Abstraction and representation: essays on the cultural evolution of thinking
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English German |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer
1996
|
| Schriftenreihe: | Boston studies in the philosophy of science
175 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Dt. übers. |
| Beschreibung: | XIV, 414 S. Ill., graph. Darst. |
| ISBN: | 0792338162 9789048146444 |
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| 650 | 7 | |a Cognition |2 ram | |
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| 650 | 7 | |a Mentale representatie |2 gtt | |
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Datensatz im Suchindex
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|---|---|
| adam_text | TABLE OF CONTENTS
INTRODUCTION
by Wolfgang Edelstein and Wolfgang Lefevre xi
ON ACTION AND COGNITION
CHAPTER 1. ACTION AND COGNITION IN PIAGET S GENETIC
EPISTEMOLOGY AND IN HEGEL S LOGIC 1
Notes 10
Bibliography 27
CHAPTER 2. REPRESENTATION AND MEANING 29
Examples of Cognitive Structures 29
Cognitive Structures and Material Action 42
Cognitive Structures and Language 46
Notes 54
Bibliography 67
EDUCATION IN CONTEXT
CHAPTER 3. PHILOSOPHICAL AND PEDAGOGICAL REMARKS
ON THE CONCEPT ABSTRACT 71
The Common Usage of the Concept in the Didactics of Mathematics 71
Abstraction as the Isolation of Qualities 72
The Concept of Abstraction of Formal Logic 73
The Empiricist Concept of Abstraction 75
Models of Abstraction Based on Constitution Theory 75
The Dialectical Concept of Abstraction 76
The Normal Pattern of Teaching 78
On the Interpretation of Learning Processes in Cognitive Psychology 79
Understanding the Facts 80
Viii TABLE OF CONTENTS
The Function of Exercises 81
Abstraction and Concretization in Mathematics Teaching 83
Bibliography 86
CHAPTER 4. WHAT IS MATHEMATICAL ABILITY AND HOW
DO ABILITY DIFFERENCES EMERGE IN MATHEMATICS
EDUCATION? 87
The Appearance of Mathematical Competence in Mathematics
Education 87
Psychometric Constructs of Ability 93
Abilities as Cognitive Structures 98
Notes 108
Bibliography 110
CHAPTER 5. MATHEMATICS EDUCATION AND SOCIETY 111
Introduction 111
The Vicinities of Mathematics— Mathematics of the Vicinities 113
Transmission of Knowledge Predetermined By Specific Ends 118
The Training of the Mind 122
Mathematics as a Profession 126
The Emergence of School Mathematics 131
Mathematics Education in the Context of Modern Institutional
Conditions 138
Notes 144
Bibliography 145
CHAPTER 6. PRELIMINARY REMARKS ON THE RELATIONSHIP
OF THE PRINCIPLES OF TEACHING ARITHMETIC TO THE EARLY
HISTORY OFMATHEMATICS 149
In Retrospect: Repetition in Unison 149
Action as the Starting Point for Mathematical Thinking? 151
On the Role of Historical Conditions of the Development of
Mathematical Thinking 152
The Early History of Arithmetic as a Touchstone 153
Arithmetic as a System of Rules for Material 154
Representatives of Numbers 154
The Arithmetic of Constructive-Additive Sign Systems 156
Developmental Stages of Mesopotamian Arithmetic 159
TABLE OF CONTENTS ix
Theoretical Perspective 167
Notes 169
Bibliography 170
CULTURAL EVOLUTION OF ARITHMETICAL
THINKING
CHAPTER 7. THE DEVELOPMENT OF ARITHMETICAL THINKING:
ON THE ROLE OF CALCULATING AIDS IN ANCIENT EGYPTIAN
AND BABYLONIAN ARITHMETIC 173
Preliminary Remarks: Reckoning Board and Rod Numerals 173
Structural Characteristics of Ancient Egyptian Arithmetic 176
The Means of Calculation in Ancient Egypt 188
The Sources for Reconstructing the History of Old Babylonian
Arithmetic 199
Structural Characteristics of Old Babylonian Arithmetic 204
The History of Mesopotamian Calculating Aids 211
CHAPTER 8. THE FIRST REPRESENTATIONS OF NUMBERS
AND THE DEVELOPMENT OF THE NUMBER CONCEPT 275
Characteristics of the Numerical Signs in the Archaic Texts 275
Earlier Attempts at Interpretation 276
Rules for Using the Signs 279
Summations 281
Statistics as a Method of Decipherment 284
The Decipherment of Calendar Entries 286
Numerical Sign Systems with Specific Areas of Application 288
The Lack of an Abstract Number Concept 291
Number Analogues 293
From Number Analogues to the Abstract Number Concept 294
Bibliography 297
CHAPTER 9. ON THE RELATIONSHIP BETWEEN ONTOGENESIS
AND HISTORIOGENESIS OF THE NUMBER CONCEPT 299
On the Preconditions of Piaget s Constructivist Conception of
Numbers 301
X TABLE OF CONTENTS
Ontogenesis of the Number Concept in Piaget s Genetic
Epistemology 302
Historiogenesis of the Number Concept in Piaget s Genetic
Epistemology 308
Symbolic Representation and Historical Transmission 314
Protoarithmetic of a Stone Age Culture 321
Protoarithmetical Techniques in the Transition to a Literate
Culture 329
Ontogenesis and Historiogenesis of the Number Concept 354
Notes 362
Bibliography 367
ON HISTORICAL EPISTEMOLOGY
CHAPTER 10. ABSTRACTION AND REPRESENTATION 371
Bibliography 381
CHAPTER 11. THE CONCEPT OF LABOR IN HISTORICAL
MATERIALISM AND THE THEORY OF SOCIO-HISTORICAL
DEVELOPMENT 383
Labor in Human History 383
Biological Evolution and Historical Development 387
CHAPTER 12. TOOLS OF SCIENCE 395
Labor and Cognition 395
The Emergence of Science 396
The Role of the Tools of Scientific Work 398
Continuity and Discontinuity of the Development of Science 401
LIST OF ORIGINAL PUBLICATIONS 405
NAME INDEX 407
SUBJECT INDEX 411
|
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| discipline | Psychologie Mathematik Philosophie |
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| indexdate | 2024-07-09T17:57:25Z |
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| isbn | 0792338162 9789048146444 |
| language | English German |
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| spelling | Damerow, Peter 1939-2011 Verfasser (DE-588)12127134X aut Abstraction and representation essays on the cultural evolution of thinking Peter Damerow Dordrecht u.a. Kluwer 1996 XIV, 414 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Boston studies in the philosophy of science 175 Aus d. Dt. übers. Abstractie gtt Abstraction ram Cognition ram Denken gtt Getalbegrip gtt Mentale representatie gtt Représentation mentale ram Abstraction Mental representation Thought and thinking Mathematik (DE-588)4037944-9 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Kognitive Entwicklung (DE-588)4133279-9 gnd rswk-swf Abstraktion (DE-588)4141162-6 gnd rswk-swf Methode (DE-588)4038971-6 gnd rswk-swf Mathematik (DE-588)4037944-9 s Methode (DE-588)4038971-6 s Geschichte (DE-588)4020517-4 s DE-604 Abstraktion (DE-588)4141162-6 s Kognitive Entwicklung (DE-588)4133279-9 s Boston studies in the philosophy of science 175 (DE-604)BV023547349 175 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007142130&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Damerow, Peter 1939-2011 Abstraction and representation essays on the cultural evolution of thinking Boston studies in the philosophy of science Abstractie gtt Abstraction ram Cognition ram Denken gtt Getalbegrip gtt Mentale representatie gtt Représentation mentale ram Abstraction Mental representation Thought and thinking Mathematik (DE-588)4037944-9 gnd Geschichte (DE-588)4020517-4 gnd Kognitive Entwicklung (DE-588)4133279-9 gnd Abstraktion (DE-588)4141162-6 gnd Methode (DE-588)4038971-6 gnd |
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| title | Abstraction and representation essays on the cultural evolution of thinking |
| title_auth | Abstraction and representation essays on the cultural evolution of thinking |
| title_exact_search | Abstraction and representation essays on the cultural evolution of thinking |
| title_full | Abstraction and representation essays on the cultural evolution of thinking Peter Damerow |
| title_fullStr | Abstraction and representation essays on the cultural evolution of thinking Peter Damerow |
| title_full_unstemmed | Abstraction and representation essays on the cultural evolution of thinking Peter Damerow |
| title_short | Abstraction and representation |
| title_sort | abstraction and representation essays on the cultural evolution of thinking |
| title_sub | essays on the cultural evolution of thinking |
| topic | Abstractie gtt Abstraction ram Cognition ram Denken gtt Getalbegrip gtt Mentale representatie gtt Représentation mentale ram Abstraction Mental representation Thought and thinking Mathematik (DE-588)4037944-9 gnd Geschichte (DE-588)4020517-4 gnd Kognitive Entwicklung (DE-588)4133279-9 gnd Abstraktion (DE-588)4141162-6 gnd Methode (DE-588)4038971-6 gnd |
| topic_facet | Abstractie Abstraction Cognition Denken Getalbegrip Mentale representatie Représentation mentale Mental representation Thought and thinking Mathematik Geschichte Kognitive Entwicklung Abstraktion Methode |
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