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While human achievements in mathematics continue to reach new levels of complexity, many of us who aren't mathematicians at heart (or engineers by trade) may struggle to remember the last time we used calculus (微积分).
It’s a fact not lost on American educators, who amid rising math failure rates are debating how math can better meet the real-life needs of students. Should we change the way math is taught in schools, or eliminate some courses entirely?
Andrew Hacker, Queens College political science professor, thinks that advanced algebra and other higher-level math should be cut from curricula in favor of courses with more routine usefulness, like statistics.
“We hear on all sides that we're not teaching enough mathematics, and the Chinese are running rings around us,” Hacker says. “I'm suggesting we're teaching too much mathematics to too many people…not everybody has to know calculus. If you're going to become an aeronautical (航空的) engineer, fine. But most of us aren't.”
Instead, Hacker is pushing for more courses like the one he teaches at Queens College: Numeracy 101. There, his students of “citizen statistics” learn to analyze public information like the federal budget and corporate reports. Such courses, Hacker argues, are a remedy for the numerical illiteracy of adults who have completed high-level math like algebra but are unable to calculate the price of, say, a carpet by area.
Hacker's argument has met with opposition from other math educators who say what's needed is to help students develop a better relationship with math earlier, rather than teaching them less math altogether.
Maria Droujkova is a founder of Natural Math, and has taught basic calculus concepts to 5-year-olds. For Droujkova, high-level math is important, and what it could use in American classrooms is an injection of childlike wonder.
“Make mathematics more available,” Droujkova says. “Redesign it so it's more accessible to more kinds of people: young children, adults who worry about it, adults who may have had bad experiences.”
Pamela Harris, a lecturer at the University of Texas at Austin, has a similar perspective. Harris says that American education is suffering from an epidemic of “fake math”—an emphasis on rote memorization (死记硬背) of formulas and steps, rather than an understanding of how math can influence the ways we see the world.
Andrew Hacker, for the record, remains skeptical.
“I'm going to leave it to those who are in mathematics to work out the ways to make their subject interesting and exciting so students want to take it,” Hacker says. “All that I ask is that alternatives be offered instead of putting all of us on the road to calculus.”
1
What does the author say about ordinary Americans?
A.They struggle to solve math problems.
B.They think math is a complex subject.
C.They find high-level math of little use.
D.They work hard to learn high-level math.
本题答案:
  • A
  • B
  • C
  • D
  • 参考答案:C
  • 系统解析:
    由题干中的 the author 和 ordinary Americans 定位到文章首段:While human acHevements in mathematics continue to reach new levels of complexity, many of us who aren't mathematicians at heart ,”(or engineers by trade) may struggle to remember the last time we used calculus (微积分)

    推理判断题。定位句指出,虽然人类数学成就的复杂性持续再创新高,但我们当中许多本身并非数学家(或者职业并非工程师)的人,可能很难记住我们最后一次使用微积分是什么时候了。也就是说,许多美国人很少使用微积分,发现高等数学的用处不大,故答案为C。

    A.“ 他们努力解决数学问题”,根据定位句的主句可知,这里并不是说许多美国人在努力解决微积分问题,而是说“我们当中许多人可能很难记住我们最后一次使用微积分是什么时候了 ”,该选项是对原文的曲解,故排除;B.“他们认为数学是一门复杂的学科”,while 引导的从句提到人类数学成就的复杂性持续再创新高,这是描述现实情况,而不是表示美国普通民众的观点,故排除;D. “他们努力学习高等数学”,原文并未提及,故排除。
2
What is the general complaint about America's math education according to Hacker?
A.America is not doing as well as China.
B.Math professors are not doing a good job.
C.Lead the trend in farming the world over.
D.Improve the quality of pastures for grazing.
本题答案:
  • A
  • B
  • C
  • D
  • 参考答案:A
  • 系统解析:
    由题干中的general complaint、America's math education和Hacker定位到文章第四段第一句:“We hear on all sides that we're not teaching enough mathematics, and the Chinese are running rings around us, " Hacker says.

    推理判断题。定位句指出,“我们听到各方都说我们并没有教授足够的数学知识,而中国人显然胜过我们,”哈克说道。也就是说,哈克认为人们普遍抱怨的是,美国的数学教育不如中国,故答案为A。

    B. “数学教授们做得不好”,定位句只提到“各方都说我们并没有教授足够的数学知识”,这里泛指数学教育工作者,并没有特指数学教授,该选项是对原文的曲解,故排除;C.“这并不能帮助学生们培养其读写能力”,第五段最后一句提到了 the numerical illiteracy,但是指《算数101》课程对于算数差的成年人是一种补救措施,原文并未提到美国的数学教育能否帮助学生数学教育能否帮助学生们培养其读写能力,故排除;D. “多年来几乎没有任何创新”,文中没有提到美国数学教育的创新问题,故排除。
3
What does Andrew Hacker's Numeracy 101 aim to do?
A.Allow students to learn high-level math step by step.
B.Enable students to make practical use of basic math.
C.Lay a solid foundation for advanced math studies.
D.Help students to develop their analytical abilities.
本题答案:
  • A
  • B
  • C
  • D
  • 参考答案:B
  • 系统解析:
    根据题干中的Numeracy 101定位到文章第五段第一句:Instead, Hacker is pushing for more courses like the one he teaches at Queens College: Numeracy 101.和第三句:Such courses, Hacker argues, are a remedy for the numerical illiteracy of adults who have completed high-level math like algebra but are unable to calculate the price of, say, a carpet by area.

    推理判断题。文章第五段第一句指出,相反,哈克正在推广更多像他在皇后学院教授的一门课程:《算数101》。接着第三句指出,哈克认为,这种课程对于算数差的成年人是一种补救措施,他们虽然学完了像代数这样的高等数学,但却无法按面积计算比如地毯之类的价格。也就是说‘安德鲁·哈克的《算数101》旨在让学生能够在实践中运用基础数学,故答案为B。A. “让学生循序渐进地学习高等数学”和C. “为高等数学的学习打下坚实的基础”,该段第三句提到这种课程对预算书差的成年人是一种补救措施,而且这些人已经学完了像代数这样的高等数学,由此可知,这门课只是补救措施,而不是让学生循序渐进地学习高等数学或者为高等数学的学习打下基础,故排除;D. “帮助学生培养他们的分析能力”,该段第二句虽然提到在这门课里,他的“公民统计学”的学生学习分析公共信息,但这门课的目的并非培养学生的分析能力,而是提高他们的算术能力,故排除。
4
What does Maria Droujkova suggest math teachers do in class?
A.Make complex concepts easy to understan
B.Start teaching children math at an early age.
C.Help children work wonders with calculus.
D.Try to arouse students' curiosity in math.
本题答案:
  • A
  • B
  • C
  • D
  • 参考答案:A
  • 系统解析:
    由题干中的 Maria Drouhkova和 in class定位到文章第七段第二句:For Drouhkova, high-level math is important, and what it could use in American classrooms is an injection of childlike wonder. 和第八段:"Make mathematics more available " Dikova says. Redesign it so it's more accessible to more kinds of people: young children, adults who worry about it, adults who may have had bad experiences.

    事实细节题。定位句指出,对于杜鲁科瓦而言,高等数学很重要,并且它可以在美国教室里使用的方法是注入孩童般的惊奇。也就是说杜鲁科瓦建议数学老师在课堂上要尽量让学生明白数学原来 如此。第八段中进一步available和more accessible to more kinds of people等表述说明要让数学教学产容易让人听懂,故答案为A。

    B. “在孩子们小的时候就开始教他们数学”,第七段第一句提到杜鲁科瓦向5岁儿童教授基本的微积分概念,但并未提到她建议数学老师在孩子们小的时候就开始教他们数学,故排除;C. “帮助学生 用微积分创造奇迹”,定位句虽然提到wonder 一词,但这里指的是让学生感到“惊奇”,而不是“奇迹”,故排除;D. “尝试引起学生对数学的好奇心”,是对第七段第二句中an injection of childlike wonder的误解, 这里是指老师要让学生产生一种“数学原来如此”的孩子般的惊奇感,而不是引起学生的好奇心,故排除。
5
What does Pamela Harris think should be the goal of math education?
A.To enable learners to understand the world better.
B.To help learners to tell fake math from real math.
C.To broaden Americans' perspectives on math.
D.To exert influence on world development.
本题答案:
  • A
  • B
  • C
  • D
  • 参考答案:C
  • 系统解析:
    由题干中的Pamela Hanis定位到文章第九段第二句:Harris says that Ameiican education is suffering from an epidemic of "fake math"—an emphasis on rote memorization (死记硬背)of formulas and steps, rather than an understanding of how math can influence the ways we see the world.

    推理判断题。定位句指出,哈里斯表示,美国教育正在遭遇“虚假数学”的泛滥——强调死记硬背公式和步骤,而不是理解数学如何影响我们看待世界的方式。也就是说,数学教育的目的应该是让学 翌鳗理解数学对人的思考方式的影响,故答案为C。

    A.“让学习者能够更好地理解世界”,原文的重点在于让学习者更加理解数学,而不是让人理 解世界,故排除;B.“帮助学习者区分真假数学”,定位句提到美国教育正在遭遇“虚假数学”的泛滥,但并没有提及要区分真假数学,故排除;D. “对世界的发展施加影响”,定位句提到的是数学影响我们看待世界的方式,而不是影响世界的发展,故排除。
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