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.
Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain. These are but a few of the wealth of fascinating observations contained here. We also discover, for example, that because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--English-speaking people can only remember seven. The book also explores the unique abilities of idiot savants and mathematical geniuses, and we meet people whose minute brain lesions render their mathematical ability useless. This new and completely updated edition includes all of the most recent scientific data on how numbers are encoded by single neurons, and which brain areas activate when we perform calculations. Perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in learning, mathematics, or the mind. "A delight." --Ian Stewart, New Scientist "Read The Number Sense for its rich insights into matters as varying as the cuneiform depiction of numbers, why Jean Piaget's theory of stages in infant learning is wrong, and to discover the brain regions involved in the number sense." --The New York Times Book Review "Dehaene weaves the latest technical research into a remarkably lucid and engrossing investigation. Even readers normally indifferent to mathematics will find themselves marveling at the wonder of minds making numbers." --Booklist
How does the brain represent number and make mathematical calculations? What underlies the development of numerical and mathematical abilities? What factors affect the learning of numerical concepts and skills? What are the biological bases of number knowledge? Do humans and other animals share similar numerical representations and processes? What underlies numerical and mathematical disabilities and disorders, and what is the prognosis for rehabilitation? These questions are the domain of mathematical cognition, the field of research concerned with the cognitive and neurological processes that underlie numerical and mathematical abilities. The Handbook of Mathematical Cognition is a collection of 27 essays by leading researchers that provides a comprehensive review of this important research field.
Demonstrates that an innate sense of numbers is as integral to the makeup of the human brain as the sense of language, arguing that there is a math gene and that mathematics is fundamental to human nature
Author: Marc S. Schwartz
Release Date: 2017-10-05
Research in Mind, Brain, and Education cuts across and unites areas of Mind, Brain, and Education (MBE) to introduce foundational and emerging topics in the field. With chapters written by leading scholars, this book offers empirical research on specific topics including autism, math, reading, and emotion, as well as conceptual guidance on the role of models and epistemological considerations relevant to MBE. Each chapter seeks to provide a platform for exploring questions, tools, and models central to current work in MBE by emphasizing investigative focus and influences. Designed both as a supplementary text for advanced undergraduate or early graduate training and as an introduction for educators, researchers, and policy makers, Research in Mind, Brain, and Education showcases the collaborative, innovative, and dynamic approach to research that is fundamental to the discipline.
Author: Kaiser Fung
Publisher: McGraw Hill Professional
Release Date: 2013-07-12
How to make simple sense of complex statistics--from the author of Numbers Rule Your World We live in a world of Big Data--and it's getting bigger every day. Virtually every choice we make hinges on how someone generates data . . . and how someone else interprets it--whether we realize it or not. Where do you send your child for the best education? Big Data. Which airline should you choose to ensure a timely arrival? Big Data. Who will you vote for in the next election? Big Data. The problem is, the more data we have, the more difficult it is to interpret it. From world leaders to average citizens, everyone is prone to making critical decisions based on poor data interpretations. In Numbersense, expert statistician Kaiser Fung explains when you should accept the conclusions of the Big Data "experts"--and when you should say, "Wait . . . what?" He delves deeply into a wide range of topics, offering the answers to important questions, such as: How does the college ranking system really work? Can an obesity measure solve America's biggest healthcare crisis? Should you trust current unemployment data issued by the government? How do you improve your fantasy sports team? Should you worry about businesses that track your data? Don't take for granted statements made in the media, by our leaders, or even by your best friend. We're on information overload today, and there's a lot of bad information out there. Numbersense gives you the insight into how Big Data interpretation works--and how it too often doesn't work. You won't come away with the skills of a professional statistician. But you will have a keen understanding of the data traps even the best statisticians can fall into, and you'll trust the mental alarm that goes off in your head when something just doesn't seem to add up. Praise for Numbersense "Numbersense correctly puts the emphasis not on the size of big data, but on the analysis of it. Lots of fun stories, plenty of lessons learned—in short, a great way to acquire your own sense of numbers!" Thomas H. Davenport, coauthor of Competing on Analytics and President’s Distinguished Professor of IT and Management, Babson College "Kaiser’s accessible business book will blow your mind like no other. You’ll be smarter, and you won’t even realize it. Buy. It. Now." Avinash Kaushik, Digital Marketing Evangelist, Google, and author, Web Analytics 2.0 "Each story in Numbersense goes deep into what you have to think about before you trust the numbers. Kaiser Fung ably demonstrates that it takes skill and resourcefulness to make the numbers confess their meaning." John Sall, Executive Vice President, SAS Institute "Kaiser Fung breaks the bad news—a ton more data is no panacea—but then has got your back, revealing the pitfalls of analysis with stimulating stories from the front lines of business, politics, health care, government, and education. The remedy isn’t an advanced degree, nor is it common sense. You need Numbersense." Eric Siegel, founder, Predictive Analytics World, and author, Predictive Analytics "I laughed my way through this superb-useful-fun book and learned and relearned a lot. Highly recommended!" Tom Peters, author of In Search of Excellence
A renowned cognitive neuroscientist?s fascinating and highly informative account of how the brain acquires reading How can a few black marks on a white page evoke an entire universe of sounds and meanings? In this riveting investigation, Stanislas Dehaene provides an accessible account of the brain circuitry of reading and explores what he calls the ?reading paradox?: Our cortex is the product of millions of years of evolution in a world without writing, so how did it adapt to recognize words? Reading in the Brain describes pioneering research on how we process language, revealing the hidden logic of spelling and the existence of powerful unconscious mechanisms for decoding words of any size, case, or font. Dehaene?s research will fascinate not only readers interested in science and culture, but also educators concerned with debates on how we learn to read, and who wrestle with pathologies such as dyslexia. Like Steven Pinker, Dehaene argues that the mind is not a blank slate: Writing systems across all cultures rely on the same brain circuits, and reading is only possible insofar as it fits within the limits of a primate brain. Setting cutting-edge science in the context of cultural debate, Reading in the Brain is an unparalleled guide to a uniquely human ability.
The authors report the results of some half dozen years of research into when and how children acquire numerical skills. They provide a new set of answers to these questions, and overturn much of the traditional wisdom on the subject. Table of Contents: 1. Focus on the Preschooler 2. Training Studies Reconsidered 3. More Capacity Than Meets the Eye: Direct Evidence 4. Number Concepts in the Preschooler? 5. What Numerosities Can the Young Child Represent? 6. How Do Young Children Obtain Their Representations of Numerosity? 7. The Counting Model 8. The Development of the How-To-Count Principles 9. The Abstraction and Order-Irrelevance Counting Principles 10. Reasoning about Number 11. Formal Arithmetic and the Young Child's Understanding of Number 12. What Develops and How Conclusions References Index Reviews of this book: The publication of this book may mark a sea change in the way that we think about cognitive development. For the past two decades, the emphasis has been on young children's limitations... Now a new trend is emerging: to challenge the original assumption of young children's cognitive incapacity. The Child's Understanding of Number represents the most original and provocative manifestation to date of this new trend. --Contemporary Psychology Reviews of this book: Here at last is the book we have been waiting for, or at any rate known we needed, on the young child and number. The authors are at once sophisticated in their own understanding of number and rich in psychological intuition. They present a wealth of good experiments to support and guide their intuitions. And all is told in so simple and unalarming a manner that even the most pusillanimous will be able to read with enjoyment. --Canadian Journal of Psychology
Why is math so hard? And why, despite this difficulty, are some people so good at it? If there's some inborn capacity for mathematical thinking—which there must be, otherwise no one could do it —why can't we all do it well? Keith Devlin has answers to all these difficult questions, and in giving them shows us how mathematical ability evolved, why it's a part of language ability, and how we can make better use of this innate talent.He also offers a breathtakingly new theory of language development—that language evolved in two stages, and its main purpose was not communication—to show that the ability to think mathematically arose out of the same symbol-manipulating ability that was so crucial to the emergence of true language. Why, then, can't we do math as well as we can speak? The answer, says Devlin, is that we can and do—we just don't recognize when we're using mathematical reasoning.