異類之不一樣的成功啟示錄 第169期:怎樣解決問(wèn)題

Schoenfeld once asked a group of high school students how long they would work on a homework question before they concluded that it was too hard for them ever to solve.

肖恩菲爾德曾經(jīng)問(wèn)一組高中生，在他們做家庭作業(yè)時(shí)，在下定結(jié)論該數(shù)學(xué)題太難而做不出之前，他們會(huì)花多長(zhǎng)時(shí)間來(lái)嘗試解答該題？

Their answers ranged from 30 seconds to five minutes, with the average answer two minutes.

他們的回答從30秒到5分鐘不等，平均時(shí)間為2分鐘。

But Renee persists. She experiments. She goes back over the same issues time and time again. She thinks out loud.

但是雷妮是個(gè)很執(zhí)著的人，她堅(jiān)持不懈，她反復(fù)在同一個(gè)問(wèn)題上推敲，并且她想出了解決辦法。

She keeps going and going. She simply won't give up.

她不斷地嘗試，不是一個(gè)輕易就屈服的人，

She knows on some vague level that there are something wrong with her theory about how to draw a vertical line, and she won't stop until she's absolutely sure she has it right.

她知道在某種程度上，她畫(huà)垂線的理論出現(xiàn)了失誤。除非她認(rèn)為自己做對(duì)了，否則她不會(huì)放棄。

Renee wasn't a math natural. Abstract concepts like "slope" and "undefined" clearly didn't come easily to her.

雷妮在數(shù)學(xué)方面并不具備天賦，類似斜率和無(wú)窮大這樣的抽象概念對(duì)她絕對(duì)不是一件容易理解的事，

But Schoenfeld could not have found her more impressive. "There is a will to make sense that drives what she does," Schoenfeld says.

但她卻給肖恩菲爾德留下了十分深刻的印象,“無(wú)論做任何事，她都有種強(qiáng)烈的意愿去弄清楚，

"She wouldn't accept the superficial 'Yeah, you're right' and walk away. That's not who she is. And that's really unusual."

她不接受敷衍了事，她不會(huì)說(shuō)‘啊，你是對(duì)的’，然后就走開(kāi)，這真不一般”。

He rewound the tape and pointed to a moment when Renee reacted with genuine surprise to something on the screen.

他將錄像帶回放到雷妮面對(duì)難題的那個(gè)時(shí)刻，并指著屏幕。

"Look, he said." She does a double take. Many students would just let that fly by.

“看，”他說(shuō)，“她做了兩次，很多學(xué)生只是繞過(guò)做下一道題，

Instead, she thought, 'That doesn't jibe with whatever I'm thinking. I don't get it. That's important. I want an explanation.'

相反，她卻去想，‘無(wú)論我怎么試，這題就是不對(duì)。我不明白。這個(gè)很重要，我需要一個(gè)說(shuō)法。’

And when she finally gets the explanation, she says 'Yeah, that fits.'"

然后當(dāng)她最終得到解釋后，她會(huì)說(shuō)。‘嗯，這才合適。’”

At Berkeley, Schoenfeld teaches a course on problem solving, the entire problem of which,

在伯克利，肖恩菲爾德教一門怎樣解決問(wèn)題的課程，

he says, it to get his students to unlearn the mathematical habits they picked up on the way to university.

整個(gè)課程的意義在于，讓學(xué)生們?cè)谏洗髮W(xué)之后，拋棄學(xué)習(xí)數(shù)學(xué)的舊習(xí)慣，

"I pick a problem that I don't know how to solve," he says. "I tell my students, 'You're going to have a two-week take-home exam.

他說(shuō)：“我挑了一個(gè)我不知道該怎樣解決的問(wèn)題，我告訴我的學(xué)生，你們?cè)趦蓚€(gè)星期后會(huì)有個(gè)考試。

I know your habits. You're going to do nothing for the first week, and start it the next week.

我了解你們的習(xí)慣。在第一周內(nèi)你們不會(huì)做任何復(fù)習(xí)，你們會(huì)在第二個(gè)禮拜開(kāi)始準(zhǔn)備，

And I want to warn you now: if you only spend one week on this, you're not going to solve it.

我現(xiàn)在要提醒你們，如果你只用一周的時(shí)間復(fù)習(xí)，那么你們不會(huì)取得好成績(jī)。