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Lesson Five


Angels on a Pin Alexander Calandra

Pre-class Work I

Read the text once for the main idea. Do not refer to the notes, dictionaries and the glossary yet.

Some time ago, I received a call from Jim, a colleague of mine, who teaches physics. He asked me if I would do him a favor and be the referee on the grading of an examination question. I said sure, but I did not quite understand why he should need my help. He told me that he was about to give a student a zero for his answer to a physics question, but the student protested that it wasn't fair. He insisted that he deserved a perfect score if the system were not set up against the student. Finally, they agreed to take the matter to an impartial instructor. And I was selected.
I went to my colleague's office and read the examination question. It said: "Show how it is possible to determine the height of a tall building with the aid of a barometer." The student had answered: "Take the barometer to the top of the building, tie a long rope to it, lower the barometer to the street, and then bring it up and measure the length of the rope. The length of the rope will be the height of the building."
I laughed and pointed out to my colleague that we must admit the student really had a pretty strong case for full credit since he had indeed answered the question completely and correctly. On the other hand, I could also see the dilemma because if full credit were given to him it could mean a high grade for the student in his physics course. A high grade is supposed to prove competence in the course, but the answer he gave did not show his knowledge on the subject. "So, what would you do if you were me?" Jim asked. I suggested that the student have another try at answering the question. I was not surprised that my colleague agreed, but I was surprised that the student did, too.
I told the student that I would give him six minutes to answer the question. But I warned him that this time his answer should show some knowledge of physics. He sat down and picked up his pen. He appeared to be thinking hard. At the end of five minutes, however, I noticed that he had not put down a single word. I asked him if he wished to give up, but he said no. He had not written anything down because he had too many possible answers to this problem. He was just trying to decide which would be the best one. I excused myself for interrupting him and asked him to go on. In the next minute, he dashed off his answer, which read: "Take the barometer to the top of the building and lean over the edge of the roof. Drop the barometer and time its fall with a stopwatch. Then, using the formula S = 1 /2 at2, calculate the height of the building."
At this point, I asked my colleague if he would give up. He nodded yes, and I gave the student almost full credit.
When I left my colleague's office, I recalled that the student had said that he had other answers to the problem. I was curious, 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 in 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. The beauty of this method is that you don't have to drop the barometer and break it."
"Fine," I said. "Any more?"
"Yes," said the student. "There is a very basic measurement method that people will like, because it is so simple and direct. In this method, you take the barometer and 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. The only trouble with this method is that it doesn't require much knowledge of physics."
"Of course, if you prefer a more sophisticated method, a method that will really show some knowledge of physics, you can tie the barometer to the end of a rope, swing it as a pendulum and determine 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 worked out."
Finally, he concluded that while there are many ways of solving the problem, "Probably the best and the most practical in a real-life situation is to take the barometer to the basement and knock on the superintendent's door. When the superintendent answers, you speak to him as follows: Mr. Superintendent, I have here a fine barometer. If you will tell me the height of this building, I will gladly give you this barometer!"
At this point, I asked the student if he really didn't know the expected answer to this question. He smiled and admitted that he did, but said he was fed up with standard answers to standard questions. He couldn't understand why there should be so much emphasis on fixed rules rather than creative thinking. So he could not resist the temptation to play a little joke with the educational system, which had been thrown into such a panic by the successful launching of the Russian Sputnik.
At that moment I suddenly remembered the question: How many angels can dance on the head of a pin? We teachers are always blaming the students for giving wrong answers. Perhaps we should ask ourselves whether we are always asking the right questions.

Read the text a second time. Learn the new words and expressions listed below.


adj. concerning teaching or studying, especially in a college or university 学术的

n. , v. help

n. a messenger and servant of God 天使

v. to fix; to fasten; to join

n. an instrument that measures the air pressure and shows when the weather is going to change 气压表

n. a floor built partly or wholly below ground level 地下室

v. to work out a number or amount from information you have 计算

n. someone you work with, especially in a professional job 同事

n. the ability and skill needed to do a particular job 能力

n. a series of lessons or lectures on a particular subject 课程

adj. to develop or use new ideas 有创造性的

n. a measure of a student's work at a university 学分

dash off
v. to run away from a place very quickly; Here: to write in a hurry

v. 该得;应受

n. a difficult choice to be made between two courses of action which seem to be equally bad 进退两难

adj. connected with education

v. to examine; investigate; often refers to previously unexamined space or ideas 探索

n. 公式

v. (AmE) to give a mark to an examination paper

adj. fair in giving judgements, unbiased etc. 不偏不倚的

adj. on the inside; close to the centre

n. a teacher

v. Here: to send into space 发射

v. 倾斜;倚;靠

n. reason 逻辑

n. fear; scare

n. 钟摆

n. 原则

n. 比例

v. to remember sth. 回想起

n. sb. In charge of a game in sports ; Here: a person who is asked to settle a disagreement

v. struggle against 抵抗

v. to choose

v. to find a way of dealing with a problem 解决

adj. complex 复杂的

n. 前苏联人造地球卫星

n. a watch to time speed 记秒表

n. a piece of thread

n. the way in which parts are formed into a whole 结构

n. Here: a person in charge of an apartment building 楼房管理处负责人员

v. to move from a fixed point 摆动

n. 系统;制度

n. 诱惑

n. (计量的)单位

v. to advise sb. to do sth. in order to avoid possible punishment or trouble 警告


We Should Cherish Our Children's Freedom to Think Kie Ho

Kie Ho, who grew up in Indonesia and is now a Southern California business executive, argues in the following article that the educational system in the United States is good because it teaches students to think and to experiment with ideas. The author criticizes educational systems that rely solely on memorization and rote learning, because those methods stifle creative impulses.

Americans who remember "the good old days" are not alone in complaining about the educational system in this country. Immigrants, too, complain, and with more up-to-date comparisons. Lately I have heard a Polish immigrant express dismay that his daughter's high school has not taught her the difference between Belgrade and Prague. A German friend was furious when he learned that the mathematics test given to his son on his first day as a freshman included multiplication and division. A Lebanese boasts that the average high-school graduate in his homeland can speak fluently in Arabic, French and English. Japanese businessmen in Los Angeles send their children to private schools staffed by teachers imported from Japan to learn mathematics at Japanese levels, generally considered at least a year more advanced than the level here.
But I wonder: If American education is so tragically inferior, why is it that this is still the country of innovation?
I think I found the answer on my short trip to the Laguna Beach Museum of Art, where the work of schoolchildren was on exhibit. Equipped only with colorful yarns, foil paper, felt pens and crayons, they had transformed simple paper lunch bags into, among other things, a waterfall with flying fish, Broom Hilda the witch* and a house with a woman in a bikini hiding behind a swinging door. Their public school had provided these children with opportunities and direction to fulfill their creativity, something that people in this country tend to take for granted.
When I was 12 in Indonesia, where education followed the Dutch system, I had to memorize the names of all the world's major cities, from Kabul to Karachi. At the same age, my son, who was brought up a Californian, thought that Buenos Aires was Spanish for "good food." However, unlike many children of his age in Asia and Europe, my son had studied creative geography. When he was only 6, he drew a map of the route that he traveled to get to school, including the streets and their names, the buildings and traffic signs and the houses that he passed.
American parents forget that in this country their children are able to experiment freely with ideas; without this they will not really be able to think or to believe in themselves.
In my high school years, back in Indonesia, we were models of dedication and obedience; we sat to listen, to answer only when asked, and to give the only correct answer. Even when studying word forms, there were no alternatives. In similes, pretty lips were always as red as cherries, and beautiful eyebrows were always like a parade of black clouds, Like children in many other countries in the world, I simply did not have a chance to choose, to make decisions. My son, on the contrary, told me that he got a good laugh—and an A—from his teacher for creating his own simile "the man was as nervous as Richard Pryor* at a Ku Klux Klan* convention."
There's no doubt that American education does not meet high standards in such basic skills as mathematics and language. And we realize that our youngsters are ignorant of Latin, put Mussolini in the same category as Dostoevski, cannot recite the Periodic Table* by heart. Would we, however, prefer to stuff the developing little heads of our children with hundreds of geometry problems, the names of rivers in Brazil and 50 lines from "the Canterbury Tales?" Do we really want to retard their impulses, frustrate their opportunities for self-expression?
When I was 18,1 had to memorize Hamlet's "To be or not to be" speech flawlessly. In his English class, my son was assigned to write a love letter to Juliet, either in Shakespearean or modern language. (He picked the latter; his Romeo would take it Juliet to an arcade for video games).
Here in America a history student can take the role of Lyndon Johnson in an open debate against another student playing Ho Chi Minh. But it is unthinkable that a youngster in Japan would dare to do the same regarding the role of their Hirohito in World War II.
Critics of American education in this country cannot grasp one thing, something that they don't truly understand because they take it for granted: freedom. This most important measurement has been omitted in the studies of the quality of education in this century, the only one, I think, that extends even to children the license to freely speak, write and be creative. Our public education certainly is not perfect, but it does have its advantages.

Broom Hilda the witch: comic strip character
Ku Klux Klan(三 K 党): secret organization of white men begun in the South after the Civil War to maintain white supremacy
Richard Pryor: black male film actor
Periodic Table: the arrangement of the chemical elements according to their atomic numbers