics for social justice in an urban, Latino classroom and about the role of an NCTM Standards- based curriculum. I was the teacher in the study and moved with the class from seventh to eighth grade. Using qualitative, practitioner-research methodology, I learned that students began to read the world (understand complex issues involving justice and equity) using mathematics, to develop mathematical power, and to change their orientation toward mathematics. A series of real-world projects was fundamental to this change, but the Standards-based curriculum was also important; such curricula can theoretically promote equity, but certain conditions may need to exist. Social justice pedagogy broadens the concept of equity work in mathematics classrooms and may help promote a more just society.
In this 1989 book Rorty argues that thinkers such as Nietzsche, Freud, and Wittgenstein have enabled societies to see themselves as historical contingencies, rather than as expressions of underlying, ahistorical human nature or as realizations of suprahistorical goals. This ironic perspective on the human condition is valuable on a private level, although it cannot advance the social or political goals of liberalism. In fact Rorty believes that it is literature not philosophy that can do this, by promoting a genuine sense of human solidarity. A truly liberal culture, acutely aware of its own historical contingency, would fuse the private, individual freedom of the ironic, philosophical perspective with the public project of human solidarity as it is engendered through the insights and sensibilities of great writers. The book has a characteristically wide range of reference from philosophy through social theory to literary criticism. It confirms Rorty's status as a uniquely subtle theorist, whose writing will prove absorbing to academic and nonacademic readers alike.
To celebrate the 25th anniversary of its publication, Michael W. Apple has thoroughly updated his influential text, and written a new preface. The new edition also includes an extended interview circa 2001, in which Apple relates the critical agenda outlined in Ideology and Curriculum to the more contemporary conservative climate. Finally, a new chapter titled "Pedagogy, Patriotism and Democracy: Ideology and Education After 9/11" is also included.
I am concerned with peace in its several dimensions: inner peace, social peace, environmental peace and military peace. This
paper addresses the global responsibilities of mathematicians and mathematics educators in the quest for peace. It is observed
that the evolution of mathematics is intimately related to the evolution of Western society, hence mathematics cannot be dissociated
of human behavior. After some reflections on the specifity of the human species and the production of knowledge, I claim a
symbiotic relation between human search of ways of explaining and coping with the environment and the development of mathematics.
This leads to a broader approach to the history and padagogy of mathematics and to some hints for the subor dination of mathematics
development to a global ethics, which incorporates the goal of peace in its multiple dimensions.
Mein Anliegen ist Frieden in seinen verschiedenen Dimensionen innerer Frieden, sozialer Frieden, ökologischer Frieden und
militärischer Frieden. Der Beitrag handelt von der globalen Verantwortung von mathematikern und Mathematikdi daktikern im
Streben nach Frieden Beobachtungen zeigen, daß die Entwicklung der Mathematik eng mit der Entwicklung der westlichen Gesellschaft
verbunden ist, Mathematik kann also nicht vom menschlichen Verhalten abgetrennt werden Nach einigen Überlegungen über das
Besondere der menschlichen Spezies behaupte ich, daß es eine symbiotische Beziehung zwischen der menschlichen Suche nach Wegen,
die Umwelt zu erklären, mit ihr umzugehen, und der Entwicklung der Mathematik gibt. Dies führt zu einem breiteren Zugang zur
Geschichte und zur Pädagogik der Mathematik sowie zu einigen Hinweisen, wie die Entwicklung der Mathematik einer globalen
Ethik unterworfen werden kann, die den Frieden in seinen verschiedenen Dimensionen als Ziel miteinschließt.
ZDM-ClassificationA30-A40-E20
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