美國(guó)人的數(shù)學(xué)到底有多差?——紐約時(shí)報(bào)

Are You Smarter Than an 8th Grader?

美國(guó)人的數(shù)學(xué)到底有多差?

I AM afraid you’re eligible to read this column only if you can answer this question faced by eighth graders around the world:

下面這個(gè)題是用來(lái)考世界各地八年級(jí)學(xué)生的，如果你答不上來(lái)，恐怕就不適合閱讀這篇專欄了：

What is the sum of the three consecutive whole numbers with 2n as the middle number?

三個(gè)連續(xù)整數(shù)，中間一個(gè)是2n，它們的總和是多少?

A. 6n+3

A. 6n+3

B. 6n

B. 6n

C. 6n-1

C. 6n-1

D. 6n-3

D. 6n-3

More than three-quarters of South Korean kids answered correctly (it is B). Only 37 percent of American kids were correct, lagging their peers from Iran, Indonesia and Ghana.

超過(guò)四分之三的韓國(guó)孩子回答正確(答案是B)。美國(guó)孩子只有37%答對(duì)，落后于伊朗、印度尼西亞和加納的同齡人。

We know Johnny can’t read; it appears that Johnny is even worse at counting.

我們知道美國(guó)小孩的閱讀能力不行;看來(lái)他們的算術(shù)能力更糟糕。

The Educational Testing Service released a global report finding that young adults from the United States rank poorly in reading but are even worse in math — the worst of all countries tested. This is the generation that will be in the labor force for the next half-century, struggling to compete with citizens of other countries.

美國(guó)教育考試服務(wù)中心(Educational Testing Service，簡(jiǎn)稱ETS)發(fā)布的一份全球報(bào)告稱，美國(guó)年輕人的閱讀能力排名不佳，但數(shù)學(xué)能力排名更糟——是所有參加測(cè)試的國(guó)家中最低的。這代人將在今后半個(gè)世紀(jì)成為勞動(dòng)者，他們難與其他國(guó)家的公民競(jìng)爭(zhēng)。

It’s not just that American results are dragged down by poverty. Even American millennials with graduate degrees score near the bottom of international ranks in numeracy.

這不僅僅是說(shuō)美國(guó)人的測(cè)試結(jié)果受到了貧困的拖累。即使有研究生學(xué)位的美國(guó)千禧一代，在算術(shù)上的得分也在國(guó)際排名中接近墊底。

We interrupt this column for another problem:

下面再試試另一個(gè)問(wèn)題：

How many degrees does a minute hand of a clock turn through from 6:20 a.m. to 8 a.m. on the same day?

從早上6:20到同一天的8點(diǎn)，時(shí)鐘的分針旋轉(zhuǎn)了多少度?

A. 680 degrees

A. 680度

B. 600 degrees

B. 600度

C. 540 degrees

C. 540度

D. 420 degrees

D. 420度

Only 22 percent of American eighth-graders correctly answered B, below Palestinians, Turks and Armenians.

只有22%的美國(guó)八年級(jí)學(xué)生給出了正確回答B(yǎng)，落后于巴勒斯坦人、土耳其人和亞美尼亞人。

In a recent column, I offered a paean to the humanities. But it’s also true, as a professor notes in a letter to the editor, that science majors do take humanities courses. In contrast, humanities majors often desperately avoid any semblance of math or science (except for classes like “Physics for Poets”).

在最近的專欄中，我為人文學(xué)科奉上了一曲贊歌。但是正如一位教授在給編輯的信中指出的，科學(xué)專業(yè)的學(xué)生事實(shí)上有在學(xué)習(xí)人文課程。相形之下，人文專業(yè)的學(xué)生往往拼命逃避任何和數(shù)學(xué)或科學(xué)沾邊的東西(除了“詩(shī)人物理學(xué)”這樣的課程)。

Numeracy isn’t a sign of geekiness, but a basic requirement for intelligent discussions of public policy. Without it, politicians routinely get away with using statistics, as Mark Twain supposedly observed, the way a drunk uses a lamppost: for support rather than illumination.

會(huì)算術(shù)不是怪咖的標(biāo)志，而是對(duì)公共政策進(jìn)行理性討論的基本要求。路燈在醉鬼的眼里是用來(lái)支撐身體而不是照明的——據(jù)說(shuō)語(yǔ)出馬克·吐溫(Mark Twain)，如果沒(méi)有算術(shù)，政客三天兩頭像醉鬼利用路燈一樣去利用統(tǒng)計(jì)數(shù)據(jù)，也不會(huì)被發(fā)現(xiàn)。

(I believe American high schools and colleges overemphasize calculus and don’t sufficiently teach statistics. Statistical literacy should be part of every citizen’s tool kit.)

(我相信美國(guó)高中和大學(xué)過(guò)分強(qiáng)調(diào)了微積分，而在統(tǒng)計(jì)方面教得比較少。統(tǒng)計(jì)應(yīng)該是每一個(gè)公民應(yīng)有的基本素養(yǎng)。)

Public debates often dance around basic statistical concepts, like standard deviation, because too few Americans understand them. And people assume far too much of “averages.”

公開(kāi)辯論常常避開(kāi)基本的統(tǒng)計(jì)概念，比如標(biāo)準(zhǔn)差，因?yàn)榱私馑鼈兊拿绹?guó)人太少了。而人們對(duì)“平均數(shù)”有太多一廂情愿的理解。

After all, American adults have, on average, one ovary and one testicle. But try finding such an “average person.”

美國(guó)成年人平均每人有一個(gè)卵巢和一個(gè)睪丸。但你找到一個(gè)這樣的“一般人”試試。

Another pop quiz:

再來(lái)一個(gè)臨時(shí)小測(cè)驗(yàn)：

A piece of wood was 40 centimeters long. It was cut into 3 pieces. The lengths in centimeters are 2x -5, x +7 and x +6. What is the length of the longest piece?

一塊木頭有40厘米長(zhǎng)。它被切成3段。以厘米為單位，三段木頭長(zhǎng)度分別是2x-5、x+7和x+6。最長(zhǎng)的那段有多長(zhǎng)?

Only 7 percent of American eighth graders got that one right (the answer is 15 centimeters). In contrast, 53 percent of Singaporean eighth graders answered correctly.

只有7%的美國(guó)八年級(jí)學(xué)生回答正確(答案是15厘米)。相比之下，新加坡八年級(jí)學(xué)生中有53%回答正確。

I know many readers will grumblingly protest that they’re just not good at math! True, there are math prodigies who are different from you and me. When the great mathematician Carl Gauss was a young boy, his teacher is said to have asked his class to calculate the sum of all the numbers from 1 to 100. Gauss supposedly supplied the answer almost instantly: 5,050.

我知道很多讀者會(huì)發(fā)牢騷抗議說(shuō)，他們只是不擅長(zhǎng)數(shù)學(xué)而已!誠(chéng)然，世界上有些數(shù)學(xué)天才異于你我常人。據(jù)說(shuō)偉大的數(shù)學(xué)家卡爾·高斯(Carl Gauss)還是一個(gè)小男孩時(shí)，他的老師在課上要求學(xué)生計(jì)算從1到100所有數(shù)字的總和，高斯幾乎瞬間就得出答案：5050。

The teacher, flabbergasted, asked how he knew. Gauss explained that he had added 1 and 100, 2 and 99, and realized that there would be 50 such pairs each summing 101. So 50 times 101 equals 5,050.

老師大吃一驚，問(wèn)他怎么知道。高斯解釋說(shuō)，他把1和100相加，2和99相加，他意識(shí)到這樣的對(duì)子有50個(gè)，每對(duì)的和為101。所以，50乘以101等于5050。

So I agree: Let’s resent the Gausses of the world for being annoyingly smart. But let’s not use that as an excuse to hide from the rigor of numbers. Countries like Singapore manage to impart extraordinary math skills in ordinary children because they work at it.

所以我同意：大家一起來(lái)怨恨高斯這種聰明得讓人惱火的人。但我們不能把那當(dāng)作借口來(lái)躲開(kāi)嚴(yán)謹(jǐn)?shù)臄?shù)字。像新加坡這樣的國(guó)家，就成功地讓普通孩子掌握了良好的數(shù)學(xué)技能，因?yàn)樗麄冊(cè)谶@方面努了力。

Numeracy isn’t just about numbers, of course. It’s also about logic. Let me leave you with a logical puzzle — a family favorite, one that I first heard as a little kid — that isn’t mathematical at all. Yet people with math training seem better at thinking it through and solving it:

算術(shù)當(dāng)然不僅僅是數(shù)字。它還涉及邏輯。下面有一個(gè)邏輯題——是我家里人最喜歡的一個(gè)，我第一次聽(tīng)到它的時(shí)候還是一個(gè)小孩——完全和數(shù)學(xué)無(wú)關(guān)。然而，接受過(guò)數(shù)學(xué)培訓(xùn)的人似乎更善于思考并解決它：

You’re in a dungeon with two doors. One leads to escape, the other to execution. There are only two other people in the room, one of whom always tells the truth, while the other always lies. You don’t know which is which, but they know that the other always lies or tells the truth. You can ask one of them one question, but, of course, you don’t know whether you’ll be speaking to the truth-teller or the liar. So what single question can you ask one of them that will enable you to figure out which door is which and make your escape?

你在一個(gè)地牢里，地牢有兩扇門，其中一扇是生門，另一扇是死門。地牢里除你之外只有兩個(gè)人，其中一人總是講真話，另一個(gè)總是說(shuō)謊。你不知道誰(shuí)講真話誰(shuí)說(shuō)謊，但他們互相知道。你可以問(wèn)他們其中一人一個(gè)問(wèn)題，當(dāng)然，你不知道你問(wèn)的究竟是老實(shí)人還是騙子。那么，這個(gè)問(wèn)題該怎么問(wèn)，才能知道哪扇是生門，哪扇是死門，從而死里逃生?

It’s not a trick question. When you hear the answer, you’ll see it’s straightforward. First reader who doesn’t know this problem, works it out and tweets me the correct answer or posts it on my Facebook page gets a signed copy of my latest book or a Saddam Hussein poster that I liberated in Iraq during the war there. I’ve posted the answer on my blog, but you won’t need the help, will you?

這不是一個(gè)腦筋急轉(zhuǎn)彎。一旦你聽(tīng)到答案，你會(huì)覺(jué)得它很簡(jiǎn)單。之前不知道這個(gè)問(wèn)題，但想出答案的人，可以在Twitter上把答案發(fā)給我，或者貼在我的Facebook頁(yè)面上，第一個(gè)給出正確答案的人，可以獲得我簽名的新書(shū)一冊(cè)，或者一張我從戰(zhàn)時(shí)的伊拉克解救出來(lái)的薩達(dá)姆·侯賽因(Saddam Hussein)海報(bào)。我已經(jīng)把答案貼在博客里了，但你不需要看答案，對(duì)嗎?