The Barometer Story
A problem in teaching critical thinking
A very interesting story about the multiple faces of creative unconventional thinking or how to solve a problem in more than the one or two usual ways.
This text appeared in Current Science, 1964, published by American Education Publications, Columbus, Ohio.
Some time ago, I received a call from a colleague who asked if I would be the referee on the grading of an examination question. It seemed that he was about to give a student a zero for his answer to a physics question, while the student claimed he should receive a perfect score and would do so if the system were not set up against the student. The instructor and the student agreed to submit this to an impartial arbiter, and I was selected.
I went to my colleague's office and read the examination question, which was: "Show how it is possible to determine the height of a tall building with the aid of a barometer."
The student answer was: "Take a barometer to the top of the building, attach a long rope to it, lower the barometer 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."
Now this is a very interesting answer, but should the student get credit for it?
I pointed out that the student really had a strong case for full credit since he had answered the question completely and correctly. On the other hand, if full credit was given, it could well contribute to a high grade for the student in his physics course. A high grade is supposed to certify that the student knows some physics, but the answer to the question did not confirm this. With this in mind, 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.
Acting in terms of the agreement, 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 had not written anything. I asked if he wished to give up, since I had another class to take care of, but he said no, he was not giving up. 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 was:
"Take the barometer to the top of the building and lean over the edge of the roof.
Drop that barometer, timing its fall with a stopwatch. Then, using the formula
S = ½ a t2, calculate the height of the building.
At this point I asked my colleague if he would give up. He conceded, and I gave the student almost full credit.
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 simple proportion, determine the height of the building."
"Fine," I asked. "And the others?"
"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."
"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' 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."
Finally, he concluded, "If you don't limit me to physics solutions to this problem, there are many other ways. "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 I have a fine barometer. If you tell me the height of this building, I will give you this barometer."
At this point, I asked the student if he really didn't know the answer to the problem. He admitted that he did, but that he was so fed up with college instructors trying to teach him how to think and to use critical thinking, instead of showing him the structure of the subject matter, that he decided to take off on what he regarded mostly as a sham.
WHAT IS SCIENCE?
In acting as a consultant for various school systems, I am often called upon to give advice on how to teach critical thinking. There is usually so much confusion on this topic that I urge the teachers to look first at the meaning of science and the method of critical thinking.
The word science originally referred to the study of the physical environment, the study of the atmosphere, the soil, the ocean, plants, animals, the stars, the planets, etc. The emphasis was on the materials of science rather than on the method. During the 18th century, it became generally recognized that science was making great progress, and it was hoped that other subjects could make advances of a similar kind. Benjamin Franklin expressed this hope:
The rapid progress true science now makes occasions my regretting sometimes that I was born too soon. It is impossible to imagine the heights to which may be carried, in a thousand years, the power of man over matter. O that moral science were in as fair a way of improvement, that men would cease to be wolves to one another, and that human beings would at length learn what they now improperly call humanity.
It was about the time of Franklin that many people began to think that progress in other subjects could be made simply by using the method of science - critical thinking. This idea is still with us, but it is quite unrealistic; for if you ask any scientist what step of critical thinking he is taking, he will probably not know what you are talking about, and if he does, he will think that you are very naive.
Most scientists operate in much the manner that P. W. Bridgman described when he said that critical thinking was nothing more than doing one's best with one's mind. Although Bridgman's definition of critical thinking was probably a reaction to pat formulas which appear in textbooks, it can also be justified on different grounds. Let us do this by examining the nature of critical thinking, and its relation to the evolutionary origin of the human mind.
EVOLUTION AND CRITICAL THINKING
Critical thinking as outlined in textbooks usually appears as some variation of the pattern of observation, hypothesis, and verification.
Now, it must be obvious that man has used this method for many of his activities for a very long time - in fact, ever since he came into existence. For if in his search for food, shelter, and a mate, he had not observed, made hypotheses, and verified them by experiment, he would never have survived. Thus, critical thinking ability is part of man's mental equipment, and in one way or another it is as natural for him to think critically as it is for him to eat and breathe.
From this point of view, we conclude that the method of critical thinking is a natural result of the evolution of the nervous system and not an invention of scientists. Thus, teachers who excitedly labor critical thinking are often in much the same position as Polonius, who was thrilled to discover that he was speaking prose.
A reasonable question to ask in this connection is: "If critical thinking is so old, how does it happen that the disciplines of physics, chemistry, and biology did not develop long before this time?" Much of the answer to this is quite simple. In the growth of a subject there is a point, the discovery of key ideas which, when reached, makes for very rapid progress. In physics, much of this occurred with the formulation of the laws of motion in the 17th century; in chemistry it took place with the discovery of oxygen in the 18th century; and in biology, it was the development of the theory of evolution in the 19th century.
Thus we conclude that science, the study of our physical environment, develops much like the solving of a jigsaw puzzle. In the beginning, it is hard to get started, but after a number of key pieces have been found and fit into place, progress is quite rapid. In fact, the last piece falls into place by itself.
The moral of all this is that critical thinking is not the thing which is characteristic of science. The characteristic feature of the scientific enterprise is that it has found many of the key pieces required for putting together the puzzle of the physical environment. The reason why this happened first in science is that the study of the physical environment is much simpler than that of our social environment.
Unless this is made clear, the teaching of critical thinking as such is misleading. In fact, as students mature, they come to realize it, and lose respect for those who have suggested otherwise, as we found in the barometer story. It seems that in the elementary grades, the youngsters are fascinated by the idea of a scientific method, in high school they accept it as a part of the folklore of science teaching, in college they begin to be bored by it, and by the time students finish college, they have usually forgotten it or resent it.
Now that the dangers of overemphasizing the method of critical thinking have been explored, let US ask the question: "Is there any advantage in showing the student some systematic ways of arriving at answers?" There is, provided that a number of precautions are taken. Here are some that seem reasonable to me:
1. Point out that the general pattern of observation, hypothesis, and verification is a method which is natural to the human mind, and is not peculiar to science except to the extent that it is easier to apply to the physical environment.
2. This pattern,used in a formal, systematic way, is more helpful in analyzing or talking about results than in obtaining them, for most discoveries are made with a great deal of trial and error, intuition, hunches, educated guesses, and repeated frustrations with results that do not agree with predictions.
3. The pattern as a systematic method of discovery is useful in the lower elementary grades (2 and 3), where the examples studied are very simple.
4. Ideas about critical thinking, especially after grade 5, are best taught in connection with the systematic development of subject matter. If method is divorced from systematic study of subject matter, it runs into the same difficulties as those for which some education courses are criticized.
5. Make a real effort to practice those techniques, namely controlled experimentation and mathematical interpretation, which scientists have found very useful in many disciplines in science. (A good case can be made for considering mathematics as the method of modern science.)
6. Avoid implying that a scientist is a different kind of person from the rest of humanity. The idea that the scientist is basically more objective as a result of his work is not borne out by his behavior outside of science. If he is more objective or honest in his work, it is because work in science is such that (a) a scientist has to be objective to get results in his scientific work, or (b) dishonest work is readily discovered because the experiments that a scientist does can usually be repeated and checked.
7. Do not give students the idea that a scientist thinks while other people do not. Not only is this untrue, but it also tends to make insufferable intellectual snobs out of children who should be learning the humility associated with the most worthwhile efforts in science.