Intuition in Science and Mathematics - E. Fischbein (2005) WW.pdf

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INTUITION IN SCIENCE AND MATHEMATICS
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TABLE OF CONTENTS
PREFACE
ix
ACKNOWLEDGMENTS
xiii
PART I: THE THEORY
CHAPTER 1 / Intuition and the Need for Certitude
3
The Complexity of the Domain
3
The Need for Certitude
7
A Preliminary Definition
13
15
C HA PTER 2 / Intuition and Mathematical Reasoning
The Real World and the Mathematical World
15
The Behavioral Meaning of Mathematical Concepts
19
Axiomatic Structures and Intuitive Procedures
22
Intuitive Concepts and the Scientific Community
24
28
CHAPTER 3 / Investigations in Overconfidence
Overconfidence and Intuitive Biases
28
Educational Implications: Overconfidence and Metacognition
41
43
CHAPTER 4 / General Characteristics ofIntuitive Cognitions
Self - Evidence
4 3
Intrinsic Certainty
45
Perseverance
47
Coerciveness
47
Extrapolativeness
50
Globality
53
Implicitness
5 4
Summary
56
57
CHAPTER 5/ The Classification ofIntuitions
Piaget’s Classification
57
Classifications of Intuitions Based on Roles and Origins
58
Summary
70
CHAPTER 6 / Inferential Intuitions and Logical Reasoning
72
v
Summary
36
Theory Status
50
vi
TABLE OF CONTENTS
PART II: FACTORS WHICH SHAPE INTUITIONS
CHAPTER 7 / Intuition and Experience
85
The Behavioral Roots of Intuitive Representations
85
Experience and Intuitive Biases
89
Summary
95
CHAPTER 8 / The Practicality of Intuitive Meanings. Analysis of an
Example: The Negative Numbers
97
CHAPTER 9 / Factors ofImmediacy
Visualization
103
Availability
106
Anchoring
107
Representativeness
108
Summary
109
CH A PTER 10/Factors of Globality
Summary
111
CHAPTER 11 /Intuition and Intuitive Models
Classification ofModel Types
121
Role of Tacit Intuitive Models
125
127
CHAPTER 12 /Models andAnalogies
The Role of Analogy in Model Construction
127
Analogic Models in Mathematics
129
Analogies as Sources of Misconceptions in Mathematics
142
143
154
CHAPTER 13 /Paradigmatic Models
CHAPTER 14/Diagrammatic Models
Summary
165
CHAPTER 15 /Phenomenological Primitives
CHAPTER 16 / Conflictsand Compromises
Impetus versus Inertia
167
176
Striving for Cognitive Compromise
181
Impact of the Impetus Model: Further Experimental Evidence
184
Conciliatory Models
187
Summary
191
CHAPTER 17 / Factors of Perseverance and Closure: The Primacy
Effect
193
Summary and Comments
198
103
120
121
Summary
122
Summary
136
176
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TABLE OF CONTENTS
vii
CHAPTER 18 /Summary and Didactical Implications
200
The Role of Intuition: A Summary
200
The Classification of Intuitions
201
Intuitions and Models
202
The Mechanisms of Intuitions
204
Conflicts and Compromises
205
Didactical Implications
206
Concluding Remarks
21 1
BIBLIOGRAPHY
215
INDEX OF NAMES
223
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