At this point, I asked my colleague if he would give up. He conceded (让步),and I gave the student almost full credit.
到这时候,我问我的同事是否肯让步。他同意了,我差不多给了这个学生满分。
In leaving my colleague's office, I recalled that the student had said he had other answers to the problem, so I asked him what they were. "Oh, yes," said the student. "There are many ways of getting the height of a tall building with the aid of a barometer. For example, you could take the barometer out on a sunny day and measure the height of the barometer, the length of its shadow, and the length of the shadow of the building, and by the use of a simple proportion, determine the height of the building."
我正要离开办公室,突然想到这学生说过他还有别的解答方法,便问他具体有哪些。“哦,有呀,”他说。“借助气压表,能有多种方式测得大楼的高度。例如,你可以在一个晴朗的日子把气压表拿到室外,量出气压表的高度及其影长,以及大楼阴影的长度,然后用个简单比例法就可求得大楼的高度。”
Fine, I said. "And the others?"
“很好,”我说。“还有呢?”
Yes, said the student. "There is a very basic measurement method that you will like. In this method, you take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give you the height of the building in barometer units. A very direct method."
“还有,”他说,“有种最基本的测量办法你一定会喜欢。用这种办法,你拿着气压表开始爬楼,一边爬一边在墙上标出气压表的髙度。然后数一下有多少个标记,这样就能用气压表的单位长度,计算出大楼的高度。这是种相当直接的办法。
Of course, if you want a more sophisticated method, you can tie the barometer to the end of a string, swing it as a pendulum(钟摆),and deter-mine the value of 'g' at the street level and at the top of the building. From the difference between the two values of 'g' the height of the building can, in principle, be calculated.
“当然,要是你想复杂一点的话,可以把气压表拴在绳子的一端,让它像钟摆那样摆动,然后分别测出它在街道水平面及大楼顶部的g值。根据这两个g值的差数,按理可计算出大楼的高度。”
Finally he concluded, there are many other ways of solving the problem. "Probably the best," he said," is to take the barometer to the basement and knock on the superintendent's (主管人)door. When the superintendent answers, you speak to him as follows: 'Mr. Superintendent, here I have a fine barometer. If you will tell me the height of this building, I will give you this barometer.' "
最后他说,这一问题有多种解答方式。“最便捷的一种办法可能是,”他说,“拿着气压表去底楼,敲敲主管人的房门。主管人来开门时,你这么跟他说:‘主管先生,我有个挺不错的气压表。要是你能告诉我这幢楼的高度,我就把气压表送给你。’”
At this point, I asked the student if he really did not know the conventional (常规的)answer to this question. He admitted that he did , but said that he was fed up with (厌烦)high school and college instructors trying to teach him how to think, to use the "scientific method," and to explore the deep inner logic of the subject in a pedantic (学究式的)way, as is often done in the new mathematics, rather than teaching him the structure of the subject. With this in mind, he decided to revive (复兴)scholasticism (烦琐经院哲学)as an academic lark (玩笑)to challenge the Sputnik-panicked classrooms of America.
这时我就问这个学生,他是否真的不知道这道题的常规解法。他承认他知道,但是他说,他厌倦了中学和大学教师们的教学方法,因为他们总想教他如何思考,如何运用“科学方法”,如何用一种学究式的方法探索学科深层的内在逻辑,就像在“新数学”中常做的那样,而不是把这一学科的结构教给他。有了这个念头,他便决定重新搬出中世纪烦琐经院哲学的那一套来开个学术性玩笑,向患有人造地球卫星恐惧症的美国课堂教育进行挑战。