美國人的數學到底有多差

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

下面這個題是用來考世界各地八年級學生的，如果你答不上來，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?

三個連續整數，中間一個是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.

超過四分之三的韓國孩子回答正確（答案是B）。美國孩子只有37%答對，落後於伊朗、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.

我們知道美國小孩的閱讀能力不行；看來他們的算術能力更糟糕。

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.

美國教育考試服務中心（Educational Testing Service，簡稱ETS）發佈的一份全球報告稱，美國年輕人的閱讀能力排名不佳，但數學能力排名更糟——是所有參加測試的國家中最低的。這代人將在今後半個世紀成爲勞動者，他們難與其他國家的公民競爭。

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.

這不僅僅是說美國人的測試結果受到了貧困的拖累。即使有研究生學位的美國千禧一代，在算術上的得分也在國際排名中接近墊底。

We interrupt this column for another problem:

下面再試試另一個問題：

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，時鐘的分針旋轉了多少度？

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%的美國八年級學生給出了正確回答B，落後於巴勒斯坦人、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，我爲人文學科奉上了一曲讚歌。但是正如一位教授在給編輯的信中指出的，科學專業的學生事實上有在學習人文課程。相形之下，人文專業的學生往往拼命逃避任何和數學或科學沾邊的東西（除了“詩人物理學”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.

會算術不是怪咖的標誌，而是對公共政策進行理性討論的基本要求。路燈在醉鬼的眼裏是用來支撐身體而不是照明的——據說語出馬克·吐溫(Mark Twain)，如果沒有算術，政客三天兩頭像醉鬼利用路燈一樣去利用統計數據，也不會被發現。

(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.)

（我相信美國高中和大學過分強調了微積分，而在統計方面教得比較少。統計應該是每一個公民應有的基本素養。）

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.”

公開辯論常常避開基本的統計概念，比如標準差，因爲了解它們的美國人太少了。而人們對“平均數”有太多一廂情願的理解。

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

美國成年人平均每人有一個卵巢和一個睾丸。但你找到一個這樣的“一般人”試試。

Another pop quiz:

再來一個臨時小測驗：

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釐米長。它被切成3段。以釐米爲單位，三段木頭長度分別是2x-5、x+7和x+6。最長的那段有多長？

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%的美國八年級學生回答正確（答案是15釐米）。相比之下，新加坡八年級學生中有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.

我知道很多讀者會發牢騷抗議說，他們只是不擅長數學而已！誠然，世界上有些數學天才異於你我常人。據說偉大的數學家卡爾·高斯(Carl Gauss)還是一個小男孩時，他的老師在課上要求學生計算從1到100所有數字的總和，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，問他怎麼知道。高斯解釋說，他把1和100相加，2和99相加，他意識到這樣的對子有50個，每對的和爲101。所以，50乘以101等於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：大家一起來怨恨高斯這種聰明得讓人惱火的人。但我們不能把那當作藉口來躲開嚴謹的數字。像新加坡這樣的國家，就成功地讓普通孩子掌握了良好的數學技能，因爲他們在這方面努了力。

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:

算術當然不僅僅是數字。它還涉及邏輯。下面有一個邏輯題——是我家裏人最喜歡的一個，我第一次聽到它的時候還是一個小孩——完全和數學無關。然而，接受過數學培訓的人似乎更善於思考並解決它：

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?

你在一個地牢裏，地牢有兩扇門，其中一扇是生門，另一扇是死門。地牢裏除你之外只有兩個人，其中一人總是講真話，另一個總是說謊。你不知道誰講真話誰說謊，但他們互相知道。你可以問他們其中一人一個問題，當然，你不知道你問的究竟是老實人還是騙子。那麼，這個問題該怎麼問，才能知道哪扇是生門，哪扇是死門，從而死裏逃生？

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?

這不是一個腦筋急轉彎。一旦你聽到答案，你會覺得它很簡單。之前不知道這個問題，但想出答案的人，可以在Twitter上把答案發給我，或者貼在我的Facebook頁面上，第一個給出正確答案的人，可以獲得我簽名的新書一冊，或者一張我從戰時的伊拉克解救出來的薩達姆·侯賽因(Saddam Hussein)海報。我已經把答案貼在博客裏了，但你不需要看答案，對嗎？