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Number Sense How the Mind Creates Mathematics

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ISBN-10: 0195132408

ISBN-13: 9780195132403

Edition: 1999

Authors: Stanislas Dehaene

List price: $46.95
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Description:

The Number Sense is an enlightening exploration of the mathematical mind. Describing experiments that show that human infants have a rudimentary number sense, Stanislas Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.
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Book details

List price: $46.95
Copyright year: 1999
Publisher: Oxford University Press, Incorporated
Publication date: 12/9/1999
Binding: Paperback
Pages: 288
Size: 6.25" wide x 9.50" long x 0.75" tall
Weight: 0.880
Language: English

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