Once upon a time, a student was in a physics class. He had achieved an otherwise perfect score, but the marker had graded him poorly on one question. The question had asked him how he would measure the height of a building using a barometer. The student had written down, “Go to the top of the building. Drop the barometer and count the seconds until it smashes on the sidewalk below. Then use the formula for acceleration by gravity to determine the height of the building.”
Of course, having referenced a barometer, the tester expected the student to use air pressure as a tool for measuring height. Since this answer did not demonstrate that the student knew how to solve questions about air pressure, he couldn’t pass that portion of the test. When the student brought up that his answer did solve the question being asked, the professor made a compromise. He said that he would let the student answer the question again with a different method. And if the student solved the problem again, he would award him the marks for the question.
Immediately the student responded that he would use the barometer to bang on the door of the landlord in the building. When the landlord answered the door, he would ask, “How tall is this building?”
At once, the professor saw what the student was doing. He asked him if he knew of any other methods to reach the answer. The student said that he did.He recommended tying a long string to the barometer and measuring the length of the string. Or swinging the string as a pendulum and inferring the height by the motion it created. The professor decided to award the student the marks. As the story goes, the student was a young Niels Bohr, later becoming the famous physicist and discovering the nature of electrons inside atoms.
This student didn’t just know how to get the answer. He also understood the entire scope for which the problem existed. Instead of seeing the problem in the same terms he had been taught, he could easily view it a number of ways.