A Quote by Donald Knuth

...methods are more important than facts. The educational value of a problem given to a student depends mostly on how often the thought processes that are invoked to solve it will be helpful in later situations. It has little to do with how useful the answer to the problem may be. On the other hand, a good problem must also motivate the students; they should be interested in seeing the answer. Since students differ so greatly, I cannot expect everyone to like the problems that please me.
To ask the 'right' question is far more important than to receive the answer. The solution of a problem lies in the understanding of the problem; the answer is not outside the problem, it is in the problem.
We cannot solve a problem by saying, "It's not my problem." We cannot solve a problem by hoping that someone else will solve it for us. I can solve a problem only when I say, "This is my problem and it's up to me to solve it."
You can't solve a problem? Well, get down and investigate the present facts and [the problem's] past history! When you have investigated the problem thoroughly, you will know how to solve it.
We shall find the answer when we examine the problem, the problem is never apart from the answer, the problem IS the answer, understanding the problem dissolves the problem.
In teaching, the other main problem related to type is the students’ interest. Intuitives and sensing types differ greatly in what they find interesting in any subject even if they like, that is, are interested in, the same subjects. Intuitives like the principle, the theory, the why. Sensing types like the practical application, the what and the how.
Solving the population problem is not going to solve the problems of racism, of sexism, of religious intolerance, of war, of gross economic inequality. But if you don't solve the population problem, you're not going to solve any of those problems. Whatever problem you're interested in, you're not going to solve it unless you also solve the population problem. Whatever your cause, it's a lost cause without population control.
The best answer to the question, 'What is the most effective method of teaching?' is that it depends on the goal, the student, the content, and the teacher. But the next best answer is, 'Students teaching other students.'
Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.
Too often the educational value of doing well what is done, however little, is overlooked. One thing well done prepares the mind to do the next thing better. Not how much, but how well, should be the motto. One problem thoroughly understood is of more value than a score poorly mastered.
An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem.
The big question isn't whether you have problems; the all-important factor is your attitude toward problems. How you think of the problem is more important than the problem itself.
Cities are never random. No matter how chaotic they might seem, everything about them grows out of a need to solve a problem. In fact, a city is nothing more than a solution to a problem, that in turn creates more problems that need more solutions, until towers rise, roads widen, bridges are built, and millions of people are caught up in a mad race to feed the problem-solving, problem-creating frenzy.
Whether you were talking about Pillsbury, Burger King, Godfather's, the National Restaurant Association, in each one of those situations, I had a daunting problem that I had to solve. And I used the same business principles to approach the problem and, more importantly, solve the problem in every one of the situations.
We academic scientists move within a certain sphere, we can go on being useless up to a point, in the confidence that sooner or later some use will be found for our studies. The mathematician, of course, prides himself on being totally useless, but usually turns out to be the most useful of the lot. He finds the solution but he is not interested in what the problem is: sooner or later, someone will find the problem to which his solution is the answer.
International adoption does not begin to solve the problems of the world's orphaned children. It's truly not the answer. At the same time, it solves a problem for a few. I think it can be a brilliant solution to the problem of adults wanting a child in their lives or wanting more children in their lives and the problem of children who want parents in their lives.
There is first of all the problem of the opening, namely, how to get us from where we are, which is, as yet, nowhere, to the far bank. It is a simple bridging problem, a problem of knocking together a bridge. People solve such problems every day. They solve them, and having solved them push on.
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