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.
2017届高考英语一轮复习全册课件:必修1 1.2 unit2《being a good language learner》(重大版)
2017届高考英语一轮复习全册课件:必修3 3.3 unit3《festivals and celebrations》(重大版)
2017届高考英语一轮复习考点真题演练:Section 12 阅读理解之史地常识类(含解析)
2017届高考英语一轮复习全册课件:必修3 3.2《challenging yourself》Ⅱ《knowing about festivals》(重大版)
2017届高考英语一轮复习考点真题演练:Section 14 完形填空之记叙文(含解析)
2017届高考英语一轮复习全册课件:必修4 4.2 unit2《stories on the wheel》(重大版)
2017届高考英语一轮复习考点真题演练:Section 14 完形填空之夹叙夹议文(含解析)
2017届高考英语一轮复习分课测试:必修4 Unit1《women of achievement》(新人教版含答案)
2017届高考英语一轮复习全册课件:必修3 3.2 unit2《attitude to life》(重大版)
2017届高考英语一轮复习全册课件:必修3 3.6 unit6《perseverance and success》(重大版)
2017届高考英语一轮复习分课测试:必修4 Unit5《theme parks》(新人教版含答案)
2017届高考英语一轮复习全册课件:必修4 4.5 unit5《art and culture》(重大版)
2017届高考英语一轮复习全册课件:必修2 2.4 unit4《unforgettable films》(重大版)
2017届高考英语一轮复习全册课件:必修2 2.2《challenging yourself》Ⅱ《enjoying sports》(重大版)
2017届高考英语一轮复习全册课件:必修3 3.3《challenging yourself ⅲ hope for life》(重大版)
2017届高考英语一轮复习考点真题演练:Section 12 阅读理解之时闻报道类(含解析)
2017届高考英语一轮复习全册课件:必修3 3.1 unit1《hope and love》(重大版)
2017届高考英语一轮复习全册课件:必修2 2.5 unit5《special clothes》(重大版)
2017届高考英语一轮复习全册课件:必修4 4.3 unit3《plants》(重大版)
2017届高考英语一轮复习全册课件:必修4 4.6 unit6《poems and poets》(重大版)
2017届高考英语一轮复习分课测试:必修5 Unit1《great scientists》(新人教版含答案)
2017届高考英语一轮复习分课测试:必修5 Unit2《the united kingdom》(新人教版含答案)
2017届高考英语一轮复习全册课件:必修3 3.4 unit4《food and culture》(重大版)
2017届高考英语一轮复习全册课件:必修2 2.3 unit3《powerful music》(重大版)
2017届高考英语一轮复习全册课件:必修2 2.6 unit6《healthy diet》(重大版)
2017届高考英语一轮复习全册课件:必修1 1.1 unit1《learning strategies and habits》(重大版)
2017届高考英语一轮复习全册课件:必修2 2.3《challenging yourself ⅲ keeping healthy》(重大版)
2017届高考英语一轮复习考点真题演练:Section 14 完形填空之议论文(含解析)
2017届高考英语一轮复习分课测试:必修4 Unit4《body language》(新人教版含答案)
2017届高考英语一轮复习分课测试:必修4 Unit3《a taste of english humour》(新人教版含答案)
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