论文部分内容阅读
Teach Perspective to Help with Geometry
My 60-second idea is that school 1）geometry should start with the science of 2）perspective. That would empower students to do some attractive， surprising， artistic things right away. They wouldn’t feel that they are passive 3）receptacles for useless information.
I’m naturally terrible at drawing， so it was a revelation to me how it’s possible， for example， to draw the way a 4）checker board actually looks from any angle by following some simple but very clever and logical steps. When I first learned that， which was quite recently， I did it dozens of times just because it’s fun. The first steps in perspective are easier and more engaging than 5）Euclidian geometry， and they can be 6）illustrated both with classic art works and with 7）striking modern photographs. I think one could package all this in a very 8）inviting way， and get geometry classes off to a beautiful start.
我的60秒奇思是教授几何学应该从（教授）透视学开始。这能够使学生立刻就去做一些吸引人的、令人惊奇的、有美感的事。他们不会觉得自己是在被动地接受无用的信息。
由于我天生就不擅长绘画，所以画画对我来说是个揭露真相的过程。例如，（我）从任意一个角度去画一个棋盘，通过采取一些简单但却非常巧妙而又富有逻辑的方法使它看起来跟实物一样。当我第一次知道这些办法，这也是最近的事了，仅仅是因为这很有趣，我就画了几十次。透视法的第一步比欧几里得几何学更简单，也更吸引人。它们可以同时用经典的艺术作品和不同寻常的现代摄影作品来举例说明。我觉得我们可以把所有这些包装得很诱人，使几何学课程有一个美丽的开端。
My 60-second idea is that school 1）geometry should start with the science of 2）perspective. That would empower students to do some attractive， surprising， artistic things right away. They wouldn’t feel that they are passive 3）receptacles for useless information.
I’m naturally terrible at drawing， so it was a revelation to me how it’s possible， for example， to draw the way a 4）checker board actually looks from any angle by following some simple but very clever and logical steps. When I first learned that， which was quite recently， I did it dozens of times just because it’s fun. The first steps in perspective are easier and more engaging than 5）Euclidian geometry， and they can be 6）illustrated both with classic art works and with 7）striking modern photographs. I think one could package all this in a very 8）inviting way， and get geometry classes off to a beautiful start.
我的60秒奇思是教授几何学应该从（教授）透视学开始。这能够使学生立刻就去做一些吸引人的、令人惊奇的、有美感的事。他们不会觉得自己是在被动地接受无用的信息。
由于我天生就不擅长绘画，所以画画对我来说是个揭露真相的过程。例如，（我）从任意一个角度去画一个棋盘，通过采取一些简单但却非常巧妙而又富有逻辑的方法使它看起来跟实物一样。当我第一次知道这些办法，这也是最近的事了，仅仅是因为这很有趣，我就画了几十次。透视法的第一步比欧几里得几何学更简单，也更吸引人。它们可以同时用经典的艺术作品和不同寻常的现代摄影作品来举例说明。我觉得我们可以把所有这些包装得很诱人，使几何学课程有一个美丽的开端。