双语有声阅读：儿童的数学能力

 Children's Numerical Skills

 

People appear to be born to compute¹. The numerical skills of children develop so early and so inexorably that it is easy to imagine an internal clock of mathematical maturity² guiding their growth. Not long after learning to walk and talk, they can set the table with impressive accuracy -- one knife, one spoon, one fork, for each of the five chairs. Soon they are capable of noting that they have placed five knives, spoons and forks on the table and, a bit later, that this amounts to fifteen pieces of silverware. Having thus mastered addition, they move on to subtraction³. It seems almost reasonable to expect that if a child were secluded⁴ on a desert island at birth and retrieved⁵ seven years later, he or she could enter a second-grade mathematics class without any serious problems of intellectual adjustment.

 

Of course, the truth is not so simple. This century, the work of cognitive⁶ psychologists has illuminated⁷ the subtle forms of daily learning on which intellectual progress depends. Children were observed as they slowly grasped -- or, as the case might be, bumped into -- concepts that adults take for granted, as they refused, for instance, to concede that quantity is unchanged as water pours from a short stout⁸ glass into a tall thin one. Psychologists have since demonstrated that young children, asked to count the pencils in a pile, readily report the number of blue or red pencils, but must be coaxed⁹ into finding the total. Such studies have suggested that the rudiments¹⁰ of mathematics are mastered gradually, and with effort. They have also suggested that the very concept of abstract numbers - the idea of a oneness, a twoness, a threeness that applies to any class of objects and is a prerequisite¹¹ for doing anything more mathematically demanding than setting a table - is itself far from innate¹².

 

儿童的数学能力

 

人似乎生来就会计算。 孩子们使用数字的技能发展得如此之早和如此必然，很容易让人想象有一个内在的精确而成熟的数字钟在指导他们的成长。 孩子们在学会走路和说话后不久，就能以令人惊叹的准确布置桌子--五把椅子前面分别摆上一把刀、一个汤匙、一把叉子。 很快地，他们就能知道他们已在桌面上摆放了五把刀、五个汤匙、五把叉子。 没有多久，他们就又能知道这些东西加起来总共是 15 把银餐具。 如此这般地掌握了加法之后，他们又转向减法。 有一种设想几乎顺理成章，那就是，即使一个孩子一出生就被隔绝到荒岛上，七年后返回世间，也能直接上小学二年级的数学课，而不会碰到任何智力调整方面的大麻烦。当然，事实并没有这么简单。 本世纪认知心理学家的工作已经揭示了智力发展所依赖的日常学习的微妙形式。 他们观察到孩子们缓慢掌握那些成年人认为理所当然的概念的过程，或者是孩子们偶然遇到这些概念的过程。 他们也观察到孩子们拒绝承认某些常识的情况。 比如：孩子们拒绝承认当水从短而粗的瓶中倒入细而长的瓶子中时，水的数量没有变化。 心理学家们而后又展示一个例子， 即：让孩子们数一堆铅笔时，他们能顺利地报出蓝铅笔或红铅笔的数目，但却需诱导才能报出总的数目。 此类研究表明：数学基础是经过逐渐努力后掌握的。 他们还表示抽象的数字概念，如可表示任何一类物品并且是在做比摆桌子有更高数学要求的任何事时都必备的一、二、三意识，远远不是天生就具备的。

1 compute   

v./n.计算，估计

参考例句：

• I compute my losses at 500 dollars.我估计我的损失有五百元。
• The losses caused by the floods were beyond compute.洪水造成的损失难以估量。

2 maturity   

n.成熟；完成；(支票、债券等)到期

参考例句：

• These plants ought to reach maturity after five years.这些植物五年后就该长成了。
• This is the period at which the body attains maturity.这是身体发育成熟的时期。

3 subtraction   

n.减法，减去

参考例句：

• We do addition and subtraction in arithmetic.在算术里,我们作加减运算。
• They made a subtraction of 50 dollars from my salary.他们从我的薪水里扣除了五十美元。

4 secluded   

adj.与世隔绝的；隐退的；偏僻的v.使隔开，使隐退( seclude的过去式和过去分词)

参考例句：

• Some people like to strip themselves naked while they have a swim in a secluded place. 一些人当他们在隐蔽的地方游泳时，喜欢把衣服脱光。 来自《简明英汉词典》
• This charming cottage dates back to the 15th century and is as pretty as a picture, with its thatched roof and secluded garden. 这所美丽的村舍是15世纪时的建筑，有茅草房顶和宁静的花园，漂亮极了，简直和画上一样。 来自《简明英汉词典》

5 retrieved   

v.取回( retrieve的过去式和过去分词 )；恢复；寻回；检索（储存的信息）

参考例句：

• Yesterday I retrieved the bag I left in the train. 昨天我取回了遗留在火车上的包。 来自《简明英汉词典》
• He reached over and retrieved his jacket from the back seat. 他伸手从后座上取回了自己的夹克。 来自辞典例句

6 cognitive   

adj.认知的，认识的，有感知的

参考例句：

• As children grow older,their cognitive processes become sharper.孩子们越长越大，他们的认知过程变得更为敏锐。
• The cognitive psychologist is like the tinker who wants to know how a clock works.认知心理学者倒很像一个需要通晓钟表如何运转的钟表修理匠。

7 illuminated   

adj.被照明的；受启迪的

参考例句：

• Floodlights illuminated the stadium. 泛光灯照亮了体育场。
• the illuminated city at night 夜幕中万家灯火的城市

8 stout   

adj.强壮的，粗大的，结实的，勇猛的，矮胖的

参考例句：

• He cut a stout stick to help him walk.他砍了一根结实的枝条用来拄着走路。
• The stout old man waddled across the road.那肥胖的老人一跩一跩地穿过马路。

9 coaxed   

v.哄，用好话劝说( coax的过去式和过去分词 )；巧言骗取；哄劝，劝诱

参考例句：

• She coaxed the horse into coming a little closer. 她哄着那匹马让它再靠近了一点。
• I coaxed my sister into taking me to the theatre. 我用好话哄姐姐带我去看戏。 来自《现代汉英综合大词典》

10 rudiments   

n.基础知识，入门

参考例句：

• He has just learned the rudiments of Chinese. 他学汉语刚刚入门。
• You do not seem to know the first rudiments of agriculture. 你似乎连农业上的一点最起码的常识也没有。

11 prerequisite   

n.先决条件；adj.作为前提的，必备的

参考例句：

• Stability and unity are a prerequisite to the four modernizations.安定团结是实现四个现代化的前提。
• It is a prerequisite of entry to the profession that you pass the exams.做这一行的先决条件是要通过了有关的考试。

12 innate   

adj.天生的，固有的，天赋的

参考例句：

• You obviously have an innate talent for music.你显然有天生的音乐才能。
• Correct ideas are not innate in the mind.人的正确思想不是自己头脑中固有的。