The Number Sense: How the Mind Creates Mathematics

by Stanislas Dehaene

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.

Genres: Science, Mathematics, Psychology, Nonfiction, Neuroscience, Education, Parenting

288 pages, Paperback

First published January 1, 1996

Reviews

[Chris · Rating 4 out of 5]

This is the earliest of Dehaene's three books about the brain and how it supports mathematics, reading, and consciousness. I have read these books in reverse order, beginning with the latest, Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts, an epic up-to-the-minute treatise that spares no detail, and which is a model of excellent scientific writing. His earlier book on reading, Reading in the Brain: The Science and Evolution of a Human Invention, was written in a similar way, and again, is thoroughly educating without an unwelcome excessive "dumbing-down," which is so common in much of modern popular science writing.

The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition is written with the same expertise as his later two books. Still, the material is somewhat dated (1998 for the original edition). Dehaene does add a new final chapter updating the state of knowledge to 2011. It would have been better for the reader to have wholly rewritten the book, integrating the new last chapter into the relevant older sections, thus relieving the reader of having to stitch and replace the new data onto what he might have remembered from the old.

My interest in the various chapters was somewhat uneven and they seemed scattered. Those covering the basic (rather simple) hypothesis on number sense are essential. Then, Dehaene spends too much time covering how a child's mathematical ability increases from birth to adolescence. His motivation is clear: he rails against the failed "new math" teaching of the 1970s, and rebuts that pedagogy with opposing scientific data. Good historical background, indeed, but we're past that true educational disaster now, I hope. Then...there is a fascinating chapter on the nature of mathematical prodigies, and the calculating techniques which they use, that "flew by." Excellent, but too short.

The last part of the book covers brain imaging and locating those brain areas responsible for particular math abilities such as numerosity recognition, number comparison, addition/subtraction, and calculation. I admit to jumping to the conclusions here: in his books on consciousness and reading, cited above, Dehaene goes deep into PET and fMRI imaging for those activities, presenting it very well and convincingly. Therefore I was already prepared to accept the application of the same techniques to mathematics processing, and go directly to the summary results without reading all the details.

I don't know of any practicing research scientist, in any field, who is writing books for an educated, intelligent public, that does it better than Dehaene. I can't wait for his next book, whatever it might be.

[Huyen · Rating 4 out of 5]

One day, a group of friends of mine and I somehow randomly came up with this random question: how universal are numbers and mathematics? Why is it that all cultures seem to have some concept of numbers? So we came up with this game, we would agree not to use any number for a day to find out how hard it was. And holy crap, it is ten thousands times harder than we could ever imagine, not only because we were a bunch of physicists, but even simplest things like: what time is it? where’s your house? became unbearably difficult to express. So we tried to figure out a way to express our ideas using other concepts. For example, if you want to say it’s 10 a.m, you say the sun is at that or that position. Or you want to say your house is 15 min away, you say follow this road, turn right at this tree, stop at that white house with a cactus in the garden. If you have 10 sheep, maybe you can name all of them, and when one is missing, you can go: hah! Bob has gone missing today. But having 100 sheep will really cause you a headache. We gave up after a few hours.
So i was thinking about this problem for a very long time. How universal are numbers? Do we have an innate sense of numbers? How would life be without them? would it even be possible? I never knew if anyone had come up with the same question but i randomly found this book, which i thought would be very interesting. And it is.
(to be cont.)

[Cynda · Rating 4 out of 5]

About the psychology of math.
Insightful.
Accessible.
Explains how babies, the average person, the mentally challenged, etc understand math.
I now know that there are no Math-Magicians. There are people impassioned about math, those who have time and resources to pursue, those who can visualize better, those who can use the tips, tricks, and components better.
As well as there no Math-Magicians, there no Math-Dummies. Math is difficult. We have re-cruit the brain. We do not have natural ability for formal math, such as learning the multiplication tables. Re-circuiting the brain requires great effort.
And we do not even agree on what numbers are.
I have only the math required to get a Bachelor of Arts--college Alegra and Trigonometry
--and I almost always understood, always enough to understand the big idea being discussed.

[Alison Rini · Rating 5 out of 5]

What an incredible window onto the brain’s construction of math and numbers! He clearly demonstrated each finding - with descriptions of brilliantly designed experiments, pictures of different areas of brain activity, or illuminating graphs. So yeah, maybe this book isn’t for everyone, but it certainly was perfect for me! “The classroom is our next lab…” Indeed!!!

[Daniel Durantes · Rating 4 out of 5]

De una forma didáctica y entretenida, Dehaene nos explica cómo se configura el sentido numérico en nuestro cerebro, haciendo especial énfasis en lo que viene dado a nivel evolutivo pero también explicando lo que puede darse a partir del lenguaje y del aprendizaje simbólico. A pesar de que en algunos puntos me he perdido un poco porque ando flojo de neuroanatomía, es interesante ver los experimentos que describe y cómo se ha ido descubriendo cómo nuestro cerebro identifica, interpreta, compara y opera los números, y cómo algunas enfermedades pueden influir en esos procesos.

[Pam]

"The squirrel that notices that a branch bears two nuts, and neglects it for another one that bears three, will have more chances of making it safely through the winter." page 23 I'm not sure I agree with this statement. I believe that the squirrel that gathers nuts from the branch with 2 nuts AND also from the branch with 3 nuts will have 5 nuts (2+3=5) and therefore have more than 3 nuts, and the BEST chance to survive. I'm not arguing with the author on whether animals have number sense (as I think the evidence shows they do), just that this particular statement doesn't make sense to me.

I'm geeking out a bit over the fact that David Premack's work is mentioned in this book. Premack's Principle is also known as "Grandma's Law" ie: First eat your meat then you can have your pudding. (First eat your vegetables then you can have dessert). A high probability behavior (ie: getting to eat dessert) will reinforce a lower probability behavior (ie: having to eat your vegetables). I use this daily in my work as an applied behavior analyst...and as a mother.

In this book, Premack's work is mentioned in relation to experiments with chimpanzees where, "When the sample stimulus was made of one-quarter apple and one-half glass, and the choice was between one-half disc or three-quarters disc, the animals chose the latter more often than chance alone would predict. They were obviously performing an internal calculation, not unlike the addition of two fractions 1/4 + 1/2 = 3/4. Presumably they did not use sophisticated calculation algorithms as we would. But they clearly had an intuitive grasp of how these proportions should combine." page 25 So this makes me think...if chimpanzees have the ability to add fractions (even while avoiding "sophisticated calculation algorithms") why can fractions be so difficult for people to learn in school. My hypothesis is that we move in with the "sophisticated calculation algorithms" too soon, which causes children to tune out their " intuitive grasp of how these proportions should combine." We as teachers/parents should spend a whole lot of time, during the early years, showing pictures and real world examples and 3D examples of fractions for children to explore and learn much in advance of adding the "sophisticated calculation algorithms."

page 34 "Fuzzy Counting" The author refers to Alice in Wonderland when the Red Queen asks her, "'What's one and one and one and one and one and one and one and one and one and one?' 'I don't know' said Alice, 'I lost count'...Presumably although she lacked enough time to count verbally, Alice would have been able to estimate the total to within a few units." Trying this with my own children...and reading a normal speed, without a heads up to "count" (I just told them to "listen carefully...ready?") they both got 10. Very cool.

"The chimp, therefore, learned to recognize the digits, 1, 2 and 3, and the point to the appropriate digit when it saw the corresponding number of biscuits. Finally, in the last stage, Sarah Boysen taught her protege the converse: It had to choose among several sets of objects, the one whose numerosity matched a given Arabic digit...At the end of this training, Sheba could fluently move back and forth between a digit and the corresponding quantity. This can be considered the essence of symbolic knowledge. A symbol, beyond it's arbitrary shape, refers to a covert meaning. Symbol comprehension implies accessing this meaning from shape alone, while symbol production requires recovering the arbitrary shape from knowledge of the intended meaning." page 37 It is difficult not to think about the many ways this in incorporated into teaching young children. Fascinating.

"Otherwise, they [babies] stick to the hypothesis that there is only one object, even if that implies that the object is constantly changing in shape, size and color. Thus, the baby's numerical module is both hypersensitive to information about object trajectory, location, and occlusion, and completely blind to changes in shape or color. Never mind the identity of the object, only location and trajectory matter." page 59 This is interesting, so babies are surprised when the think there should be 1 object and instead there are 2, or when they think there are 2 objects and there is only 1...but seeing 1 bird go behind a screen and seeing 1 truck come out doesn't surprise them at all. "Yet in order to learn something, one must not be to prejudiced." page 59. Dehaene argues that things in the baby's environment often change shape, size, and color...(he used the example of a small piece of red rubber easily and quickly inflating to a large pink balloon), so babies must remain open to the prospect that an object can change all of it's attributes and still be one object. Lots to think about here.

I can see some outdated information in this book (which was published in 1997) "Right after birth, they learn to recognize their mother's voice and face..." page 61...but, we now know that babies recognize their own mother's voice even BEFORE birth.

I feel that Dehaene contradicts himself on pages 65, 66, when he states, "Georges Ifrah, in his comprehensive book on the history of numerical notations, shows that in all civilizations, the first three numbers were initially denoted by repeatedly writing down the symbol for 'one' as many times as necessary, exactly as in Roman numerals. And most, if not all civilizations stopped using this beyond the number 3 (see Figure 3.1)." but then provides a Figure (Figure 3.1) where actually Cuneform Notation, Etruscan Notation, Mayan Notation, and I might even argue Ancienr Indian Notation (as there are two lines intersecting at a right angle - where you could count the lines from the midpoint as 4 separate lines representing the number 4) DO represent the number 4 (and in the case of Cuneform Notation, the number 5) with drawings of that many lines - just like one, two or three lines are represented with 1, 2, or 3 lines.

I love thinking about where things relating to language come from. It was interesting to hear Dehaene surmise that the numbers 2 and 3, "Our digit 1 is a single bar, and our digits 2 and 3 actually derive from 2 or 3 horizontal bars that become tied together when they were deformed by being handwritten." (page 65) I can almost see it in the arabic number 4 as well, if you count each part of the bisected right hand line as a separate line - you get 4 lines!

When I was a child I was obsessed with the idea that if you make an invisible "x" in the air with your pointed finger, there is no way to prevent a joining curve to happen between drawing the first diagonal line and drawing the second. That really bothered me as a kid, I remember drawing and redrawing x's with my finger while riding the elementary school bus. So the above quote ("Our digit 1 is a single bar, and our digits 2 and 3 actually derive from 2 or 3 horizontal bars that become tied together when they were deformed by being handwritten." page 65) brings that back to mind, and connects me with the humans of the ancient past, in my opinion. That makes me feel innovative and connected to antiquity.

My favorite part of this book by far is the section called, "Do numbers have colors?" This is, of course, because I have always seen numbers in color! Dehaen states, "Between 5$ and 10% is thoroughly convinced that numbers have colors and occupy very precise locations in space." (page 83). I remember the gentleman who wrote "Born on a Blue Day" saw numbers as an undulating, mountain type shape. While that is not the case for me, I am heartened to learn that others see numbers in color, too!

I made a quick list of the colors I see for the numbers from 1-9:
0 - clear
1 - white *
2 - yellow*
3 - red*
4- green (light)
5 - blue* (5 is not mentioned by Dehaene, but as it is so close to 4, I'm adding the *)
6 - tan*
7 - green (dark)
8 -brown*
9 - yellow/tan*

So 7/10 of my numbers' colors in some light match up with other peoples. (if you count 5 as a "small number" and count tan as a brown). How is that possible? The colors of numbers is not something we teach children, or learn about as children...after all the majority of people that I have told about seeing numbers in color think I sound a bit crazy. So how can there be similarities across people? Something else is going on here.

Dehaene states that, "Most people associate black and white with either 0 and 1 or 8 and 9; yellow, red and blue with small numbers such as 2, 3, and 4; and brown, purple and gray with larger numbers such as 6, 7 and 8." (page 83) I have placed a * next to the number colors that I see which correlate with Dehaene's statement.

I have always called seeing numbers in color synesthesia (well, always since I first learned the term as an adult). I was glad that Dehaene mentioned synesthesia in this book. He explains why he thinks some people see numbers in color as follows, "Because the total number of neurons remains constant, the growth of the numerical network must occur at the expense of the surrounding cortical maps, including those coding for color, form and location. In some children, perhaps the shrinkage of nonnumerical areas may not reach its fullest term. In this case, some overlap between the cortical areas coding for numbers, space, and color may remain. Subjectively, this might translate into an irrepressible sensation of "seeing" the color and location of numbers. A similar account might explain the related phenomenon of synesthesia--the impression, familiar to poets or musicians, that sounds have shapes and that tastes evoke colors." (page 85)

I don't love that on page 86 Dehaene refers to my special, valuable and in my view instrumental in evolution with respect to human beings, and our language of words and numbers, as "bizarre numerical hallucinations."

I just saw this in my goodreads feed, and the idea that number sense originates from our perception of color (as the caption about the book states) is fascinating! Sounds like an excellent read!

[Murilo Andrade · Rating 3 out of 5]

This book covers a lot of different subjects to study/explain Mathematical Reasoning.

The chapters follow a certain logic, starting with math comprehension in animals, then babies, then adults, and finally geniuses/prodigies. The book is based on intense research from several fields as phrenology, psychology, etc. Then it concludes with a more philosophical discussion about maths as a subject, its existence, its "purity" and matching with physical phenomena.

Chapter 1 - Talented and Gifted Animals

The author describes situations in which humans perceive animals to have a "number sense". It turns out some of these perceptions are erroneous, as in the case of the horse named Hans, which merely responded to the trainer expectations, like an unintended non-verbal communication. In other cases, animals (e.g. rats) can indeed manifest some sort of number understanding, with a certain accuracy. Chimpanzees can also compare quantities, for example.

Chapter 2 - Babies who count

Dehaene describes a few nice experiences with babies, showing evidence that they seem to have some sort of innate "number sense", from birth. After a few months, they are also capable to perform a few simple calculations as 1 + 1 , 2 + 1.

Chapter 3 - The adult number line

The author describes the (natural) evolution of number writings (romans, etc), and the increasing advantage of each writing compared to the previous ones. He also introduces the magnitude effect when comparing 2 numbers (e.g. 4 vs 5 is much slower than 1 vs 9 ),which permeates all the book.

Chapter 4 - The language of numbers

Now the object is the (mathematical) language, and how it evolved through civilizations. The Eastern languages, such as japanese and chinese have shorter words for the numbers, as well as more structured "number language", what explains chinese can memorize more digits (9 against 7, on average) than western.

Chapter 5 - Small heads for big calculations

This is a very interesting chapter. Stanislas enters in the world of pre-schoolers, when they learn to count, sum, subtract, etc. Basically, in order to be able to produce faster results in these operations children need to refine the algorithms. Just remind when you used to count in your fingers to sum 4 + 3. In this chapter the author also discusses the introduction of calculators in schools, which can help students, despite its bad reputation.

Chapter 6 - Geniuses/Prodigies

The big discussion of the chapter is about innate mathematical talent, and the probable answer is there is no such thing. Although it is hard to separate effects and find any causality, there is positive correlation between math ability and myopia, allergy, first-born, left-handedness.

Chapter 7 - Losing Number Sense

Here the author discusses brain damage and brain plasticity. Even though brain parts can specialize and almost replace completely other parts, in some cases this is impossible. The author show some interesting cases here.

Chpater 8 - The computing Brain

This chapter enters into brain location of mathematical reasoning, etc.

Chapter 9 - What is a number ?

In the author vision mathematics is an evolutionary field, and not as perfect as mathematicians think (an example is the sum 1-1+1-1... which Leibniz proved to be 1/2). Another thing discussed in the chapter is that the axiomatic system , as Peano's axioms, and long chain computations are not as suitable for a brain as it is for a computer. The book ends with discussion on the "unreasonable effectiveness of math".

[Jay Cruz · Rating 3 out of 5]

The Number Sense is Stanislas Dehaene's argument that the human brain is wired to understand numbers, or "numerosity" as Dehaene puts it. Before we acquire language, learn number symbols, learn to count, and basically learn mathematics, we already come equipped to spot when there is less or more of something. Even animals have this number sense which is discussed in the first chapter of the book. Babies and children also come equipped with the "sense" and the second chapter gives many examples of this. The book then goes on to explain why going beyond counting and simple addition, mathematics starts to get really weird and a bit difficult for the brain to handle.

It's definitely an interesting read, but at times I found myself a bit overwhelmed by how in depth Dehaene goes. Chapters 7 and 8 deal with neurobiology, the brain, and brain imagining. These chapters went beyond of what I needed to know to understand that mapping where and how the brain works with numbers it's still a mystery and a work in progress. But I'm still glad I read it. I learned that like language, mathematics has been with us since the beginning and has been an ongoing evolutionary process.

[Riccardo · Rating 5 out of 5]

Il libro è favoloso, anche se probabilmente la mia opinione possa essere influenzato dalla mia passione per le Neuroscienze. Comunque sia, il primo punto a favore è l'autore: non si tratta del solito giornalista scientifico che, eccitato da qualche frase sentita da qualche scienziato, decide di scrivere un libro sulla concezione dei numeri senza sapere niente né di matematica né del cervello. Qui si parla di un matematico che ha preso un PhD in psicologia cognitiva arrivando così ad occuparsi della rappresentazione cerebrale dei numeri e della matematica. Insomma, un tipo che sa perfettamente ciò di cui sta parlando. E si vede: il libro è incredibilmente chiaro, nonostante arrivi a trattare argomenti piuttosto complessi.
Il secondo punto a favore sono le molteplici riflessioni che suscita: la matematica è un'entità astratta che esiste indipendentemente dall'uomo o è frutto dell'uomo stesso? È possibile pensare qualcosa di universale oppure sul cervello agisce la selezione darwiniana di modo che i nostri pensieri sono efficienti ma non necessariamente coerenti? (Se no, la cosa mi spaventa un po'). Esiste l'anima o è solo un'illusione?

[Almudena · Rating 5 out of 5]

Un libro fascinante sobre la capacidad humana para los números. Desde las primeras intuiciones cuantitativas hasta la abstracción más pura sobre el que se yerguen las matemáticas.

Dehaene describe las habilidades aproximativas que compartimos con otras especies animales, las capacidades aritméticas más básicas observadas incluso en bebés y cómo estas afectaron, probablemente, a la historia de las matemáticas a lo largo y ancho del planeta, con sus distintas bases numéricas y su enorme pero acotada diversidad. Esa cota la impone, según Dehaene, nuestra habilidad para el número como especie, el sustrato neuronal que ha dado lugar a ese invento cultural conocido como "números".

El neurocientífico describe en detalle, además, cómo el cerebro representa esos números, qué regiones se ven involucradas cuando realizamos tareas cuantitativas y cómo pueden verse alteradas por distintas lesiones. En base a ello, explora la cuestión "¿qué es un número?", ¿las matemáticas se descubren o se inventan?

[Scott · Rating 3 out of 5]

As a radiologist and medical physicist, I found the early chapters on early childhood development of a number sense and the later chapters on number-processing deficits experienced by brain-damaged patients and brain imaging to be a little slow and not particularly revealing, most likely due to my prior exposure to these topics through my professional training. The middle chapters that discussed how adults think about numbers and do calculations, however, were fascinating.

[Megan · Rating 3 out of 5]

Interesting review of the psychology of numbers. This guy has been featured a few times on the RadioLab podcast, which I love. I think its strength is the really interesting discussion of what animals and humans are inherently capable of when it comes to numbers and mathematics. Its weakness is when it tries to apply evolutionary arguments to the "fitness" of mathematical concepts, which I find kinda dumb.

Fun if you're interested in this kind of thing.

[Charly · Rating 5 out of 5]

Besides an overly enthusiastic usage of the phrase "in the final analysis," this book is near-flawless. Thorough, accurate, insightful, useful, even damned funny in parts . . . call me a Dehaenophile through and through!

It will appeal most to those interested in the intersection between neuroscience and math education.

[Roberto Liebheart · Rating 4 out of 5]

Muy buen libro que nos explica muy científicamente como es que se producen los números en el cerebro y como es que existe gente a la que aparentemente se les da mejor las matemáticas. Genética,don o aprendizaje? Leer es libro y os haréis una idea

[Behrooz Parhami · Rating 4 out of 5]

The original 1997 edition of this book, written some 15 years before the current edition, had three parts and 9 chapters.

Part One: Our Numerical Heritage (Chs. 1-3)

Part Two: Beyond Approximation (Chs. 4-6)

Part Three: Of Neurons and Numbers (Chs. 7-9)

The author has added Part Four, The Contemporary Science of Numbers and Brain, consisting of the single Ch. 10, to review the most-important developments in the field since the book's original publication. The book ends with two appendices and a bibliography. A most-exciting advance in the intervening 15 years is the discovery of single neurons that code for number in the monkey brain.

Numbers are all around us. It's not an exaggeration to say that we cannot live without them. Even poets must be able to count in order to follow the rules of various poetic forms! As early as 5 months after birth, a baby knows that 1 plus 1 makes 2. Animals possess a mental module called "accumulator" that can hold quantities, recognize small sets with a handful of elements, or approximately add two quantities. This accumulator mechanism isn't digital but analog; not dealing with discrete values, but with continuous ones.

The complexities of the various classes of numbers, and all of abstract mathematics, for that matter, arise from and are supported by a small set of features or capabilities in the human brain. Research on animals has revealed an age-old competence for handling approximate quantities, an ability that may be as old as life. Mathematician Richard Dedekind, however, was of the opinion that numbers are "free creations of the human mind."

We now understand that animals will never be able to do exact arithmetic or tell the difference between 49 and 50; such fine distinctions are made by humans, only because of our ability to devise and use symbols, which in turn enable precision and abstraction. One should not forget that the notation for dealing with multi-digit numbers, which seems like child's play now, took centuries to be devised and refined.

Aside from the approximate, analog accumulator that we share with rats and other animals, our brain does not seem to contain an "arithmetic unit" to allow us to perform multiplication and other mathematical tasks. The brain uses alternative circuits, that have evolved for other functions, to do math. The brains of gifted mathematicians are essentially the same as those of ordinary people; the difference is in one group's clever methods to get around the brain's limitations.

The Number Sense is perhaps the most-important book of its kind. Other books that contribute to our understanding of how the brain deals with numbers and mathematics include:

The Mathematical Brain (by B. Butterworth, 1999)

Where Mathematics Comes From (by G. Lakoff and R. Nunez, 2000)

The Handbook of Mathematical Cognition (ed. by J. I. D. Campbell, 2005)

[A YOGAM · Rating 4 out of 5]

Stanislas Dehaene: La bosse des maths
(„Die Mathe-Macke gibt es“)
Aus neurowissenschaftlicher Perspektive vertritt Stanislas Dehaene die These, dass die grundlegende Fähigkeit zur Arithmetik – der sogenannte Zahlensinn – tief im menschlichen Gehirn verankert und angeboren ist. Das Buch stützt sich auf eine Vielzahl von Experimenten und bildgebenden Verfahren, die zeigen, dass bereits Säuglinge und sogar Tiere über eine intuitive, approximative Form des Rechnens verfügen. Zudem lassen sich spezifische kortikale Areale identifizieren, die auf Zahlenverarbeitung spezialisiert sind.
Für Dehaene bilden diese angeborenen „Rechnen-Neuronen“ das biologische Fundament, auf dem der Mensch mithilfe von Sprache und symbolischen Systemen – insbesondere Ziffern – schrittweise eine präzisere und komplexere Mathematik aufbaut. Seine Argumentation liefert damit eine naturwissenschaftliche Erklärung dafür, dass ein grundlegendes mathematisches Potenzial universell vorhanden ist, auch wenn es zunächst ungenau und vorbewusst bleibt.
Natur als Möglichkeit, Kultur als Wirklichkeit
Stanislas Dehaenes La bosse des maths zeigt aus neurowissenschaftlicher Perspektive, dass ein grundlegender Zahlensinn zur biologischen Ausstattung des Menschen gehört. Mathematik erscheint hier als eine kognitive Möglichkeit, die tief im Gehirn verankert ist und universell vorhanden sein dürfte. Clémence Perronnets La bosse des maths n’existe pas macht dagegen sichtbar, warum dieses Potenzial in der sozialen Realität so ungleich zur Entfaltung kommt. Ihr soziologischer Blick legt offen, wie Bildungssysteme, Erwartungen und Machtverhältnisse darüber entscheiden, wer seine mathematischen Fähigkeiten weiterentwickeln kann – und wer nicht.
Zusammengenommen widersprechen sich die beiden Bücher nicht, sondern ergänzen einander. Dehaene beschreibt die neuronale Grundlage, Perronnet die gesellschaftlichen Bedingungen. Erst im Zusammenspiel beider Perspektiven wird verständlich, warum mathematische Begabung zugleich universell angelegt und sozial ungleich verteilt ist. Die entscheidende Lehre lautet daher: Mathematik ist weder reines Naturtalent noch bloßes soziales Konstrukt. Sie entsteht dort, wo biologische Möglichkeiten auf kulturelle Ermutigung treffen – oder an ihr scheitern.

[Fernando Pestana da Costa · Rating 5 out of 5]

This book's subtitle (How the mind creates mathematics) is a clear description of the leitmotif of the book: to understand the neurological basis of elementary mathematical calculations. The author is a cognitive neuropsychologist (with a first degree in mathematics) and his main thesis is that Evolution has endowed humans (and other higher animal species) with an innate ability for intuitive counting which, coupled with the human capacity for language, is the basis of the unique mathematical capacity of the human species. In support of this thesis Dehaene amasses an extraordinary variety of evidence, namely a number of very intelligently designed animal experiments, as well as psychologist's tests with humans, even amazing experiments with babies as young as five months that clearly established the erroneous nature of some aspects of Piaget's constructivist theory of child development. These, together with evidence from modern brain imaging techniques and clinical data about several types of brain lesions, helps to build a very compelling case about the physiological mechanism behind the human ability to do mathematics. In the last chapter, Dehaene allows himself a more philosophically minded speculation about the implications his analysis and conclusions have for pedagogical matters, as well as for the philosophical debate among Platonists, Formalists, and Intuitionists on the foundations of mathematics, with some surprisingly reasonable arguments in favor of (a mild version of) intuitionism. Summing up: reading this book was a wondrous experience and I am sure I will often return to parts of it in the future. Nobody interested in Mathematics, its teaching, or the mechanisms of brain functioning, should miss this book!

[Renard · Rating 4 out of 5]

Explique de façon scientifique comment les mathématiques et le calcul fonctionnent dans notre cerveau. On apprend quelles sont les aires en jeux, mais plus globalement comment des stimuli (vision, audition) amène à la capacité à compter.
Chaque enseignement est accompagné de l'explication d'une ou plusieurs expériences qui le prouvent. Ces expériences sont en général vraiment bien pensée.
Cet ouvrage ne livre par contre pas une méthode clé en main pour bien enseigner les nombres et les mathématiques à un enfant, mais en lisant entre les lignes, et en cherchant sur internet on peut trouver des méthodes.
J'ai trouvé la fin moins éclairante/utile.

[Görkem Saylam · Rating 4 out of 5]

The Number Sense | Stanislas Dehaene
Scoring Rubric
1: baseline
2: creative contextualization bcs of covering almost all studies on mathing to combine them
1: creative conceptualization bcs of no new holistic and groundbreaking comprehension on theory of mathing
4: total points by 5

[Seth the Zest · Rating 5 out of 5]

The best book on math I've ever read, and I've read entire math textbooks. This is the first book I've read that actually gives insight into how the mind understands math. I skimmed a bit about the brain science, especially because the book is nearly thirty years old, but the processes described make so much sense that I'm surprised they didn't come up in any math teaching courses.

[Özgün Şen · Rating 4 out of 5]

Great scientific explanation and tests of human and other species learn and format math and numbers. Even babies, sea mammals, birds have known numbers. Chapters of neurological accidents were quite interesting that cause how it affects number sense, loss of math and numbering. Take care of your parietal and frontal lobes:)

[Adnan Khaleel · Rating 3 out of 5]

This book has lots of good theories but the author likes to ramble on and on for the sake of filling pages. He even states as much in the beginning on his approach to writing this book.
I would recommend it, but don’t feel like you have to read every page, which unfortunately I did.

[Kazuya Sakakihara · Rating 3 out of 5]

Enjoyed the first parts about numeracy, but then it dwindled down towards the end, which is almost a metaphysical bullshit.
Anyways it's pretty outdated, some of psychological experiments might not stands scrutiny of reproducibility, so read it with a grain of salt.

[D P · Rating 4 out of 5]

I like the parts about childhood and language, less the parts about genius and the philosophy of numbers. Which is to say that it is a stronger book of experimental cognitive science than it is one of philosophy.

[Olya · Rating 3 out of 5]

A lot more neuroscience than I had bargained for. And a lot more math than I've had to deal with in a decade at least. That said, there are some very fascinating facts in here and the writing style is relatively approachable - for the subject matter.

[Cody · Rating 5 out of 5]

Outstanding adventure into the way our evolved brains intuit about math!

[Rachid Rd · Rating 5 out of 5]

Well written book to discover mathemical cognition!

[Jukka Paulin · Rating 5 out of 5]

Excellent. Clear, with plenty of relatable examples of our human and animal
companions' sense of numeracy. Founded on research.

[Olivia · Rating 3 out of 5]

There were some confusing parts about mathematical logic, but for the most part, this book outlines a clear map of how our number sense develops and where it occurs in the brain.

[Nicholas · Rating 2 out of 5]

Not very engaging.