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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.
肖恩菲爾德曾經問一組高中生，在他們做家庭作業時，在下定結論該數學題太難而做不出之前，他們會花多長時間來嘗試解答該題？
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.
但是雷妮是個很執著的人，她堅持不懈，她反復在同一個問題上推敲，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，她畫垂線的理論出現了失誤。除非她認為自己做對了，否則她不會放棄。
Renee wasn't a math natural. Abstract concepts like "slope" and "undefined" clearly didn't come easily to her.
雷妮在數學方面并不具備天賦，類似斜率和無窮大這樣的抽象概念對她絕對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,“無論做任何事，她都有種強烈的意愿去弄清楚，
"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，她不會說‘啊，你是對的’，然后就走開，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難題的那個時刻，并指著屏幕。
"Look, he said." She does a double take. Many students would just let that fly by.
“看，”他說，“她做了兩次，很多學生只是繞過做下一道題，
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，‘無論我怎么試，這題就是不對。我不明白。這個很重要，我需要一個說法。’
And when she finally gets the explanation, she says 'Yeah, that fits.'"
然后當她最終得到解釋后，她會說。‘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.
整個課程的意義在于，讓學生們在上大學之后，拋棄學習數學的舊習慣，
"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：“我挑了一個我不知道該怎樣解決的問題，我告訴我的學生，你們在兩個星期后會有個考試。
I know your habits. You're going to do nothing for the first week, and start it the next week.
我了解你們的習慣。在第一周內你們不會做任何復習，你們會在第二個禮拜開始準備，
And I want to warn you now: if you only spend one week on this, you're not going to solve it.
我現在要提醒你們，如果你只用一周的時間復習，那么你們不會取得好成績。
