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 ...
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.
A quantitative representation, inherited from our evolutionary past, underlies our intuitive understanding of numbers. If we did not already posses some internal non-verbal representation of the quantity "eight", we would probably be unable to attribute a meaning to the digit 8. We would then be reduced to purely formal manipulations of digital systems, in exactly the same way that a computer follows an algorithm without ever understanding its meaning.
I would like to suggest that these mathematical entities are so difficult for us to accept and so defy intuition because they do not correspond to any preexisting category in our brain. Positive integers naturally find an echo in the innate representation of numerosity; hence a four-year-old can understand them. Other sorts of numbers, howev... (查看原文)
Place-value coding is a must if one wants to perform calculations using simple algorithms. Just try to compute XIV * VII using Roman numerals! Calculations are also inconvenient in the Greek alphabetical notation, because nothing betrays that number N (50) is ten times greater than number E (5). This is the main reason the Greeks and the Romans never performed computations without the help of an abacus. By contrast, our Arabic numerals, based on the place-value principle, make the magnitude relations between 5, 50, 500, and 5,000 completely transparent. Place-value notations are the only ones that reduce the complexity of multiplication to the mere memorization of a table of products from 2 * 2 up to 9 * 9. Their invention revolutionized the art of numerical computation. (查看原文)
麦兜小胖
浙江教育出版社2022版
苦瓜美语Cary
0 有用 春云 2013-01-17 21:11:41
对我这种刚入门的小白来说，Dahaene的书就算是启蒙篇啦
0 有用 Marvin 2015-08-02 14:06:49
Education is wiping out the treasure we're born with
1 有用 文化 2018-04-15 09:05:58
转载一段：serendipitous“本书讲了动物和人类天生的数感、大脑处理数字和数量的区域和方式、数感与空间感的关系、计算能力（和数感不是一回事，数感关键是右脑叶中专门处理数量的区域，跟空间和位置有关；计算能力跟记忆力以及左脑主语言的区域有关）、数学天才和计算天才、合理的数学教学方法（应该发挥儿童天生的数感）、数学是客观存在还是人为创造（作为认为柏拉图派能想象出一个数学世界，不是因为那个世界存在... 转载一段：serendipitous“本书讲了动物和人类天生的数感、大脑处理数字和数量的区域和方式、数感与空间感的关系、计算能力（和数感不是一回事，数感关键是右脑叶中专门处理数量的区域，跟空间和位置有关；计算能力跟记忆力以及左脑主语言的区域有关）、数学天才和计算天才、合理的数学教学方法（应该发挥儿童天生的数感）、数学是客观存在还是人为创造（作为认为柏拉图派能想象出一个数学世界，不是因为那个世界存在，而是数字在大脑里是空间式呈现的）、为何数学能巧妙的解释世界（人类的数感是进化塑造的，进化的大脑必然有一套适用的能认知周围世界的机制；另外那些不能合理解释世界的数学都被淘汰了。不是上帝用数学创造了世界，而是人脑只能用数学认知世界）、以及后天可以培养数感等问题。没有谈到人类的逻辑本能是怎么回事……” (展开)
1 有用 文化 2018-04-15 09:05:58
转载一段：serendipitous“本书讲了动物和人类天生的数感、大脑处理数字和数量的区域和方式、数感与空间感的关系、计算能力（和数感不是一回事，数感关键是右脑叶中专门处理数量的区域，跟空间和位置有关；计算能力跟记忆力以及左脑主语言的区域有关）、数学天才和计算天才、合理的数学教学方法（应该发挥儿童天生的数感）、数学是客观存在还是人为创造（作为认为柏拉图派能想象出一个数学世界，不是因为那个世界存在... 转载一段：serendipitous“本书讲了动物和人类天生的数感、大脑处理数字和数量的区域和方式、数感与空间感的关系、计算能力（和数感不是一回事，数感关键是右脑叶中专门处理数量的区域，跟空间和位置有关；计算能力跟记忆力以及左脑主语言的区域有关）、数学天才和计算天才、合理的数学教学方法（应该发挥儿童天生的数感）、数学是客观存在还是人为创造（作为认为柏拉图派能想象出一个数学世界，不是因为那个世界存在，而是数字在大脑里是空间式呈现的）、为何数学能巧妙的解释世界（人类的数感是进化塑造的，进化的大脑必然有一套适用的能认知周围世界的机制；另外那些不能合理解释世界的数学都被淘汰了。不是上帝用数学创造了世界，而是人脑只能用数学认知世界）、以及后天可以培养数感等问题。没有谈到人类的逻辑本能是怎么回事……” (展开)
0 有用 Marvin 2015-08-02 14:06:49
Education is wiping out the treasure we're born with
0 有用 春云 2013-01-17 21:11:41
对我这种刚入门的小白来说，Dahaene的书就算是启蒙篇啦