陳蕙雅思教材 - 雅思閱讀精選 (Children's Numerical Skills)

Children's Numerical Skills

People appear to be bornto compute. The numerical skills of children

develop so early and soinexorably that it is easy to imagine an internal

clock of mathematicalmaturity guiding their growth. Not long after

learning to walk       and talk, they can set the table withimpressive accuracy

-- one knife, one spoon,one fork, for each of the five  chairs.Soon they

are capable of notingthat they have placed five knives, spoons and forks

on the table and, a bitlater, that this amounts to fifteen pieces of

silverware. Having  thus mastered addition, they move on to       subtraction.

It seems almostreasonable to expect  that if a childwere secluded  on a

desert  island at birth  and retrieved seven years later, he or shecould

enter a second-grademathematics class without any serious problems of

intellectual adjustment.

Of course, the truth isnot so simple. This century, the work of cognitive

psychologists hasilluminated  the subtle forms of dailylearning on which

intellectual  progress depends.  Children were observedas they slowly

grasped --     or, as the case might be, bumped into --concepts that adults

take for granted, as theyrefused, for instance, to          concedethat quantity

is unchanged as waterpours from a short stout glass into a tall thin one.

Psychologists have sincedemonstrated that young children, asked to count

the pencils in a pile,readily report the number of blue or        redpencils,

but must be coaxed intofinding the total. Such studies have suggested that

the rudiments of      mathematics are mastered gradually, andwith effort. They

have also suggested thatthe very concept of abstract   numbers -the idea of

a oneness, a twoness, athreeness that applies to any class of objects and

is  a prerequisite for doing anything more  mathematically demanding than

setting a table - isitself far from innate.

兒童的數學能力

人似乎生來就會計算。  孩子們使用數字的技能發展得如此之早和如此必然，很容易讓 人想像有一個內在的精確而成熟的數字鐘在指導他們的成長。  

孩子們在學會走路和說話後 不久，就能以令人驚歎的準確佈置桌子--五把椅子前面分別擺上一把刀、一個湯匙、一把叉

子。  很快地，他們就能知道他們已在桌面上擺放了五把刀、五個湯匙、五把叉子。  沒有多 久，他們就又能知道這些東西加起來總共是 15 把銀餐具。

如此這般地掌握了加法之後，他 們又轉向減法。  有一種設想幾乎順理成章，那就是，即使一個孩子一出生就被隔絕到荒島

上，七年後返回世間，也能直接上小學二年級的數學課，而不會碰到任何智力調整方面的大 麻煩。當然，事實並沒有這麼簡單。  

本世紀認知心理學家的工作已經揭示了智力發展所依 賴的日常學習的微妙形式。  他們觀察到孩子們緩慢掌握那些成年人認為理所當然的概念的

過程，或者是孩子們偶然遇到這些概念的過程。  他們也觀察到孩子們拒絕承認某些常識的 情況。 比如：

孩子們拒絕承認當水從短而粗的瓶中倒入細而長的瓶子中時，水的數量沒有 變化。  心理學家們而後又展示一個例子，  

即：讓孩子們數一堆鉛筆時，他們能順利地報出 藍鉛筆或紅鉛筆的數目，但卻需誘導才能報出總的數目。  此類研究表明：數學基礎是經過 逐漸努力後掌握的。  

他們還表示抽象的數字概念，如可表示任何一類物品並且是在做比擺 桌子有更高數學要求的任何事時都必備的一、二、三意識，遠遠不是天生就具備的。