Dehaene / Brannon Space, Time and Number in the Brain

Searching for the Foundations of Mathematical Thought
1. Auflage 2011
ISBN: 978-0-12-385949-5
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 374 Seiten

The study of mathematical cognition and the ways in which the ideas of space, time and number are encoded in brain circuitry has become a fundamental issue for neuroscience. How such encoding differs across cultures and educational level is of further interest in education and neuropsychology. This rapidly expanding field of research is overdue for an interdisciplinary volume such as this, which deals with the neurological and psychological foundations of human numeric capacity. A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology. - The first comprehensive and authoritative volume dealing with neurological and psychological foundations of mathematical cognition - Uniquely integrative volume at the frontier of a rapidly expanding interdisciplinary field - Features outstanding and truly international scholarship, with chapters written by leading experts in a variety of fields

Autoren/Hrsg.

Dehaene, Stanislas

Brannon, Elizabeth

Inhaltsverzeichnis

1;Front Cover;1
2;Space, Time and Number in the Brain;4
3;Copyright Page;5
4;Contents;6
5;Contributors;8
6;Foreword;10
6.1;Quantity Codes;11
6.2;Developmental Origins;11
6.3;Cross-Dimensional Interactions and Metaphors;11
6.4;Quantitative Computations;12
6.5;Thought with or Without Symbols;12
6.6;Human Turing Machine;12
6.7;Impact of Culture and Education;12
6.8;Acknowledgments;13
7;Section I. Mental Magnitudes and their Transformations;14
7.1;Chapter 1. Mental Magnitudes;16
7.1.1;Computational Implications of Behavioral Results;18
7.1.2;Constraints on Mental Magnitudes;19
7.1.3;Conclusions;24
7.1.4;References;24
7.2;Chapter 2. Objects, Sets, and Ensembles;26
7.2.1;Representing Individual Items in Working Memory;28
7.2.2;Representing Sets of Items in Working Memory;29
7.2.3;Representing Ensembles in Working Memory;30
7.2.4;Conclusions;33
7.2.5;References;33
7.3;Chapter 3. Attention Mechanisms for Counting in Stabilized and in Dynamic Displays;36
7.3.1;Explicit Counting;36
7.3.2;Experiment 1: What is the Limit for Explicit Counting in Afterimages?;41
7.3.3;What is the Limit for Explicit Counting in Moving Displays?;44
7.3.4;Conclusions;45
7.3.5;Acknowledgments;47
7.3.6;References;47
8;Section II. Neural Codes for Space, Time and Number;50
8.1;Chapter 4. A Manifold of Spatial Maps in the Brain;54
8.1.1;Spatial Maps in the Brain;54
8.1.2;Hippocampal Maps;55
8.1.3;Entorhinal Maps;58
8.1.4;Relation Between Entorhinal and Hippocampal Maps;61
8.1.5;The Manifold of Entorhinal and Hippocampal Maps;61
8.1.6;Dynamic Maps;63
8.1.7;Can Several Maps Be Active Simultaneously?;65
8.1.8;Concluding Remarks;65
8.1.9;Acknowledgments;67
8.1.10;References;67
8.2;Chapter 5. Temporal Neuronal Oscillations can Produce Spatial Phase Codes;72
8.2.1;A Functional Role for Interference Between Neuronal Oscillations;73
8.2.2;An Oscillatory Interference Model of Grid Cell Firing;75
8.2.3;Oscillatory Interference and Representations of Sequential Order?;78
8.2.4;Summary and Conclusions;80
8.2.5;Acknowledgments;80
8.2.6;References;81
8.3;Chapter 6. Population Clocks: Motor Timing with Neural Dynamics;84
8.3.1;The Problem of Time;84
8.3.2;Motor Timing;86
8.3.3;Models of Timing;87
8.3.4;Dynamics in Recurrent Networks;90
8.3.5;Neural Correlates of Timing;92
8.3.6;Concluding Remarks;94
8.3.7;Acknowledgments;95
8.3.8;References;95
8.4;Chapter 7. Discrete Neuroanatomical Substrates for Generating and Updating Temporal Expectations;100
8.4.1;Temporal Orienting of Attention: Temporal Expectations Derived from Learned Cues;101
8.4.2;Rhythm and Speed: Temporal Expectations Derived from Regular Stimulus Dynamics;107
8.4.3;The Hazard Function: Temporal Expectations Derived from the Flow of Time Itself;107
8.4.4;Conclusions: Generating vs Updating Temporal Expectations;108
8.4.5;References;111
8.5;Chapter 8. The Neural Code for Number;116
8.5.1;Neurons Encoding Numerical Quantity;117
8.5.2;Coding of Continuous and Discrete Quantity;125
8.5.3;Coding of Proportions;127
8.5.4;Towards Symbolic Number Representations;128
8.5.5;References;130
9;Section III. Shared Mechanisms for Space, Time and Number?;132
9.1;Chapter 9. Synesthesia: Gluing Together Time, Number, and Space;136
9.1.1;Is it Really Synesthesia?;137
9.1.2;The Effect of TNS Synesthesia on Everyday Cognitive Processes;138
9.1.3;Neural Processes of TNS Synesthesia;140
9.1.4;TNS Synesthesia: Symbolic or Non-Symbolic?;142
9.1.5;Conclusions;142
9.1.6;Acknowledgments;142
9.1.7;References;143
9.2;Chapter 10. How is Number Associated with Space? The Role of Working Memory;146
9.2.1;Dissociating the Number Interval Bisection Bias from the Line Bisection Bias;149
9.2.2;Dissociating Snarc from the Number Line: Conceptual Vs Visuospatial Representations;151
9.2.3;The Snarc Effect: A Crucial Role for Working Memory;152
9.2.4;General Discussion;155
9.2.5;References;159
9.3;Chapter 11. Neglect “Around the Clock”: Dissociating Number and Spatial Neglect in Right Brain Damage;162
9.3.1;Number–Space Association in the Healthy Brain;163
9.3.2;Neglect in Visual and Number Space;170
9.3.3;A Further Twist to Number Space Neglect: Bisecting “Around the Clock”;174
9.3.4;Discussion and Conclusions;180
9.3.5;Acknowledgments;183
9.3.6;References;183
9.4;Chapter 12. Saccades Compress Space, Time, and Number;188
9.4.1;Space, Time, and Number as Visual Primitives;189
9.4.2;A Common Metric for Magnitude;189
9.4.3;A Visual Sense of Number;189
9.4.4;Interactions Between Space, Time, and Number;190
9.4.5;Effects of Saccades on Space, Time, and Number;193
9.4.6;Conclusions;196
9.4.7;Acknowledgments;197
9.4.8;References;197
10;Section IV. Origins of Proto-Mathematical Intuitions;200
10.1;Chapter 13. Origins of Spatial, Temporal, and Numerical Cognition: Insights from Comparative Psychology;204
10.1.1;Researching Human Cognition Through the Study of other Species;205
10.1.2;Are Some Cognitive Capacities in Place at Birth?;205
10.1.3;What is the Evolutionary Endowment of Human Cognition?;208
10.1.4;Closely Related Animal Models;208
10.1.5;Which Cognitive Abilities are Uniquely Human?;213
10.1.6;Distantly Related Animal Models;213
10.1.7;Concluding Remarks;215
10.1.8;References;217
10.2;Chapter 14. Evolutionary Foundations of the Approximate Number System;220
10.2.1;Shared Systems for Number Representation;222
10.2.2;The Relationship Between Time, Space, and Number;228
10.2.3;Arithmetic Reasoning;230
10.2.4;Conclusions;233
10.2.5;References;234
10.3;Chapter 15. Origins and Development of Generalized Magnitude Representation;238
10.3.1;The Big Three: Spatial Extent, Number, and Time;239
10.3.2;Beyond the Big Three Magnitudes and Cross-Modal Transfer;245
10.3.3;Particulars of the General Magnitude System;249
10.3.4;Conclusions;252
10.3.5;Acknowledgments;252
10.3.6;References;252
11;Section V. Representational Change and Education;258
11.1;Chapter 16. Foundational Numerical Capacities and the Origins of Dyscalculia;262
11.1.1;Why are People Bad at Learning Arithmetic?;262
11.1.2;Domain-Specific Foundational Capacities for Arithmetic;264
11.1.3;The Approximate Number System;266
11.1.4;The Small Numerosity System;267
11.1.5;Numerosity Coding;268
11.1.6;The Role of Language;270
11.1.7;The Neural Basis of Dyscalculia;271
11.1.8;Intervention;273
11.1.9;Concluding Remarks;273
11.1.10;Acknowledgments;275
11.1.11;References;275
11.2;Chapter 17. Neurocognitive Start-Up Tools for Symbolic Number Representations;280
11.2.1;The Approximate Number System;281
11.2.2;The Object Tracking System;283
11.2.3;The Role of the ANS and the OTS in the Acquisition of Symbolic Number Representations;285
11.2.4;Evidence for a Foundational Role of the ANS in Symbolic Number Processing;286
11.2.5;Evidence for a Foundational Role of the OTS in Symbolic Number Processing;291
11.2.6;Concluding Remarks;293
11.2.7;References;295
11.3;Chapter 18. Natural Number and Natural Geometry;300
11.3.1;A Core System of Number;302
11.3.2;A Core System of Geometry;307
11.3.3;More Core Systems;316
11.3.4;Constructing Natural Number;317
11.3.5;Constructing Natural Geometry;318
11.3.6;Conclusion and Prospects;326
11.3.7;References;327
11.4;Chapter 19. Geometry as a Universal Mental Construction;332
11.4.1;Universal Geometric Intuitions;334
11.4.2;Perception of Abstract Geometric Features;334
11.4.3;Normative Geometric Concepts;339
11.4.4;Conclusion;342
11.4.5;Acknowledgments;344
11.4.6;References;344
11.5;Chapter 20. How Languages Construct Time;346
11.5.1;The Axes of Time;347
11.5.2;Motion in Time;349
11.5.3;Reversing the Direction of Time;349
11.5.4;Duration;350
11.5.5;Representations of Time in Absolute Space;350
11.5.6;Summary;351
11.5.7;References;352
11.6;Chapter 21. Improving Low-Income Children’s Number Sense;356
11.6.1;Does Playing Numerical Board Games Improve Children’s Number Sense?;360
11.6.2;Generality of Learning Across Tasks and Time;361
11.6.3;Game Playing in the Everyday Environment;362
11.6.4;Which Features of Board Games Influence Learning?;363
11.6.5;Effects of other Preschool Mathematics Interventions;364
11.6.6;Conclusions;365
11.6.7;References;366
12;Index;368