My answers:

1. How do you know which approach to take for a given problem?
Do you mean a given problem (to find an answer) or proving?
I can't say proving is better than finding answer in this sense.

2. How do you compare different approaches, and how do you know your answer is correct?
Problem solving encourages taking various approaches to confirm your answers.
When you get the same answer from different apporaches, you are more certain that the answer is correct.

While in proofs, the correct answer is already there. So I, for instance, would stop looking for different approaches to solve the same problem once I hit the correct statement. In this sense, problem solving is better than proofs.

3. There are many proofs hidden under the "solving" or "computational" part, unless, you were taught by other people and you don't bother to challenge.

I think that is the point I am trying to make.
In addition, in proofs, there is a correct answer. I would never think about challenging that.--Not sure if this addresses your issue.

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• It seems that we have totally different understanding of what is -trivial- ♀ (100 bytes) () 01/15/2015 postreply 13:40:18