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.
Author(s): Eric Vandendriessche, Rik Pinxten
Publisher: Springer
Year: 2023
Language: English
Pages: 292
City: Cham
Introduction
Contents
Ethnography and Mathematics
Re/Creating ‘Evocative Images’ (sunannguanik iqqaigutinik): Procedural Knowledge and the Art of Memory in the Inuit Practice of String Figure-Making
1 Introduction: String Figure-Making as a Widespread Activity Involving Procedural Knowledge
2 String Figure-Making in Pre-colonial Inuit Societies
2.1 A Practice Referring to Different Spatiotemporal Scales
2.2 A Procedural Activity Relating to Memory and Knowledge Sharing
3 Symbolic Meanings Ascribed to Some Structural Features of ajaraaq (ayarr’ar, ayaqhaaq): An Insight into Mathematical Ideas as Embedded in Inuit Cosmology
3.1 String Figure- and Knot-Making: Generative/Ordered Thread Crossings Versus Tangles
3.2 Cultural Interpretations of Some Geometrical Ideas Involved in Inuit String Figure-Making
References
Modeling of Implied Strategies of Solo Expert Players
1 Introduction
1.1 My Ethnographic Fieldwork and the Object of My Research
1.2 What Are Abstract Combinatorial Games ?
1.3 Why the ``Sowing Game'' Appellation?
1.4 Presentation of the Next Sections of this Chapter
2 Sowing Games
2.1 Some Artifacts
2.2 Common Characteristics
2.3 Two Classes of Sowing Games
2.4 Geographical Distribution
2.5 Diagrams
3 The Zanzibar Bao
3.1 The Bao la Kujifunza
3.2 The Bao la Kiswahili
3.3 Notation of the Games
4 The Other solo
4.1 A 4 times4 Katro from the ``Hauts Plateaux'' of Madagascar
4.2 The 4 times8 fanga by Flacourt
4.3 The 4 times8 mraha of Mahajanga
4.4 The 4 times8 mraha of Mayotte
5 Regulated Movements and Optimized Movements
6 Modeling
6.1 Some Preliminary Definitions
6.2 An Enlightening Interview
6.3 A Modeling Proposal
7 Conclusion
References
Sand Drawing Versus String Figure-Making: Geometric and Algorithmic Practices in Northern Ambrym, Vanuatu
1 Introduction
2 Cultural and Symbolic Aspects of String Figures and Sand Drawings: Some Elements of Comparison
3 Ethnomathematics of String Figures and Sand Drawings
3.1 Algorithmic/Procedural Aspects of String-Figure and Sand Drawing Practice
3.2 Shared Mathematical Properties
4 In Conclusion: From Epistemological to Educational Issues
References
Impact of Indigenous Culture on Education in General, and on Mathematics Classes in Particular
Indigenous School Education: Brazilian Policies and the Implementation in Teacher Education
1 Introduction
2 Socio-historical and Demographic Panorama of the Brazilian Indigenous Population
2.1 Invasion and Destruction of Indigenous Peoples in Brazil
2.2 Protection of Indigenous Peoples
3 The Implementation of Indigenous School Education in Brazil
4 The Advances and Setbacks of Indigenous School Education in Brazil
5 An Experience of Collaboration with Xukuru of Ororubá Teachers
6 Final Considerations
References
Indigenous Mathematical Knowledge and Practices: State of the Art of the Ethnomathematics Brazilian Congresses (2000–2016)
1 Introduction
2 The Brazilian Ethnomathematics Congresses
3 Methodology
4 Results
4.1 Works on Indigenous Themes
4.2 Ethnicities Represented in the Works
4.3 Indigenous Authorship
4.4 Research Themes
4.5 Anthropology and Ethnography in the Works
5 Indigenous Ethnomathematics and Anthropology
6 Final Considerations
References
Subverting Epistemicide Through ‘the Commons’: Mathematics as Re/making Space and Time for Learning
1 Epistemicide
2 Land and Locals: Tracing Signs of Epistemicide
3 The Commons: A Matter of Learning to Subvert Epistemicide
4 Learning and ‘The School’: Α Radical Pedagogy for ‘The Commons’
5 Mathematics: Re/making Space and Time for Learning
References
Meta-studies
The Tapestry of Mathematics—Connecting Threads: A Case Study Incorporating Ecologies, Languages and Mathematical Systems of Papua New Guinea
1 Introduction
2 Threads of the Tapestry
2.1 Caveat on This Perspective of the Tapestry
3 The Diversity of Cultures
3.1 Time and Place
3.2 Time and Language
3.3 Migrations and Languages
3.4 DNA Assessments
3.5 Displacement and Migration
3.6 Proto Languages
3.7 Social Values, Sociopolitics, and Language
4 The Tapestry Section on Number Systems—A Window into Diversity
5 Mathematics in Cultural Activities
5.1 Trade
5.2 Group Decision Making and Displays
5.3 Valuing Culture in the Mathematical Language
5.4 Intergenerational Relationships
6 The Need for Large Numbers for Cultural Reasons
7 The Tapestry Section on Time and Work Patterns
8 The Tapestry of Transactions
9 The Tapestry of Mathematics in Art
10 Discussion
11 Conclusion
12 PostScript
References
Indigenous Mathematics in the Amazon: Kinship as Algebra and Geometry Among the Cashinahua
1 Introduction
2 Note on the Cashinahua
3 Cashinahua Name-Sake Classes
4 The Group Structure of Same-Sex Cashinahua Kinship Terms
4.1 Definition of a Group
4.2 The Klein Group of Cashinahua Alliance: Same-Gender Kinship Terms
5 Cashinahua Structure of Eight Name-Sake Classes
5.1 The Cashinahua Eight-Sections Group
5.2 Different Representations of the Dihedral Group Structure
6 Conclusions
References
The Western Mathematic and the Ontological Turn: Ethnomathematics and Cosmotechnics for the Pluriverse
1 Introduction
2 Multiple Technics, Multiple Natures, and Multiple Ontologies
3 Mathematics, Technology and the Technoecological Condition
4 The Ontological Turn and Technodiversity
5 Computational Mathematics: Singularity Versus Pluriversality
6 Ethnomathematics and Cosmotechnics
References
Conclusions. Some Possible Lines for Further Research in Ethnomathematics
More Ethnography of Diverse, Local Mathematical Knowledge
More Anthropological Research
Mathematics Education and Ethnomathematics
References
