Posing the Question
It is well known that in physics research (and probably other areas as well, but I am not qualified to talk about them) asking the right question is often the crucial step to solving a problem.
Einstein famously obtained his insights into special relativity by wondering what it would be like to ride on a light beam. The mother of the physicist I. I. Rabi, who later won a Nobel prize, used to ask him every day, not if he had answered questions in class, but if he had asked a good question. I have known researchers step back from a problem saying "We weren't asking the right questions."
However, it seems to me that the art of questioning is perhaps not taught as much as the art of answering. We learnt how to complete homework problems, take tests, sit for exams, etc. where someone else has performed the difficult and subtle task of framing the question (for those who like this sort of thing the Clay Mathematical Institute offers a significant sum of money for solving one of their posted problems).
We are only responsible and rewarded for answering. In the physics curriculum we are taught a great number of formal techniques for finding solutions. We are of course, encouraged to ask questions in class, but rarely taught formally how to frame questions.
Implications for Research
One of the consequences of this approach is that it defines a type of student as 'good' who might not be suitable for research. I have seen on many occasions, students with good classroom grades flounder in the research environment, where the framing of questions can be a crucial skill.
I have also seen the reverse where a student who takes three tries to pass the academic qualifying exam ends up with a strong research resume and several good publications (part of the reason many universities are doing away with GREs; they have low correlation to research success).
Another example, which I found quaint when I first came across it, was talking to a colleague from a different field (high energy physics) where perhaps the questions posed by Nature are well known to all practitioners of the field, and the only interest is in solving them (which is not something that I am trivializing).
This person asked me once what the main questions in my field (atomic, molecular and optical physics) were. I was taken aback because I did not know the answer. I was not aware of any such agenda set by my field - other than that of cooking up interesting questions, each of which had set off an unexpected revolution. And nobody knew what the next interesting question would be - that was part of the excitement.
Here are two examples of such questions: Can you build a laser? Can you cool the motion of atoms with lasers?
When the first laser was built, no one was trying to solve a grand problem with it; in fact it famously became known as a 'solution looking for a problem'. Of course, many uses for lasers were eventually found. Today there is a 20 billion USD worldwide laser market.
When laser cooling of atoms was first realized, it was not the result of widespread competition; only three research groups were working in this then obscure area. Later, two Nobel prizes and atomic clocks for the GPS came out of this research.
A Possible Solution - I mean - Question
I am not formally trained in the techniques of pedagogy, though I do teach for a living, and try to follow best practices. So what I am about to suggest is very crude, but I think it involves the right philosophy. For example a freshman mechanics question which could perform the required exercise might be:
A diver jumps off a cliff and into a lake. We would like to know with what velocity she hits the water. Neglect friction due to air. What information do you need to solve this problem? Give a stepwise account of the process by which you will arrive at the answer.
In answering this question, the student participates more in its framing than they would if numerical values of the relevant quantities (initial velocity, acceleration due to gravity, time the diver spends in the air) were supplied.
In fact, some students might find a different way to pose and solve the problem (using initial velocity, acceleration due to gravity and height of cliff). This can be used to show them that different procedures can be devised to determine the same physical quantity.
A few questions like this - I'm only asking for maybe 10% market share here - would help train students in sharpening questions, in addition to finding answers.
留言