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Renee was in her mid-twenties, with long black hair and round glasses.
其中一名叫雷妮的女生给他留下了深刻的印象，雷妮大概20多岁，黑色长发，带一个银边眼镜。
In the tape, she is playing with a software program designed to teach algebra.
在录影带中，她正在操作一套用来教学的代数软件程序。
On the screen is an x and a y axis.The program asks you to punch in the set of coordinates and then draws a line view on the screen.
屏幕上出现了Y轴和X轴，教学程序要求使用者划一条线穿过座标轴，举个例子，如果我们在Y轴上标出5，在X轴上也标出5，那么计算机就会作出反应。
At this point, I'm sure, some vague memory of your middle-school algebra is coming back to you.
我相信，这时候，很多有关高中时的代数知识就会模糊地浮现在脑海中。
But rest assured, you don't need to remember any of it to understand the significance of Renee's example.
但是请放心，你不需要记住任何相关的知识，就可以理解雷妮案例的重要性。
In fact, as you listen to Renee talking, don't focus on what she's saying, but rather on why and how she's talking the way she is.
实际上，在文中的下面几段里，当你听到雷妮的谈话时，请不要关注她所说的内容，而是注意她谈话的方式和为什么她会谈到这些。
The point of the computer program, which Shoenfeld had created, was to teach students about how they can calculate the slope of a line.
肖恩菲尔德设计的计算程序是想教授学生如何计算直线的倾斜程度。
Slope, as I'm sure you remember (or, more accurately, as I'll bet you don't remember; I certainly didn't), is rise over run.
斜线，我相信，你一定记得（或者说，你记不得了，我就忘记了），就是横坐标与纵坐标上两点相连所形成的一条直线。
So that if you type in 5 on the y axis, and 5 on the x axis, the slope would be 1, 5 over 5. So there is Renee.
这个案例中要求画出的斜线只要一条，横轴和纵轴的数字都是5。
She's sitting at the keyboard, and she's trying to figure out what numbers to enter
现在雷妮坐在键盘前，试图计算出，输入哪些数字可以让计算机划出一条垂线，
in order to get the computer to draw a line that is absolutely vertical, that is directly superimposed over the y axis.
直接同Y轴垂直相交。
No, those of you who remember your high school math will know that this is, in fact, impossible. A vertical line has an undefined slope.
现在，高中时的数学知识会帮助你得出答案。实际上，这是不可能实现的，
It's rise is infinite: any number on the y axis starting at zero and going on forever.
垂线是一种特殊的斜线它的斜率无穷大：纵轴上的数字是无穷大的，Y轴上的数都以零开始且无穷大。
It's run, on the x axis, meanwhile, is zero. Infinity divided by zero is not a number.
当它穿过X轴的时候，数值为零，无穷大除以零，还是无穷大。
And the reason why Schoenfeld likes to show this particular tape is that it is a perfect demonstration of how Renee came to resolve this misconception.
但是雷妮没有意识到她在尝试做一件没有答案的数学题，她正陷入被肖恩菲尔德称为“美丽的理解误区”中。
