Correct and wrong mindsets for problem solving [closed]

Question

Is there one right answer in a math or physics problem?How does one approach a problem?With what mindsets? Is it necessary to have a mindset that you should find the correct combination of elements, make a synthesis and you have found it or something else? What role intuition plays in problem solving?I think intuition is like knowing something or the answer to a problem without knowing how you know it or without knowing the reasoning behind what you know.I think you know it in an unexplainable way somehow.

How does one improve intuition, especially on math and physics?I read some proofs from my notes and textbooks in math and sometimes I can not answer and when I read the answer I know perhaps I could not find it even if I would spend very much time.

Are undergraduate courses programmed for students capable of answering the questions in math and physics?

Perhaps my mindsets are wrong in math and I can not answer most times math and physics problems in undergraduate courses, although I think I do well with my memory.

Thank you.

Answer 1

For some undergraduate math problems, yes, there is one correct answer, though there might be several approaches to obtaining it.

For "intuition" in your post, perhaps you should substitute "insight". Insight sometimes comes in a flash, but more often only after hard work on several related problems.

Many people find that in the early years of learning things seem easy and they don't need to work to achieve success. But some (many) of those eventually hit a point where it isn't easy anymore and if they don't yet have good work habits (solving problems, reading, asking questions...) they may give up thinking that the next steps are impossible.

Probably you have an instructor to whom you can ask questions. Instead of asking for solutions, see if you can work out a system where you explain what you've done and ask for the flaw. Or ask for a minimal hint that will get you past the block. Good instructors know to do this, I hope.

If you can't solve a problem, find a similar problem, or several such. See if you can't get some insight from the set of them that didn't come from a single problem. I once gained quite a lot of insight about the behavior of functions by graphing (by hand with no computer - yes, I'm that old) a huge number of rational functions using derivative information. The fact that it was hard to do was probably an advantage in my understanding. I doubt I'd have learned as much by asking the internet to graph them for me and just looking at the results.