their knowledge and develop their ability to solve problems. A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted. There remains always something to do; with sufficient study and penetration, we could improve and, in any we can always improve our understanding of the solution.
The student has now carried through his plan. He has written down the solution, checking each step. Thus, he should have good reasons to believe that his solution is correct. Nevertheless, errors are always possible, especially if the argument is long and involved. Hence, verifications are desirable. Especially, if there is some rapid and intuitive procedure to test either the result or the argument, it should not be overlooked. Can you check the result? Can you check the argument?
In order to convince ourselves of the presence or of the quality of an object, we like to see and to touch it. And e prefer perception through two different senses, so we prefer conviction by two different proofs: Can you derive the result diferently? We prefer, of course, a short and intuitive argument to a long and heavy one: Can you see it at a glance?
their knowledge and develop their ability to solve problems. A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted. There remains always something to do; with sufficient study and penetration, we could improve and, in any we can always improve our understanding of the solution. The student has now carried through his plan. He has written down the solution, checking each step. Thus, he should have good reasons to believe that his solution is correct. Nevertheless, errors are always possible, especially if the argument is long and involved. Hence, verifications are desirable. Especially, if there is some rapid and intuitive procedure to test either the result or the argument, it should not be overlooked. Can you check the result? Can you check the argument? In order to convince ourselves of the presence or of the quality of an object, we like to see and to touch it. And e prefer perception through two different senses, so we prefer conviction by two different proofs: Can you derive the result diferently? We prefer, of course, a short and intuitive argument to a long and heavy one: Can you see it at a glance?
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