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Of course, the truth is not so simple. This century, the work of cognitive psychologists has illuminated 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 stout 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 into finding the total. Such studies have suggested that the rudiments of mathematics are mastered gradually, and with effort. They have also suggested that the very concept of abstract numbers--the idea of aloneness, a prerequisite for doing anything more mathematically demanding than setting a table¡ªis itself far from innate.
¡¡¡¡ 1. What's the main idea about this passage?
¡¡¡¡¡¡¡¡ A. The use of mathematics in child psychology.
¡¡¡¡¡¡¡¡ B. Trends in teaching mathematics to children.
¡¡¡¡¡¡¡¡ C. The development of mathematical ability in children.
¡¡¡¡¡¡¡¡ D. The fundamental concepts of mathematics that children must learn.
¡¡¡¡ 2. It can be inferred from the passage that children normally learn simple counting¡ª¡ª.
¡¡¡¡¡¡¡¡ A. soon after they learn to talk
B. after they reach second grade in school
¡¡¡¡¡¡¡¡ C. by looking at the clock
¡¡¡¡¡¡¡¡ D. when they begin to be mathematically mature
¡¡¡¡ 3. According to the passage, when small children were asked to count a pile of red and blue pencils they¡ª¡ª.
¡¡¡¡¡¡¡¡ A. counted the number of pencils of each color
¡¡¡¡¡¡¡¡ B. counted only the pencils of their favorite color
¡¡¡¡¡¡¡¡ C. guessed at the total number of pencils
¡¡¡¡¡¡¡¡ D. subtracted the number of red pencils from the number of blue pencils
¡¡¡¡ 4. What does the word ¡°They¡± (Para. 3, Line 5) refer?
¡¡¡¡¡¡¡¡ A. Children¡¡¡¡ B. Pencils¡¡¡¡ C. Mathematicians ¡¡¡¡ D. Studies
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People appear to be born to compute. The numerical skills of children develop so early and so inexorably that it is easy to imagine an internal clock of mathematical maturity guiding their growth. Not long after learning to walk and talk, they can set the table with impressive accuracy¡ªone plate, 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, which this amounts to fifteen pieces of silverware. Having thus mastered addition, they move on to subtraction. It seems almost reasonable to expect that if a child were secluded on a desert island at birth and received 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 cognitive psychologists has illuminated 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 stout 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 into finding the total. Such studies have suggested that the rudiments of mathematics are mastered gradually, and with effort. They have also suggested that the very concept of abstract numbers--the idea of aloneness, a prerequisite for doing anything more mathematically demanding than setting a table¡ªis itself far from innate.
¡¡¡¡ 1. What's the main idea about this passage?
¡¡¡¡¡¡¡¡ A. The use of mathematics in child psychology.
¡¡¡¡¡¡¡¡ B. Trends in teaching mathematics to children.
¡¡¡¡¡¡¡¡ C. The development of mathematical ability in children.
¡¡¡¡¡¡¡¡ D. The fundamental concepts of mathematics that children must learn.
¡¡¡¡ 2. It can be inferred from the passage that children normally learn simple counting¡ª¡ª.
¡¡¡¡¡¡¡¡ A. soon after they learn to talk
B. after they reach second grade in school
¡¡¡¡¡¡¡¡ C. by looking at the clock
¡¡¡¡¡¡¡¡ D. when they begin to be mathematically mature
¡¡¡¡ 3. According to the passage, when small children were asked to count a pile of red and blue pencils they¡ª¡ª.
¡¡¡¡¡¡¡¡ A. counted the number of pencils of each color
¡¡¡¡¡¡¡¡ B. counted only the pencils of their favorite color
¡¡¡¡¡¡¡¡ C. guessed at the total number of pencils
¡¡¡¡¡¡¡¡ D. subtracted the number of red pencils from the number of blue pencils
¡¡¡¡ 4. What does the word ¡°They¡± (Para. 3, Line 5) refer?
¡¡¡¡¡¡¡¡ A. Children¡¡¡¡ B. Pencils¡¡¡¡ C. Mathematicians ¡¡¡¡ D. Studies
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When I was young,my parents ran a snack bar in our small town.
One evening in early April,my mother told me to fill in at the snack bar 36¡¡ a worker who had the flu.I told her I would mess it up, 37 I had never worked at the bar before.I ¡¡38¡¡
that instead of making money,I would end up owing it.
¡°You can do it,¡±said my mother.¡°¡¡ 39¡¡ ,you won¡¯t get much business until lunch.¡±
¡°But I¡¯ll never remember the orders,and I¡¯m no good ___40_ money.Please,Mom,don¡¯t
¡¡ 41¡¡ me.¡±
¡°Then I¡¯ll help you,¡±she said.
I shrugged my shoulders.I thought my mother¡¯s¡¡¡¡ 42¡¡¡¡ was a bad one,but I ¡¡¡¡ 43¡¡¡¡ .
When I got to the bar the next day,I found my mother was¡¡ 44¡¡ .Because the weather that day was rainy and cold,people wanted hot snacks and drinks.¡¡ 45¡¡ ,I was really slow at taking the orders and making change.The line of people grew,and everybody seemed¡¡ 46¡¡ .I was so nervous that my hands shook,and I ¡¡ 47 a cup into pieces.What a mess!Then my mother came to¡¡ 48 me,and she also showed me how to make¡¡ 49¡¡ .If someone gave me $5 for something that cost $3.25,I handed over¡¡ 50¡¡ quarters and a dollar and said,¡°75 cents makes four dollars,plus one dollar makes five.¡±Things went more¡¡ 51¡¡ after that.
By the end of the day,I could remember orders,¡¡ 52¡¡ the bill,and make change quickly with a smile.I was even a little¡¡ 53¡¡ when the sun came out and dried up business.My mother said she was proud of me,and when she¡¡ 54¡¡ that I work at the snack bar again next year,I did not even shrug.I was too busy¡¡ 55¡¡ the restaurant I would open one day.
36.A.to¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.for¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.after¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.over
37.A.because¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.though¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.until¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.while
38.A.promised¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.noticed¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.worried¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.hoped
39.A.Therefore¡¡¡¡¡¡¡¡¡¡¡¡ B.However¡¡¡¡¡¡¡¡¡¡ C.Besides¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.Yet
40.A.of¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.on¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.about¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.with
41.A.blame¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.fool¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.frighten¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.make
42.A.idea¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.bar¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.day¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.answer
43.A.guessed¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.obeyed¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.begged¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.admitted
44.A.angry¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.sad¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.wrong¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.ashamed
45.A.At least¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.At last¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.At most¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.At first
46.A.surprised¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.impolite¡¡¡¡¡¡¡¡¡¡¡¡ C.pleased¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.impatient
47.A.damaged¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.destroyed¡¡¡¡¡¡¡¡¡¡ C.broke¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.ruined
48.A.scold¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.help¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.beat¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.save
49.A.money¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.lunch¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.coffee¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.change
50.A.two¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.three¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.four¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.five
51.A.smoothly¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.fairly¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.simply¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.conveniently
52.A.turn in¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.count out¡¡¡¡¡¡¡¡¡¡ C.take over¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.add up
53.A.discouraged¡¡¡¡¡¡¡¡ B.disturbed¡¡¡¡¡¡¡¡¡¡ C.disappointed¡¡¡¡¡¡¡¡¡¡¡¡ D.distrusted
54.A.thought¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ B.stated¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ C.announced¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.suggested
55.A.imagining¡¡¡¡¡¡¡¡¡¡¡¡ B.preparing¡¡¡¡¡¡¡¡¡¡ C.examining¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ D.describing
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