People appear to born to compute. The numerical skills of children develop so early and so inexorably(冷酷地,无情地) that it is easy to imagine an internal clock of mathematical maturity(成熟,完备) guiding their growth. Not long after learning to walk and talk, they can set the table with impress accuracy---one knife, one spoon, one fork, for each of the five chairs. Soon they are capable of nothing that they have placed five knives, spoons and forks on the table and, a bit later, that this amounts to fifteen pieces ofsilverware(银器) . Having thus mastered addition, they move on to subtraction(减少,差集) . It seems almost reasonable to expect that if a child were secluded(隔绝) on a desert island at birth andretrieved(取回,寻回) seven years later, he or she could enter a second 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 cognitive(认知的,认识的) psychologists has illuminated(照明,启发) the subtle(微妙的,敏感的) 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 quantity is unchanged as water pours from a short 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 coaxed(哄骗,劝诱) into finding the total. Such studies have suggested that the rudiments(入门,初步) 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(二重性) , a threeness that applies to any class of objects and is a prerequisite(先决条件)for doing anything more mathematically demanding than setting a table -- is itself far from innate.
考生必读:雅思阅读的所有句型结构分析
考生必读:如何攻克雅思段落细节信息配对题
备考分享:详解雅思听力中的对话与独白
“烤鸭”必读:雅思听力训练的三个注意要点
经验分享:高中生考雅思的弱势及解决方法
“雅思口语”实用模板与答题范例整理
实例分析:别让小错误毁了你的雅思写作
考生必读:雅思词汇之常见医学类词汇一览
考生必读:备考雅思听力的三大必备技能
雅思听力高分备考秘籍分享:从声音到全篇
必读:雅思阅读选择题如何应对干扰项
“烤鸭”必读:提高雅思口语的四个方面
雅思阅读填空题五大解题技巧
雅思8分学霸经验分享:三周如何突破四难关
四级刚过如何考到雅思7分:烤鸭二战破7心得
论背单词的重要性与雅思词汇手册的选择
活用技巧:巧拿“雅思口语”高分
高分技能:雅思听力长段子的五条精听技巧
高分技能:20句雅思写作经典句型背诵
如何打破雅思写作地图题的“魔咒”
从技巧到能力:手把手教你雅思9分备考攻略
为什么你的雅思听力上不了6.5?
雅思口语:中国考生如何避免说中式英语
中国考生雅思口语低分三大原因分析
笔译专家支招雅思考试技巧:攻核心词勤练手
雅思阅读备考中常见的三类问题
备考分享:如何保证雅思阅读的做题质量
考生必读:雅思听力的几个长期练习方法
雅思高分攻略:议论文题型各个击破
雅思听力备考秘籍:常用信号词分类整理
不限 |
英语教案 |
英语课件 |
英语试题 |
不限 |
不限 |
上册 |
下册 |
不限 |