Indigenous Knowledge And Ethnomathematics

The book presents a series of ethnographic studies, which illustrate issues of wider importance, such as the role of cultural traditions, concepts and learning procedures in the development of formal (or mathematical) thinking outside of the western tradition. It focuses on research at the crossroads of anthropology and ethnomathematics to document indigenous mathematical knowledge and its inclusion in specific cultural patterns. More generally, the book demonstrates the heuristic value of crossing ethnographical, anthropological and ethnomathematical approaches to highlight and analyze—or "formalize" with a pedagogical outlook—indigenous mathematical knowledge. The book is divided into three parts. The first part extensively analyzes theoretical claims using particular ethnographic data, while revealing the structural mathematical features of different ludic, graphic, or technical/procedural practices in their links to other cultural phenomena. In the second part, new empirical studies that add data and perspectives from the body of studies on indigenous knowledge systems to the ongoing discussions in mathematics education in and for diverse cultural traditions are presented. This part considers, on the one hand, the Brazilian work in this field; on the other hand, it brings ethnographic innovation from other parts of the world. The third part comprises a broad philosophical discussion of the impact of intuitive or "ontological" premises on mathematical thinking and education in the light of recent developments within so-called indigenously inspired thinking. Finally, the editors’ conclusions aim to invite the broad and diversified field of scholars in this domain of research to seek alternative approaches for understanding mathematical reasoning and the adjacent adequate educational goals and means. This book is of interest to scholars and students in anthropology, ethnomathematics, history and philosophy of science, mathematics, and mathematics education, as well as other individuals interested in these topics.

Mapping Time, Space and the Body: Indigenous Knowledge and Mathematical Thinking in Brazil brings people, land and numbers together in the fight for justice. On this extraordinary voyage through ancestral territories in central and southern Brazil, the Xavante, Suyá, Kayabi, and other local nations use mapping as a tool to protect their human rights to lands and resources they have traditionally owned and acquired. Mathematics activities inside the classroom and in everyday life help explain how Indigenous Peoples understand the cosmos and protect the living beings that helped create it. The book is a welcome contribution to a growing literature on the mathematical and scientific thinking of Indigenous Peoples around the globe. It makes mathematics alive and culturally relevant for students of all national backgrounds worldwide. “A brilliant marriage of ethnography and mathematics written with deep understanding and obvious affection for the peoples she observed.” – James A. Wiley, Ph.D. Professor, University of California at San Francisco, USA “This original and beautifully illustrated book offers a vivid study of Indigenous Peoples in Brazil. The author develops theoretical approaches and research methodologies to understand the way cultural groups deal with their natural and social environments.” – Ubiratan D’Ambrosio, Ph.D. Emeritus Professor, Universidade Estadual de Campinas, Brazil “Mapping Time, Space and the Body is destined to create new and enlightened research in Ethnomathematics. It is an essential read for all of us working with culture and social justice in the realm of mathematics.” – Daniel Clark Orey, Ph.D. Professor, Universidade Federal de Ouro Preto, Minas Gerais, Brazil. Emeritus Professor, California State University, Sacramento, USA Cover photo by Mariana K. Leal Ferreira, 1998: Romdó Suyá, ceremonial leader of the Suyá people in the Xingu Indigenous Park

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

This book presents a collection of ethnomathematical studies of diverse mathematical practices in Afro-Brazilian, indigenous, rural and urban communities in Brazil. Ethnomathematics as a research program aims to investigate the interrelationships of local mathematical knowledge sources with broader universal forms of mathematics to understand ideas, procedures, and practices found in distinct cultural groups. Based on this approach, the studies brought together in this volume show how this research program is applied and practiced in a culturally diverse country such as Brazil, where African, indigenous and European cultures have generated different forms of mathematical practice. These studies present ethnomathematics in action, as a tool to connect the study of mathematics with the students’ real life experiences, foster critical thinking and develop a mathematics curriculum which incorporates contributions from different cultural groups to enrich mathematical knowledge. By doing so, this volume shows how ethnomathematics can contribute in practice to the development of a decolonial mathematics education. Ethnomathematics in Action: Mathematical Practices in Brazilian Indigenous, Urban and Afro Communities will be of interest to educators and educational researchers looking for innovative approaches to develop a more inclusive, democratic, critical, multicultural and multiethnic mathematics education.

Although the manifestation of what is taken to be indigenous knowledge could presumably be traced back roughly to the origins of humankind, the idea of indigenous knowledge is a fairly recent phenomenon. It has arguably gained conceptual and discursive currency only over the past half century, with a veritable slew of conferences, workshops, special journal editions, and anthologies devoted to the topic. Yet, there has been no treatise that offers a comprehensive, critical examination of this notion. Accounts of indigenous knowledge usually focus on explanations of “indigenous,” “local,” “traditional,” “African” and the like – but to date not a single defense of indigenous knowledge has bothered to explain the particular understanding of “knowledge” the authors are working with. Indigenous Knowledge: Philosophical and Educational Considerations’s critique of the idea of indigenous knowledge should in no way be understood as an endorsement of the evils of colonial conquest and (ongoing) exploitation, oppression, and subjugation. Nor should it be taken as an indication of a failure on the part of the Kai Horsthemke to sympathize with the struggle of indigenous peoples the world over for a dignified and sustainable way of life, for personal and communal space, and for self-determination. The aim of the book is to provide especially “indigenous” educators with theoretical tools for critical reflection and interrogation of their own and others’ preconceptions, assumptions, and epistemic practices and customs.

This survey on the modernity of ethnomathematics addresses numerous themes related to both ethnomathematics and mathematics education. It offers a broader view of mathematics, including ideas, procedures, concepts, processes, methods, and practices rooted in distinct cultural environments. In addition, by reflecting on the social and political dimensions of ethnomathematics, another important aspect of this research program is the development of innovative approaches for a dynamic and glocalized society. Ethnomathematics recognizes that members of different cultures develop unique mathematical techniques, methods, and explanations that allow for an alternative understanding and transformation of societal norms. The theoretical basis of ethnomathematics offers a valid alternative to traditional studies of history, philosophy, cognition, and pedagogical aspects of mathematics. The current agenda for ethnomathematics is to continue an ongoing, progressive trajectory that contributes to the achievement of social justice, peace, and dignity for all. The debates outlined in this book share a few of the key ideas that provide for a clearer understanding of the field of ethnomathematics and its current state of the art by discussing its pedagogical actions, its contributions for teacher education, and its role in mathematics education.

In this book, Ubiratan D’Ambrosio presents his most recent thoughts on ethnomathematics—a sub-field of mathematics history and mathematics education for which he is widely recognized to be one of the founding fathers.

The purpose of the edited volume is to provide an international lens to examine evidence-based investigations in Ethno-STEM research: Ethno-science, Ethno-technology, Ethno-engineering, and Ethno-mathematics. These themes grew out of multi-national, multi-institutional and multi-disciplinary efforts to preserve as well as epitomize the role that Indigenous Knowledge Systems (IKS) play in cognitive development and its vital contributions to successful and meaningful learning in conventional and non-conventional contexts. Principled by the Embodied, Situated, and Distributed Cognition (ESDC), this innovative book will provide evidence supporting the embeddedness of a thinking-in-acting model as a fundamental framework that explains and supports students’ acquisition of scientific knowledge. So often ‘western’ science curricula are experienced as irrelevant, since it does not take cognizance of the daily experiences and world in which the learner finds himself. This book takes a socio-cultural look at IKS and applies research in neuroscience to make a case its incorporation in the STEM (Science, Technology, Engineering and Mathematics) classroom. We use the Embodied Situated Distributed Cognition (ESDC) Model as conceptual framework in this book. Although the value of IKS is often acknowledged in curriculum policy documents, teachers are most often not trained in incorporating IK in the classroom. Teachers’ lack of the necessary pedagogical content knowledge (PCK) in effectively incorporating IK in their classrooms is a tremendous problem internationally. Another problem is that IK is often perceived as “pseudo-science”, and scholars advocating for the incorporation of IK in the school curriculum often do not contextualize their arguments within a convincing theoretical and conceptual framework.