PBS高端访谈:关于教学中数学课重要性的探讨

 　　JUDY WOODRUFF: Now a look at how required math classes may factor into the academic success or failure of high school and college students.

　　Hari Sreenivasan has the story as part of our weekly education series, Making the Grade.

　　ANDREW HACKER¹, Author, "The Math Myth": Words and numbers, we use them both. We use them for different reasons.

　　HARI SREENIVASAN: Even if you aren't going to be an engineer, getting through high school or college means getting through math.

　　MICHAEL GENAO, Student, Queens College: Why do we need to take all these math classes? It's not necessary. It's not needed for what we are actually learning.

　　HARI SREENIVASAN: Andrew Hacker, the college professor teaching at the front of this classroom at New York's Queens College, agrees.

　　ANDREW HACKER: The goal is to have everybody do a full menu of mathematics, up to and including calculus².

　　And I don't see any rational reason for this at all. What I'm suggesting is that at least there should be other options, alternatives, instead of this rigid³ math curriculum for everyone.

　　HARI SREENIVASAN: Minimum requirements for math are different across the country, but many states today demand getting through the quadratic equations and two years of algebra⁴ to graduate high school, and most college degrees also require some math credits.

　　Hacker writes about this perceived disconnect between academic requirements and the everyday needs of graduates in his recent book, "The Math Myth."

　　关于教学中数学课重要性的探讨

　　ANDREW HACKER: It's actually several myths. One of the myths is that every one of us is going to have to know algebra, geometry, trigonometry in the 21st century, because that's the way a high-tech⁵ age is going.

　　It's a total myth. At most, 5 percent of people really use math, advanced math, in their work.

　　HARI SREENIVASAN: You're also drawing a distinction in your book between mathematics and arithmetic. Explain that.

　　ANDREW HACKER: Yes.

　　We use math, the term, indiscriminately. I think we teach arithmetic really very well up through grades, let's say, five or six. We do it. But then, instead of continuing with arithmetic to what I would call adult arithmetic, or sophisticated arithmetic, we immediately plunge⁶ people into geometry and algebra.

　　And, as a result, Americans are really quite illiterate⁷ in terms of numbers.

　　HARI SREENIVASAN: Hacker's alternative? Teaching what he calls numeracy.

　　ANDREW HACKER: It's income per hour, essentially⁸, per person. Is Norway well ahead of the United States? OK. Let's continue with that.

　　HARI SREENIVASAN: Where he focuses on developing his students' mathematical literacy by giving them some real-world perspective on the subject.

　　ANDREW HACKER: How to read a corporate⁹ report, how to look at the federal budget, how to parse¹⁰ the numbers on the campaign trail, how votes are cast, and how many seats are won, all sorts of assignments like this, which only require arithmetic, but adult arithmetic.

　　HARI SREENIVASAN: A political scientist by training, Hacker and his assertions have predictably put college and high school math departments across the country on the defensive¹¹.

　　DIANE BRIARS, President, National Council of Teachers of Mathematics: We need algebra as a basic way of making sense of our world. Many mathematical relationships are described using algebra.

　　HARI SREENIVASAN: Diane Briars is president of the National Council of Teachers of Mathematics. We chatted with her on nearly her home turf, the National Museum of Mathematics in Manhattan.

　　DIANE BRIARS: Algebra gives us a way of representing relationships in general, so that we can reason about them in the general case, instead of specific cases. Algebraic equations and expressions are also ways of describing patterns that we may see and differences between those patterns.

　　ANDREW HACKER: This is put about by the mathematicians¹². I think they have to say this: Mathematics trains the mind.

　　There's no evidence for this whatever. Mathematics trains the mind for mathematics.

　　HARI SREENIVASAN: Hacker thinks math is a powerful divider of high school success. A number of students succeed and move onward¹³, while a sizable fraction do not.

　　ANDREW HACKER: One out of every five of our citizens has not finished high school. We have a 20 percent dropout¹⁴ rate. It's one of the highest in the developed world. And the chief academic reason for this dropout rate is algebra in the ninth grade.

　　HARI SREENIVASAN: The fail rate is something Diane Briars doesn't dispute.

　　DIANE BRIARS: The fact that failing algebra I as a ninth grader is — makes a student more likely to drop out is a huge problem that the mathematics education community is actively¹⁵ engaged in. One of the ways we're addressing that is by building a stronger foundation in K-8 mathematics.

　　With a more solid conceptual understanding in K-8 mathematics, students are going to be much better prepared to be successful in algebra I.

　　HARI SREENIVASAN: But Hacker says the math failure is greater than just high school.

　　ANDREW HACKER: Forty-seven percent of people who start a four-year college do not get a degree. That's a very high dropout rate, close to half. Chief academic reason, freshman¹⁶ math course, which people fail and don't make up. And why don't we ask ourselves, look at the talent we're losing.

　　HARI SREENIVASAN: Why are the institutions in high school and in college structured the way they are to emphasize math, as we do today?

　　ANDREW HACKER: Here's the big word I always hear: Let's be rigorous, the big R. Let's be rigorous, so let's make everybody coming into community college pass a stiff algebra test. That shows how rigorous we are.

　　Same thing at a higher level. If you take Princeton, Stanford, Yale, they want virtually all of their incoming students, except for athletes and a few alumni children, to have an SAT score on math of at least 700. That's very high. That's the top 7 percent. Why? We're Princeton, we're rigorous.

　　And in the name of rigor¹⁷, we have this irrational¹⁸ math barrier.

　　HARI SREENIVASAN: Diane Briars agrees with that too, but only up to a point.

　　DIANE BRIARS: You can argue that, for some of them, that requirement may have been put there to ensure that they filter people out. On the other hand, being able to be facile with symbols and equations is necessary for a number of trades. For example, the electricians union has passing a course in algebra I as a requirement for an apprenticeship¹⁹ program.

　　HARI SREENIVASAN: So both sides agree that the formula for the right amount of math isn't optimal²⁰. Figuring out the right equation may be one of the first major problems for new graduates everywhere.

　　For the "PBS NewsHour," I'm Hari Sreenivasan in New York.

1 hacker   

n.能盗用或偷改电脑中信息的人，电脑黑客

参考例句：

• The computer hacker wrote that he was from Russia.这个计算机黑客自称他来自俄罗斯。
• This site was attacked by a hacker last week.上周这个网站被黑客攻击了。

2 calculus   

n.微积分；结石

参考例句：

• This is a problem where calculus won't help at all.对于这一题，微积分一点也用不上。
• After studying differential calculus you will be able to solve these mathematical problems.学了微积分之后，你们就能够解这些数学题了。

3 rigid   

adj.严格的，死板的；刚硬的，僵硬的

参考例句：

• She became as rigid as adamant.她变得如顽石般的固执。
• The examination was so rigid that nearly all aspirants were ruled out.考试很严，几乎所有的考生都被淘汰了。

4 algebra   

n.代数学

参考例句：

• He was not good at algebra in middle school.他中学时不擅长代数。
• The boy can't figure out the algebra problems.这个男孩做不出这道代数题。

5 high-tech   

adj.高科技的

参考例句：

• The economy is in the upswing which makes high-tech services in more demand too.经济在蓬勃发展，这就使对高科技服务的需求量也在加大。
• The quest of a cure for disease with high-tech has never ceased. 人们希望运用高科技治疗疾病的追求从未停止过。

6 plunge   

v.跳入，(使)投入，(使)陷入；猛冲

参考例句：

• Test pool's water temperature before you plunge in.在你跳入之前你应该测试水温。
• That would plunge them in the broil of the two countries.那将会使他们陷入这两国的争斗之中。

7 illiterate   

adj.文盲的；无知的；n.文盲

参考例句：

• There are still many illiterate people in our country.在我国还有许多文盲。
• I was an illiterate in the old society,but now I can read.我这个旧社会的文盲，今天也认字了。

8 essentially   

adv.本质上，实质上，基本上

参考例句：

• Really great men are essentially modest.真正的伟人大都很谦虚。
• She is an essentially selfish person.她本质上是个自私自利的人。

9 corporate   

adj.共同的，全体的；公司的，企业的

参考例句：

• This is our corporate responsibility.这是我们共同的责任。
• His corporate's life will be as short as a rabbit's tail.他的公司的寿命是兔子尾巴长不了。

10 parse   

v.从语法上分析；n.从语法上分析

参考例句：

• I simply couldn't parse what you just said.我完全无法对你刚说的话作语法分析。
• It causes the parser to parse an NP.它调用分析程序分析一个名词短语。

11 defensive   

adj.防御的；防卫的；防守的

参考例句：

• Their questions about the money put her on the defensive.他们问到钱的问题，使她警觉起来。
• The Government hastily organized defensive measures against the raids.政府急忙布置了防卫措施抵御空袭。

12 mathematicians   

数学家( mathematician的名词复数 )

参考例句：

• Do you suppose our mathematicians are unequal to that? 你以为我们的数学家做不到这一点吗？ 来自英汉文学
• Mathematicians can solve problems with two variables. 数学家们可以用两个变数来解决问题。 来自哲学部分

13 onward   

adj.向前的，前进的；adv.向前，前进，在先

参考例句：

• The Yellow River surges onward like ten thousand horses galloping.黄河以万马奔腾之势滚滚向前。
• He followed in the steps of forerunners and marched onward.他跟随着先辈的足迹前进。

14 dropout   

n.退学的学生；退学；退出者

参考例句：

• There is a high dropout rate from some college courses.有些大学课程的退出率很高。
• In the long haul,she'll regret having been a school dropout.她终归会后悔不该中途辍学。

15 actively   

adv.积极地，勤奋地

参考例句：

• During this period all the students were actively participating.在这节课中所有的学生都积极参加。
• We are actively intervening to settle a quarrel.我们正在积极调解争执。

16 freshman   

n.大学一年级学生(可兼指男女)

参考例句：

• Jack decided to live in during his freshman year at college.杰克决定大一时住校。
• He is a freshman in the show business.他在演艺界是一名新手。

17 rigor   

n.严酷，严格，严厉

参考例句：

• Their analysis lacks rigor.他们的分析缺乏严谨性。||The crime will be treated with the full rigor of the law.这一罪行会严格依法审理。

18 irrational   

adj.无理性的，失去理性的

参考例句：

• After taking the drug she became completely irrational.她在吸毒后变得完全失去了理性。
• There are also signs of irrational exuberance among some investors.在某些投资者中是存在非理性繁荣的征象的。

19 apprenticeship   

n.学徒身份；学徒期

参考例句：

• She was in the second year of her apprenticeship as a carpenter. 她当木工学徒已是第二年了。
• He served his apprenticeship with Bob. 他跟鲍勃当学徒。

20 optimal   

adj.最适宜的；最理想的；最令人满意的

参考例句：

• What is the optimal mix of private and public property rights in natural resources?私人和国家的自然资源产权的最适宜的组合是什么？
• Optimal path planning is a key link for the sailing contest.帆船最优行驶路径规划是帆船比赛取胜的关键环节。