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.

肖恩菲尔德曾经问一组高中生，在他们做家庭作业时，在下定结论该数学题太难而做不出之前，他们会花多长时间来尝试解答该题？

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

他们的回答从30秒到5分钟不等，平均时间为2分钟。

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

但是雷妮是个很执着的人，她坚持不懈，她反复在同一个问题上推敲，并且她想出了解决办法。

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

她不断地尝试，不是一个轻易就屈服的人，

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.

她知道在某种程度上，她画垂线的理论出现了失误。除非她认为自己做对了，否则她不会放弃。

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

雷妮在数学方面并不具备天赋，类似斜率和无穷大这样的抽象概念对她绝对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.

但她却给肖恩菲尔德留下了十分深刻的印象,“无论做任何事，她都有种强烈的意愿去弄清楚，

"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，她不会说‘啊，你是对的’，然后就走开，这真不一般”。

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

他将录像带回放到雷妮面对难题的那个时刻，并指着屏幕。

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

“看，”他说，“她做了两次，很多学生只是绕过做下一道题，

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，她却去想，‘无论我怎么试，这题就是不对。我不明白。这个很重要，我需要一个说法。’

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

然后当她最终得到解释后，她会说。‘嗯，这才合适。’”

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

在伯克利，肖恩菲尔德教一门怎样解决问题的课程，

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

整个课程的意义在于，让学生们在上大学之后，抛弃学习数学的旧习惯，

"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.

他说：“我挑了一个我不知道该怎样解决的问题，我告诉我的学生，你们在两个星期后会有个考试。

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

我了解你们的习惯。在第一周内你们不会做任何复习，你们会在第二个礼拜开始准备，

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

我现在要提醒你们，如果你只用一周的时间复习，那么你们不会取得好成绩。