The Number Sense: How the Mind Creates Mathematics

Several years ago I was trying to organize a conference on the topic of how we learn mathematics. I needed someone who could present for two and one-half days on the subject. I called some of the top researchers in the United States and they all declined because, as they said, no one on the planet knew enough to be able to fill all of that time. By 2009 that had changed. By then there was enough research to have the conference I wanted. Most of it was hidden in scientific journals.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.

Hard to read but intriguing

Terrific math book that shows its importance and how it is logically tied to an array of human issues. .Favorite chapter? SIx - 'Geniuses and prodigies'. This book will instill an abiding appreciation of math in most everyone that reads it.

Great research and examples and studies of how we learn math and how the brain struggles with it.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.

I enjoyed this book very much and was impressed by the knowledge of the author. He explained some quite complicated science in an easy to understand manner. He combined a historic review with new research in an impressive way. I look forward to reading more from this author.

Dr. Dehanae has continued his research. Neuroscience has advanced so far in the last 10 years that there is very little to glean from this this book. See instead, Reading in the brain and for information on number processing, Dr. Dehanae's latest publications.

Great background for understanding our innate sense for math. Well written and logical. Anyone teaching mathematics to any age will benefit from reading it.

Let me start by saying that I have a large interest in both the fields of mathematics and neuroscience. And so when I came across this book with its outstandingly positive reviews, I decided to give it a try.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!

Nothing wrong with the book but a little dry as a read!

「２と７はどちらが大きい数か？」と聞かれたらあなたは即座に７と答えられるだろう。「では４と５はどちらが大きい数か？」と聞かれても即座に５と答えられるだろう。取るに足らない問いであると思われるかもしれない。しかし前者に比べ、後者の問いの答えにあなたはより長い時間を要したことに気付いたであろうか。言語機能が正常でも、このような数の大小に関する問いに答えられない障害をもった人々がいることをあなたは知っているだろうか。これら数認知に関する知見に加え、生後どの時期からどれだけ正確にそして脳のどの部位がかかわることにより数が認知されているのか、これまでの研究で得られた知見は決して少なくない。数を扱った情報が飛び交う現代社会では日常生活の場はもちろん、算数教育の現場においても数認知の知見が有用であることは疑うべくもない。本書では、数の錯覚や、動物や赤ちゃんの数認知、数認知疾患の症例、最近の脳機能イメージング手法による数認知の研究を幅広く、一般の読者にも分かるよう丁寧に説明されている。日本語版が出版されなかったため我々日本人にとっては読むのに時間がかかるのが残念だが、一読すればあなたの好奇心が掻き立てられることは信じて疑わない。