Abstract
Swapna Mukhopadhyay & Wolff-Michael Roth (eds), Alternative forms of knowing (in) mathematics: Celebrations of diversity of mathematical practices, The Netherlands: Sense Publishers, Rotterdam, 2012; 323 pp.: ISBN 978-94-6091-919-0, £42.73 (pbk)
A compilation of 14 papers from a yearly public lecture series hosted at Portland State University since 2006 (and later Portland Community College since 2009), this book is another salvo in the can(n)on of the culturally responsive agenda in mathematics education research. Readers are encouraged to access the talks 1 by contributors on the front lines, including mathematics education specialists, historians, anthropologists, and other education professionals (a few speakers are not included in the volume). Wolff-Michael Roth, the second editor, is also a contributor and provides a further political perspective. A third author, Brian Greer, contributes to the Prologue, Celebrating diversity, Realizing alternatives: An Introduction, and the Epilogue, Why bother about diversity of mathematical practices?
The underlying tone and message of the book is that mathematics and mathematics education, far from being inert and value-free, are inherently political as they are inseparably connected to questions of values and power. The key ideas here are diversity, knowing, and alternatives (Žižek provides the inspiration for ‘realizing’ alternatives, realizing in the sense both of ‘becoming aware of’ and of ‘making happen’). The book is organized into four parts: ‘Mathematics and politics of knowledge’, ‘Ethnomathematics’, ‘Learning to see mathematically’, and ‘Mathematics education for social justice’, each with an Introduction for which the editors claim collective responsibility. In Part I, the authors address notions of mathematics and mathematics education (similar to language) as weapons of cultural violence and oppression in suppressing traditional systems and thought. Gary Urton examines how mathematics and accounting practices in the Andes were suppressed by the Spanish conquest. Gregory Cajete presents a personal synthesis of his experience as an Indian educator, addressing Indian orientations to learning and teaching, and calling on those involved in Indigenous education to make the case for transformation, resistance, and solidarity as redress. Washington et al. frame mathematics as crisis in the discourse of achievement gaps and deficit models with a focus on Black children. Lastly, Marta Civil and Núria Planas consider the politics of access and power relations in the learning and teaching of mathematics in two-language contexts.
Part II, Ethnomathematics, is compelling in its display of lived experience of diversity in mathematics and mathematics teaching in cultural contexts. The term, ethnomathematics, is a contested one, raising questions of whose mathematics, whose worldview, what mathematics, and what is mathematics education for? Having emerged as resistance to the cultural hegemony of mathematics as it is codified and taught, the subfield has become embroiled in political and theoretical considerations. Still, it has provided a way to present alternative knowledges and conceptions in mathematics. These include explorations of the use of mathematics in divinations (foretelling the future) in various cultures (including Chinese, Tibetan, and German), examples of map-making and Indigenous knowledges and mathematics in Brazil, and an alternative learning trajectory in the Yup’ik community of Alaska. Two new terms are proposed: ethnomodeling as a methodological basis for ethnomathematics with examples of land measurement, freedom quilts, and tipis, and ethno computing which describes the use of computational media in capturing and exploring the phenomena of ethnomathematics.
So far the book is lively and varied, but there is a nagging feeling of little attention to underlying theory and theoretical perspectives. The remaining two parts present other aspects of mathematics education, such as learning to see mathematically, making sense of big numbers, and mathematics for social justice. Taken as a whole, the book as an edited volume focuses on applications with occasional references to theory. I had the impression that the editors were hard put to impose some order on the selections and to make each part cohere under some common theme. Finally, the Epilogue is a conversation among the two editors and Brian Greer around why we should concern ourselves with the diversity of mathematical practices, offering interesting glimpses into personal philosophies and political leanings with respect to the practices of mathematics teaching and learning.
The area of mathematics education research covered in this book is fraught with challenge as researchers and those who teach mathematics struggle with the ways in which mathematics is conceived (mathematics-as-a-discipline, mathematics-as-a-school-subject, mathematics-as-a-set-of-practices, etc.), straddling the extremes in math wars (on the one side those who would perpetrate an abstract decontextualized view of mathematics as opposed to a socially and culturally oriented view of mathematics). The Common Core Standards of The National Council of Teachers of Mathematics (NCTM), which is considered the ‘enlightened mainstream,’ contains little or no reference to cultural contexts and culturally responsive pedagogy or to the subjective and psychoanalytic issues in the teaching and learning of mathematics. A flavor of these considerations is captured by the editors in their various introductions and in the front and back matter.
The contributors to this book from their various fields and disciplines reflect the diversity of researchers working in and around mathematics education, testifying to the centrality of mathematics and its place in our society and world. While covering similar ground as many titles in the field (Greer et al., 2009; Skovsmose and Greer, 2012), this book presents further experiences and the thoughts of researchers grappling with the larger questions within; Why mathematics, and Is mathematics for all? This collection asks us to re-examine the many meanings of mathematics and the many perspectives of teaching mathematics, and to keep central the theme of humanization consistent in the work of Freire. It seeks to connect expressions of mathematics with our lived experiences, to celebrate mathematics as many (as opposed to a single mathematics), and to understand that mathematics in praxis is inherently social and political and therefore inextricably bound up with value and power. It reminds us that the important questions are political and that in order to enable meaningful lives, we must resist the dominant status of formal knowledge and celebrate the diversity of and within mathematics.