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| Preface | |
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| Introduction | |
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| Our Numerical Heritage | |
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| Talented and Gifted Animals | |
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| A Horse Named Hans | |
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| Rat Accountants | |
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| How Abstract Are Animal Calculations? | |
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| The Accumulator Metaphor | |
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| Number-Detecting Neurons? | |
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| Fuzzy Counting | |
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| The Limits of Animal Mathematics | |
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| From Animal to Human | |
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| Babies Who Count | |
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| Baby Building: Piaget's Theory | |
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| Piaget's Errors | |
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| Younger and Younger | |
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| Babies' Power of Abstraction | |
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| How Much Is 1 plus 1? | |
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| The Limits of Infant Arithmetic | |
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| Nature, Nurture, and Number | |
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| The Adult Number Line | |
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| 1, 2, 3, and Beyond | |
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| Approximating Large Numbers | |
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| The Quantity Behind the Symbols | |
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| The Mental Compression of Large Numbers | |
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| Reflexive Access to Number Meaning | |
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| A Sense of Space | |
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| Do Numbers Have Colors? | |
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| Intuitions of Number | |
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| Beyond Approximation | |
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| The Language of Numbers | |
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| A Short History of Number | |
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| Keeping a Permanent Trace of Numerals | |
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| The Place-Value Principle | |
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| An Exuberant Diversity of Number Languages | |
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| The Cost of Speaking English | |
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| Learning to Label Quantities | |
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| Round Numbers, Sharp Numbers | |
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| Why Are Some Numerals More Frequent Than Others? | |
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| Cerebral Constraints on Cultural Evolution | |
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| Small Heads for Big Calculations | |
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| Counting: The ABC of Calculation | |
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| Preschoolers as Algorithm Designers | |
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| Memory Appears on the Scene | |
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| The Multiplication Table: An Unnatural Practice? | |
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| Verbal Memory to the Rescue | |
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| Mental Bugs | |
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| Pros and Cons of the Electronic Calculator | |
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| Innumeracy: Clear and Present Danger? | |
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| Teaching Number Sense | |
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| Geniuses and Prodigies | |
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| A Numerical Bestiary | |
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| The Landscape of Numbers | |
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| Phrenology and the Search for Biological Bases of Genius | |
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| Is Mathematical Talent a Biological Gift? | |
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| When Passion Produces Talent | |
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| Ordinary Parameters for Extraordinary Calculators | |
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| Recipes for Lightning Calculation | |
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| Talent and Mathematical Invention | |
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| Of Neurons and Numbers | |
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| Losing Number Sense | |
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| Mr. N, the Approximate Man | |
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| A Clear-Cut Deficit | |
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| A Champion in Numerical Non-sense | |
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| Inferior Parietal Cortex and the Number Sense | |
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| Seizures Induced by Mathematics | |
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| The Multiple Meanings of Numbers | |
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| The Brain's Numerical Information Highways | |
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| Who Orchestrates the Brain's Computations? | |
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| At the Origins of Cerebral Specialization | |
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| The Computing Brain | |
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| Does Mental Calculation Increase Brain Metabolism? | |
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| The Principle of Positron Emission Tomography | |
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| Can One Localize Mathematical Thought? | |
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| When the Brain Multiplies or Compares | |
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| The Limits of Positron Emission Tomography | |
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| The Brain Electric | |
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| The Time Line of the Number Line | |
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| Understanding the Word "Eighteen" | |
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| Numerate Neurons | |
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| What Is a Number? | |
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| Is the Brain a Logical Machine? | |
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| Analog Computations in the Brain | |
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| When Intuition Outruns Axioms | |
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| Platonists, Formalists, and Intuitionists | |
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| The Construction and Selection of Mathematics | |
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| The Unreasonable Effectiveness of Mathematics | |
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| Appendix | |
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| Notes and References | |
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| Index | |