异类之不一样的成功启示录 第168期:学习数学的秘密
时间：2019-02-17 作者：英语课 分类：异类:不一样的成功启示录
英语课
She types in 80. The line steeper still, but it's not totally vertical 1.
她输入80，线更斜了，但是还是没有变成垂线。
"Ohhh, it's infinity 2, isn't it? It's never going to get there."
“数值是无穷大是吗？我永远都划不出一条垂线是吧？”
Renee is close. But then she reverts 3 to her original misconception.
雷妮的发现已接近事实的真相，但是她又绕回了她最初的“思维误区”。
“So what do I need? 100? Everytime you double the number, you get half way to the y axis 4. But it never gets there..."
“那我该怎么办呢？100吗？每一次我输入加倍的数字，它就会更接近，但是却总是达不到我想要的结果。”
She types in 100. "It's closer, but not quite there yet." She starts to think out loud. It's obvious she's on the verge 5 of figuring something out.
她输入100。“接近了，但依旧不大理想。”她开始更大胆的想象，很明显她就要得出事实的真相了。
"Well, I knew this, though, but... I knew that. For each one up, it goes that many over. I'm still somewhat confused as to why..."
“好吧，我知道了，尽管……但是……我知道了，每加大一个数字，线就更接近Y轴一点。至于为什么会这样，我仍然感到困惑不解……”
She pauses, squinting 6 at the screen. "I'm getting confused. It's a tenth way to the one. But I don't want it to be..."
之后她停顿了一下，紧紧盯着屏幕，“我有点糊涂了，这里只是十分之一，但我没有意识到 ……”
And then she sees it. "Oh! It's any number up and zero over. It's any number divided by zero!" Her face lights up.
然后她突然明白了，她的脸闪耀着光芒：
"A vertical line is anything divided by zero. And that's an undefined number. Ohhh, Okay, now I see.
“噢，任何一条垂线都被零整除，因此就会无穷大。嗯，好，现在我明白了，
The slope of a vertical line is undefined. Ahhhh.That means something now. I won't forget that!"
垂直的斜率是无穷大的，嗯，现在总算是明白了，我永远也不会忘记这堂课。”
Over the course of his career, Schoenfeld has videotaped countless 7 students as they worked on math problems.
在肖恩菲尔德任教时，他曾用录影机记录了许多学生的数学课。
But the Renee tape is one of his favorites, because of how beautifully it illustrates 8 what he considers to be the secret to learning mathematics.
但是雷妮的录影带是他最喜欢的一个，因为这个录影带贴切地诠释了学习数学的秘密。
Twenty-two minutes pass from the moment Renee begins playing with the computer to the moment she says, "Ahhh. That means something now."
从雷妮开始操作计算程序，直到第22分钟，她才说了声：“嗯，现在有些眉目了。”
That's a long time. "This is eighth grade mathematics," Schoenfeld said.
那是一段很长的时间，肖恩菲尔德说道：
If I put the average eighth grader in the same position as Renee, I'm guessing that after the first few attempts, they would have said,'I don't get it, I need you to explain it.'"
“这是道八年级的数学题，如果我把给雷妮布置的数学题目，同样布置给与雷妮程度相同的八年级学生，我想，在他们试试之后就会说，‘我做不出来，我需要你来讲解一下。’”
adj.垂直的，顶点的，纵向的；n.垂直物，垂直的位置
- The northern side of the mountain is almost vertical.这座山的北坡几乎是垂直的。
- Vertical air motions are not measured by this system.垂直气流的运动不用这种系统来测量。
n.无限，无穷，大量
- It is impossible to count up to infinity.不可能数到无穷大。
- Theoretically,a line can extend into infinity.从理论上来说直线可以无限地延伸。
恢复( revert的第三人称单数 )； 重提； 回到…上； 归还
- The mind reverts to the earliest days of colonial history. 我们回想到早期的殖民地历史。
- Macau reverts to Chinese sovereignty at midnight on December19. 澳门主权于十二月十九日零时回归中国。
n.轴，轴线，中心线；坐标轴，基准线
- The earth's axis is the line between the North and South Poles.地轴是南北极之间的线。
- The axis of a circle is its diameter.圆的轴线是其直径。
n.边，边缘；v.接近，濒临
- The country's economy is on the verge of collapse.国家的经济已到了崩溃的边缘。
- She was on the verge of bursting into tears.她快要哭出来了。
斜视( squint的现在分词 )； 眯着眼睛； 瞟； 从小孔或缝隙里看
- "More company," he said, squinting in the sun. "那边来人了，"他在阳光中眨巴着眼睛说。
- Squinting against the morning sun, Faulcon examined the boy carefully. 对着早晨的太阳斜起眼睛，富尔康仔细地打量着那个年轻人。
adj.无数的，多得不计其数的
- In the war countless innocent people lost their lives.在这场战争中无数无辜的人丧失了性命。
- I've told you countless times.我已经告诉你无数遍了。
给…加插图( illustrate的第三人称单数 )； 说明； 表明； （用示例、图画等）说明
- This historical novel illustrates the breaking up of feudal society in microcosm. 这部历史小说是走向崩溃的封建社会的缩影。
- Alfred Adler, a famous doctor, had an experience which illustrates this. 阿尔弗莱德 - 阿德勒是一位著名的医生，他有过可以说明这点的经历。 来自中级百科部分
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