泥窯中的碎渣兒

學生寄來的一個故事，也是網路流傳多時的。我們的想法，我們的教育，可以再活絡些的。
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給「天才的想法」一點空間，而不是「不要想那麼多」！ 

核子物理學之父歐尼斯特‧拉瑟福當他在擔任皇家學院校長時，有一天接到一位教授打來的電話：「校長大人，我有個不情之請，要拜託你幫忙。」

「大家都是老同事，幹嘛這麼客氣？ 」

「是這樣的，我出了一道物理學的考題，給了一個學生零分，但這個學生堅持他應該得到滿分。我和學生同意找一個公平的仲裁人，想來想去就閣下你最合適......」

「你出的是什麼題目？」

「題目是：如何利用氣壓計測量一座大樓的高度？校長大人，如果是你怎麼回答？」

「還不簡單，用氣壓計測出地面的氣壓，再到頂樓測出樓頂的氣壓，兩壓相差換算回來，答案就出來了。當然也可以先上樓頂量氣壓，再下到地面量氣壓。只要是本校的學生都應該答得出來。」

「對，你猜這個學生怎麼答？他答說：先把氣壓計拿到頂樓，然後綁上一根繩子，再把氣壓計垂到一樓，在繩子上做好記號，把氣壓計拉上來，測量繩子的長度，繩子有多長，大樓就有多高。」

「哈，這傢伙挺滑頭的。不過，他確實是用氣壓計測出大樓的高度，不應該得到零分吧？」

「他是答出一個答案，但是這個答案不是物理學上的答案，沒辦法表示他可以合格升等到下一個進階的課程啊！」

拉瑟福第二天把學生找到辦公室，給學生六分鐘的時間，請他就同樣的問題，再作答一次。拉瑟福特別提醒答案要能顯示物理學的程度。

一分，兩分，三分，四分，五分鐘過去了，拉瑟福看學生的紙上仍然一片空白，便問：「你是想放棄嗎？」

「噢！不，拉瑟福校長，我沒有要放棄。這個題目的答案很多，我在想用哪一個來作答比較好，你跟我講話的同時，我正好想到一個挺合適的答案呢！」

「對不起，打擾你作答，我會把問話的時間扣除，請繼續。」

學生聽完，迅速在白紙上寫下答案：把氣壓計拿到頂樓，丟下去，用碼錶計算氣壓計落下的時間，用 x = 0.5 x a x t^2 的公式，就可以算出大樓的高度。 拉瑟福轉頭問他的同事，說：「你看怎樣？」「我同意給他九十九分。」

「同學，我看事情就等你同意，便可以圓滿解決。」

「校長，教授，我接受這個分數。」

「同學，我很好奇，你說有很多答案，可不可以說幾個來聽聽？」

「答案太多了，」學生說：「你可以在晴天時，把氣壓計放在地上，看它的影子有多長，再量出氣壓計有多高，然後去量大樓的影子長度，同比例就算出大樓的高度。」

「還有一種非常基本的方法，你帶著氣壓計爬樓梯，一邊爬一邊用氣壓計做標記，最後走到頂樓，你做了幾個標記，大樓就是幾個氣壓計的高度。」

「還有複雜的辦法，你可以把氣壓計綁在一根繩子的末端，把它像鐘擺一樣擺動透過重力在樓頂和樓底的差別，來計算大樓的高度。或者把氣壓計垂到即將落地的位置，一樣像鐘擺來擺動它，再根據『徑動』的時間長短來計算大樓的高度。」「好孩子，這才像上過皇家學院物理課的學生。」

「當然，方法是很多，或許最好的方法就是把氣壓計帶到地下室找管理員，跟他說：『先生，這是一根很棒的氣壓計，價錢不便宜，如果你告訴我大樓有多高，我就把這個氣壓計送給你。』」「我問你，你真的不知道這個問題傳統的標準答案嗎？」「我當然知道，校長。」學生說：「我不是沒事愛搗蛋，我是對老師限定我的『思考』感到厭煩！」

拉瑟福遇到的學生名叫尼爾斯‧波爾（Niels Bohr），是丹麥人，他後來成為著名的物理學家，在一九二二年得到諾貝爾獎。

Some Questions Have Many Answers：Niels Bohr on Learning
Sir Ernest Rutherford, President of the Royal Academy, and recipient of the Nobel Prize in Physics, related the following story. .

Some time ago I received a call from a colleague. He was about to give a student a zero for his answer to a physics question, while the student claimed a perfect score. The instructor and the student agreed to an impartial arbiter, and I was selected.

I read the examination question: "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, attach a long rope to it, lower it to the street, and then bring it up, measuring the length of the rope. The length of the rope is the height of the building."

The student really had a strong case for full credit since he had really answered the question completely and correctly! On the other hand, if full credit were given, it could well contribute to a high grade in his physics course and certify competence in physics, but the answer did not confirm this.

I suggested that the student have another try. I gave the student six minutes to answer the question with the warning that the answer should show some knowledge of physics. At the end of five minutes, he hadn't written anything. I asked if he wished to give up, but he said he had many answers to this problem; he was just thinking of the best one. I excused myself for interrupting him and asked him to please 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, timing its fall with a stopwatch. Then, using the formula x=0.5*a*t^2, calculate the height of the building." At this point, I asked my colleague if he would give up. He conceded, and gave the student almost full credit.

While leaving my colleague's office, I recalled that the student had said that he had other answers to the problem, so I asked him what they were.

"Well," 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 simple proportion, determine the height of the building."

"Fine," I said, "and others?"

"Yes," said the student, "there is a very basic measurement method 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."

"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, and determine the value of g [gravity] 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, in principle, can be calculated."

"On this same tack, you could take the barometer to the top of the building, attach a long rope to it, lower it to just above the street, and then swing it as a pendulum. You could then calculate the height of the building by the period of the precession".

"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 door. When the superintendent answers, you speak to him as follows: 'Mr. Superintendent, here is a fine barometer. If you will tell me the height of the building, I will give you this barometer."

At this point, I asked the student if he really did not know the conventional answer to this question. He admitted that he did, but said that he was fed up with high school and college instructors trying to teach him how to think.

The name of the student was Niels Bohr." (1885-1962) Danish Physicist; Nobel Prize 1922; best known for proposing the first 'model' of the atom with protons & neutrons, and various energy state of the surrounding electrons -- the familiar icon of the small nucleus circled by three elliptical orbits ... but more significantly, an innovator in Quantum Theory.

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在我們的小學學校考試，考試題目是：下列哪一個答案不是植物？ A 桃子，B 竹子， C 麥子，D 桌子，E 獅子。 

小朋友只選了獅子，老師說：「錯，桌子也不是植物。」   

小朋友不服氣，說：「桌子是木頭做的，木頭是樹砍下來的，樹是植物吧，那桌子怎麼不是植物呢？」   

 老師說：「不是就不是，你想太多了！」   

小朋友回家問媽媽，他媽告訴他：「不要想那麼多！」

 老師錯了嗎？也未必，因為桌子不一定都是木頭做的，也有鐵的、塑膠的，但問題不在答案是什麼？而在思考能不能展開四方？ 

像釋迦牟尼說的，有八萬四千個法門，每一個法門都是方便法。從哪個門進去，都可以到羅馬。 

如果我們不給孩子思考的空間，不給他詢問解惑的機會，那他得到的不是「教育」只是「教訓」。