Cultural development of mathematical ideas: Papua New Guinea studies
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u. a.]
Cambridge Univ. Press
2012
|
| Edition: | 1. publ. |
| Series: | Learning in doing
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XXXIII, 362 S. Ill., graph. Darst., Kt. |
| ISBN: | 9780521761666 |
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Record in the Search Index
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| adam_text |
Cultural Development of
Mathematical Ideas
Papua New Guinea Studies
GEOFFREY B SAXE
University of California, Berkeley
with
INDIGO ESMONDE
University of Toronto
CAMBRIDGE
UNIVERSITY PRESS
Contents
List of Figures page xiii
Series Foreword xxi
Preface xxiii
A Trajectory of Research - Tensions and Partial
Resolutions xxiii
Acknowledgments xxxi
Introduction 1
Part I The Origins of Number: Enduring Questions 5
1 Culture-Cognition Relations 7
Culture and Cognition: Separate Variables with
External Links 7
Culture and Cognition: Jointly Rooted in Activity
with Intrinsic Relations 16
Toward a Genetic Treatment of Intrinsic Relations • 22
The Promise of the Oksapmin Case 39
2 Cultural Forms of Number Representation Used
in Oksapmin Communities 40
Body Counting in the New Guinea Highlands 43
The Oksapmin Counting System 44
Reproduction and Alterations in Numerical
Representations and Ideas 48
Part II Economic Exchange 49
3 Collective Practices of Economic Exchange: A Brief
Social History 51
ix
Contents
Pre-contact 51
Period 1 (1938-1960) 55
Period 2 (-1960-1980) ' 59
Period 3 (-1980-2001) 66
4 Reproduction and Alteration of Numerical
Representations 71
Study 4-1 Body Arithmetic in 1980 74
Study 4-2 The Body and Tok Pisin: Forms Used for
Number Representation in 2001 96
Study 4-3 Languages of Quantification Used in Stores
in 2001 and the Accomplishment of Emergent
Arithmetical Problems 107
Study 4-4 Emergent Arithmetic in Store Transactions
in 2001 116
Notes across Studies 123
5 Reproduction and Alteration in Currency Token
Representations 126
Study 5 -1 Shifting Ways of Naming Tokens 128
Study 5-2 Shifting Quantification Practices with Currency 144
Discussion 158
6 Representational Forms, Functions, Collective Practices,
and Fu: A Microcosm 160
Leading Observations 163
Study 6-1 Shifting Meanings, Locations, and Uses for Fu 166
Study 6-2 Distribution of Fu Use in Representing Values
of Currency and Numbers of Stones: Additional Analysis
of Study 5-2 Data : 179
Study 6-3 Fu Use in the Reading of Prices Written with
Hindu-Arabic Numerals 181
Shifting Forms and Functions of Fu in Collective Practices
of Exchange: Coordinating Synchronic and Diachronic
Analyses 184
Collective Practices and the Micro-, Socio-, and
Ontogenesis of Form-Function Relations 190
Part III Schooling 193
7 A Brief History: Collective Practices of Schooling
in Oksapmin 196
No Western Schooling (Before 1962) 196
The Bible School (-1962) 199
Contents xi
Colonial and Postcolonial Community Schools (1967) 200
The School Reforms (1998) ' 201
8 Unschooled Children's Developing Uses of the Body
System 203
Study 8-1 Counting to Compare and Reproduce Sets 204
Study 8-2 Comparing Numerical Values of Body Parts 209
Study 8-3 Measuring with the Body 215
9 Children's Adaptations of the Body System in School
in 1980: An Unintended Consequence of
Postcolonial Schooling 223
Study 9-1 Observations in Classrooms 224
Study 9-2 Arithmetic with the Body: Unintended
Consequences 228
10 Some 20 Years Later: Schooling and Number 237
Study 10-1 Grade 3 School Mathematics in 2001 239
Study 10-2 Quantification Practices Known by Grade
3 Children in 2001 249
Discussion 262
11 Teachers and Students as (Unintentional) Agents of Change 265
The Elementary School as a Research Site 265
Study 11-1 Observations of Classroom Instruction in 2 001 267
Study 11-2 Elementary Lesson Plans 280
Part IV Toward an Integrated Treatment
of Sociohistorical and Cognitive
Developmental Processes 293
12 What Develops? A Focus on Form-Function Relations • 295
Key Properties of Form-Function Relations in
Quantification 295
Form-Function Relations in Quantification Practices as
Units of Analysis 298
13 How Do Form-Function Relations Develop? 299
Genetic Continuity and Discontinuity of Forms in
Quantifications 300
Genetic Continuity and Discontinuity of Functions in
Quantification Practices 301
Changing Niches and Implications for Genetic Shifts
in Form-Function Relations 303
Continuities and Discontinuities in Forms, Functions,
and Collective Practices over Historical Time 307
xii Contents
14 Why Do Form-Function Relations Develop? 308
Regulative Processes in Microge/iesis 308
Regulative Processes in Sociogenesis 312
Regulative Processes in Ontogenesis 321
The Interplay between Micro-, Socio-, and
Ontogenetic Developments 325
Epilogue 328
Appendix A The Five Oksapmin Conversational Number Words 331
Appendix B Currency Tokens, Images, and Physical Descriptions 332
Appendix C Notes on Age Determination, Back-Translation,
and Interview Settings 335
Appendix D Record Form Used in Trade Store Diary Study
(Sample Page) 337
Appendix E Auxiliary Words Used in Quantification 339
Appendix F Tit Fu Interview Used with Adults 341
References 343
Index 355 |
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| discipline | Psychologie Sozial-/Kulturanthropologie / Empirische Kulturwissenschaft |
| edition | 1. publ. |
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| spelling | Saxe, Geoffrey B. Verfasser aut Cultural development of mathematical ideas Papua New Guinea studies Geoffrey B. Saxe ; Indigo Esmonde 1. publ. Cambridge [u. a.] Cambridge Univ. Press 2012 XXXIII, 362 S. Ill., graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Learning in doing Literaturangaben Lokales Wissen (DE-588)4518241-3 gnd rswk-swf Oksapmin (DE-588)4365025-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Papua-Neuguinea (DE-588)4044569-0 gnd rswk-swf 1\p (DE-588)4522595-3 Fallstudiensammlung gnd-content Papua-Neuguinea (DE-588)4044569-0 g Oksapmin (DE-588)4365025-9 s Mathematik (DE-588)4037944-9 s Lokales Wissen (DE-588)4518241-3 s DE-604 Esmonde, Indigo Verfasser aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024979939&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Saxe, Geoffrey B. Esmonde, Indigo Cultural development of mathematical ideas Papua New Guinea studies Lokales Wissen (DE-588)4518241-3 gnd Oksapmin (DE-588)4365025-9 gnd Mathematik (DE-588)4037944-9 gnd |
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| title | Cultural development of mathematical ideas Papua New Guinea studies |
| title_auth | Cultural development of mathematical ideas Papua New Guinea studies |
| title_exact_search | Cultural development of mathematical ideas Papua New Guinea studies |
| title_full | Cultural development of mathematical ideas Papua New Guinea studies Geoffrey B. Saxe ; Indigo Esmonde |
| title_fullStr | Cultural development of mathematical ideas Papua New Guinea studies Geoffrey B. Saxe ; Indigo Esmonde |
| title_full_unstemmed | Cultural development of mathematical ideas Papua New Guinea studies Geoffrey B. Saxe ; Indigo Esmonde |
| title_short | Cultural development of mathematical ideas |
| title_sort | cultural development of mathematical ideas papua new guinea studies |
| title_sub | Papua New Guinea studies |
| topic | Lokales Wissen (DE-588)4518241-3 gnd Oksapmin (DE-588)4365025-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Lokales Wissen Oksapmin Mathematik Papua-Neuguinea Fallstudiensammlung |
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