- Paperback: 288 pages
- Publisher: Oxford University Press; 1 edition (December 9, 1999)
- Language: English
- ISBN-10: 0195132408
- ISBN-13: 978-0195132403
- Product Dimensions: 9 x 0.8 x 6 inches
- Shipping Weight: 12 ounces (View shipping rates and policies)
- Average Customer Review: 18 customer reviews
- Amazon Best Sellers Rank: #1,156,708 in Books (See Top 100 in Books)
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The Number Sense: How the Mind Creates Mathematics 1st Edition
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This may surprise those who have trouble carrying the remainder in division or figuring out a 15 percent tip on a $20 lunch bill, but according to mathematician and psychologist Stanislas Dehaene, mathematics is an inborn skill. In The Number Sense, Dehaene makes a compelling case for the human mind's innate grasp of mathematics. Take, for example, the fact that place value systems (such as the Arabic numeral system we use) arose independently in four separate civilizations--evidence of a universal sense of number. Dehaene's book is filled with examples to support his thesis, from young babies' ability to "count" (i.e., to react when single objects are replaced by two or more) to examples of how brain damage affects various individuals' number sense. Even more fascinating is his discussion of the relationship between language and numbers. Though Dehaene's book is about mathematics, even those readers with the worst math anxiety will find The Number Sense an intriguing exploration of the world of numbers--and the human mind. --This text refers to the Digital edition.
From Library Journal
This interesting and informative book sets forth the latest findings by Dehaene (research affiliate, Institut de la Sante et de la Recherche Medicale, Paris) and other psychologists trying to determine how the brain understands and manipulates numbers and other forms of mathematical information. Included are many startling results of experiments involving animals and infants that shed light on the extent and nature of our inborn number sense. Dahaene also describes how brain scans and computer simulations can help us understand possible differences in the ways the brain handles similar mathematical topics such as approximation, arithmetic computations, and algebra. These findings, if they receive the consideration they merit, should have a major impact on the way mathematics is taught at the elementary and secondary level. Highly recommended.?Harold D. Shane, Baruch College, CUNY
Copyright 1997 Reed Business Information, Inc. --This text refers to the Digital edition.
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This book is among the first to get the word out more generally about what we know about learning mathematics. It features solid science, is accessible to a general audience, and in some parts so amusingly handled that I found myself laughing out loud.
As a math teacher, I had long suspected mathematics was an unnatural act of the mind. Dehaene confirms my suspicion. The chapter on patients with severed corpora callosa put me in mind of similar split brain findings in the field of linguistics.
I'm not sure about the limits on subitizing. The handful of my students with innate math reasoning seems to be able to subitize beyond what Dehaene suggests.
Dehaene is a bit heavy-handed with the evolutionary build-up. Can we just observe the increasingly complex organization of living things along a continuum without making the presumption that nature is showing us a time-lapse film?
As MisterNumbers on Youtube it helps me understand what helps kids learn math. The Outliers by Malcolm Boyd has an amazing chapter that is based on this book.
After having read it I can say that this work definitely deserves the positive attention it has garnered thus far. This book is a very comprehensive start to what may be an ultimate understanding of the human (and indeed even animal!) affinity to numbers. Like others who reviewed before me have said, it is very cleanly organized, presents a wealth of compelling evidence from a variety of fascinating and ingenious experiments, and is a pleasure to read by both experts and laymen alike. In short, I recommend Dehaene's The Number Sense to anyone who is curious about how our brains deal with math.
Dehaene covers a wide range of topics throughout the course of this book, discussing what he calls the "number sense" in infants, adolescents, adults, and animals in the context of both classic and more modern experimentation. Fascinatingly, he talks about how even animals have a basic ability to approximate numbers and how some (such as chimpanzees and macaques) can even be trained to perform rudimentary arithmetic with Arabic numerals! Furthermore, he asserts that even human infants are born with an innate knowledge (albeit extremely limited) of numbers that can be detected using very clever experiments. In this way Dehaene has perhaps dispelled forever the long-held notion that mathematics is a purely human science learned after birth by means of human language. In all cases he provides solid, detailed evidence supporting his arguments and clearly explains every conclusion he reaches such that the information is readily accessible by even those modestly educated in the subject.
One of the more interesting and readily appreciable points Dehaene makes is the animal (humans included) inability to comprehend large numbers. He posits that we innately understand and grasp numbers only up to the number four; thus we are to able estimate and differentiate these discrete quantities quickly and accurately. Naturally Dehaene provides satisfactory experimental evidence to this conclusion. Beyond this however, our ability to discern exact quantities fades dramatically. What's more is that our ability to discern the difference between two nearly equal quantities drops rapidly as a function of quantity magnitude and the distance between them. More concisely, given two sets of chocolate chips, many higher life-forms can distinguish between the set that contains one versus the set that contains two, but none can distinguish 99 from 100 if they were laid out randomly. However, one could probably distinguish between sets of 50 and 100, but would be unable to accurately approximate the number of chips in either. This is perhaps something that we've all thought about (I know I have), but Dehaene takes it several steps further by giving it a name, establishing its ubiquity in all intelligent organisms, and by providing an evolutionarily sound explanation to this phenomenon.
Among other topics, Dehaene talks of the notion that a small percentage of people associate numbers with color and position in space, the ability of humans and some monkeys to understand fractions, differences in mathematical abilities based on the language one learns to count in, whether or not the human brain is a logic machine that calculates based on set algorithms like a computer, and why the number crunching capacity of a trained prodigy is still vastly inferior to that of a modern calculator. In all, there were a great number of highly fascinating topics about the science, psychology, neuroscience, and philosophy of mathematics to be read about in this work.
Perhaps the part I least enjoyed about this book was reading through all of the data that Dahaene provides. Make no mistake, Dehaene writes in great form and provides ample support for every claim he asserts. Equally importantly, he clearly labels his own conjecture as such. He writes how a scientist should write in my opinion. However, he provides so much detail in the way of experimental evidence that I found the reading to be rather slow at points. Long after a point Dehaene is trying to make is firmly established in my mind, I still find myself reading evidence in support of his argument. But among the list of things that could be considered wrong with a book, my grievance ranks pretty low, and by no means did the reading get slow all the time.
In summary I highly recommend this book to both experts and laymen alike. It is full of fascinating information and interesting experiments that elucidate some of the neuoscientific basis of mathematics. Furthermore, it uses clear, concise, and at times humorous logic to explain the number sense that is so obviously present in humans and animals alike. My only complaint is a very minor one about a slight excess of detail in some areas. But I would nonetheless say that this was a highly enjoyable read and a great learning experience for me. If I've piqued your interest in this review, then make sure to read this book!