We have not been taught how to think for ourselves, we have been taught what to think based on what past thinkers thought. We are taught to think reproductively, not productively. What most people call thinking is simply reproducing what others have done in the past. We have been trained to seek out the neural path of least resistance, searching out responses that have worked in the past, rather than approach a problem on its own terms.
Educators discourage us from looking for alternatives to prevailing wisdom. When confronted with a problem, we are taught to analytically select the most promising approach based on past history, excluding all other approaches and then to work logically within a carefully defined direction towards a solution. Instead of being taught to look for possibilities, we are taught to look for ways to exclude them. This kind of thinking is dehumanizing and naturalizes intellectual laziness which promotes an impulse toward doing whatever is easiest or doing nothing at all. It’s as if we entered school as a question mark and graduated as a period.
Once when I was a young student, I was asked by my teacher, “What is one-half of thirteen?” I answered six and one half or 6.5. However, I exclaimed there are many different ways to express thirteen and many different to halve something. For example, you can spell thirteen, then halve it (e.g., thir/teen). Now half of thirteen becomes four (four letters in each half). Or, you can express it numerically as 13, and now halving 1/3 gives you 1 and 3. Another way to express a 13 is to express it in Roman numerals as XIII and now halving XI/II gives you XI and II, or eleven and two. Consequently one-half of thirteen is now eleven and two. Or you can even take XIII, divide it horizontally in two (XIII) and half of thirteen becomes VIII or 8.
My teacher scolded me for being silly and wasting the class’s time by playing games. She said there is only one right answer to the question about thirteen. It is six and one-half or 6.5. All others are wrong. I’ll never forget what she said “When I ask you a question, answer it the way you were taught or say you don’t know. If you want to get a passing grade, stop making stuff up.”
When we learn something, we are taught to program it into our brain and stop thinking about or looking for alternatives. Over time these programs become stronger and stronger, not only cognitively but physiologically as well. To get a sense of how strong these programs are, try solving the following problem.
Even when we actively seek information to test our ideas to see if we are right, we usually ignore paths that might lead us to discover alternatives. Following is an interesting experiment, which was originally conducted by the British psychologist Peter Wason that demonstrates this attitude. Wason would present subjects with the following triad of three numbers in sequence.
2 4 6
He would then ask subjects to write other examples of triads that follow the number rule and explain the number rule for the sequence. The subjects could ask as many questions as they wished without penalty.
He found that almost invariably most people will initially say, “4, 6, 8,” or “20, 22, 24,” or some similar sequence. And Watson would say, yes, that is an example of a number rule. Then they will say, “32, 34, 36″ or “50, 52, 54″ and so on– all numbers increasing by two. After a few tries, and getting affirmative answers each time, they are confident that the rule is numbers increasing by two without exploring alternative possibilities.
Actually, the rule Wason was looking for is much simpler– it’s simply numbers increasing. They could be 1, 2, 3 or 10, 20, 40 or 400, 678, 10,944. And testing such an alternative would be easy. All the subjects had to say was 1, 2, 3 to Watson to test it and it would be affirmed. Or, for example, a subject could throw out any series of numbers, for example, 5, 4, and 3 to see if they got a positive or negative answer. And that information would tell them a lot about whether their guess about the rule is true.
The profound discovery Wason made was that most people process the same information over and over until proven wrong, without searching for alternatives, even when there is no penalty for asking questions that give them a negative answer. In his hundreds of experiments, he, incredibly, never had an instance in which someone spontaneously offered an alternative hypothesis to find out if it were true. In short, his subjects didn’t even try to find out if there is a simpler or even, another, rule.
On the other hand, creative thinkers have a vivid awareness of the world around them and when they think, they seek to include rather than exclude alternatives and possibilities. They have a “lantern awareness” that brings the whole environment to the forefront of their attention. So, by the way, do children before they are educated. This kind of awareness is how you feel when you visit a foreign country; you focus less on particulars and experience everything more globally because so much is unfamiliar.
I am reminded of a story about a student who protested when his answer was marked wrong on a physics degree exam at the University of Copenhagen. The imaginative student was purportedly Niels Bohr who years later was co-winner of the Nobel Prize for physics.
In answer to the question, “How could you measure the height of a skyscraper using a barometer?” he was expected to explain that the barometric pressures at the top and the bottom of the building are different, and by calculating, he could determine the building’s height. Instead, he answered, “You tie a long piece of string to the neck of the barometer, then lower the barometer from the roof of the skyscraper to the ground. The length of the string plus the length of the barometer will equal the height of the building.
This highly original answer so incensed the examiner that the student was failed immediately. The student appealed on the grounds that his answer was indisputably correct, and the university appointed an independent arbiter to decide the case.
The arbiter judged that the answer was indeed correct, but did not display any noticeable knowledge of physics. To resolve the problem it was decided to call the student in and allow him six minutes in which to provide a verbal answer that showed at least a minimal familiarity with the basic principles of physics.
For five minutes the student sat in silence, forehead creased in thought. The arbiter reminded him that time was running out, to which the student replied that he had several extremely relevant answers, but couldn’t make up his mind which to use. On being advised to hurry up the student replied as follows:
“Firstly, you could take the barometer up to the roof of the skyscraper, drop it over the edge, and measure the time it takes to reach the ground. The height of the building can then be worked out from the formula H = 0.5g x t squared. But bad luck on the barometer.”
“Or if the sun is shining you could measure the height of the barometer, then set it on end and measure the length of its shadow. Then you measure the length of the skyscraper’s shadow, and thereafter it is a simple matter of proportional arithmetic to work out the height of the skyscraper.”
“But if you wanted to be highly scientific about it, you could tie a short piece of string to the barometer and swing it like a pendulum, first at ground level and then on the roof of the skyscraper. The height is worked out by the difference in the gravitational restoring force T =2 pi sqr root (I /9).”
“Or if the skyscraper has an outside emergency staircase, it would be easier to walk up it and mark off the height of the skyscraper in barometer lengths, then add them up.”
“If you merely wanted to be boring and orthodox about it, of course, you could use the barometer to measure the air pressure on the roof of the skyscraper and on the ground, and convert the difference in millibars into feet to give the height of the building.”
“But since we are constantly being exhorted to exercise independence of mind and apply scientific methods, undoubtedly the best way would be to knock on the janitor’s door and say to him ‘If you would like a nice new barometer, I will give you this one if you tell me the height of this skyscraper’.”
The obvious moral here is that education should not consist merely of stuffing students’ heads full of information and formulae to be memorized by rote and regurgitated upon demand, but of teaching students how to think and solve problems using whatever tools are available. In the mangled words of a familiar phrase, students should be educated in a way that enables them to figure out their own ways of catching fish, not simply taught a specific method of fishing.