The number sense how the mind creates mathematics
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His working hypothesis was that the horse could not but be totally inept in mathematics. Even then, they should never be imposed on the child, but rather they should always be justified by a demand for greater simplicity and effectiveness. 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. His solution -- let children use calculators! I tend to find a hard line on this debate to be a bit unpalatable and find myself agreeing more with 's stance in his excellent book, , namely that mathematics is a little bit of both a creation and discovery. In their first experiment, the chimpanzee's task was simple: It was rewarded for selecting, among two objects, the one that was physically identical to a third one. This seems to reinforce the idea of allowing children to solve contextual problems in an open-format and to share their insights into how they solved the problems with each other as a means of allowing them to develop conceptual understanding of ideas through intuition prior to developing procedural skills. 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.

Thorough, accurate, insightful, useful, even damned funny in parts. Japanese effectively has three different ways to name each digit. Pfungst eventually deduced that Hans's truly amazing ability lay in detecting minuscule movements of its master's head or eyebrows that invariably announced the time to stop the series of knocks. The rats had to discriminate between the two melodies. Fun if you're interested in this kind of thing. Finally, and more facetiously, the anecdote shows how the forces of Darwinian selection also apply to the arithmetical domain. If you have 10 sheep, maybe you can name all of them, and when one is missing, you can go: hah! Tracing the history of numbers, we learn that in early times, people indicated numbers by pointing to part of their bodies, and how Roman numerals were replaced by modern numbers.

The second tray contains a pile with five pieces of chocolate and, separate from it, a single piece. Initially, the rats were conditioned to press the left lever when they heard two tones, and the right lever when they heard four tones. If the chimp could not do the additions, but was content with choosing the tray with the largest single pile of chocolates, it should have been wrong in this particular example because while the pile with five chips on the second tray exceeds each of the piles on the first tray, the total amount of chips on the first tray is larger. As we grow and develop, we refine this predisposition with language that gives us a much more precise sense of number through education and exposure to our culture. They can add two quantities and spontaneously choose the larger of two sets. Injecting rats with metamphetamine, for instance, seems to accelerate the internal counter. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind.

The spine of the book is still in great condition and the front cover is generally unmarked. First, the rats often squeezed lever A a little more than the minimum required—five times instead of four, for instance. And we meet people whose minute brain lesions render their mathematical ability useless--one man, in fact, who is certain that two and two is three. However, mathematics and nature follow rules that aren't governed by human beings. Even after considerable training, a rat seems unable to press exactly four times on a lever, but it can press four, five, or six times on different trials. If this could be done I would be very interested in learning of the results.

I was initially worried that the tpinformation would be outdated, but dehaene had some great insights most of which were corroborated by future research, which is summarized in the last, lengthy chapter. If you ever see a show in which an animal adds numbers, spells words, or some surprising deed of this kind, you may safely bet that its behavior rests, like Hans's, on a hidden communication with its human trainer. Now, in The quantity Sense, Stanislas Dehaene deals a desirable examine this fresh study, in an enlightening exploration of the mathematical brain. In fact, Pfungst never doubted that the trainer was sincere. Although the results were slow to come, they eventually exceeded all his expectations. Even the most elementary of organisms, after all, are confronted with a never-ending search for the best environment with the most food, the fewest predators, the most partners of the opposite sex, and so on.

To prove this, Pfungst invented a way of dissociating Hans's knowledge of a problem from what its master knew. It bridges the gap between research and practice in teaching and outlines ways to improve teacher education. Make no mistake, Dehaene writes in great form and provides ample support for every claim he asserts. Rats generalized just as easily on duration as on number. But that is another story. 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.

Neither did three, then four, then five men fool the clever bird. 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. Il libro è favoloso, anche se probabilmente la mia opinione possa essere influenzato dalla mia passione per le Neuroscienze. Chapters 7 and 8 deal with neurobiology, the brain, and brain imagining. A clear drawback of the accumulator is that numbers, although they form a discrete set, are represented by a continuous variable: water level.

The variability in the internal representation of numbers grows in direct proportion to the quantity represented. 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. While providing access to contemporary views on the issue, the papers illustrate the wide variety of functions of metaphors and analogies, as well as the many connections between the study of some of these functions and other subjects and disciplines. Cerebral circuitry is far from having revealed all its secrets. It strikes a sincere balance between psychology and mathematics. In The Number Sense, Stanislas Dehaene offers readers an enlightening exploration of the mathematical mind. However, I found other chapters dragged on a little bit.